Regression Modelling 01. Model Comparisons, Assumptions & Predictions in Cars City Miles Efficiency.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "# Regression Modelling 1\n",
    "## Model Comparisons, Assumptions & Predictions in Cars City Miles Efficiency"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this report I am going to compare the efficacy of two variables in predicting the City Miles capabilities for various cars.\n",
    "\n",
    "**Predictors**\n",
    "- Engine Size (Liters) - *Eng*\n",
    "- Volume (Both Interior Passanger and Cargo)(Hundeds of Cubic Feet) - *Vol*\n",
    "\n",
    "**Response**\n",
    "- City Gallons Per Hundred Miles - *Cgphm*\n",
    "\n",
    "The response variable Cgphm is made with the following forumla: 100/Cmpg\n",
    "\n",
    "### Import & Transform Data"
   ]
  },
  {
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    "\n",
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     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Name</th><th scope=col>Cmpg</th><th scope=col>Eng</th><th scope=col>Vol</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Acura TL 2wd 3.5L                </td><td>18                               </td><td>3.5                              </td><td>1.11                             </td></tr>\n",
       "\t<tr><td>Audi A3 2L                       </td><td>22                               </td><td>2.0                              </td><td>1.09                             </td></tr>\n",
       "\t<tr><td>Audi A4 2L                       </td><td>22                               </td><td>2.0                              </td><td>1.03                             </td></tr>\n",
       "\t<tr><td>Audi A5 Cabriolet 2L             </td><td>22                               </td><td>2.0                              </td><td>0.91                             </td></tr>\n",
       "\t<tr><td>Audi A6 3.2L                     </td><td>21                               </td><td>3.2                              </td><td>1.14                             </td></tr>\n",
       "\t<tr><td>Buick Lacrosse 2.4L              </td><td>19                               </td><td>2.4                              </td><td>1.16                             </td></tr>\n",
       "\t<tr><td>Buick Lacrosse 3.6L              </td><td>17                               </td><td>3.6                              </td><td>1.16                             </td></tr>\n",
       "\t<tr><td>Buick Lucerne 4.6L               </td><td>15                               </td><td>4.6                              </td><td>1.21                             </td></tr>\n",
       "\t<tr><td>Buick Lucerne FFV 3.9L           </td><td>17                               </td><td>3.9                              </td><td>1.21                             </td></tr>\n",
       "\t<tr><td>Buick Regal 2.4L                 </td><td>19                               </td><td>2.4                              </td><td>1.11                             </td></tr>\n",
       "\t<tr><td>Buick Regal FFV 2L               </td><td>18                               </td><td>2.0                              </td><td>1.11                             </td></tr>\n",
       "\t<tr><td>Cadillac DTS 4.6L                </td><td>15                               </td><td>4.6                              </td><td>1.32                             </td></tr>\n",
       "\t<tr><td>Chevrolet Aveo 1.6L              </td><td>25                               </td><td>1.6                              </td><td>1.03                             </td></tr>\n",
       "\t<tr><td>Chevrolet Aveo 5 1.6L            </td><td>25                               </td><td>1.6                              </td><td>0.98                             </td></tr>\n",
       "\t<tr><td>Chevrolet Cruze 1.4L             </td><td>24                               </td><td>1.4                              </td><td>1.10                             </td></tr>\n",
       "\t<tr><td>Chevrolet Cruze 1.8L             </td><td>22                               </td><td>1.8                              </td><td>1.10                             </td></tr>\n",
       "\t<tr><td>Chevrolet Cruze ECO 1.4L         </td><td>26                               </td><td>1.4                              </td><td>1.10                             </td></tr>\n",
       "\t<tr><td>Chevrolet Impala FFV 3.5L        </td><td>19                               </td><td>3.5                              </td><td>1.24                             </td></tr>\n",
       "\t<tr><td>Chevrolet Impala FFV 3.9L        </td><td>17                               </td><td>3.9                              </td><td>1.24                             </td></tr>\n",
       "\t<tr><td>Chevrolet Malibu 2.4L            </td><td>22                               </td><td>2.4                              </td><td>1.11                             </td></tr>\n",
       "\t<tr><td>Chevrolet Malibu 3.6L            </td><td>17                               </td><td>3.6                              </td><td>1.11                             </td></tr>\n",
       "\t<tr><td>Chevrolet Malibu FFV 2.4L        </td><td>22                               </td><td>2.4                              </td><td>1.11                             </td></tr>\n",
       "\t<tr><td>Chrysler 200 2.4L                </td><td>21                               </td><td>2.4                              </td><td>1.15                             </td></tr>\n",
       "\t<tr><td>Chrysler 200 Convertible 2.4L    </td><td>20                               </td><td>2.4                              </td><td>1.01                             </td></tr>\n",
       "\t<tr><td>Chrysler 200 Convertible FFV 3.6L</td><td>19                               </td><td>3.6                              </td><td>1.01                             </td></tr>\n",
       "\t<tr><td>Chrysler 200 FFV 3.6L            </td><td>19                               </td><td>3.6                              </td><td>1.15                             </td></tr>\n",
