# Simple Linear Regression

By | March 25, 2023

Simple linear regression is a statistical technique used to study the relationship between two continuous variables, where one variable is considered the dependent variable and the other variable is considered the independent variable. The goal of simple linear regression is to develop a linear equation that best describes the relationship between the two variables.

The linear equation takes the form of:

Y = a + bX

Where:

• Y is the dependent variable (also known as the response variable)
• X is the independent variable (also known as the predictor variable)
• a is the intercept (the value of Y when X=0)
• b is the slope (the change in Y per unit change in X)

The slope (b) of the linear equation describes the direction and strength of the relationship between the two variables. If b is positive, it indicates a positive relationship between the variables, meaning that as X increases, Y also tends to increase. If b is negative, it indicates a negative relationship between the variables, meaning that as X increases, Y tends to decrease.

The intercept (a) of the linear equation is the value of Y when X is zero. In many cases, the intercept may not have a meaningful interpretation.

To perform a simple linear regression, we need a dataset that includes values of both the dependent and independent variables. We can use this data to estimate the values of a and b in the linear equation. Once we have estimated the equation, we can use it to predict the value of the dependent variable (Y) for any given value of the independent variable (X).

Simple linear regression is a useful tool in many fields, including finance, economics, and social sciences, where it is used to study the relationship between variables and make predictions about future values.

Statistics 101

Four videos hosted on YouTube by Brandon Foltz provide step by step guide with examples to understand the concept of simple linear regression. Look no further and only watch these 4 videos. Total duration of videos is approximately 2 hours.

Simple linear regression in R

How to plot simple linear regression model in R is explained by Christoph Scherber. He used the dataset of airquality and utilized the commands plot, abline, and lm.