NN_v1_k.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From C:\\Users\\a95826ar.DS\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\keras\\src\\losses.py:2976: The name tf.losses.sparse_softmax_cross_entropy is deprecated. Please use tf.compat.v1.losses.sparse_softmax_cross_entropy instead.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd \n",
    "import numpy as np \n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from sklearn.model_selection import train_test_split\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import dataset and select x and y data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset=pd.read_csv('./data/driver_clean_data.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will first select all the possible data that we might consider as input data. Then, we will try different networks with different subsets of this big X vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xall = dataset[['Year','RaceResults','GridPos','QualiRes','NumRaces','AvgFinalPos','StdDevFinalPos','MedianFinalPos','AvgStartPos','StdDevStartPos','MedianStartPos']]\n",
    "y = dataset['Championship Position']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Split in train and test datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xall_train, Xall_test, y_train, y_test = train_test_split(Xall, y, random_state=111,test_size=0.3,shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AvgFinalPos</th>\n",
       "      <th>StdDevFinalPos</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>8.500000</td>\n",
       "      <td>8.817596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>664</th>\n",
       "      <td>7.421053</td>\n",
       "      <td>5.696867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>757</th>\n",
       "      <td>12.250000</td>\n",
       "      <td>3.973349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>573</th>\n",
       "      <td>14.947368</td>\n",
       "      <td>6.108438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>487</th>\n",
       "      <td>15.055556</td>\n",
       "      <td>5.512332</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     AvgFinalPos  StdDevFinalPos\n",
       "59      8.500000        8.817596\n",
       "664     7.421053        5.696867\n",
       "757    12.250000        3.973349\n",
       "573    14.947368        6.108438\n",
       "487    15.055556        5.512332"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xall_train[['AvgFinalPos','StdDevFinalPos']].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "46"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset['Championship Position'].max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since all the input and output values have similar size and there is no more than an order of magnitude of difference between minimum and maximum, there is no need to normalize the values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, I will construct different models with different inputs to compare their predictive power.\n",
    "They will all use dense layers. I will also test different hyperparameter configurations.\n",
    "The output  will not be hardcoded, i.e. the last layer will give a number between 1 and 46, which is the maximum Championship position found in the dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model 1: Final position average and standard deviation as input"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define model architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From C:\\Users\\a95826ar.DS\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\keras\\src\\backend.py:873: The name tf.get_default_graph is deprecated. Please use tf.compat.v1.get_default_graph instead.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "model1=Sequential()\n",
    "model1.add(Dense(10,activation='relu',input_shape=(2,)))\n",
    "model1.add(Dense(20,activation='relu'))\n",
    "model1.add(Dense(10,activation='relu'))\n",
    "model1.add(Dense(1,activation='linear'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compile model and show summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From C:\\Users\\a95826ar.DS\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\keras\\src\\optimizers\\__init__.py:309: The name tf.train.Optimizer is deprecated. Please use tf.compat.v1.train.Optimizer instead.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "model1.compile(optimizer='adam',loss='mean_squared_error',metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense (Dense)               (None, 10)                30        \n",
      "                                                                 \n",
      " dense_1 (Dense)             (None, 20)                220       \n",
      "                                                                 \n",
      " dense_2 (Dense)             (None, 10)                210       \n",
      "                                                                 \n",
      " dense_3 (Dense)             (None, 1)                 11        \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 471 (1.84 KB)\n",
      "Trainable params: 471 (1.84 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "xmod1_train=np.float32(Xall_train[['AvgFinalPos','StdDevFinalPos']].values)\n",
    "xmod1_test=np.float32(Xall_test[['AvgFinalPos','StdDevFinalPos']].values)\n",
    "ymod_train=np.float32(y_train.values)\n",
    "ymod_test=np.float32(y_test.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(592, 2)\n",
      "(592,)\n",
      "(255, 2)\n",
      "(255,)\n"
     ]
    }
   ],
   "source": [
    "print(xmod1_train.shape)\n",
    "print(ymod_train.shape)\n",
    "print(xmod1_test.shape)\n",
    "print(ymod_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/10\n",
      "WARNING:tensorflow:From C:\\Users\\a95826ar.DS\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\keras\\src\\utils\\tf_utils.py:492: The name tf.ragged.RaggedTensorValue is deprecated. Please use tf.compat.v1.ragged.RaggedTensorValue instead.\n",
      "\n",
      "WARNING:tensorflow:From C:\\Users\\a95826ar.DS\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\keras\\src\\engine\\base_layer_utils.py:384: The name tf.executing_eagerly_outside_functions is deprecated. Please use tf.compat.v1.executing_eagerly_outside_functions instead.\n",
      "\n",
      "19/19 [==============================] - 1s 9ms/step - loss: 258.6527 - accuracy: 0.0051 - val_loss: 222.7406 - val_accuracy: 0.0314\n",
      "Epoch 2/10\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 166.3397 - accuracy: 0.0321 - val_loss: 131.2444 - val_accuracy: 0.0471\n",
      "Epoch 3/10\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 93.9967 - accuracy: 0.0338 - val_loss: 63.1019 - val_accuracy: 0.0471\n",
      "Epoch 4/10\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 44.4842 - accuracy: 0.0338 - val_loss: 28.4412 - val_accuracy: 0.0471\n",
      "Epoch 5/10\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 23.6998 - accuracy: 0.0338 - val_loss: 19.7606 - val_accuracy: 0.0471\n",
      "Epoch 6/10\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 19.3385 - accuracy: 0.0338 - val_loss: 19.7950 - val_accuracy: 0.0471\n",
      "Epoch 7/10\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 18.4998 - accuracy: 0.0338 - val_loss: 19.1091 - val_accuracy: 0.0471\n",
      "Epoch 8/10\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.9859 - accuracy: 0.0338 - val_loss: 18.6367 - val_accuracy: 0.0471\n",
      "Epoch 9/10\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.4360 - accuracy: 0.0338 - val_loss: 18.3324 - val_accuracy: 0.0471\n",
      "Epoch 10/10\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 16.9638 - accuracy: 0.0338 - val_loss: 18.1335 - val_accuracy: 0.0471\n"
     ]
    }
   ],
   "source": [
    "histo1=model1.fit(xmod1_train,ymod_train,epochs=10,validation_data=(xmod1_test,ymod_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x129642b7d00>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(histo1.history['loss'])\n",
    "plt.plot(histo1.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 76ms/step\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[16.894089 ],\n",
       "       [14.038999 ],\n",
       "       [ 9.4175205]], dtype=float32)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.predict(xmod1_test[:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16., 18.,  7.], dtype=float32)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ymod_test[:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model 2: Final position average, standard deviation and median as input"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define model architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2=Sequential()\n",
    "model2.add(Dense(10,activation='relu',input_shape=(3,)))\n",
    "model2.add(Dense(20,activation='relu'))\n",
    "model2.add(Dense(10,activation='relu'))\n",
    "model2.add(Dense(1,activation='linear'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compile model and show summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_1\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense_4 (Dense)             (None, 10)                40        \n",
      "                                                                 \n",
      " dense_5 (Dense)             (None, 20)                220       \n",
      "                                                                 \n",
      " dense_6 (Dense)             (None, 10)                210       \n",
      "                                                                 \n",
      " dense_7 (Dense)             (None, 1)                 11        \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 481 (1.88 KB)\n",