       "\t<tr><td>Dodge Avenger 2.4L               </td><td>21                               </td><td>2.4                              </td><td>1.14                             </td></tr>\n",
       "\t<tr><td>Dodge Avenger FFV 3.6L           </td><td>19                               </td><td>3.6                              </td><td>1.14                             </td></tr>\n",
       "\t<tr><td>Dodge Caliber 2.4L               </td><td>22                               </td><td>2.4                              </td><td>1.12                             </td></tr>\n",
       "\t<tr><td>Dodge Caliber 2L                 </td><td>23                               </td><td>2.0                              </td><td>1.12                             </td></tr>\n",
       "\t<tr><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><td>Scion xB 2.4L                          </td><td>22                                     </td><td>2.4                                    </td><td>1.23                                   </td></tr>\n",
       "\t<tr><td>Scion xD 1.8L                          </td><td>27                                     </td><td>1.8                                    </td><td>0.95                                   </td></tr>\n",
       "\t<tr><td>Suzuki Kizashi 2.4L                    </td><td>23                                     </td><td>2.4                                    </td><td>1.05                                   </td></tr>\n",
       "\t<tr><td>Suzuki Kizashi S 2.4L                  </td><td>23                                     </td><td>2.4                                    </td><td>1.05                                   </td></tr>\n",
       "\t<tr><td>Suzuki Swift + 1.6L                    </td><td>25                                     </td><td>1.6                                    </td><td>0.98                                   </td></tr>\n",
       "\t<tr><td>Suzuki SX4 2L                          </td><td>23                                     </td><td>2.0                                    </td><td>0.98                                   </td></tr>\n",
       "\t<tr><td>Suzuki SX4 Sedan 2L                    </td><td>25                                     </td><td>2.0                                    </td><td>1.04                                   </td></tr>\n",
       "\t<tr><td>Suzuki SX4 Sport Anniversary Edition 2L</td><td>23                                     </td><td>2.0                                    </td><td>1.04                                   </td></tr>\n",
       "\t<tr><td>Toyota Avalon 3.5L                     </td><td>20                                     </td><td>3.5                                    </td><td>1.21                                   </td></tr>\n",
       "\t<tr><td>Toyota Camry 2.5L                      </td><td>22                                     </td><td>2.5                                    </td><td>1.16                                   </td></tr>\n",
       "\t<tr><td>Toyota Camry 3.5L                      </td><td>20                                     </td><td>3.5                                    </td><td>1.16                                   </td></tr>\n",
       "\t<tr><td>Toyota Corolla 1.8L                    </td><td>26                                     </td><td>1.8                                    </td><td>1.04                                   </td></tr>\n",
       "\t<tr><td>Toyota Corolla 2.4L                    </td><td>22                                     </td><td>2.4                                    </td><td>1.04                                   </td></tr>\n",
       "\t<tr><td>Toyota Corolla Matrix 1.8L             </td><td>25                                     </td><td>1.8                                    </td><td>1.14                                   </td></tr>\n",
       "\t<tr><td>Toyota Corolla Matrix 2.4L             </td><td>21                                     </td><td>2.4                                    </td><td>1.14                                   </td></tr>\n",
       "\t<tr><td>Toyota Yaris 1.5L                      </td><td>29                                     </td><td>1.5                                    </td><td>1.00                                   </td></tr>\n",
       "\t<tr><td>Volkswagen CC 2L                       </td><td>22                                     </td><td>2.0                                    </td><td>1.07                                   </td></tr>\n",
       "\t<tr><td>Volkswagen EOS 2L                      </td><td>22                                     </td><td>2.0                                    </td><td>0.88                                   </td></tr>\n",
       "\t<tr><td>Volkswagen GOLF 2.5L                   </td><td>24                                     </td><td>2.5                                    </td><td>1.09                                   </td></tr>\n",
       "\t<tr><td>Volkswagen GTI 2L                      </td><td>24                                     </td><td>2.0                                    </td><td>1.09                                   </td></tr>\n",
       "\t<tr><td>Volkswagen Jetta 2.5L                  </td><td>24                                     </td><td>2.5                                    </td><td>1.10                                   </td></tr>\n",
       "\t<tr><td>Volkswagen Jetta 2L                    </td><td>23                                     </td><td>2.0                                    </td><td>1.10                                   </td></tr>\n",
       "\t<tr><td>Volkswagen Jetta Sportwagen 2.5L       </td><td>24                                     </td><td>2.5                                    </td><td>1.25                                   </td></tr>\n",
       "\t<tr><td>Volvo C30 Fwd 2.5L                     </td><td>21                                     </td><td>2.5                                    </td><td>1.04                                   </td></tr>\n",
