Statistics for Machine Learning

Assumptions of linear regression

Linear regression has the following assumptions, failing which the linear regression model does not hold true:

• The dependent variable should be a linear combination of independent variables
• No autocorrelation in error terms
• Errors should have zero mean and be normally distributed
• No or little multi-collinearity
• Error terms should be homoscedastic

These are explained in detail as follows:

• The dependent variable should be a linear combination of independent variables: Y should be a linear combination of X variables. Please note, in the following equation, X2 has raised to the power of 2, the equation is still holding the assumption of a linear combination of variables:

How to diagnose: Look into residual ...