Discuss in your own terms the similarities and differences between simple linear regression analysis and multiple regression analysis.

Similarities and differences between simple linear regression analysis and multiple regression analysis

Simple linear regression is when you have only one predictor, or X variable, predicting the response or Y variable. Simple linear regression occurs in 2 dimension. Multiple regression you can have multiple X predictors that all contribute to predicting Y. Multiple linear regression can occur in an infinite number of dimensions. They both have one Y variable that is explained by either 1, or many X variables.

The similarities between simple linear and multiple regression are:

Both models predict a dependent variable with the help of independent variable. The error terms of both the models should be normally distributed with mean zero and constant variance, in both the cases. The dependent variable should be continuous in both the cases. The error terms should be independent of each other in both the cases. Finally, there should be a linear relationship between the dependent and independent variables in both cases.

The similarities between simple linear and multiple regression are:

Simple Linear Regression:

One independent variable. Multi collinearity problem cannot exist. The coefficient of determination is the square of the correlation coefficient between x and y

Multi Linear Regression: More than one independent variable. Multi collinearity problem can exist. The coefficient of determination is not simply the square of r. It needs to be computed from model