       "\t<tr><td>Volvo C70 Fwd 2.5L                     </td><td>19                                     </td><td>2.5                                    </td><td>0.97                                   </td></tr>\n",
       "\t<tr><td>Volvo S40 Fwd 2.5L                     </td><td>21                                     </td><td>2.5                                    </td><td>1.05                                   </td></tr>\n",
       "\t<tr><td>Volvo S80 Fwd 3.2L                     </td><td>19                                     </td><td>3.2                                    </td><td>1.13                                   </td></tr>\n",
       "\t<tr><td>Volvo V50 Fwd 2.5L                     </td><td>21                                     </td><td>2.5                                    </td><td>1.25                                   </td></tr>\n",
       "\t<tr><td>Volvo XC60 Fwd 3.2L                    </td><td>18                                     </td><td>3.2                                    </td><td>1.33                                   </td></tr>\n",
       "\t<tr><td>Volvo XC70 Fwd 3.2L                    </td><td>18                                     </td><td>3.2                                    </td><td>1.35                                   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       " Name & Cmpg & Eng & Vol\\\\\n",
       "\\hline\n",
       "\t Acura TL 2wd 3.5L                 & 18                                & 3.5                               & 1.11                             \\\\\n",
       "\t Audi A3 2L                        & 22                                & 2.0                               & 1.09                             \\\\\n",
       "\t Audi A4 2L                        & 22                                & 2.0                               & 1.03                             \\\\\n",
       "\t Audi A5 Cabriolet 2L              & 22                                & 2.0                               & 0.91                             \\\\\n",
       "\t Audi A6 3.2L                      & 21                                & 3.2                               & 1.14                             \\\\\n",
       "\t Buick Lacrosse 2.4L               & 19                                & 2.4                               & 1.16                             \\\\\n",
       "\t Buick Lacrosse 3.6L               & 17                                & 3.6                               & 1.16                             \\\\\n",
       "\t Buick Lucerne 4.6L                & 15                                & 4.6                               & 1.21                             \\\\\n",
       "\t Buick Lucerne FFV 3.9L            & 17                                & 3.9                               & 1.21                             \\\\\n",
       "\t Buick Regal 2.4L                  & 19                                & 2.4                               & 1.11                             \\\\\n",
       "\t Buick Regal FFV 2L                & 18                                & 2.0                               & 1.11                             \\\\\n",
       "\t Cadillac DTS 4.6L                 & 15                                & 4.6                               & 1.32                             \\\\\n",
       "\t Chevrolet Aveo 1.6L               & 25                                & 1.6                               & 1.03                             \\\\\n",
       "\t Chevrolet Aveo 5 1.6L             & 25                                & 1.6                               & 0.98                             \\\\\n",
       "\t Chevrolet Cruze 1.4L              & 24                                & 1.4                               & 1.10                             \\\\\n",
       "\t Chevrolet Cruze 1.8L              & 22                                & 1.8                               & 1.10                             \\\\\n",
       "\t Chevrolet Cruze ECO 1.4L          & 26                                & 1.4                               & 1.10                             \\\\\n",
       "\t Chevrolet Impala FFV 3.5L         & 19                                & 3.5                               & 1.24                             \\\\\n",
       "\t Chevrolet Impala FFV 3.9L         & 17                                & 3.9                               & 1.24                             \\\\\n",
       "\t Chevrolet Malibu 2.4L             & 22                                & 2.4                               & 1.11                             \\\\\n",
       "\t Chevrolet Malibu 3.6L             & 17                                & 3.6                               & 1.11                             \\\\\n",
       "\t Chevrolet Malibu FFV 2.4L         & 22                                & 2.4                               & 1.11                             \\\\\n",
       "\t Chrysler 200 2.4L                 & 21                                & 2.4                               & 1.15                             \\\\\n",
       "\t Chrysler 200 Convertible 2.4L     & 20                                & 2.4                               & 1.01                             \\\\\n",
       "\t Chrysler 200 Convertible FFV 3.6L & 19                                & 3.6                               & 1.01                             \\\\\n",
       "\t Chrysler 200 FFV 3.6L             & 19                                & 3.6                               & 1.15                             \\\\\n",
       "\t Dodge Avenger 2.4L                & 21                                & 2.4                               & 1.14                             \\\\\n",
       "\t Dodge Avenger FFV 3.6L            & 19                                & 3.6                               & 1.14                             \\\\\n",
       "\t Dodge Caliber 2.4L                & 22                                & 2.4                               & 1.12                             \\\\\n",
       "\t Dodge Caliber 2L                  & 23                                & 2.0                               & 1.12                             \\\\\n",
