I would be negligent if I failed to mention the boring but very critical topic of the assumptions of linear models, and how to detect violations of those assumptions. Just like the assumptions of the hypothesis tests in Chapter 6, Testing Hypotheses, linear regression has its own set of assumptions, the violation of which jeopardizes the accuracy of our model and any inferences derived from it to varying degrees. The checks and tests that ensure these assumptions are met are called diagnostics.
There are five major assumptions of linear regression:
- That the errors (residuals) are normally distributed with a mean of zero
- That the error terms are uncorrelated
- That the errors have a constant variance
- That the effect of the independent variables on the dependent variable are linear and additive
- That multi-collinearity is at a minimum
We'll briefly touch on these assumptions, and how to check for them in this section here. To do this, we will be using a residual-fitted...