      "Trainable params: 481 (1.88 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model2.compile(optimizer='adam',loss='mean_squared_error',metrics=['accuracy'])\n",
    "\n",
    "model2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(592, 3)\n",
      "(592,)\n",
      "(255, 3)\n",
      "(255,)\n"
     ]
    }
   ],
   "source": [
    "xmod2_train=np.float32(Xall_train[['AvgFinalPos','StdDevFinalPos','MedianFinalPos']].values)\n",
    "xmod2_test=np.float32(Xall_test[['AvgFinalPos','StdDevFinalPos','MedianFinalPos']].values)\n",
    "ymod_train=np.float32(y_train.values)\n",
    "ymod_test=np.float32(y_test.values)\n",
    "\n",
    "print(xmod2_train.shape)\n",
    "print(ymod_train.shape)\n",
    "print(xmod2_test.shape)\n",
    "print(ymod_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train and evaluate model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "19/19 [==============================] - 1s 9ms/step - loss: 212.0776 - accuracy: 0.0338 - val_loss: 189.2169 - val_accuracy: 0.0471\n",
      "Epoch 2/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 137.9911 - accuracy: 0.0338 - val_loss: 113.0977 - val_accuracy: 0.0471\n",
      "Epoch 3/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 73.3451 - accuracy: 0.0338 - val_loss: 54.8376 - val_accuracy: 0.0471\n",
      "Epoch 4/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 40.0928 - accuracy: 0.0338 - val_loss: 36.8735 - val_accuracy: 0.0471\n",
      "Epoch 5/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 32.2570 - accuracy: 0.0338 - val_loss: 31.7043 - val_accuracy: 0.0471\n",
      "Epoch 6/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 27.9786 - accuracy: 0.0338 - val_loss: 27.9223 - val_accuracy: 0.0471\n",
      "Epoch 7/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 24.8204 - accuracy: 0.0338 - val_loss: 24.8538 - val_accuracy: 0.0471\n",
      "Epoch 8/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 22.5560 - accuracy: 0.0338 - val_loss: 22.9267 - val_accuracy: 0.0471\n",
      "Epoch 9/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 21.2277 - accuracy: 0.0338 - val_loss: 21.4689 - val_accuracy: 0.0471\n",
      "Epoch 10/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 20.2330 - accuracy: 0.0338 - val_loss: 20.7734 - val_accuracy: 0.0471\n",
      "Epoch 11/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 19.5035 - accuracy: 0.0338 - val_loss: 20.1227 - val_accuracy: 0.0471\n",
      "Epoch 12/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 19.0086 - accuracy: 0.0338 - val_loss: 19.8902 - val_accuracy: 0.0471\n",
      "Epoch 13/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 18.5695 - accuracy: 0.0338 - val_loss: 19.5542 - val_accuracy: 0.0471\n",
      "Epoch 14/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 18.2430 - accuracy: 0.0338 - val_loss: 19.2463 - val_accuracy: 0.0471\n",
      "Epoch 15/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.9461 - accuracy: 0.0338 - val_loss: 19.1145 - val_accuracy: 0.0471\n",
      "Epoch 16/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.6793 - accuracy: 0.0338 - val_loss: 18.9962 - val_accuracy: 0.0471\n",
      "Epoch 17/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.5010 - accuracy: 0.0338 - val_loss: 18.9016 - val_accuracy: 0.0471\n",
      "Epoch 18/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.2325 - accuracy: 0.0338 - val_loss: 18.9714 - val_accuracy: 0.0471\n",
      "Epoch 19/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.0601 - accuracy: 0.0338 - val_loss: 18.9716 - val_accuracy: 0.0471\n",
      "Epoch 20/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 16.7838 - accuracy: 0.0338 - val_loss: 18.2538 - val_accuracy: 0.0471\n"
     ]
    }
   ],
   "source": [
    "histo2=model2.fit(xmod2_train,ymod_train,epochs=17,validation_data=(xmod2_test,ymod_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12962a883a0>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(histo2.history['loss'])\n",
    "plt.plot(histo2.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 57ms/step\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[16.271484 ],\n",
       "       [13.511462 ],\n",
       "       [ 7.3186097]], dtype=float32)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.predict(xmod2_test[:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16., 18.,  7.], dtype=float32)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ymod_test[:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model 3: Mean and standard deviation of grid and final race position"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define model architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3=Sequential()\n",
    "model3.add(Dense(10,activation='relu',input_shape=(4,)))\n",
    "model3.add(Dense(20,activation='relu'))\n",
    "model3.add(Dense(10,activation='relu'))\n",
    "model3.add(Dense(1,activation='linear'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compile model and show summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_2\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense_8 (Dense)             (None, 10)                50        \n",
      "                                                                 \n",
      " dense_9 (Dense)             (None, 20)                220       \n",
      "                                                                 \n",
      " dense_10 (Dense)            (None, 10)                210       \n",
      "                                                                 \n",
      " dense_11 (Dense)            (None, 1)                 11        \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 491 (1.92 KB)\n",
      "Trainable params: 491 (1.92 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model3.compile(optimizer='adam',loss='mean_squared_error',metrics=['accuracy'])\n",
    "\n",
    "model3.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Year', 'RaceResults', 'GridPos', 'QualiRes', 'NumRaces', 'AvgFinalPos',\n",
       "       'StdDevFinalPos', 'MedianFinalPos', 'AvgStartPos', 'StdDevStartPos',\n",
       "       'MedianStartPos'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xall_train.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(592, 4)\n",
      "(592,)\n",
      "(255, 4)\n",
      "(255,)\n"
     ]
    }
   ],
   "source": [
    "xmod3_train=np.float32(Xall_train[['AvgFinalPos','StdDevFinalPos','AvgStartPos','StdDevStartPos']].values)\n",
    "xmod3_test=np.float32(Xall_test[['AvgFinalPos','StdDevFinalPos','AvgStartPos','StdDevStartPos']].values)\n",
    "ymod_train=np.float32(y_train.values)\n",
    "ymod_test=np.float32(y_test.values)\n",
    "\n",
    "print(xmod3_train.shape)\n",
    "print(ymod_train.shape)\n",
    "print(xmod3_test.shape)\n",
    "print(ymod_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train and evaluate model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "19/19 [==============================] - 1s 8ms/step - loss: 246.4675 - accuracy: 0.0034 - val_loss: 232.4904 - val_accuracy: 0.0196\n",
      "Epoch 2/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 189.5083 - accuracy: 0.0338 - val_loss: 167.6683 - val_accuracy: 0.0471\n",
      "Epoch 3/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 130.3597 - accuracy: 0.0338 - val_loss: 101.3702 - val_accuracy: 0.0471\n",
      "Epoch 4/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 70.2211 - accuracy: 0.0338 - val_loss: 42.2355 - val_accuracy: 0.0471\n",
      "Epoch 5/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 29.3897 - accuracy: 0.0338 - val_loss: 21.6815 - val_accuracy: 0.0471\n",
      "Epoch 6/20\n",
      "19/19 [==============================] - 0s 4ms/step - loss: 21.1809 - accuracy: 0.0338 - val_loss: 21.3681 - val_accuracy: 0.0471\n",
      "Epoch 7/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 20.0785 - accuracy: 0.0338 - val_loss: 20.1044 - val_accuracy: 0.0471\n",
      "Epoch 8/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 18.4531 - accuracy: 0.0338 - val_loss: 19.2773 - val_accuracy: 0.0471\n",
      "Epoch 9/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.0686 - accuracy: 0.0338 - val_loss: 18.3863 - val_accuracy: 0.0471\n",
      "Epoch 10/20\n",
      "19/19 [==============================] - 0s 4ms/step - loss: 15.7794 - accuracy: 0.0338 - val_loss: 17.5394 - val_accuracy: 0.0471\n",
      "Epoch 11/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 14.2198 - accuracy: 0.0321 - val_loss: 16.0674 - val_accuracy: 0.0392\n",
      "Epoch 12/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 13.4681 - accuracy: 0.0253 - val_loss: 15.6434 - val_accuracy: 0.0353\n",
      "Epoch 13/20\n",
      "19/19 [==============================] - 0s 4ms/step - loss: 12.9510 - accuracy: 0.0270 - val_loss: 15.2408 - val_accuracy: 0.0353\n",
      "Epoch 14/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.6761 - accuracy: 0.0270 - val_loss: 15.0909 - val_accuracy: 0.0353\n",
      "Epoch 15/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.5232 - accuracy: 0.0287 - val_loss: 15.0922 - val_accuracy: 0.0353\n",
      "Epoch 16/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.3726 - accuracy: 0.0287 - val_loss: 14.6895 - val_accuracy: 0.0353\n",
      "Epoch 17/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.3244 - accuracy: 0.0287 - val_loss: 14.7475 - val_accuracy: 0.0353\n",
      "Epoch 18/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.2526 - accuracy: 0.0304 - val_loss: 14.6607 - val_accuracy: 0.0431\n",
      "Epoch 19/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.1819 - accuracy: 0.0338 - val_loss: 14.7803 - val_accuracy: 0.0431\n",
      "Epoch 20/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.1172 - accuracy: 0.0338 - val_loss: 14.6873 - val_accuracy: 0.0471\n"
     ]
    }
   ],
   "source": [