       "\t ... & ... & ... & ...\\\\\n",
       "\t Scion xB 2.4L                           & 22                                      & 2.4                                     & 1.23                                   \\\\\n",
       "\t Scion xD 1.8L                           & 27                                      & 1.8                                     & 0.95                                   \\\\\n",
       "\t Suzuki Kizashi 2.4L                     & 23                                      & 2.4                                     & 1.05                                   \\\\\n",
       "\t Suzuki Kizashi S 2.4L                   & 23                                      & 2.4                                     & 1.05                                   \\\\\n",
       "\t Suzuki Swift + 1.6L                     & 25                                      & 1.6                                     & 0.98                                   \\\\\n",
       "\t Suzuki SX4 2L                           & 23                                      & 2.0                                     & 0.98                                   \\\\\n",
       "\t Suzuki SX4 Sedan 2L                     & 25                                      & 2.0                                     & 1.04                                   \\\\\n",
       "\t Suzuki SX4 Sport Anniversary Edition 2L & 23                                      & 2.0                                     & 1.04                                   \\\\\n",
       "\t Toyota Avalon 3.5L                      & 20                                      & 3.5                                     & 1.21                                   \\\\\n",
       "\t Toyota Camry 2.5L                       & 22                                      & 2.5                                     & 1.16                                   \\\\\n",
       "\t Toyota Camry 3.5L                       & 20                                      & 3.5                                     & 1.16                                   \\\\\n",
       "\t Toyota Corolla 1.8L                     & 26                                      & 1.8                                     & 1.04                                   \\\\\n",
       "\t Toyota Corolla 2.4L                     & 22                                      & 2.4                                     & 1.04                                   \\\\\n",
       "\t Toyota Corolla Matrix 1.8L              & 25                                      & 1.8                                     & 1.14                                   \\\\\n",
       "\t Toyota Corolla Matrix 2.4L              & 21                                      & 2.4                                     & 1.14                                   \\\\\n",
       "\t Toyota Yaris 1.5L                       & 29                                      & 1.5                                     & 1.00                                   \\\\\n",
       "\t Volkswagen CC 2L                        & 22                                      & 2.0                                     & 1.07                                   \\\\\n",
       "\t Volkswagen EOS 2L                       & 22                                      & 2.0                                     & 0.88                                   \\\\\n",
       "\t Volkswagen GOLF 2.5L                    & 24                                      & 2.5                                     & 1.09                                   \\\\\n",
       "\t Volkswagen GTI 2L                       & 24                                      & 2.0                                     & 1.09                                   \\\\\n",
       "\t Volkswagen Jetta 2.5L                   & 24                                      & 2.5                                     & 1.10                                   \\\\\n",
       "\t Volkswagen Jetta 2L                     & 23                                      & 2.0                                     & 1.10                                   \\\\\n",
       "\t Volkswagen Jetta Sportwagen 2.5L        & 24                                      & 2.5                                     & 1.25                                   \\\\\n",
       "\t Volvo C30 Fwd 2.5L                      & 21                                      & 2.5                                     & 1.04                                   \\\\\n",
       "\t Volvo C70 Fwd 2.5L                      & 19                                      & 2.5                                     & 0.97                                   \\\\\n",
       "\t Volvo S40 Fwd 2.5L                      & 21                                      & 2.5                                     & 1.05                                   \\\\\n",
       "\t Volvo S80 Fwd 3.2L                      & 19                                      & 3.2                                     & 1.13                                   \\\\\n",
       "\t Volvo V50 Fwd 2.5L                      & 21                                      & 2.5                                     & 1.25                                   \\\\\n",
       "\t Volvo XC60 Fwd 3.2L                     & 18                                      & 3.2                                     & 1.33                                   \\\\\n",
       "\t Volvo XC70 Fwd 3.2L                     & 18                                      & 3.2                                     & 1.35                                   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| Name | Cmpg | Eng | Vol |\n",
       "|---|---|---|---|\n",
       "| Acura TL 2wd 3.5L                 | 18                                | 3.5                               | 1.11                              |\n",
       "| Audi A3 2L                        | 22                                | 2.0                               | 1.09                              |\n",
       "| Audi A4 2L                        | 22                                | 2.0                               | 1.03                              |\n",
