# Assumption tests to be run on each independent variable or on the entire model in a multiple linear regression?

Here are important assumptions that one has to check when performing a linear

• Assumption 1: Homoscedasticity of residuals or equal variance (with Breusch-Pagan test for example)
• Assumption 2: Normalcy of residuals (with Shapiro-Wilk test for example)
• Assumption 3: No autocorrelation of residuals (for time series with Durbin Watson test for example)

Here is my question: When performing a multiple linear regression (with more than ond independent variable), should one do each of the above-mentioned test on the entire model or should one run each of the above-mentioned test for each individual independent variable with the dependent variable?

• VIF is only available for the entire matrix of predictors (independent variables) – ERT Jul 24 '18 at 20:24
• Thank you @ERT you are right: I removed that point of the list – ecjb Jul 24 '18 at 20:26
• I'd suggest to look through the many, many questions on our site on OLS assumptions. – Michael M Jul 24 '18 at 20:57

1. You can only check the homoscedasticity of residuals after fitting your model.
Residuals are 'what's left' that isn't explained by your model; they're in a way an estimate of the random noise in your assumed model, i.e. the $\epsilon$ in $$Y = X\beta + \epsilon$$