Lesson 3 of 8 · 13 min
The four assumptions and residual plots
OLS conclusions are valid only if the relationship is linear and the residuals have constant variance, are independent and are normally distributed. Residual plots are how you spot violations.
In short
- Linearity: Y and X are linearly related, and X is not random. A curved residual pattern signals a violation.
- Homoskedasticity: the residual variance is the same for all observations. If not, the residuals are heteroskedastic.
- Independence: the (X, Y) pairs are independent, so residuals are uncorrelated. Patterns such as seasonality signal autocorrelation.
- Normality: the residuals (not X or Y) are normally distributed. Matters most in small samples; the central limit theorem helps in large ones.
- Good residual plots look like random noise around zero with an even band.
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