       "| Audi A5 Cabriolet 2L              | 22                                | 2.0                               | 0.91                              |\n",
       "| Audi A6 3.2L                      | 21                                | 3.2                               | 1.14                              |\n",
       "| Buick Lacrosse 2.4L               | 19                                | 2.4                               | 1.16                              |\n",
       "| Buick Lacrosse 3.6L               | 17                                | 3.6                               | 1.16                              |\n",
       "| Buick Lucerne 4.6L                | 15                                | 4.6                               | 1.21                              |\n",
       "| Buick Lucerne FFV 3.9L            | 17                                | 3.9                               | 1.21                              |\n",
       "| Buick Regal 2.4L                  | 19                                | 2.4                               | 1.11                              |\n",
       "| Buick Regal FFV 2L                | 18                                | 2.0                               | 1.11                              |\n",
       "| Cadillac DTS 4.6L                 | 15                                | 4.6                               | 1.32                              |\n",
       "| Chevrolet Aveo 1.6L               | 25                                | 1.6                               | 1.03                              |\n",
       "| Chevrolet Aveo 5 1.6L             | 25                                | 1.6                               | 0.98                              |\n",
       "| Chevrolet Cruze 1.4L              | 24                                | 1.4                               | 1.10                              |\n",
       "| Chevrolet Cruze 1.8L              | 22                                | 1.8                               | 1.10                              |\n",
       "| Chevrolet Cruze ECO 1.4L          | 26                                | 1.4                               | 1.10                              |\n",
       "| Chevrolet Impala FFV 3.5L         | 19                                | 3.5                               | 1.24                              |\n",
       "| Chevrolet Impala FFV 3.9L         | 17                                | 3.9                               | 1.24                              |\n",
       "| Chevrolet Malibu 2.4L             | 22                                | 2.4                               | 1.11                              |\n",
       "| Chevrolet Malibu 3.6L             | 17                                | 3.6                               | 1.11                              |\n",
       "| Chevrolet Malibu FFV 2.4L         | 22                                | 2.4                               | 1.11                              |\n",
       "| Chrysler 200 2.4L                 | 21                                | 2.4                               | 1.15                              |\n",
       "| Chrysler 200 Convertible 2.4L     | 20                                | 2.4                               | 1.01                              |\n",
       "| Chrysler 200 Convertible FFV 3.6L | 19                                | 3.6                               | 1.01                              |\n",
       "| Chrysler 200 FFV 3.6L             | 19                                | 3.6                               | 1.15                              |\n",
       "| Dodge Avenger 2.4L                | 21                                | 2.4                               | 1.14                              |\n",
       "| Dodge Avenger FFV 3.6L            | 19                                | 3.6                               | 1.14                              |\n",
       "| Dodge Caliber 2.4L                | 22                                | 2.4                               | 1.12                              |\n",
       "| Dodge Caliber 2L                  | 23                                | 2.0                               | 1.12                              |\n",
       "| ... | ... | ... | ... |\n",
       "| Scion xB 2.4L                           | 22                                      | 2.4                                     | 1.23                                    |\n",
       "| Scion xD 1.8L                           | 27                                      | 1.8                                     | 0.95                                    |\n",
       "| Suzuki Kizashi 2.4L                     | 23                                      | 2.4                                     | 1.05                                    |\n",
       "| Suzuki Kizashi S 2.4L                   | 23                                      | 2.4                                     | 1.05                                    |\n",
       "| Suzuki Swift + 1.6L                     | 25                                      | 1.6                                     | 0.98                                    |\n",
       "| Suzuki SX4 2L                           | 23                                      | 2.0                                     | 0.98                                    |\n",
       "| Suzuki SX4 Sedan 2L                     | 25                                      | 2.0                                     | 1.04                                    |\n",
       "| Suzuki SX4 Sport Anniversary Edition 2L | 23                                      | 2.0                                     | 1.04                                    |\n",
       "| Toyota Avalon 3.5L                      | 20                                      | 3.5                                     | 1.21                                    |\n",
       "| Toyota Camry 2.5L                       | 22                                      | 2.5                                     | 1.16                                    |\n",