    "histo3=model3.fit(xmod3_train,ymod_train,epochs=20,validation_data=(xmod3_test,ymod_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x129650aaa40>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(histo3.history['loss'])\n",
    "plt.plot(histo3.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 56ms/step\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[13.980842],\n",
       "       [16.149017],\n",
       "       [ 6.568536]], dtype=float32)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model3.predict(xmod3_test[:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16., 18.,  7.], dtype=float32)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ymod_test[:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model 4: Median and standard deviation of grid and final race position"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define model architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From C:\\Users\\a95826ar.DS\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\keras\\src\\backend.py:873: The name tf.get_default_graph is deprecated. Please use tf.compat.v1.get_default_graph instead.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "model4=Sequential()\n",
    "model4.add(Dense(10,activation='relu',input_shape=(4,)))\n",
    "model4.add(Dense(20,activation='relu'))\n",
    "model4.add(Dense(10,activation='relu'))\n",
    "model4.add(Dense(1,activation='linear'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compile model and show summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From C:\\Users\\a95826ar.DS\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\keras\\src\\optimizers\\__init__.py:309: The name tf.train.Optimizer is deprecated. Please use tf.compat.v1.train.Optimizer instead.\n",
      "\n",
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense (Dense)               (None, 10)                50        \n",
      "                                                                 \n",
      " dense_1 (Dense)             (None, 20)                220       \n",
      "                                                                 \n",
      " dense_2 (Dense)             (None, 10)                210       \n",
      "                                                                 \n",
      " dense_3 (Dense)             (None, 1)                 11        \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 491 (1.92 KB)\n",
      "Trainable params: 491 (1.92 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model4.compile(optimizer='adam',loss='mean_squared_error',metrics=['accuracy'])\n",
    "\n",
    "model4.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Year', 'RaceResults', 'GridPos', 'QualiRes', 'NumRaces', 'AvgFinalPos',\n",
       "       'StdDevFinalPos', 'MedianFinalPos', 'AvgStartPos', 'StdDevStartPos',\n",
       "       'MedianStartPos'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xall_train.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(592, 4)\n",
      "(592,)\n",
      "(255, 4)\n",
      "(255,)\n"
     ]
    }
   ],
   "source": [
    "xmod4_train=np.float32(Xall_train[['MedianFinalPos','StdDevFinalPos','MedianStartPos','StdDevStartPos']].values)\n",
    "xmod4_test=np.float32(Xall_test[['MedianFinalPos','StdDevFinalPos','MedianStartPos','StdDevStartPos']].values)\n",
    "ymod_train=np.float32(y_train.values)\n",
    "ymod_test=np.float32(y_test.values)\n",
    "\n",
    "print(xmod4_train.shape)\n",
    "print(ymod_train.shape)\n",
    "print(xmod4_test.shape)\n",
    "print(ymod_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train and evaluate model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "WARNING:tensorflow:From C:\\Users\\a95826ar.DS\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\keras\\src\\utils\\tf_utils.py:492: The name tf.ragged.RaggedTensorValue is deprecated. Please use tf.compat.v1.ragged.RaggedTensorValue instead.\n",
      "\n",
      "WARNING:tensorflow:From C:\\Users\\a95826ar.DS\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\keras\\src\\engine\\base_layer_utils.py:384: The name tf.executing_eagerly_outside_functions is deprecated. Please use tf.compat.v1.executing_eagerly_outside_functions instead.\n",
      "\n",
      "19/19 [==============================] - 1s 10ms/step - loss: 193.7970 - accuracy: 0.0321 - val_loss: 183.5309 - val_accuracy: 0.0471\n",
      "Epoch 2/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 152.5099 - accuracy: 0.0338 - val_loss: 133.5065 - val_accuracy: 0.0471\n",
      "Epoch 3/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 102.3183 - accuracy: 0.0338 - val_loss: 76.9590 - val_accuracy: 0.0471\n",
      "Epoch 4/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 55.9799 - accuracy: 0.0338 - val_loss: 42.1324 - val_accuracy: 0.0471\n",
      "Epoch 5/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 36.0420 - accuracy: 0.0338 - val_loss: 32.4222 - val_accuracy: 0.0471\n",
      "Epoch 6/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 28.4685 - accuracy: 0.0338 - val_loss: 27.6759 - val_accuracy: 0.0471\n",
      "Epoch 7/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 23.4769 - accuracy: 0.0338 - val_loss: 24.7606 - val_accuracy: 0.0471\n",
      "Epoch 8/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 19.9501 - accuracy: 0.0338 - val_loss: 22.4530 - val_accuracy: 0.0471\n",
      "Epoch 9/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.4700 - accuracy: 0.0338 - val_loss: 20.9231 - val_accuracy: 0.0471\n",
      "Epoch 10/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 16.0535 - accuracy: 0.0338 - val_loss: 19.8906 - val_accuracy: 0.0471\n",
      "Epoch 11/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 15.4299 - accuracy: 0.0338 - val_loss: 19.3895 - val_accuracy: 0.0471\n",
      "Epoch 12/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 15.0911 - accuracy: 0.0338 - val_loss: 18.6241 - val_accuracy: 0.0471\n",
      "Epoch 13/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 14.8026 - accuracy: 0.0338 - val_loss: 18.3117 - val_accuracy: 0.0471\n",
      "Epoch 14/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 14.6262 - accuracy: 0.0338 - val_loss: 17.7161 - val_accuracy: 0.0471\n",
      "Epoch 15/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 14.4386 - accuracy: 0.0338 - val_loss: 17.7982 - val_accuracy: 0.0471\n",
      "Epoch 16/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 14.4342 - accuracy: 0.0338 - val_loss: 16.9460 - val_accuracy: 0.0471\n",
      "Epoch 17/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 14.1813 - accuracy: 0.0338 - val_loss: 16.9499 - val_accuracy: 0.0471\n",
      "Epoch 18/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 13.9654 - accuracy: 0.0338 - val_loss: 16.7409 - val_accuracy: 0.0471\n",
      "Epoch 19/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 13.8428 - accuracy: 0.0338 - val_loss: 16.4177 - val_accuracy: 0.0471\n",
      "Epoch 20/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 13.7937 - accuracy: 0.0338 - val_loss: 16.5601 - val_accuracy: 0.0471\n"
     ]
    }
   ],
   "source": [
    "histo4=model4.fit(xmod4_train,ymod_train,epochs=20,validation_data=(xmod4_test,ymod_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f71ad50070>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(histo4.history['loss'])\n",
    "plt.plot(histo4.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 75ms/step\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[14.116458],\n",
       "       [18.545294],\n",
       "       [ 6.897211]], dtype=float32)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model4.predict(xmod4_test[:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16., 18.,  7.], dtype=float32)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ymod_test[:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model 5: Mean and standard deviation of grid and final race position and number of entered races"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define model architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "model5=Sequential()\n",
    "model5.add(Dense(10,activation='relu',input_shape=(5,)))\n",
    "model5.add(Dense(20,activation='relu'))\n",
    "model5.add(Dense(10,activation='relu'))\n",
    "model5.add(Dense(1,activation='linear'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compile model and show summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_1\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense_4 (Dense)             (None, 10)                60        \n",
      "                                                                 \n",
      " dense_5 (Dense)             (None, 20)                220       \n",
      "                                                                 \n",
      " dense_6 (Dense)             (None, 10)                210       \n",
      "                                                                 \n",
      " dense_7 (Dense)             (None, 1)                 11        \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 501 (1.96 KB)\n",
      "Trainable params: 501 (1.96 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model5.compile(optimizer='adam',loss='mean_squared_error',metrics=['accuracy'])\n",
    "\n",
    "model5.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Year', 'RaceResults', 'GridPos', 'QualiRes', 'NumRaces', 'AvgFinalPos',\n",
       "       'StdDevFinalPos', 'MedianFinalPos', 'AvgStartPos', 'StdDevStartPos',\n",
       "       'MedianStartPos'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xall_train.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(592, 5)\n",
      "(592,)\n",
      "(255, 5)\n",
      "(255,)\n"
     ]
    }
   ],
   "source": [
    "xmod5_train=np.float32(Xall_train[['AvgFinalPos','StdDevFinalPos','AvgStartPos','StdDevStartPos','NumRaces']].values)\n",
