Assumptions of Regression Analysis

Regression Assumptions

For the simple and multiple regression model to hold there are some assumptions we need to make:

• The chosen sample is representative of the population.
• There is a linear relationship between the independent variable(s) and the dependent variable.
• All the variables are normally distributed; to check, plot a histogram of the residuals.
• There are no outliers, (if there are outliers they need to be removed); to check use a test for detecting outliers.
• The independent variables are all linearly independent (no variable dependents of the other variables); to check plot the independent values against each other and look for a correlation.
• For multiple regression there should be at least five times as many pairs of data than dependent variables.

Linear Assumptions

• The mean of the distribution of errors is $0$.
• The variance of errors is constant across all levels of the independent variable, this is called homoscedasticity; to check plot the residuals versus the predicted values of $y$.
• The distribution of errors is normal; to check this draw a histogram of the errors.
• All the errors are independent; to check plot the residuals versus the time periods.

See Also

• Simple Linear Regression
• Multiple Regression
• Residuals
• Coefficient of Determination, R-squared