       "| Toyota Camry 3.5L                       | 20                                      | 3.5                                     | 1.16                                    |\n",
       "| Toyota Corolla 1.8L                     | 26                                      | 1.8                                     | 1.04                                    |\n",
       "| Toyota Corolla 2.4L                     | 22                                      | 2.4                                     | 1.04                                    |\n",
       "| Toyota Corolla Matrix 1.8L              | 25                                      | 1.8                                     | 1.14                                    |\n",
       "| Toyota Corolla Matrix 2.4L              | 21                                      | 2.4                                     | 1.14                                    |\n",
       "| Toyota Yaris 1.5L                       | 29                                      | 1.5                                     | 1.00                                    |\n",
       "| Volkswagen CC 2L                        | 22                                      | 2.0                                     | 1.07                                    |\n",
       "| Volkswagen EOS 2L                       | 22                                      | 2.0                                     | 0.88                                    |\n",
       "| Volkswagen GOLF 2.5L                    | 24                                      | 2.5                                     | 1.09                                    |\n",
       "| Volkswagen GTI 2L                       | 24                                      | 2.0                                     | 1.09                                    |\n",
       "| Volkswagen Jetta 2.5L                   | 24                                      | 2.5                                     | 1.10                                    |\n",
       "| Volkswagen Jetta 2L                     | 23                                      | 2.0                                     | 1.10                                    |\n",
       "| Volkswagen Jetta Sportwagen 2.5L        | 24                                      | 2.5                                     | 1.25                                    |\n",
       "| Volvo C30 Fwd 2.5L                      | 21                                      | 2.5                                     | 1.04                                    |\n",
       "| Volvo C70 Fwd 2.5L                      | 19                                      | 2.5                                     | 0.97                                    |\n",
       "| Volvo S40 Fwd 2.5L                      | 21                                      | 2.5                                     | 1.05                                    |\n",
       "| Volvo S80 Fwd 3.2L                      | 19                                      | 3.2                                     | 1.13                                    |\n",
       "| Volvo V50 Fwd 2.5L                      | 21                                      | 2.5                                     | 1.25                                    |\n",
       "| Volvo XC60 Fwd 3.2L                     | 18                                      | 3.2                                     | 1.33                                    |\n",
       "| Volvo XC70 Fwd 3.2L                     | 18                                      | 3.2                                     | 1.35                                    |\n",
       "\n"
      ],
      "text/plain": [
       "    Name                                    Cmpg Eng Vol \n",
       "1   Acura TL 2wd 3.5L                       18   3.5 1.11\n",
       "2   Audi A3 2L                              22   2.0 1.09\n",
       "3   Audi A4 2L                              22   2.0 1.03\n",
       "4   Audi A5 Cabriolet 2L                    22   2.0 0.91\n",
       "5   Audi A6 3.2L                            21   3.2 1.14\n",
       "6   Buick Lacrosse 2.4L                     19   2.4 1.16\n",
       "7   Buick Lacrosse 3.6L                     17   3.6 1.16\n",
       "8   Buick Lucerne 4.6L                      15   4.6 1.21\n",
       "9   Buick Lucerne FFV 3.9L                  17   3.9 1.21\n",
       "10  Buick Regal 2.4L                        19   2.4 1.11\n",
       "11  Buick Regal FFV 2L                      18   2.0 1.11\n",
       "12  Cadillac DTS 4.6L                       15   4.6 1.32\n",
       "13  Chevrolet Aveo 1.6L                     25   1.6 1.03\n",
       "14  Chevrolet Aveo 5 1.6L                   25   1.6 0.98\n",
       "15  Chevrolet Cruze 1.4L                    24   1.4 1.10\n",
       "16  Chevrolet Cruze 1.8L                    22   1.8 1.10\n",
       "17  Chevrolet Cruze ECO 1.4L                26   1.4 1.10\n",
       "18  Chevrolet Impala FFV 3.5L               19   3.5 1.24\n",
       "19  Chevrolet Impala FFV 3.9L               17   3.9 1.24\n",
       "20  Chevrolet Malibu 2.4L                   22   2.4 1.11\n",
       "21  Chevrolet Malibu 3.6L                   17   3.6 1.11\n",
       "22  Chevrolet Malibu FFV 2.4L               22   2.4 1.11\n",
       "23  Chrysler 200 2.4L                       21   2.4 1.15\n",
       "24  Chrysler 200 Convertible 2.4L           20   2.4 1.01\n",
       "25  Chrysler 200 Convertible FFV 3.6L       19   3.6 1.01\n",
       "26  Chrysler 200 FFV 3.6L                   19   3.6 1.15\n",
       "27  Dodge Avenger 2.4L                      21   2.4 1.14\n",
       "28  Dodge Avenger FFV 3.6L                  19   3.6 1.14\n",
       "29  Dodge Caliber 2.4L                      22   2.4 1.12\n",
       "30  Dodge Caliber 2L                        23   2.0 1.12\n",
       "... ...                                     ...  ... ... \n",
       "98  Scion xB 2.4L                           22   2.4 1.23\n",
       "99  Scion xD 1.8L                           27   1.8 0.95\n",
       "100 Suzuki Kizashi 2.4L                     23   2.4 1.05\n",
       "101 Suzuki Kizashi S 2.4L                   23   2.4 1.05\n",
       "102 Suzuki Swift + 1.6L                     25   1.6 0.98\n",
       "103 Suzuki SX4 2L                           23   2.0 0.98\n",
       "104 Suzuki SX4 Sedan 2L                     25   2.0 1.04\n",
       "105 Suzuki SX4 Sport Anniversary Edition 2L 23   2.0 1.04\n",
       "106 Toyota Avalon 3.5L                      20   3.5 1.21\n",
       "107 Toyota Camry 2.5L                       22   2.5 1.16\n",
       "108 Toyota Camry 3.5L                       20   3.5 1.16\n",
       "109 Toyota Corolla 1.8L                     26   1.8 1.04\n",
       "110 Toyota Corolla 2.4L                     22   2.4 1.04\n",
       "111 Toyota Corolla Matrix 1.8L              25   1.8 1.14\n",
       "112 Toyota Corolla Matrix 2.4L              21   2.4 1.14\n",
       "113 Toyota Yaris 1.5L                       29   1.5 1.00\n",
       "114 Volkswagen CC 2L                        22   2.0 1.07\n",
       "115 Volkswagen EOS 2L                       22   2.0 0.88\n",
       "116 Volkswagen GOLF 2.5L                    24   2.5 1.09\n",
       "117 Volkswagen GTI 2L                       24   2.0 1.09\n",
       "118 Volkswagen Jetta 2.5L                   24   2.5 1.10\n",
       "119 Volkswagen Jetta 2L                     23   2.0 1.10\n",
       "120 Volkswagen Jetta Sportwagen 2.5L        24   2.5 1.25\n",
       "121 Volvo C30 Fwd 2.5L                      21   2.5 1.04\n",
       "122 Volvo C70 Fwd 2.5L                      19   2.5 0.97\n",
       "123 Volvo S40 Fwd 2.5L                      21   2.5 1.05\n",
       "124 Volvo S80 Fwd 3.2L                      19   3.2 1.13\n",
       "125 Volvo V50 Fwd 2.5L                      21   2.5 1.25\n",
       "126 Volvo XC60 Fwd 3.2L                     18   3.2 1.33\n",
       "127 Volvo XC70 Fwd 3.2L                     18   3.2 1.35"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cars2_df <- read.table(url(\"http://jupyter-regressions.s3-eu-west-1.amazonaws.com/cars2.csv\"), \n",
    "                           sep=\",\", header = T, stringsAsFactors = F)\n",
    "cars2_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "cars2_df[,5] <- 100/ cars2_df[,2]\n",
    "names(cars2_df)[5] <- \"Cmphg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating a linear model for Engine Size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Cmphg ~ Eng, data = cars2_df[])\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.61401 -0.22593 -0.04419  0.15520  1.32962 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   2.5894     0.1026   25.24   <2e-16 ***\n",
       "Eng           0.8183     0.0397   20.61   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.3351 on 125 degrees of freedom\n",
       "Multiple R-squared:  0.7726,\tAdjusted R-squared:  0.7708 \n",
       "F-statistic: 424.8 on 1 and 125 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the linear regression and print summary\n",
    "lmEng = lm(Cmphg~Eng, data = cars2_df[]) \n",
    "summary(lmEng)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model for Interior & Cargo Volume"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Cmphg ~ Vol, data = cars2_df[])\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-1.2039 -0.4521 -0.1067  0.3734  2.3482 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   1.8760     0.5337   3.515 0.000613 ***\n",
       "Vol           2.5010     0.4849   5.157 9.53e-07 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.6382 on 125 degrees of freedom\n",
       "Multiple R-squared:  0.1755,\tAdjusted R-squared:  0.1689 \n",
       "F-statistic:  26.6 on 1 and 125 DF,  p-value: 9.527e-07\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the linear regression and print summary\n",
    "lmVol = lm(Cmphg~Vol, data = cars2_df[]) \n",
    "summary(lmVol) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitted Line Plots\n",
    "### Using a Dataframe to store all Model, Fortfify and Predict values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n",
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n"
     ]
    },
    {
     "data": {
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QcBAACgmxSEAADQj6LZDnZ0xu9bNurJVcMzmbdH4rHMWdMazj6+IRbL5HxqFKkG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BodwICL2YJWYoKyuznDKGN+Gb68XcJyB07kjaLHzSDOMAACAASURBVIlbv4/Z8kOM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\nhzXwJf9ls9l+/etfv/baa1ZrBL7naWlpXYNAp9Pp48ErAACa3njjjQGv8XN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vRAadSlelHX3uQB+ux05eThzRwq7JYKQIUOAAAAThAQAgQx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12nRpIk165d29NyTUuWLHFxo8N9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\nAAByoECoOclXqv/jx/rpOUbPksSa+ZP7nasTZZN1uyRdAAAAAADtIEs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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predsEng = predict(lmEng, interval = \"confidence\")\n",
    "predsVol = predict(lmVol, interval = \"confidence\")\n",
    "\n",
    "fortifyEng = fortify(lmEng)\n",
    "fortifyVol = fortify(lmVol)\n",
    "\n",
    "modEng <- cbind(fortifyEng,predsEng)\n",
    "modVol <- cbind(fortifyVol,predsVol)\n",
    "\n",
    "# summary(modVol)\n",
    "\n",
    "theme <- theme(\n",
    "        axis.text=element_text(size = rel(1.7)),\n",
    "        axis.title=element_text(size = rel(1.7)),\n",
    "        plot.title=element_text(size = rel(2))\n",
    "    )\n",
    "points <- geom_point(size=3)\n",
    "smooth <- stat_smooth(method=\"lm\", level=0.95)\n",
    "geom_ribbon <- geom_ribbon( aes(ymin = lwr, ymax = upr), alpha = .15) \n",
    "\n",
    "plotEng <- ggplot(modEng, aes(x=Eng, y=Cmphg)) + points + theme + geom_ribbon + \n",
    "    geom_smooth(aes(x=Eng, y=.fitted))\n",
    "\n",
    "plotVol <- ggplot(modVol, aes(x=Vol, y=Cmphg)) + points + theme + geom_ribbon +\n",
    "    geom_smooth(aes(x=Vol, y=.fitted)) \n",
    "\n",