    "xmod5_test=np.float32(Xall_test[['AvgFinalPos','StdDevFinalPos','AvgStartPos','StdDevStartPos','NumRaces']].values)\n",
    "ymod_train=np.float32(y_train.values)\n",
    "ymod_test=np.float32(y_test.values)\n",
    "\n",
    "print(xmod5_train.shape)\n",
    "print(ymod_train.shape)\n",
    "print(xmod5_test.shape)\n",
    "print(ymod_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train and evaluate model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "19/19 [==============================] - 1s 9ms/step - loss: 251.9569 - accuracy: 0.0338 - val_loss: 232.9885 - val_accuracy: 0.0471\n",
      "Epoch 2/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 187.9537 - accuracy: 0.0338 - val_loss: 166.5904 - val_accuracy: 0.0471\n",
      "Epoch 3/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 118.7348 - accuracy: 0.0338 - val_loss: 90.2136 - val_accuracy: 0.0471\n",
      "Epoch 4/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 54.4107 - accuracy: 0.0338 - val_loss: 40.8329 - val_accuracy: 0.0471\n",
      "Epoch 5/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 24.6282 - accuracy: 0.0338 - val_loss: 29.0164 - val_accuracy: 0.0471\n",
      "Epoch 6/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.7913 - accuracy: 0.0338 - val_loss: 24.2476 - val_accuracy: 0.0471\n",
      "Epoch 7/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 15.6775 - accuracy: 0.0338 - val_loss: 21.2350 - val_accuracy: 0.0471\n",
      "Epoch 8/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 14.1349 - accuracy: 0.0338 - val_loss: 18.9303 - val_accuracy: 0.0431\n",
      "Epoch 9/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 13.2221 - accuracy: 0.0338 - val_loss: 17.6514 - val_accuracy: 0.0431\n",
      "Epoch 10/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.4472 - accuracy: 0.0338 - val_loss: 16.8629 - val_accuracy: 0.0431\n",
      "Epoch 11/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.0436 - accuracy: 0.0338 - val_loss: 16.2767 - val_accuracy: 0.0392\n",
      "Epoch 12/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 11.6428 - accuracy: 0.0321 - val_loss: 15.9362 - val_accuracy: 0.0392\n",
      "Epoch 13/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 11.3182 - accuracy: 0.0321 - val_loss: 15.3709 - val_accuracy: 0.0392\n",
      "Epoch 14/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 11.0609 - accuracy: 0.0321 - val_loss: 15.1794 - val_accuracy: 0.0392\n",
      "Epoch 15/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 10.8175 - accuracy: 0.0321 - val_loss: 15.1040 - val_accuracy: 0.0392\n",
      "Epoch 16/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 10.5295 - accuracy: 0.0321 - val_loss: 14.7492 - val_accuracy: 0.0392\n",
      "Epoch 17/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 10.2923 - accuracy: 0.0321 - val_loss: 14.6658 - val_accuracy: 0.0392\n",
      "Epoch 18/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 10.1291 - accuracy: 0.0321 - val_loss: 14.2969 - val_accuracy: 0.0392\n",
      "Epoch 19/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 9.8746 - accuracy: 0.0321 - val_loss: 14.3876 - val_accuracy: 0.0431\n",
      "Epoch 20/20\n",
      "19/19 [==============================] - 0s 4ms/step - loss: 9.6672 - accuracy: 0.0338 - val_loss: 14.1223 - val_accuracy: 0.0431\n"
     ]
    }
   ],
   "source": [
    "histo5=model5.fit(xmod5_train,ymod_train,epochs=20,validation_data=(xmod5_test,ymod_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f71df81330>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OjHWKexGRyadwH02oBObfMCzcP7xoBiWhgL7AQ0SymsL9QuqaoW0HnBsM8tKiIB9aNIPNmgJYRLKYwv1C6lZ7y6HfztQQZn97F4c7ujNQlIjIxSncL2TW1VA8dcSpCAA2a9SMiGQphfuFBEOw8KZh4V5XU8686ik8p/HuIpKlFO4XU9cMHfugc/DbAs2MWxpqeWnfSXoHNCRSRLKPwv1i6pq95dB+96VhuvuibDl4aoQHiYhklsL9YmqvgCnVw4dELp5BcTCgq1VFJCsp3C8mEICFN3vhnvQF2WXFIa6vq9Y8MyKSlRTuY1HXDJ2H4dSBlObVDWF2t57j6OnzGSpMRGRkCvexiI93H9I1c+uyWgCeeU9n7yKSXRTuY1FTDxUzh4X74rA3S+TGHa0ZKkxEZGQK97Ew87pmDryQ0u9uZrQ01vLyvpOc6x3IYIEiIqkU7mNVtwq62qB9V0rz2qaZ9EVjPK9RMyKSRRTuYxUf7z6ka2bF/OlUlRWpa0ZEsorCfayqFsL0+XDguZTmUDDArctqeWZXGwPRWGZqExEZQuF+Keqa4eCLEEsN8bWNEU5397P1kK5WFZHsoHC/FHWroec0tL6d0ryqIUxxMMDGneqaEZHsoHC/FAtXecsh/e4VJSE+vHgGG3a04pJG04iIZIrC/VJMmwUz6oeFO0BLU4SDJ7vZ134uA4WJiKRSuF+qumY49BJE+1OaWxq9q1U37NDVqiKSeQr3S1XXDH3n4IM3U5pnVU7hyjmV6ncXkaxw0XA3s6+ZWZuZvZPUVm1mG8xsj7+s8tvNzP7WzPaa2XYzW5HO4jMi0e/+3LBNLY0R3nj/FCfO9U5yUSIiqcZy5v4N4M4hbZ8FNjnn6oFN/n2Au4B6//Yg8MjElJlFymdA5EpvKoIhWppqcU4TiYlI5l003J1zzwMdQ5rvAx731x8HPpLU/k3neQWYbmazJqjW7FG3Cg6/Cv09Kc1Ns6Yxu7JUV6uKSMZdbp97xDl3zF8/DkT89TnA4aT9jvhtw5jZg2a2xcy2tLfn2Lwsdc0w0ANHXk9pNjNamiK8sOcEPf36blURyZxxf6DqvIHdlzy42zn3qHNupXNuZTgcHm8Zk2vBjWCBkYdENkY43x/l53tPZKAwERHP5YZ7a7y7xV/GO5mPAvOS9pvrt+WX0kqYfc2I4f6hRdVUlIQ0akZEMupyw309sM5fXwf8OKn9k/6omRuAzqTum/xS1wxHt0BfV0pzSSjI6qVhNu5sIxbT1aoikhljGQr5beBlYKmZHTGzB4A/B9aa2R6gxb8P8CSwH9gLPAb8dlqqzgYLV0FsAN5/edimtY0R2s/2sv1oZwYKExGB0MV2cM59fJRNa0bY1wEPjbeonDD/BggUeV0zS1pSNt2yNEwwYGzc0cryedMzU5+IFDRdoXq5isth7nUj9rtPLyvmuoVV6ncXkYxRuI9HXTMcewvOD5/HvaUxwnvHz3K4ozsDhYlIoVO4j8eSNeBisPOJYZvWNnlD/zfogiYRyQCF+3jMvQ5qGuCNx4dtWjCjnPraCnXNiEhGKNzHwwyu/ZR3perxd4ZtXtsU4dUDHXR29w9/rIhIGincx+vqj0OweMSz95amCNGYY/NuTSQmIpNL4T5eZdXQdB+89V3oS/3wdPnc6dRUFLNxp8JdRCaXwn0irFgHvZ2w40cpzYGAsWZZhM272ugbiGWmNhEpSAr3ibDwZqheDFtH7po52zPA6weHzposIpI+CveJEP9g9fAr0LYzZdPNS2ooCQU0JFJEJpXCfaIs/xVvOoIhZ+9TioOsqq9hw45WvNkZRETST+E+UcproPE/wFvfHvYNTS2NEY6ePs97x89mqDgRKTQK94l07TroOQ0716c0r2mMYIa+fk9EJo3CfSItbIaqOtj6jZTm8NQSls+brqtVRWTSKNwnUiDgnb0f+jm0707Z1NIY4a0jnbSe6RnlwSIiE0fhPtGW/yoEQsOuWI1PJLZJFzSJyCRQuE+0ilpY9ouw7V9hoDfRXF9bwfzqMjbsOJ7B4kSkUCjc02HFOjjfATv/PdFkZrQ0Rvj5vpN09Q5ksDgRKQQK93RYdCtMnz/sg9WWplr6BmK8sOdEZuoSkYKhcE+HQMA7ez/4ApzYm2i+bmE100pDGjUjImmncE+Xa34NLJjywWpRMMBty2p55r02ojFdrSoi6aNwT5epM2HpXf4Hq32J5pamCB1dfbz5/vDvXRURmSgK93S69lPQfQJ2/STR1NwQpihobFDXjIikkcI9nRbfBpXzUj5YnVZaxA2LZmgqAhFJK4V7OgWCsOKTsH8zdOxPNLc0RtjX3sX+9nOZq01E8prCPd2u+TWwALzxzUTTmsZaAI2aEZG0Ubin27TZ0HAnvPktiPYDMLeqjMZZ09i4Q1MRiEh6KNwnw4p10NUGu36aaFrbFGHLoQ46uvou8EARkcujcJ8MS1pg2pyUD1bXNkaIOXj2PZ29i8jEU7hPhmAIrvkE7HsGTh0E4BfmTCMyrUT97iKSFgr3yXLNr3lfpP3GPwODE4k9t7udnv5ohosTkXyjcJ8s0+fBkrXw5r9A1JsV8o4rZtLdF+VfX30/w8WJSL4ZV7ib2UEze9vMtpnZFr+t2sw2mNkef1k1MaXmgWvXwbnjsOcpAFbV13DL0jB/+dQuDp3synBxIpJPJuLM/Vbn3HLn3Er//meBTc65emCTf18A6u+AipmJD1bNjD/7pSsJBYw/+P52YppMTEQmSDq6Ze4D4lMhPg58JA3PkZuCIVjxCdizAU4fBmBW5RT+8BcbeWV/B//6mrpnRGRijDfcHfC0mW01swf9tohz7pi/fhyIjPRAM3vQzLaY2Zb29vZxlpFDrvmEt3zzXxJNv3zdPG5eUsOfPbmTI6e6M1SYiOST8Yb7zc65FcBdwENm1py80Tnn8A4AwzjnHnXOrXTOrQyHw+MsI4dULYAla+DNf058sBrvnnHA537wNt7LJiJy+cYV7s65o/6yDfghcD3QamazAPylrtIZasU6OHMU9m5MNM2rLuNzdy3jhT0n+N6WwxksTkTywWWHu5mVm9nU+DpwO/AOsB5Y5++2DvjxeIvMO0vvgvLaYd+x+qsfWsCH6qr50yd2cqzzfGZqE5G8MJ4z9wjwopm9BbwG/MQ59zPgz4G1ZrYHaPHvS7JgkXdR056noPNoojkQMP7iP15FfyzG/1T3jIiMw2WHu3Nuv3Puav92hXPui377SefcGudcvXOuxTnXMXHl5pEVnwQXg23fSmleWFPO/7hjGc/uaueHbx4d5cEiIhemK1QzpboOFt3qzfMeS51+4FM3LuTaBVX873/fQduZngwVKCK5TOGeSdc9AJ2H4et3w/G3E83BgPGlj11FT3+UP/rRO+qeEZFLpnDPpGX3wH1/Byf3wD82w0//AHo6AVgcruB31zbw9I5Wnth+7CI/SEQklcI9k8y8D1Y/vQVW/ga8+o/wlZXw1nfAOR64uY6r51byv9a/y8lzvZmuVkRyiMI9G5RVwy9+GR58FqbPhx/+V/j63YRO7OQv/9PVnOsZ4PPr3810lSKSQxTu2WT2NfDABrj3K9D+HvzDKhre/DN+b/VMfrL9GD97R90zIjI2oUwXIEMEAt4wyWX3wDN/Aq/8PQ9W/BudMz7BH/2wiA/VzaCqvDjTVYpIltOZe7Yqq4Z7/gb+yyZs2mx+v+uv+Lv+z/Po93+S6cpEJAco3LPdnGvhNzfBPf+Xq4o/4Hf3PcChb/8O9J7NdGUiksUU7rkgEISVv07wv21lQ0kL83Z9ndhXVsLb/wYaAy8iI1C455DiaWHmffIxPtb/xxwdqITvPwDfuAe2fB3adyvoRSRBH6jmmCvnVvKhVbezenMdP1u1n4b3HoEnHvY2lodhwY2w4CZvWXuF9wGtiBQchXsO+syaejbsaOVT23+Bpx7eztTuw3Do53Dw53DoJdjhz7JcWgnzP+wH/s0w6ypvRkoRyXuWDfOWrFy50m3ZsiXTZeSUN94/xcceeYn7r5/P//nolakbT78Ph172Av/QS970BgBF5TDv+sEz+znXQlHp5BcvIhPCzLY651aOtE1n7jlqxfwqHri5jsdeOMDBE13ct3w2d14xi8qyIu8q1+nz4epf9nY+2wrvv+QF/aGX4Nk/9dqDJTBnBdQ2wox6qGmAmiVQOc/7EFdEcpbO3HNYT3+Uf3xuPz/adpQDJ7ooChqrG2q5d/lsWhprKSse5djd3QHvv+Kd2R9+DU7sSkxYBnihP2Mx1NT7oV8/uF46bXJ+ORG5qAuduSvc84BzjrePdrJ+2wc8sf0Yx8/0UFYcpKUxwr1Xz6a5IUxx6AIfrDoHXSe87psTe+DEbji511s/dRBc0nzzFRE/8Jd4Z/oz6r2/EirnQMnUtP+uIjJI4V5AYjHHawc7WP/WBzz59jFOd/dTOaWIu35hJvcun82H6mYQDNjYf+BAH5w64AX9yT1wYq8f/nvg/KnUfUune106lXOH3Py2qTPV3SMygRTuBapvIMaLe9tZv+0Dnt7RSndflNqpJdxz1WzuXT6bq+dWYnYJQT9U10nvDL/zsH87knQ7nNrVAxAIwdTZMD3pADBtjjfVQmmld3CYMt1bllbqQCByEQp34XxflE3vtbJ+2wds3tVOXzTGghll3H3lLOprK5hZWcrMaaXMrCwdva/+UvWcgTNHB8N+aPif+QBiA6M/vmTakNCvHAz+5INAcTkUTYGiMm+Zcr8MQiXe3PkieUbhLik6z/fz1DvHWf/WB7y07wSxIW+BaaUhZlVOIVJZyiw/8BO3aaXMqiylckrR+M76wfvu2HNtXvdOz2nvTP/86Quvn/fv93ddwhOZF/LFZamhHz8YhEogVOov/fVgsd9WPLgtWDJyW7DI+6skfgsWeX91BIqG3A8NtuniMpkACncZVXffAMc7e7zbmR6OdfbQOmR54lzvsJkNSkIBZlWWEplWSk1FCVXlRVSXFVNVXkx1eTFVZf6yvJgZ5cWUFk1wF8tAnxfy8aDvPw/93d6yr3twPbHtPPQN2a/f32+gN+nWA9G+wWW6WGAw7INFqQeNYEnSevHgQSdYMvK6Bb2DhQW8dQt4BxMLDN4S90faboBdxhJvmTiADT3A+Qe1xLYiCIZSf2/9RTUuGucuoyorDrEoXMGicMWo+/RHY7Sd7U05CBzvPM/xM720dvawq/UsHV19nOruG3V6mylFQT/siwaDv8y7VZSGKC8OUlbiL4tDlJcEKYuvF4coKwlSFEw62w0VQ0XYu6VLLJYa9AM9qQeCaPxgMOB1L8X6/WUUov1Jbcn3k27xtsTP7vN/ZtKt7xx0n0x6vuR6er2fn8viB5ihB4+R2pIPKMkHpaF/LQWLhhxw4geVohH2i1+x7fy5mRy4WNJ60tLFhreBX2/8LzN/mTh4B5O2+W0p+wZh7vVQt2rCX1qFu1xUUTDAnOlTmDN9ygX3i8YcZ87309Hdx6muvkTgn+yK3+/nVLfX/n5HNx1dfZztuUCf+xDFwQBlJUHKi0NMKQ4mDgRlxUFKi4NMKfJvxUFK4+tFAaYUB5lSHEraHhjcXuwdNIoCAUJB89aD5nU5BQIQKM3uq3hjMW+oqot5BxGXfD825H7yduffj44cZCMuGbk9cbBKOshF/YNaYn3oQS3poDdiaMYD9QI1xR+XckBNer7k5+3r9rcNrTH+/osfVEb7K2Wkv3D8NhcbrCE2MML9qPdvkVj394m76WGFu2S3YMCo8rtiGOMJdX80RndflO6+Abp6hyz7onT3pi7Px9v9/bp6B2g928/5vig9/TG6+wY43++tj/d3CQWM4qAX+qFggKKAv/QPAqGgEQoEhu0T31YUDBAKGEWhwceGgv7PTBxMLLEeCnj7BwNGKOgv421Br574vvH6QoEAwYARDEAwECBoAYLBIEEzAgES2+PrgQAEzXv8uD8zkcuXfHAlPf8OCnfJqKJggMopASqnTOyEZrGYo3cgxvn+qHfri9Ljr3f3pd7vj8bojzoGojEGYo6+gRgDsRgDUUd/1NEf9e7H9xlsc/5jY/QNxOjqi/rb/ccmfkbSY/3HZMFHXQQsNfAD/oElse4fBOK3gOEvU9vj+3kHncEDVNAGD0rxg1EwMHjQGvy5yQcnbz35+ePPN9hGSg0Bi9/AbLDWgBnmL0fabjb8dwoFRvvdk7bF9xvysy6JmddVlMYIVrhLXgoEzO+Oyc6x8tHY4AEi6h8IojE3/H7UefuOdD/qGIjFiMYg6hwx//GxmCPqktZjjph/PxpL2m/IPvGfEXX+/ZgjGoOYG9wejY62n6O3P8ZALJrSNuDXHX/sQMwNv5/0c3JV/CBhlnxQGjxIJZbxNv++GXz8+vn85qpFE16Twl0kA7wzwuw88GRS8kEjflCJxfAOEs5bTxxc/H2dc8Tc4EHI+evxtsT2xP5J24ce5IYcsFIOekkHxWgMokMOrDGXvG/8OQZ/l5Tak56/pqIkLa+lwl1EskYgYAQwJnrkbCHSlRQiInlI4S4ikocU7iIieSht4W5md5rZLjPba2afTdfziIjIcGkJdzMLAn8H3AU0AR83s6Z0PJeIiAyXrjP364G9zrn9zrk+4DvAfWl6LhERGSJd4T4HOJx0/4jflmBmD5rZFjPb0t7enqYyREQKU8Y+UHXOPeqcW+mcWxkOp3FmPxGRApSui5iOAvOS7s/120a0devWE2Z26DKfqwY4cZmPnQzZXh9kf42qb3xU3/hkc30LRtuQli/rMLMQsBtYgxfqrwO/4px7Nw3PtWW0yeqzQbbXB9lfo+obH9U3Ptle32jScubunBsws08DTwFB4GvpCHYRERlZ2uaWcc49CTyZrp8vIiKjy4crVB/NdAEXke31QfbXqPrGR/WNT7bXN6Ks+IJsERGZWPlw5i4iIkMo3EVE8lDOhPvFJiIzsxIz+66//VUzWziJtc0zs2fNbIeZvWtmnxlhn1vMrNPMtvm3z09Wff7zHzSzt/3n3jLCdjOzv/Vfv+1mtmISa1ua9LpsM7MzZvbwkH0m/fUzs6+ZWZuZvZPUVm1mG8xsj7+sGuWx6/x99pjZukms7y/N7D3/3/CHZjZ9lMde8P2Qxvq+YGZHk/4d7x7lsWmfeHCU+r6bVNtBM9s2ymPT/vqNm/O/hiqbb3jDKfcBi4Bi4C2gacg+vw38g79+P/DdSaxvFrDCX5+KN8Z/aH23AE9k8DU8CNRcYPvdwE/xvor9BuDVDP5bHwcWZPr1A5qBFcA7SW1fAj7rr38W+IsRHlcN7PeXVf561STVdzsQ8tf/YqT6xvJ+SGN9XwD++xjeAxf8/56u+oZs/zLw+Uy9fuO95cqZ+1gmIrsPeNxf/zdgjV3yV5JfHufcMefcG/76WWAnQ+bSyQH3Ad90nleA6WY2KwN1rAH2Oecu94rlCeOcex7oGNKc/D57HPjICA+9A9jgnOtwzp0CNgB3TkZ9zrmnnXMD/t1X8K4Oz4hRXr+xmJSJBy9Un58d/xn49kQ/72TJlXC/6ERkyfv4b+5OYMakVJfE7w66Bnh1hM0fNrO3zOynZnbF5FaGA542s61m9uAI28fyGk+G+xn9P1QmX7+4iHPumL9+HIiMsE+2vJa/gffX2Egu9n5Ip0/73UZfG6VbKxtev1VAq3NuzyjbM/n6jUmuhHtOMLMK4PvAw865M0M2v4HX1XA18BXgR5Nc3s3OuRV4c+w/ZGbNk/z8F2VmxcC9wP8bYXOmX79hnPf3eVaOJTazPwQGgG+Nskum3g+PAIuB5cAxvK6PbPRxLnzWnvX/n3Il3McyEVliH/PmtqkETk5Kdd5zFuEF+7eccz8Yut05d8Y5d85ffxIoMrOayarPOXfUX7YBP8T70zfZJU32liZ3AW8451qHbsj065ekNd5d5S/bRtgno6+lmX0KuAf4Vf8ANMwY3g9p4Zxrdc5FnXMx4LFRnjfTr18I+CXgu6Ptk6nX71LkSri/DtSbWZ1/dnc/sH7IPuuB+KiEjwHPjPbGnmh+/9xXgZ3Oub8eZZ+Z8c8AzOx6vNd+Ug4+ZlZuZlPj63gfur0zZLf1wCf9UTM3AJ1J3Q+TZdSzpUy+fkMkv8/WAT8eYZ+ngNvNrMrvdrjdb0s7M7sT+H3gXudc9yj7jOX9kK76kj/H+egozzuW/+/p1AK855w7MtLGTL5+lyTTn+iO9YY3mmM33qfof+i3/THemxigFO/P+b3Aa8CiSaztZrw/z7cD2/zb3cBvAb/l7/Np4F28T/5fAW6cxPoW+c/7ll9D/PVLrs/wvhpxH/A2sHKS/33L8cK6Mqkto68f3oHmGNCP1+/7AN7nOJuAPcBGoNrfdyXwT0mP/Q3/vbgX+PVJrG8vXn91/H0YH0E2G3jyQu+HSarvn/3313a8wJ41tD7//rD/75NRn9/+jfj7LmnfSX/9xnvT9AMiInkoV7plRETkEijcRUTykMJdRCQPKdxFRPKQwl1EJA8p3EVE8pDCXUQkD/1/8YrspCyl9QEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(histo5.history['loss'])\n",
    "plt.plot(histo5.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 51ms/step\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[18.285011 ],\n",
       "       [20.209135 ],\n",
       "       [ 7.8709855]], dtype=float32)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model5.predict(xmod5_test[:3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model 6: Mean and standard deviation of final race position and number of entered races"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define model architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "model6=Sequential()\n",
    "model6.add(Dense(10,activation='relu',input_shape=(3,)))\n",
    "model6.add(Dense(20,activation='relu'))\n",
    "model6.add(Dense(10,activation='relu'))\n",
    "model6.add(Dense(1,activation='linear'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compile model and show summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_3\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense_12 (Dense)            (None, 10)                40        \n",
      "                                                                 \n",
      " dense_13 (Dense)            (None, 20)                220       \n",
      "                                                                 \n",
      " dense_14 (Dense)            (None, 10)                210       \n",
      "                                                                 \n",
      " dense_15 (Dense)            (None, 1)                 11        \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 481 (1.88 KB)\n",
      "Trainable params: 481 (1.88 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model6.compile(optimizer='adam',loss='mean_squared_error',metrics=['accuracy'])\n",
    "\n",
    "model6.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(592, 3)\n",
      "(592,)\n",
      "(255, 3)\n",
      "(255,)\n"
     ]
    }
   ],
   "source": [
    "xmod6_train=np.float32(Xall_train[['AvgFinalPos','StdDevFinalPos','NumRaces']].values)\n",
    "xmod6_test=np.float32(Xall_test[['AvgFinalPos','StdDevFinalPos','NumRaces']].values)\n",
    "ymod_train=np.float32(y_train.values)\n",
    "ymod_test=np.float32(y_test.values)\n",
    "\n",
    "print(xmod6_train.shape)\n",
    "print(ymod_train.shape)\n",
    "print(xmod6_test.shape)\n",
    "print(ymod_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train and evaluate model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "19/19 [==============================] - 1s 8ms/step - loss: 225.1812 - accuracy: 0.0338 - val_loss: 218.5652 - val_accuracy: 0.0471\n",
      "Epoch 2/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 174.6737 - accuracy: 0.0338 - val_loss: 164.2532 - val_accuracy: 0.0471\n",
      "Epoch 3/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 119.1077 - accuracy: 0.0338 - val_loss: 95.7908 - val_accuracy: 0.0471\n",
      "Epoch 4/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 63.9408 - accuracy: 0.0338 - val_loss: 57.3773 - val_accuracy: 0.0471\n",
      "Epoch 5/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 48.9896 - accuracy: 0.0338 - val_loss: 47.6588 - val_accuracy: 0.0471\n",
      "Epoch 6/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 44.5962 - accuracy: 0.0338 - val_loss: 41.9261 - val_accuracy: 0.0471\n",
      "Epoch 7/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 39.2017 - accuracy: 0.0338 - val_loss: 36.6774 - val_accuracy: 0.0471\n",
      "Epoch 8/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 34.4110 - accuracy: 0.0338 - val_loss: 32.2389 - val_accuracy: 0.0471\n",
      "Epoch 9/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 31.2765 - accuracy: 0.0338 - val_loss: 29.4710 - val_accuracy: 0.0471\n",
      "Epoch 10/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 28.7358 - accuracy: 0.0338 - val_loss: 27.2352 - val_accuracy: 0.0471\n",
      "Epoch 11/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 26.4879 - accuracy: 0.0338 - val_loss: 25.2513 - val_accuracy: 0.0471\n",
      "Epoch 12/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 24.2607 - accuracy: 0.0338 - val_loss: 23.5385 - val_accuracy: 0.0471\n",
      "Epoch 13/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 22.2755 - accuracy: 0.0338 - val_loss: 22.1269 - val_accuracy: 0.0471\n",
      "Epoch 14/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 20.7348 - accuracy: 0.0338 - val_loss: 21.0169 - val_accuracy: 0.0471\n",
      "Epoch 15/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 19.4696 - accuracy: 0.0338 - val_loss: 20.1512 - val_accuracy: 0.0471\n",
      "Epoch 16/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 18.5776 - accuracy: 0.0338 - val_loss: 19.2089 - val_accuracy: 0.0471\n",
      "Epoch 17/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.3793 - accuracy: 0.0338 - val_loss: 18.7457 - val_accuracy: 0.0471\n",
      "Epoch 18/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 16.6819 - accuracy: 0.0338 - val_loss: 18.0551 - val_accuracy: 0.0471\n",
      "Epoch 19/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 15.9821 - accuracy: 0.0338 - val_loss: 17.7276 - val_accuracy: 0.0471\n",
      "Epoch 20/20\n",
      "19/19 [==============================] - 0s 2ms/step - loss: 15.4018 - accuracy: 0.0338 - val_loss: 17.5158 - val_accuracy: 0.0471\n"
     ]
    }
   ],
   "source": [
    "histo6=model6.fit(xmod6_train,ymod_train,epochs=20,validation_data=(xmod6_test,ymod_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f721b27fd0>]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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risxsu5kd8ZeF/nozs2+Z2VEz+8DM1k5n8Qkz5wYIZV/UmhmaSOzVWk0kJiKJNZEj9+8D945a91Vgp3NuGbDTvw1wH7DMvzwKfHdqypxhgiF/vPubF23aUl1OZyTK28c1kZiIJM5lw9059zowOqkeBJ72rz8NPDRi/Q+cZzdQYGaVU1TrzLJwAzQcgO7mC1bfvqyUzFBAJzSJSEJdbc+93DlX518/B5T71+cCH4/Y77S/7iJm9qiZ7TWzvY2NSfgB5NB4949+fcHqrPQgG5eWaiIxEUmoSX+g6rwEu+IUc8494Zxb55xbV1paOtky4m/ODZCWNeaQyLv9icQO1nUkoDARkasP9/qhdou/bPDXnwHmj9hvnr8u9aSlw4Jbxuy737mqTBOJiUhCXW24Pwc84l9/BPiXEes/54+auRVoH9G+ST0LN0L9fui58COJkpwMblxQqHAXkYSZyFDIHwFvASvM7LSZfQH4a2CLmR0BNvu3AbYBx4GjwJPAY9NS9Uyx9C7AwYc/v2jT5upyDpzt4EybJhITkfibyGiZzzrnKp1zIefcPOfc95xzzc65u5xzy5xzm51zLf6+zjn3uHNuiXNujXNu7/T/ExJo7lqYdxPs/g7EBi/YpInERCSRdIbqZN36GLSegMMvXrB6SWkOi0vDas2ISEIo3Cdr1acgfz689Z2LNg1NJNbeq4nERCS+FO6TFUyDW/6TN7/72fcu2HR3dTnRmOO12oax7ysiMk0U7lNh7ee8Od53X3j0fv38Qkpy0tlxSOEuIvGlcJ8Kmflww3+E/c9Ax/mRn8GAcdfKcl6raaA/qonERCR+FO5T5ZYveSNm3nnygtVbqsvp7Ivy9onmce4oIjL1FO5TpWgRrLwf9j4F/T3DqzcuKyEzFNCoGRGJK4X7VFr/OPS2wvs/Gl6VGQpy+7JSdmgiMRGJI4X7VFqw3ptQbPd3IXa+x76lupyz7REOnNVEYiISHwr3qWQGtz4OzUfg6Pbh1XetLCNg8LJaMyISJwr3qbb6IcidA2/93fCq4pwMblyoicREJH4U7lMtGIKbvwgndsG54a+dZUt1OYfqOvi4pecSdxYRmRoK9+lw4+95X6A94qSmLdUVAOzU1++JSBwo3KdDdhFc/zvw4c+g0wvzRSVhlpblsF3hLiJxoHCfLrd8GQb7Ye/3hldtqS7n7eMtmkhMRKadwn26lCyF5ffBO9+DAe8LO7ZoIjERiROF+3Ra/xj0NMEHPwXg+nkFlORkaEikiEw7hft0qrodytd4JzU5RyBgbF5Vxq7aRvqig5e/v4jIVVK4Tycz7+i98RAcewXwWjNdfVF2H2+5zJ1FRK6ewn26XfPvIKd8+KSmDUtLyAoF2X7wXIILE5FUpnCfbmkZcNMX4dhOaKghMxTkjuUl7DjYoInERGTaKNzjYd3nIS1z+KSmLdUVnOuI8OGZ9gQXJiKpSuEeD+FiuO5heP/H0N3Enf5EYjs0akZEponCPV5ufQwG+2DvUxSF01lXVaQhkSIybRTu8VK6ApZuhj1PQrSPu6vLqTnXqYnERGRaKNzjaf3j0N0A+59h86pyAE0DLCLTQuEeT4s/CWXV8NbfUVWczbKyHIW7iEwLhXs8mcGtX4b6/XDidbZUl7PnZAsNnZFEVyYiKUbhHm9rPgPZJbD7Ozx0w1yCAePhf9jNR83qvYvI1FG4x1soE276Azj8IsuD5/jhH9xCS08/v/ndN3n/47ZEVyciKULhngg3fQGC6bD7u9xUVcQzX76NzFCQh5/YrW9qEpEpoXBPhJwyrz3z/o+gp4UlpTn84rHbWFqWwxd/sJcfvn0q0RWKSJJTuCfK+sdgoAf2fR+AstxMfvzorWxaXspfPLufb7xYo7lnROSqKdwTpXw1LP4E7HkC+r0PU8MZaTz5uXV89uYFfOe1Y/zJT96jPxpLbJ0ikpQU7om04SvQWQf/+yb48OfgHGnBAP/j09fwX+5ZwT+/d5ZHntqj71wVkSumcE+kJZ+E33sBsgvhmS/AU/fAmX2YGY9/cinf/Mx1vHOyhd/++19ztq030dWKSBJRuCda1UZ4dBd86tvQchyevBOe/RJ0nOU3187j6c/fTF1bhE9/500Onu1IdLUikiQU7jNBIAhrPwd/9K7Xqtn/DHz7Rtj1DTYsDPOzL6/HMD7zD2/xxpHGRFcrIklgUuFuZifN7EMze8/M9vrrisxsu5kd8ZeFU1PqLJCZB1v+Gzy+x5tB8tWvw7fXsbLxZZ59bD3zCrP4/X98h5/vO53oSkVkhpuKI/dPOueud86t829/FdjpnFsG7PRvy5UoWgT//p/gkeeH+/GVzzzEzx/M4JbFRfzpz97nWzuPaKikiIxrOtoyDwJP+9efBh6ahseYHRbdfkE/Pufpu/lB4T/y+9ek883th/nzX3zIwKCGSorIxWwyR39mdgJoBRzwD865J8yszTlX4G83oHXo9qj7Pgo8CrBgwYIbT53SWZmXFOmAN/4Wdn8HF0jjzYrf5QtH1nPL8rl8edMSblhQQGYomOgqRSSOzGzfiK7JhdsmGe5znXNnzKwM2A78EfDcyDA3s1bn3CX77uvWrXN79+696jpmlZYTsP0v4dBzdGdW8F+7fot/jd5MMC2ddVWF3LakhNuWFLNmbj5pQX1eLpLKpi3cRz3I14Au4IvAJ5xzdWZWCbzmnFtxqfsq3K/CiTfgpT+Hcx/Sn17Ah3mb+FnvTfyseSGDBMnJSOOWRUWsX1LMhqUlrCjPJRCwRFctIlNoWsLdzMJAwDnX6V/fDvwVcBfQ7Jz7azP7KlDknPuzS/0shftVig3C4Rdh/y+g9pcw0E0su4SPy7fwcmA9Pz43j2PN3heBFIXTWb+4mPVLirltSTGLSsJ4XTMRSVbTFe6LgWf9m2nA/3POfd3MioGfAguAU8BnnHMtl/pZCvcp0N8DR7fDgWfh8EvepGQ55XQtuZ+94U/wfOsC3jzeQl27F/aV+Zl+0JfwyRWlFOdkJPgfICJXKi5tmclQuE+x/m4v4A88C0dehmgEcitx1Q9SN28rr3Yv4NfHW3nrWDMt3f0EDG6qKuKe1RXcvbqceYXZif4XiMgEKNxns77OEUG/HQb7IG8erH6IWPWnOWhLeflgPS8dqKe2vhOAa+bmcU91BfdcU8Gyshy1b0RmKIW7eCIdXm/+wLNwdAfEBqBgAax8AFZs5UT4Wl461MRLB87xbx+1AbCoJMw9qyu4Z3U5180r0IeyIjOIwl0u1tsGtdvgwD/D8de8I/qsQlh2D6zcSkPZRl462sXLB87x1rFmojFHeV4Gd1dXcM/qCm5ZXERIQy1FEkrhLpfW1wXHXvHC/vCL0NsKwQxYvAlWbKVjwWZ2nDZeOnCOXYcbiQzEyM8KcdeqMu5ZXcHGpSWEM9IS/a8QmXUU7jJxg1H4eDfUbIPaF6D1pLd+7jpYuZXI4nvZ1VrESwfq2XGono5IlFDQuKmqiE3LS9m0opQV5bnq04vEgcJdro5z0HDIC/maF+Dsv3nrixbDiq1El9/HnoFl7Drawq7DjdSc8z6QrcjLHA76DUtLyM8KJfAfIZK6FO4yNTrOeq2bmm1w4nXvA9nsYli0CRZvoqHkVl5tyGbX4UbeONJEZyRKMGDcML+ATctL+cSKMlbPydOHsiJTROEuUy/S4Y24OfwSnNjlfRcseKNvFt3B4MI7+DD9enaehl2HG/ngdDsAxeF07lheyqblpdy+rEQnT4lMgsJdppdz0HTEC/njr8HJNyDihTmlq2DxJjoq17OrfwU7j0d4/UgTLd39mME1c/K5bn4+qyrzWFWZx8qKXLLT9eGsyEQo3CW+YoNQ974X9ideh1NvQbQXLABzbsBVbeJE3o282L6QXSe6OHi2g86+KABmsKg47Id97nDoV+Zn6kNakVEU7pJY0T44/Q4c3+UF/um94Aa94Zbzb8aVX0NreDFH3Fze7SnjvSbjUF0nH7X0DP+IguwQqyryhkO/ek4eS8tyyEjTHPYyeyncZWbp6/SO5k/sgpO/gsZa78h+SLgMSlfQX7ScutACagbnsLe7jD2NadTWdxIZ8L59Ki1gLC3LYUlpDotKwiwuDXvLkhzyszVCR1Kfwl1mtlgM2j/yQn74UgNNh6Gv4/x+mQW40pV05C7hdHAeBwbmsKerhH0tWXzU1sdg7PxruSiczuISL+wXlXqBv7g0zIKibH1jlaQMhbskJ+e8UTiNNdB42F/6wd87YhbpYAauYAG94Xk0hyo5beUcGyjmg+5C9rTlcbLrfJibwdyCLBaVhIeP+BcUZ7OgKJu5BVkKfkkqlwp3DUuQmcsM8uZ4lyV3Xritu+l82LeexNpOkd16kuyGd5kfaWf9iF1dQSG9OfNpzZjDWSvj2EAp+9sK2f1RPv+3L5/oiF+DirxMFhRlM7/IC/wFxVne7cJsSnMz9KGuJA2FuySncAmEN0LVxou39bZC6ylv6oS2U1jrSS/4W48wt20nN8UGvP0MXFaAgewKOjPKaQqWcSZWxImeQmqa8nmxO48zrpgOwoCRGQowvzD7gvA/v8zSEE6ZUfRqlNSTVehd5lx/8bbYoHembZsX/tZ6kvT2MxS3f0xx+2FWdJyBwX5vX//8qmhamK6McpqDpZxxJZw4V0jN8TxejhZx1hVT7wrpI52SnHTm+eE/FPjz/aP+yvxMfWG5xJV67iIjxWLQ3Qjtp6H9Y395GjpOn7/e3XjR3SJpebQFi2mkkNPRfE7253IuVki9K6TBFdBkRYTyK6kszr8g9BcUZTO3MIvicLpaPnLF1HMXmahAAHLLvcu8G8feZ6DXO/ofCv/OOjI766norKOi8xxrOo/g3DksFr3wfr3QcSaP+tMFnB0soMEV8AaFNLs82gP5WLiUUF4p2QUV5BVXUFmUy5yCLO+Sn0VWuj7slYlTuItcqVAWFC/xLuOwWMwb0dNZB53n/GU9eZ115HWeY3HHWWIdRwj2NBBwg96dIv6lwbvZ7rJpdnm0kMcxl0tnsIBoZjEuXEIot5TMgnJyCivIKywlv7iUkqJicjND+gtAAIW7yPQIBPwPfUugYs1Fm4P+hVgMIm3e6J+eJq/l093EYFcTgdZz5Hc0kNvVSFVvMxl9J8iOtBGMxKD54oeMugBthOkOhOkN5tKflsdgRh4uo4BAdgGhcCEZuUVk5RWTW1BCdl4xllUAGbmQnuO9aemNIWUo3EUSKRCA7CLvwvLh1UEgd6z9h94Meprpbq2jrbGOnvZmIl3NRLvaiPW2YpE2gv0dpA90EI7UkeO6yKObdBu8ZCmDBOgPhhkIZjMYCuPScyA9h0BmLmlZeaRn5xHKysMycs6/IQxdz8j3l/4lPaw3igRTuIskkxFvBuGSZYSXXf4usZijtbuP5rYO2loa6GxroqejmUhnMwNdrcQinbi+Tqy/i+BAF6H+HsK9vYSJkGMNhPmIsEXIwVsXusybBIAjQDQUZjA9F5fuBX4gM49AVh5pWflYRi5k5HlvBGkZ3iWYAWnpo5YZEEwftRyxPRjSm8g4FO4iKS4QMIpzMynOzYT5ZZfdfzDm6OgdoKWnn7aefj7uHqC1p5+2ngFau/vo7O4m0t1OX3c7A72dWF8ngf5O0qJdZLtecugh13rJifaSG+klB29djrWQS6+3jV6yrW8K/nXmtZNC2f4lC9KzR90Oj7HPiHXBdO9NIhCCQPD89WCavxzrdtqF97Gg98Y7gyjcReQCwYBRGE6nMJx+RfdzztEXjdHVF6W7L0pnxFt29UVp7otyqm/o9iBdkSi9kQj9vR309fbQ29tNb28vfZFeov0R0omSbgPekgEyRtzOT4+RlxYjNxQjNy1GONBPlvWTTR+Zg31k9PaT0R0hw7URivURivUSHIyQNthLINqLMV3Dv21E0I9YXrQu4C/TvHVrPwfrH5/yahTuIjIlzIzMUJDMUJCSSXzD1sBgjI7eAdp6B2jrGaC91/uroa3HW9fe089Zf1tbTz89/YP09A8SGfCWvQOXahs5Mhggiz6y6CfbIoQYJCsQIxxy5IQc4aAjOy1GdpojKxgjK+jIDsbIDMbIDHjrMgKDZARiZFiMUCBGyBwhi5FmjjSLkRbwlkEcaQySZo4gMQLEvBPp3CDEot717JKrfq4uReEuIjNKKBigOCfjqr+CMRbz/oLo6Y/SOzBIrx/4Q8Hf2+9degYG6e2P0tsfo2cgSmTEfu2j9/dvR/z7jZyB9EoEA0ZmWoDMUJAMf/k7cxbwB1f10y5N4S4iKSUQMLLSg9N20pdzjoFB579BRIkMxOiLDhIZiBEZ8P6C6It61/sGYkSi/nJgkMiI/Yb2mcxfOZeicBcRuQJmRnqakZ4WIJ+Z+6UwM+vjXRERmRIKdxGRFKRwFxFJQQp3EZEUpHAXEUlBCncRkRSkcBcRSUEKdxGRFDQjvkPVzBqBU1d59xKgaQrLmWozvT6Y+TWqvslRfZMzk+tb6JwrHWvDjAj3yTCzveN9QexMMNPrg5lfo+qbHNU3OTO9vvGoLSMikoIU7iIiKSgVwv2JRBdwGTO9Ppj5Naq+yVF9kzPT6xtT0vfcRUTkYqlw5C4iIqMo3EVEUlDShLuZ3WtmtWZ21My+Osb2DDP7ib/9bTOrimNt883sVTM7aGYHzOyPx9jnE2bWbmbv+Ze/jFd9/uOfNLMP/cfeO8Z2M7Nv+c/fB2a2No61rRjxvLxnZh1m9pVR+8T9+TOzp8yswcz2j1hXZGbbzeyIvywc576P+PscMbNH4ljf/zSzGv//8FkzKxjnvpd8PUxjfV8zszMj/h+3jnPfS/6+T2N9PxlR20kze2+c+0778zdpzrkZfwGCwDFgMZAOvA9Uj9rnMeDv/esPAz+JY32VwFr/ei5weIz6PgE8n8Dn8CRQcontW4FfAgbcCrydwP/rc3gnZyT0+QPuANYC+0es+wbwVf/6V4G/GeN+RcBxf1noXy+MU313A2n+9b8Zq76JvB6msb6vAX86gdfAJX/fp6u+Udv/FvjLRD1/k70ky5H7zcBR59xx51w/8GPgwVH7PAg87V//OXCXmVk8inPO1Tnn3vWvdwKHgLnxeOwp9CDwA+fZDRSYWWUC6rgLOOacu9ozlqeMc+51oGXU6pGvs6eBh8a46z3Adudci3OuFdgO3BuP+pxzLzvnov7N3cC8qX7ciRrn+ZuIify+T9ql6vOz4zPAj6b6ceMlWcJ9LvDxiNunuTg8h/fxX9ztQHFcqhvBbwfdALw9xub1Zva+mf3SzFbHtzIc8LKZ7TOzR8fYPpHnOB4eZvxfqEQ+f0PKnXN1/vVzQPkY+8yU5/LzeH+NjeVyr4fp9Id+2+ipcdpaM+H5ux2od84dGWd7Ip+/CUmWcE8KZpYDPAN8xTnXMWrzu3ithuuAbwP/HOfyNjrn1gL3AY+b2R1xfvzLMrN04FPAz8bYnOjn7yLO+/t8Ro4lNrO/AKLAD8fZJVGvh+8CS4DrgTq81sdM9FkufdQ+43+fkiXczwDzR9ye568bcx8zSwPygea4VOc9Zggv2H/onPvF6O3OuQ7nXJd/fRsQMrOSeNXnnDvjLxuAZ/H+9B1pIs/xdLsPeNc5Vz96Q6KfvxHqh9pV/rJhjH0S+lya2e8BDwD/wX8DusgEXg/TwjlX75wbdM7FgCfHedxEP39pwG8CPxlvn0Q9f1ciWcL9HWCZmS3yj+4eBp4btc9zwNCohN8CXhnvhT3V/P7c94BDzrlvjrNPxdBnAGZ2M95zH5c3HzMLm1nu0HW8D932j9rtOeBz/qiZW4H2Ee2HeBn3aCmRz98oI19njwD/MsY+LwF3m1mh33a421837czsXuDPgE8553rG2Wcir4fpqm/k5zifHudxJ/L7Pp02AzXOudNjbUzk83dFEv2J7kQveKM5DuN9iv4X/rq/wnsRA2Ti/Tl/FNgDLI5jbRvx/jz/AHjPv2wFvgR8yd/nD4EDeJ/87wZui2N9i/3Hfd+vYej5G1mfAX/nP78fAuvi/P8bxgvr/BHrEvr84b3R1AEDeH3fL+B9jrMTOALsAIr8fdcB/2fEfT/vvxaPAr8fx/qO4vWrh16HQyPI5gDbLvV6iFN9/+S/vj7AC+zK0fX5ty/6fY9Hff767w+97kbsG/fnb7IXTT8gIpKCkqUtIyIiV0DhLiKSghTuIiIpSOEuIpKCFO4iIilI4S4ikoIU7iIiKej/Ay0m4dsmVja+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(histo6.history['loss'])\n",
    "plt.plot(histo6.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 45ms/step\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[19.724798],\n",
       "       [12.709128],\n",
       "       [ 8.678424]], dtype=float32)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model6.predict(xmod6_test[:3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model 7: Shallow and wide - Mean and standard deviation of grid and final race position and number of entered races"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define model architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "model7=Sequential()\n",
    "model7.add(Dense(200,activation='relu',input_shape=(5,)))\n",
    "model7.add(Dense(1,activation='linear'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compile model and show summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_5\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense_18 (Dense)            (None, 200)               1200      \n",
      "                                                                 \n",
      " dense_19 (Dense)            (None, 1)                 201       \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 1401 (5.47 KB)\n",
      "Trainable params: 1401 (5.47 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model7.compile(optimizer='adam',loss='mean_squared_error',metrics=['accuracy'])\n",
    "\n",
    "model7.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Year', 'RaceResults', 'GridPos', 'QualiRes', 'NumRaces', 'AvgFinalPos',\n",
       "       'StdDevFinalPos', 'MedianFinalPos', 'AvgStartPos', 'StdDevStartPos',\n",
       "       'MedianStartPos'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xall_train.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(592, 5)\n",
      "(592,)\n",
      "(255, 5)\n",
      "(255,)\n"
     ]
    }
   ],
   "source": [
    "xmod7_train=np.float32(Xall_train[['AvgFinalPos','StdDevFinalPos','AvgStartPos','StdDevStartPos','NumRaces']].values)\n",
    "xmod7_test=np.float32(Xall_test[['AvgFinalPos','StdDevFinalPos','AvgStartPos','StdDevStartPos','NumRaces']].values)\n",
    "ymod_train=np.float32(y_train.values)\n",
    "ymod_test=np.float32(y_test.values)\n",
    "\n",
    "print(xmod7_train.shape)\n",
    "print(ymod_train.shape)\n",
    "print(xmod7_test.shape)\n",
    "print(ymod_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train and evaluate model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "19/19 [==============================] - 0s 7ms/step - loss: 214.1116 - accuracy: 0.0135 - val_loss: 107.4000 - val_accuracy: 0.0471\n",
      "Epoch 2/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 62.3843 - accuracy: 0.0338 - val_loss: 61.4872 - val_accuracy: 0.0471\n",
      "Epoch 3/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 40.9646 - accuracy: 0.0338 - val_loss: 44.9529 - val_accuracy: 0.0471\n",
      "Epoch 4/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 25.8612 - accuracy: 0.0338 - val_loss: 32.3926 - val_accuracy: 0.0471\n",
      "Epoch 5/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 17.7606 - accuracy: 0.0304 - val_loss: 26.1366 - val_accuracy: 0.0392\n",
      "Epoch 6/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 14.3441 - accuracy: 0.0236 - val_loss: 22.2729 - val_accuracy: 0.0235\n",
      "Epoch 7/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.6377 - accuracy: 0.0220 - val_loss: 19.7559 - val_accuracy: 0.0235\n",
