Regression Definition

There are two basic types of regression:

1. Simple Linear Regression: In this type of regression, there is only one x and one y variable. 
2. Multiple Linear Regression: In this type of regression, there is one y variable and two or more x variables. 

It is important to note that the aforementioned regressions are methods of linear regression and cannot be used for non-linear data. Linear regression involves relating variables with a straight line while nonlinear regression relates the variables in a nonlinear (curved) relationship. For more complicated data and analysis, there are other methods of non-linear regression. 

Simple Linear Regression

Simple linear regression involves using one independent variable (x) to explain the outcome of the dependent variable (y). 

The formula for simple linear regression is: 

Y = a + bX + u

Where,

• Y = the variable that you are trying to predict (dependent variable).
• X = the variable that you are using to predict Y (independent variable).
• a = the intercept.
• b = the slope.
• u = the regression residual

To understand when the appropriate use of linear regression, let’s consider the following example: 

If we were to assume height as the singular determinant of body weight, we could use the simple linear regression model to predict or explain the impact of a change in height on weight. 

Multiple Linear Regression

Multiple linear regression involves using two or more independent variables (x) to explain the outcome of the dependent variable (y).  

The formula for multiple linear regression is as follows: 

Y = a + b1X1 + b2X2 + b3X3 + … + btXt + u

Multiple linear regression is used when simple linear regression is not enough to account for the multiple real-life factors that influence the outcome of a dependent variable. 

Let’s continue with the previous example involving height and weight. Realistically, height is not the only determinant of weight. There are a lot of different factors that influence a person’s weight, such as diet and exercise, and therefore a more realistic model would contain multiple x variables (independent variable).