Regression Analysis in R

Regression Analysis is a statistical method used in finance, investing, and other disciplines that attempt to determine the strength and character of the relationship between one dependent variable (usually denoted by Y) and a series of other variables (known as independent variables).

In this tutorial, we will explore how to perform regression analysis in R.

Getting Started: Installing and Loading Necessary Packages

To perform regression analysis in R, you will need to install and load the necessary packages. Here is how to do it:

install.packages("ggplot2")
install.packages("dplyr")

# Load the libraries
library(ggplot2)
library(dplyr)

Understanding the Data

For this tutorial, we will use the mtcars dataset which is included in R. This dataset contains various car attributes like mpg, cyl, hp, etc. Before running a regression analysis, we first need to understand the data.

# View the first few rows of the dataset
head(mtcars)

Simple Linear Regression

Simple linear regression is used when we want to predict a dependent variable based on the value of an independent variable.

For example, we might want to predict mpg (miles per gallon) based on hp (horsepower). Here is how to do this:

# Run the regression
model <- lm(mpg ~ hp, data = mtcars)

# View the summary of the regression model
summary(model)

The summary() function provides a lot of information. The most important parts are the coefficients table, which shows the regression coefficients, and the multiple R-squared, which provides the R² value.

Multiple Linear Regression

Multiple linear regression is used when we want to predict a dependent variable based on the values of multiple independent variables.

For example, we might want to predict mpg based on hp and wt (weight). Here is how to do this:

# Run the regression
model <- lm(mpg ~ hp + wt, data = mtcars)

# View the summary of the regression model
summary(model)

Interpreting the Results

The coefficients table shows the value of the regression coefficients. For example, in the simple linear regression model, the coefficient for hp is the amount by which mpg will change if hp increases by one unit.

The R² value, shown in the summary as "Multiple R-squared", tells us the proportion of the variance in the dependent variable that is predictable from the independent variable(s). A higher R² indicates a better fit of the model.

Conclusion

This tutorial introduced you to regression analysis in R, including how to perform simple and multiple linear regression and how to interpret the results. Practice with different datasets and variables to get a better understanding of regression analysis. Remember, the goal of regression analysis is to understand the relationship between variables, not just to create models that predict well.