    "grid.arrange(plotEng, plotVol, ncol=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparisons of Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- M1: Cmphg = b0 + b1(Eng) \n",
    "- M2: Cmphg = b0 + b1(Vol)\n",
    "\n",
    "#### S (Regression Standard Error)\n",
    "- $S_{M1}$=0.3351 vs $S_{M2}$=0.6382\n",
    "- This means there is a smaller error when using Engine size to Predict City Miles (Per Hundred Gallon) than when using car Volume.\n",
    "- Another way of phrasing this is that fitted values further away from predicted values on average in the second model. \n",
    "\n",
    "#### R2 (Coefficient of Determination)\n",
    "- $R2_{M1}$=77% vs $R2_{M2}$=17%\n",
    "- The R2 is also much larger when Engine size is the input variable, meaning more variation around the mean of City Miles (per hundred gallon) is explained from its linear relationship with Engine Size, than its linear relationship with Car Volume.\n",
    "- This can also be thought of as, more of the variation in city miles (per hundred gallon) is explained via the linear assoication with engine size than car volume.\n",
    "\n",
    "#### Slope of $b_{1}$\n",
    "- $T_{M1}$=20.61 $T_{M2}$=5.157\n",
    "- The test statistic for zero population slope is much higher for Engine size than Car Volume.\n",
    "- This confirms that the slope is taller for engine sizes than car volume, meaning that there is a larger association between engine size and city miles (per hundred gallon) than car volume"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residual Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotResidEng <- ggplot(modEng, aes(x = .fitted, y = .resid)) + points + theme + \n",
    "    ggtitle(\"Engine Size - Resid Vs Fit\") +\n",
    "    geom_hline(yintercept = 0)\n",
    "plotResidVol <- ggplot(modVol, aes(x = .fitted, y = .resid)) + points + theme + \n",
    "    ggtitle(\"Car Volume - Resid Vs Fit\") +\n",
    "    geom_hline(yintercept = 0)\n",
    "\n",
    "grid.arrange(plotResidEng, plotResidVol, ncol=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QQ Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "qqVol <- ggplot(modEng, aes(sample=.resid)) + \n",
    "    stat_qq() +\n",
    "    theme +\n",
    "    geom_qq_line(line.p = c(0.25, 0.75), col = \"blue\") + \n",
    "    ggtitle(\"QQ Plot - Engine Size\") \n",
    "\n",
    "qqEng <- ggplot(modVol, aes(sample=.resid)) + \n",
    "    stat_qq() + \n",
    "    theme +\n",
    "    geom_qq_line(line.p = c(0.25, 0.75), col = \"blue\") +\n",
    "    ggtitle(\"QQ Plot - Car Volume\")\n",
    "\n",
    "grid.arrange(qqVol, qqEng, ncol=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Not recommended as sample size is large and even small deviations from normality will produce a failed test\n",
    "ad.test(modVol$.resid) \n",
    "ad.test(modEng$.resid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Assumptions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With respect to the model errors and model assumptions the following observations were made:\n",
    "- **Zero Mean**: A mean close to zero seems to be present for both models, with a slight deviation caused by approx 2 observations in the engine size model with the lower values.\n",
    "- **Constant Variance**: Data looks to be homoscedastic, with very little noticable deviation in variance from the left to right of the graph in both models.\n",
    "- **Normality**: Slight deviations from Normality noticed in both models, but nothing significant.\n",
    "- **Independance**: No patterns noticed in residuals vs fitted graphs for both models. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Interpretations\n",
    "- Model 1 shows that for each 1 litre increase in Engine size you can expect a 0.818 increase in car miles per 100 gallon on average. \n",
    "- So for a car with an engine size of 2.4 we can expect the following city miles per 100 gallon.\n",
    "- We can also quantify our certainty on this point estimate with a confidence interval. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predict a population average\n",
    "- Confidence Interval: ${\\hat{Y}}$ ±t-percentile($S_{\\hat{Y}}$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "b0 <- 2.58942273998879 # intercept\n",
    "b1 <- 0.818255593593726 # slope\n",
    "xp <- 3 # X to predict\n",
    "y <- b0 + b1*(xp) # point estimate for eng=3\n",
    "\n",
    "mx <- mean(modEng$Eng) # mean for all x values\n",
    "s <- 0.3351 # regression standard error\n",
    "\n",
    "sq_diff <- (xp-mx)^2 # squared difference between predictor x and mean of x\n",
    "ss_error = 0 # sum of squared errors for x value\n",
    "for(xi in modEng$Eng) { \n",
    "    ss_error = ss_error + (xi-mx)^2\n",
    "} \n",
    "\n",
    "n_scale <- 1/125\n",
    "s_yhat <- s*sqrt(n_scale+(sq_diff/ss_error))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cat('95% CI:(',y-1.96*s_yhat,',', y+1.96*s_yhat,')')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Estimated vs Observed Values\n",
    "We can also use the lm.predict() variables in our DataFrame to confirm the best point estimate and confidence interval script above.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "filter(modEng, Eng==3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predict a population single value\n",
    "Lets continue with the example of cars with engine sizes of 2.4 Litres, but this time in the context of a prediction on a single vehicles performance. Here we can also make a point estimate, which will be the same as the estimate for mean, but we will also calculate a wider prediction interval for this estimate.\n",
    "- Confidence Interval: ${\\hat{Y}}$ ±t-percentile($S_{\\hat{Y}*}$)\n",
    "- $S_{\\hat{Y}*}$: Standard Error for Prediction\n",
    "- We can also make the approximation that about 95% of the observed Y-values lie within ±2s of their fitted ${\\hat{Y}}$-values. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s_ystar <- s*sqrt(1 + n_scale+(sq_diff/ss_error))\n",
    "cat('95% PI:(',y-1.96*s_ystar,',', y+1.96*s_ystar,')')"
   ]
  }
 ],
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