      "Epoch 8/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 11.6049 - accuracy: 0.0220 - val_loss: 17.9266 - val_accuracy: 0.0275\n",
      "Epoch 9/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 10.6829 - accuracy: 0.0236 - val_loss: 16.0785 - val_accuracy: 0.0275\n",
      "Epoch 10/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 10.0172 - accuracy: 0.0253 - val_loss: 15.5329 - val_accuracy: 0.0392\n",
      "Epoch 11/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 9.6442 - accuracy: 0.0270 - val_loss: 13.9159 - val_accuracy: 0.0235\n",
      "Epoch 12/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 9.1405 - accuracy: 0.0236 - val_loss: 13.4351 - val_accuracy: 0.0353\n",
      "Epoch 13/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 8.8159 - accuracy: 0.0236 - val_loss: 13.1564 - val_accuracy: 0.0392\n",
      "Epoch 14/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 8.7714 - accuracy: 0.0236 - val_loss: 12.3140 - val_accuracy: 0.0392\n",
      "Epoch 15/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 8.3262 - accuracy: 0.0270 - val_loss: 12.0815 - val_accuracy: 0.0392\n",
      "Epoch 16/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 8.1437 - accuracy: 0.0236 - val_loss: 11.7587 - val_accuracy: 0.0392\n",
      "Epoch 17/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 8.0516 - accuracy: 0.0270 - val_loss: 12.2214 - val_accuracy: 0.0392\n",
      "Epoch 18/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 7.9800 - accuracy: 0.0270 - val_loss: 11.6633 - val_accuracy: 0.0392\n",
      "Epoch 19/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 7.8309 - accuracy: 0.0270 - val_loss: 11.7627 - val_accuracy: 0.0392\n",
      "Epoch 20/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 7.8871 - accuracy: 0.0287 - val_loss: 11.5621 - val_accuracy: 0.0392\n"
     ]
    }
   ],
   "source": [
    "histo7=model7.fit(xmod7_train,ymod_train,epochs=20,validation_data=(xmod7_test,ymod_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f722cbddb0>]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(histo7.history['loss'])\n",
    "plt.plot(histo7.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 36ms/step\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[15.390786],\n",
       "       [18.253681],\n",
       "       [ 7.160033]], dtype=float32)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model7.predict(xmod5_test[:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16., 18.,  7.], dtype=float32)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ymod_test[:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model 8: Deep and narrow - Mean and standard deviation of grid and final race position and number of entered races"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define model architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "model8=Sequential()\n",
    "model8.add(Dense(10,activation='relu',input_shape=(5,)))\n",
    "model8.add(Dense(10,activation='relu'))\n",
    "model8.add(Dense(10,activation='relu'))\n",
    "model8.add(Dense(10,activation='relu'))\n",
    "model8.add(Dense(10,activation='relu'))\n",
    "model8.add(Dense(10,activation='relu'))\n",
    "model8.add(Dense(10,activation='relu'))\n",
    "model8.add(Dense(10,activation='relu'))\n",
    "model8.add(Dense(10,activation='relu'))\n",
    "model8.add(Dense(10,activation='relu'))\n",
    "model8.add(Dense(1,activation='linear'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compile model and show summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_7\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense_31 (Dense)            (None, 10)                60        \n",
      "                                                                 \n",
      " dense_32 (Dense)            (None, 10)                110       \n",
      "                                                                 \n",
      " dense_33 (Dense)            (None, 10)                110       \n",
      "                                                                 \n",
      " dense_34 (Dense)            (None, 10)                110       \n",
      "                                                                 \n",
      " dense_35 (Dense)            (None, 10)                110       \n",
      "                                                                 \n",
      " dense_36 (Dense)            (None, 10)                110       \n",
      "                                                                 \n",
      " dense_37 (Dense)            (None, 10)                110       \n",
      "                                                                 \n",
      " dense_38 (Dense)            (None, 10)                110       \n",
      "                                                                 \n",
      " dense_39 (Dense)            (None, 10)                110       \n",
      "                                                                 \n",
      " dense_40 (Dense)            (None, 10)                110       \n",
      "                                                                 \n",
      " dense_41 (Dense)            (None, 1)                 11        \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 1061 (4.14 KB)\n",
      "Trainable params: 1061 (4.14 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model8.compile(optimizer='adam',loss='mean_squared_error',metrics=['accuracy'])\n",
    "\n",
    "model8.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Year', 'RaceResults', 'GridPos', 'QualiRes', 'NumRaces', 'AvgFinalPos',\n",
       "       'StdDevFinalPos', 'MedianFinalPos', 'AvgStartPos', 'StdDevStartPos',\n",
       "       'MedianStartPos'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xall_train.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(592, 5)\n",
      "(592,)\n",
      "(255, 5)\n",
      "(255,)\n"
     ]
    }
   ],
   "source": [
    "xmod8_train=np.float32(Xall_train[['AvgFinalPos','StdDevFinalPos','AvgStartPos','StdDevStartPos','NumRaces']].values)\n",
    "xmod8_test=np.float32(Xall_test[['AvgFinalPos','StdDevFinalPos','AvgStartPos','StdDevStartPos','NumRaces']].values)\n",
    "ymod_train=np.float32(y_train.values)\n",
    "ymod_test=np.float32(y_test.values)\n",
    "\n",
    "print(xmod8_train.shape)\n",
    "print(ymod_train.shape)\n",
    "print(xmod8_test.shape)\n",
    "print(ymod_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train and evaluate model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "19/19 [==============================] - 1s 10ms/step - loss: 280.8605 - accuracy: 0.0000e+00 - val_loss: 305.1512 - val_accuracy: 0.0000e+00\n",
      "Epoch 2/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 278.9410 - accuracy: 0.0000e+00 - val_loss: 302.8116 - val_accuracy: 0.0000e+00\n",
      "Epoch 3/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 276.1984 - accuracy: 0.0000e+00 - val_loss: 299.1490 - val_accuracy: 0.0000e+00\n",
      "Epoch 4/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 271.6507 - accuracy: 0.0000e+00 - val_loss: 292.5057 - val_accuracy: 0.0000e+00\n",
      "Epoch 5/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 261.7198 - accuracy: 0.0338 - val_loss: 273.7503 - val_accuracy: 0.0471\n",
      "Epoch 6/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 212.2216 - accuracy: 0.0338 - val_loss: 155.2225 - val_accuracy: 0.0471\n",
      "Epoch 7/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 102.4805 - accuracy: 0.0338 - val_loss: 74.5457 - val_accuracy: 0.0471\n",
      "Epoch 8/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 50.8889 - accuracy: 0.0338 - val_loss: 39.0196 - val_accuracy: 0.0471\n",
      "Epoch 9/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 25.6625 - accuracy: 0.0338 - val_loss: 21.1106 - val_accuracy: 0.0471\n",
      "Epoch 10/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 16.0430 - accuracy: 0.0338 - val_loss: 16.6914 - val_accuracy: 0.0471\n",
      "Epoch 11/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 13.4491 - accuracy: 0.0338 - val_loss: 16.2710 - val_accuracy: 0.0471\n",
      "Epoch 12/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 12.8512 - accuracy: 0.0338 - val_loss: 14.6973 - val_accuracy: 0.0471\n",
      "Epoch 13/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 10.8979 - accuracy: 0.0338 - val_loss: 14.3964 - val_accuracy: 0.0471\n",
      "Epoch 14/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 10.5273 - accuracy: 0.0338 - val_loss: 12.9194 - val_accuracy: 0.0471\n",
      "Epoch 15/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 9.9381 - accuracy: 0.0338 - val_loss: 12.8176 - val_accuracy: 0.0471\n",
      "Epoch 16/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 9.9484 - accuracy: 0.0338 - val_loss: 12.7151 - val_accuracy: 0.0471\n",
      "Epoch 17/20\n",
      "19/19 [==============================] - 0s 4ms/step - loss: 9.3115 - accuracy: 0.0338 - val_loss: 12.5055 - val_accuracy: 0.0471\n",
      "Epoch 18/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 9.1171 - accuracy: 0.0338 - val_loss: 11.7132 - val_accuracy: 0.0471\n",
      "Epoch 19/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 8.8780 - accuracy: 0.0338 - val_loss: 11.5556 - val_accuracy: 0.0471\n",
      "Epoch 20/20\n",
      "19/19 [==============================] - 0s 3ms/step - loss: 8.6654 - accuracy: 0.0338 - val_loss: 11.4384 - val_accuracy: 0.0471\n"
     ]
    }
   ],
   "source": [
