Before we can trust the results from our linear regression analysis to be valid, we need to assess our model to check that it does not violate any of the fundamental assumptions of linear regression.
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Checklist
Continuous and normally distributed outcome
The y-variable has to be continuous. It should also be normally distributed. Check this with a histogram. If it is not normally distributed, you might need to consider another alternative. For example, you can transform your y-variable (e.g. through categorisation, or log transformation).
Correct model specification
Your model should be correctly specified. This means that the x-variables that are included should be meaningful and contribute to the model. No important (confounding) variables should be omitted (often referred to as omitted variable bias).
No outliers
Outliers are individuals who do not follow the overall pattern of data. Sometimes referred to as influential observations (however, not all outliers are influential).
Homoscedasticity
The variance around the regression line should be constant across all values of the x-variable(s).
Normality
The residuals for our x-variables should be normally distributed.
Linearity
The effect of x on y should be linear.
No multicollinearity
Multicollinearity may occur when two or more x-variables that are included simultaneously in the model are strongly correlated with each another. Actually, this does not violate the assumptions, but it does create greater standard errors which makes it harder to reject the null hypothesis.
Types of model diagnostics
Link test
Assess model specification
Residual plot
Check for linearity, homoscedasticity, and outliers
