Regression.Rmd

---
title: "Regression"
author: "north-tower"
date: "2023-08-17"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```


```{r echo=TRUE}
#Loading required R packages
library(tidyverse)
```


```{r}
# Reading in the data
data <- data.frame(
  x1 = c(19, 19, 10, 17, 19, 12, 18, 10, 15, 15),
  y = c(61, 47, 75, 63, 79, 75, 67, 47, 71, 84),
  x2 = c(11, 4, 8, 12, 5, 12, 6, 14, 13, 11)
)

# Estimates the parameters B1, B2 in the regression model y=B0 + B1x1 + B2x2 + e where e ~ N(0, δ2)
#Building Model 
model <- lm(y ~ x1 + x2, data = data)
model$coefficients
```

```{r}
# Estimates the parameters a,b,c in the regression  model y=a + b *x1 +exp(c*x2) +e where e ~ N(0, δ2)

# Transforming the equation
# Taking logarithm of both sides: log(y - a - b * x1) = c * x2 + log(e)
# Now it's in a linear form: log(y - a - b * x1) = c * x2 + log(e)
# So, we can perform linear regression on this transformed equation
# Perform linear regression
model <- lm(log(y) ~ x2 + x1, data = data)
model$coefficients
```