    "histo8=model8.fit(xmod8_train,ymod_train,epochs=20,validation_data=(xmod8_test,ymod_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f7240396c0>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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r8ruqgUn+8hRgb9jT9vltPf+sVWa21szW1tTUDLVuGYrOK0RWvR2xu6K8gP11J3QhMZEkMuhwN7Ns4FHgy865bnvfnHMOcEN5YefcaufcEufckqKioqE8VYaqK9w3RuyuKM8HYL223kWSxqDC3cxS8YL9QefcY37zwc7hFn/eeZrjfqAs7OmlfpvEy7hC776qfYy7zy/JJS0YYMNejbuLJIvBHC1jwD3ANufc98K6ngRW+ssrgSfC2j/pHzWzDKgPG76ReOnnTNX0lCDzSnI17i6SRAaz5f5h4CbgEjPb6E9XAd8CPmJm24HL/McATwE7gUrgbuC2kS9bhqykAo7uhuO1EbsryvPZtK+O9o5QbOsSkahIGWgF59yrgPXRfWmE9R1w+zDrkpEWPu4+85Je3RXlBfz0td28W93Igil5sa1NREaczlAdK4rP8uYDncyki4iJJAWF+1iRWQCFM/oM99KCTCZkp+tkJpEkoXAfS0oq+ry2u5lRUZ7PRu1UFUkKCvexpKQC6vdC0+GI3RXl+ew83MTRptYYFyYiI03hPpZ03XZvY8TuirICADbuq4tJOSISPQr3sWSAnapnluYRMF0hUiQZKNzHkoxcGD+7z3DPSk/htMm52qkqkgQU7mNNP2eqgjfuvnFvHaHQkC4VJCIJRuE+1pRUQOMBaKyO2F1Rlk9jczs7Dx+LcWEiMpIU7mNN55mqfe1ULfd2quoKkSKjm8J9rJl8Bligz6GZGROyyMtM1U5VkVFO4T7WpGfDhNP6DPdAwFhYlq+dqiKjnMJ9LOrcqeoi7zStKM/n/YONHGtpj3FhIjJSFO5jUclCaDoEjZEvs19RXkDIwSadzCQyaincx6KunaqRh2YWluYDOplJZDRTuI9FkxaABfsM97xxqcwsylK4i4xiCvexKG0cTDx9gJOZCtiw5yiuj3F5EUlsCvexqmThgDtVjzS1srf2RGzrEpERoXAfq0oq4PgR7xLAEXReIXLDXh0SKTIaKdzHqgF2qs6ZlM24tKDG3UVGKYX7WDVpAQRS+wz3lGCAM0vzdDKTyCilcB+rUtIHtVN1y4EGmts6YliYiIwEhftY1nlP1b52qpbl0x5ybDlQH9u6RGTYFO5jWUkFNNfB0d0RuxeW5wM6mUlkNFK4j2VlS7357lcidk/MyaC0IFPhLjIKDRjuZnavmR0ys81hbV83s/1mttGfrgrr+3szqzSz98zsimgVLiNg4jzILYX3/9DnKp0nM4nI6DKYLff7gOUR2r/vnFvoT08BmNk84Hpgvv+cH5lZcKSKlRFmBnOugB0vQHtLxFUqyvI5UN9MdX1zjIsTkeEYMNydcy8DtYP881YADznnWpxzu4BKYOkw6pNom7Mc2pr6HJqp8MfdN+pkJpFRZThj7l8ws03+sE2B3zYFCD/lcZ/f1ouZrTKztWa2tqamZhhlyLBMvwBSx/U5NDOvJJe0YEDj7iKjzKmG+53ATGAhUAX851D/AOfcaufcEufckqKiolMsQ4YtNQNmXATv/z7iIZHpKUHmT8lVuIuMMqcU7s65g865DudcCLibk0Mv+4GysFVL/TZJZHOugLo9UPNuxO5F5QVs2l9HW0coxoWJyKk6pXA3s+Kwh9cAnUfSPAlcb2bpZjYdmA28ObwSJepmX+7N33s6YndFeT7NbSHeq26MYVEiMhyDORTyl8DrwGlmts/MbgG+Y2bvmNkm4GLgKwDOuS3Ar4CtwO+B251zOnc90eWWQPFZfY67V5T7V4jUIZEio0bKQCs4526I0HxPP+t/E/jmcIqSOJhzJbz8HWg6Alnju3WV5GUwMSedDXvquOncONUnIkOiM1TFM+cKcCGo/GOvLjOjojyfDXvrYl+XiJwShbt4ihdC9iR4v69x9wJ2HW7iaFNrbOsSkVOicBdPIODtWK18DjraenVXlOUDsFFb7yKjgsJdTjrtSmhpgD2v9+o6ozSPYMBYr52qIqOCwl1Omn4hBNMjHjUzLi2FuZNzdDKTyCihcJeT0rNh+vn9Hu++cW8dHaHIN/cQkcShcJfu5iyH2h1wuLJXV0VZAcda2tlRcywOhYnIUCjcpbs5/iX43/99r66KrjszadxdJNEp3KW7/HKYOD9iuE+fkEVeZqrG3UVGAYW79DbnCu+ImRN13Zq7TmZSuIskPIW79DZnOYTaYcdzvboqygp4/1Ajjc29j4UXkcShcJfeSpfAuPERD4msKM/HOdi0rz4OhYnIYCncpbdA0DtbdfszEOp+Uc+z/DNVtVNVJLEp3CWyOVfAiaOwt/vl+PMyU5k1MVvj7iIJTuEukc28BAIpkQ+JLPOuEOki3JZPRBKDwl0iy8iDqR/qY9y9gNqmVvbUHo9DYSIyGAp36duc5VCzDY7u7tZ88mSmupiXJCKDo3CXvs1Z7s17bL3PmZRDVlpQO1VFEpjCXfo2fiaMn91r3D0YMM4q052ZRBKZwl36N+cK2P0qtDR2a64oz2frgQaa23T/c5FEpHCX/s1ZDh2tsPPFbs0VZQW0hxyb9+tkJpFEpHCX/pUv846c6TE0s1A7VUUSmsJd+hdMhVmXwfvPQCjU1TwhO53ywnFs2KudqiKJSOEuA5uzHJoOwYEN3Zp1hUiRxDVguJvZvWZ2yMw2h7UVmtmzZrbdnxf47WZmPzCzSjPbZGaLolm8xMisy8ACvYZmKsryqapvpqr+RJwKE5G+DGbL/T5geY+2rwHPOedmA8/5jwGuBGb70yrgzpEpU+JqXCGUndMr3M+eXgjAM1sOxqMqEenHgOHunHsZqO3RvAK431++H7g6rP0B53kDyDez4hGqVeJpznKo3gT1+7ua5hXnsqg8n7tf2Ul7R6ifJ4tIrJ3qmPsk51yVv1wNTPKXpwB7w9bb57f1YmarzGytma2tqak5xTIkZjrPVt1+8mxVM+PzF81i39ET/O6dqj6eKCLxMOwdqs67NOCQLw/onFvtnFvinFtSVFQ03DIk2opOg/ypvS5FcOncicyemM2dL+7QVSJFEsiphvvBzuEWf37Ib98PlIWtV+q3yWhn5m2973wRWk9eDTIQMFZdMIN3qxt58X39AhNJFKca7k8CK/3llcATYe2f9I+aWQbUhw3fyGh32nJob4ZdL3drXrFwCsV5Gdz14o44FSYiPQ3mUMhfAq8Dp5nZPjO7BfgW8BEz2w5c5j8GeArYCVQCdwO3RaVqiY+pH4a07F5HzaSlBLjlvOms2VWrK0WKJIiUgVZwzt3QR9elEdZ1wO3DLUoSVEo6zLzYG3d3zhuq8d2wtJwfPl/JXS/t4Mc3LYljkSICOkNVhmrOcmg8ANXvdGvOSk/hk+dO5ZmtB6k8dCxOxYlIJ4W7DM3sywGLeG/VlR+aRlowwOqXNfYuEm8Kdxma7IkwZXHEcJ+Qnc7HlpTx+Ib9VNc3x6E4EemkcJehm7Mc9q+DY4d6da26YAYhB/e+tisOhYlIJ4W7DN2cK7z59md6dZUVjuPPzijmwTc+oP54W4wLE5FOCncZuslnQO4UeO/piN2fu3AGTa0d/HzNBzEuTEQ6Kdxl6My8rfcdL0B7S6/u+SV5XDCniJ++tkv3WBWJE4W7nJo5y6Gtybt5dgSfv3Amh4+18si6fTEuTERA4S6navoFkJLZ60JinZbNKOSssnxWv6zLAYvEg8JdTk1qJsy4EN5/2jtbtQcz4/MXzmBP7XGe3lwdhwJFxjaFu5y6OVdA3R7vJh4RfGTeZGZMyOKul3Q5YJFYU7jLqTv9LyAjD373NxDqveM06F8OeMuBBl6tPByHAkXGLoW7nLqsCXDld2Hfm/D6HRFXuWbRFCbmpHPXS7okgUgsKdxleM78GMz9KDz/TTj0bq/u9JQgt5w3ndcqj7BpX13s6xMZoxTuMjxm8NHvQ1oW/OZW6Oh9VurHzyknJyNFW+8iMaRwl+HLnugF/IEN8Or3e3XnZKTyiWVTeXpzNbsON8WhQJGxR+EuI2P+1bDgWnjp21DV++iZT394GqnBAKtf3hn72kTGIIW7jJyr/gPGjYfffB7aW7t1TczJ4LrFpTy6bh+HGnQ5YJFoU7jLyBlXCH/+X3Bws7cF38Oq82fQHgpx72u7Y1+byBijcJeRddqVcNbHvbH3/eu6dU2bkMWVC7zLATc063LAItGkcJeRt/z/QPYkePzz0NZ9CObWC2fS2NLOL9bsiVNxImODwl1GXmY+rLgDDr8HL/xbt64zSvM4b9YE7nlVlwMWiSaFu0THrEth8afhT3fAnje6dd164UxqGlt4fMP+OBUnkvwU7hI9l/8r5JfB47dC68nj2z88azwLpuSy+uWddIR0QTGRaBhWuJvZbjN7x8w2mtlav63QzJ41s+3+vGBkSpVRJz0HVvwIju6CP369q9nMuPXCmew63MQzW3Q5YJFoGIkt94udcwudc0v8x18DnnPOzQae8x/LWDX9fDjnVnhzNex8qav5ygXFTB0/TpcDFomSaAzLrADu95fvB66OwmvIaHLpv0DhTHjiC9DcAJy8HPDb++o19i4SBcMNdwc8Y2brzGyV3zbJOVflL1cDkyI90cxWmdlaM1tbU1MzzDIkoaWNg6vvhIZ98Mz/6mq+bnEp50wv5G8f2aThGZERNtxwP885twi4ErjdzC4I73Te7+2Iv7mdc6udc0ucc0uKioqGWYYkvPJz4ENfhPX3w/Y/At7lgO/51NmcMSWPL/xiA69s15e8yEgZVrg75/b780PA48BS4KCZFQP480PDLVKSxEX/AEVz4ckvwomjAGSnp3D/p5cyoyiLzz6wljd31ca5SJHkcMrhbmZZZpbTuQxcDmwGngRW+qutBJ4YbpGSJFIz4Jq74NhBePrkfva8can87JZzKMnP5Ob73tJNPURGwHC23CcBr5rZ28CbwO+cc78HvgV8xMy2A5f5j0U8JRVw/ldh00Pw7u+6moty0nnwM+eQPy6VT977Ju9VN8axSJHRzxLhMLQlS5a4tWvXxrsMiZX2VvjJJdBYDbetgazxXV17jhznr378JzpC8Otbz2X6hKw4FiqS2MxsXdhh6N3oDFWJvZQ0uPouOFEHT321W1f5+HE8+JllOOe48e432Hf0eHxqFBnlFO4SH5MXwEVfgy2Pw+//vtvNPWZNzOaBW5ZyrKWdG3+yRjf3EDkFCneJnw9/GZaugjd+BD9dDkd3d3XNL8njvpuXUtPYwo0/WUNtU2uff4yI9KZwl/gJpsBV34WPPQCHK+GuC2Db/+vqXlRewD0rz2ZP7XE+ee8a3eBDZAgU7hJ/81bA516C8TPh4U/AU38H7S0AnDtzPHd9YjHvVTfy6Z++xfHW9jgXKzI6KNwlMRROh5v/AMtugzd/DPdcDrU7Abh47kR+cH0FG/Yc5bMPrNVNPkQGQeEuiSMlzbtF3/W/9Mbf77oANj8GwJVnFPPd687itcoj3P7geto6QvGtVSTBKdwl8cy9Cm59BSbOhUc+Db/9CrQ1c+3iUv716gU89+4hvvLwRt3oQ6QfKfEuQCSi/HL49NPw/L/Ca/8Fe9+Cv7qPm5bN4kRrO//+1Ltkpgb59rVnEghYvKsVSTjacpfEFUyFj3wDPv5raNgPqy+ETb9m1QUz+dKls/n1un1847dbdbMPkQi05S6Jb87lcOur8Ogt8NhnYPfLfHn5tzje2s7dr+zipfdruGFpGdctLqMwKy3e1YokBF1bRkaPjnZ48d/hle/BxNNx1/2UJw/k8LPXP2DtB0dJCwa4YsFkPr60nGUzCjHTcI0kt/6uLaNwl9Gn8jl4bBW0HYer/gPOup73a47zizV7eGz9Phqa25kxIYsblpZz7eJSbc1L0lK4S/JprIZHPwO7X4GUDJh4Okw+g7YJ83ntWDH3bh/Hy3tbtTUvSU3hLskp1AFbfwP710P1O3BwMxw/0tXdmlPGzsA0XqyfxIbWUpry53LhOWdz7ZJybc1LUlC4y9jgnLdFX/0OHHwHqjfDwc24I5WY8056OuYyeM+Vc7zwdEpOO5sZ88/G0nO9I3MCQQikQiAl8mMLgLb8JYH0F+46WkaShxnkFnvTnMtPNrceh5ptUL2Ztp3rmLB7I4V1z5Cz5glYM8TX6Bn+wTRIz4GMPMjIh8z8Hsv+487lzv70PAjoSGSJHoW7JL+0cTBlMUxZTMHilRQAJ1raeerNtWzb9BbHGhtoON6Ma28laCFS6SBIByl0kJduFGQYeWlGXrqRmwbZaZCTamSlOsYFQ6S0HcOa66C5zrtsQnMdNNdDqL+LnBlk5HpBH0wDC3pfFp3z8GULel8EgZTIbWnZJ79QMvL8KTds2Z/SsvXLYwzRsIwI4Jyjobmd6vpmqupPcLChmar6Zqrrm6luaPbbm6k/EfmywykBIzUYIC0lQGowQHrQyA22UBA4TkHgOPl2nDw7Tp41kcsxcjhGtmsiyzWRGeggIwjpQUgLONKDjrSAI9UcKRbyhpRCHd6Xhevwlrva2qC1yfsyaRvgrlUWgPQIoR8IAuYHf3/zQNgyg3xO2NwCYW30+HMD/pdWoO+pr/6UdH/K9OcZ3s3YU8Km1LC+QHC4H5eEoWEZkQGYGXmZqeRlpnLa5Jw+1zvR2kF1w8kvgIMNLZxo7aCtI0RbR4jW9hCtHa5rua0jRHN7iD1h/W1h/S3tIeqOt9LUGvlKl8GAUTAulcKsNAqz0hifld613DmlpwRICRoprp209mOktx8jraORtLZG0tobSGk7RmpbIymtDaS0NhBsayTY2kCgpYFA0y7MtWM4DDDnAOd9eXQtd87p8TjSOn3N6f85zv/CcjG4IFwgtfsXQNeXW+cXRthy+JdaeHvPvm7LRPgy67luWP/pfw4Lbxjxv6bCXWQIMtOCTJ+QNeI37m5u6+Do8VaOHGultsmbjjS1ctSf1za1UNvUyrvVDdQ2tVJ3oo2Bf3QHgHx/GpxgwEgNGmlhv0LCf5GkBbv/QkkNBoY90pMSMNJSAidfM2BkpDjSg+b9mglCWoCTy0EjPeBIC0Ba0JFCO8GOZoKhVlJCLQQ7Wgj680CohZRQC4EObwp2dC43d7WZ68AI+e+Y9+XjfdmFMH8ZHOZCXrtzgP+LquvLCm8e6qDfL0AXotcXW3Pd8N7Avt7XqPypIjIkGalBivMyKc7LHNT67R0h6k60cbSpldaOEB0hR3vIefMOfx7q0R5ydIRCYf2O9o4Q7SFHa0eItnZHa0cHbR2u61dH57ytw1vn5OMQTa0dtLYPb0vbOa+Wzj/b++Vzcn5qo8YBINOfoscMgmYEzLzlwMnlgJn/2PtVGPDXNTNvV4mZ/xhuaCvnM1GoT+EuMgqlBANMyE5nQnZ6vEuJGue8L6C2PoK/sy3kIOQcIee8jWfnvLaQO7nsHC5sOeROfrF0tfnLHV3LXr/rbAtfJ7yf3q8VCnV/rV79YctFOdH5N1S4i0hCMvOGiFKDAcbpnLMh04G2IiJJKGrhbmbLzew9M6s0s69F63VERKS3qIS7mQWB/wauBOYBN5jZvGi8loiI9BatLfelQKVzbqdzrhV4CFgRpdcSEZEeohXuU4C9YY/3+W1dzGyVma01s7U1NTVRKkNEZGyK2w5V59xq59wS59ySoqKieJUhIpKUohXu+4GysMelfpuIiMRAtML9LWC2mU03szTgeuDJKL2WiIj0ELWrQprZVcD/BYLAvc65b/azbg3wwSm+1ATg8Ck+NxYSvT5I/BpV3/CovuFJ5PqmOucijmsnxCV/h8PM1vZ1yctEkOj1QeLXqPqGR/UNT6LX1xedoSoikoQU7iIiSSgZwn11vAsYQKLXB4lfo+obHtU3PIleX0SjfsxdRER6S4YtdxER6UHhLiKShEZNuA90CWEzSzezh/3+NWY2LYa1lZnZC2a21cy2mNmXIqxzkZnVm9lGf/rnWNXnv/5uM3vHf+21EfrNzH7gv3+bzGxRDGs7Lex92WhmDWb25R7rxPz9M7N7zeyQmW0Oays0s2fNbLs/L+jjuSv9dbab2coY1vddM3vX/zd83Mzy+3huv5+HKNb3dTPbH/bveFUfz436JcP7qO/hsNp2m9nGPp4b9fdv2Jx/+6lEnvBOhNoBzADSgLeBeT3WuQ24y1++Hng4hvUVA4v85Rzg/Qj1XQT8No7v4W5gQj/9VwFPAwYsA9bE8d+6Gu/kjLi+f8AFwCJgc1jbd4Cv+ctfA74d4XmFwE5/XuAvF8SovsuBFH/525HqG8znIYr1fR34m0F8Bvr9/x6t+nr0/yfwz/F6/4Y7jZYt98FcQngFcL+//Ahwqdlw78s+OM65Kufcen+5EdhGj6tgjgIrgAec5w0g38yK41DHpcAO59ypnrE8YpxzLwO1PZrDP2f3A1dHeOoVwLPOuVrn3FHgWWB5LOpzzj3jnGv3H76Bd12nuOjj/RuMmFwyvL/6/Oz4GPDLkX7dWBkt4T7gJYTD1/E/3PXA+JhUF8YfDqoA1kToPtfM3jazp81sfmwrwwHPmNk6M1sVoX8w73EsXE/f/6Hi+f51muScq/KXq4FJEdZJlPfyZrxfY5EM9HmIpi/4w0b39jGslQjv3/nAQefc9j764/n+DcpoCfdRwcyygUeBLzvnGnp0r8cbajgL+CHwmxiXd55zbhHe3bFuN7MLYvz6A/IvMvcXwK8jdMf7/evFeb/PE/JYYjP7R6AdeLCPVeL1ebgTmAksBKrwhj4S0Q30v9We8P+fRku4D+YSwl3rmFkKkAcciUl13mum4gX7g865x3r2O+canHPH/OWngFQzmxCr+pxz+/35IeBxvJ++4RLhMs1XAuudcwd7dsT7/QtzsHO4yp8firBOXN9LM/sU8FHgRv8LqJdBfB6iwjl30DnX4ZwLAXf38brxfv9SgL8EHu5rnXi9f0MxWsJ9MJcQfhLoPCrhOuD5vj7YI80fn7sH2Oac+14f60zu3AdgZkvx3vuYfPmYWZaZ5XQu4+1029xjtSeBT/pHzSwD6sOGH2Klz62leL5/PYR/zlYCT0RY5w/A5WZW4A87XO63RZ2ZLQf+DvgL59zxPtYZzOchWvWF78e5po/Xjfclwy8D3nXO7YvUGc/3b0jivUd3sBPe0Rzv4+1F/0e/7Rt4H2KADLyf85XAm8CMGNZ2Ht7P803ARn+6CrgVuNVf5wvAFrw9/28AH4phfTP8133br6Hz/Quvz/Buar4DeAdYEuN/3yy8sM4La4vr+4f3RVMFtOGN+96Ctx/nOWA78Eeg0F93CfCTsOfe7H8WK4FPx7C+Srzx6s7PYecRZCXAU/19HmJU38/8z9cmvMAu7lmf/7jX//dY1Oe339f5uQtbN+bv33AnXX5ARCQJjZZhGRERGQKFu4hIElK4i4gkIYW7iEgSUriLiCQhhbuISBJSuIuIJKH/D6J28657tTlgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(histo8.history['loss'])\n",
    "plt.plot(histo8.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 19ms/step\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[15.12937  ],\n",
       "       [17.847494 ],\n",
       "       [ 5.8829994]], dtype=float32)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model8.predict(xmod8_test[:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16., 18.,  7.], dtype=float32)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ymod_test[:3]"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}