7.8 ANOVA for regression

Since an ANOVA is an analysis of the variance due to a model, compared to the unexplained variance, it can be used to test the overall model fit. This will give us the same general answer to the question of “is there an association between X and Y” that testing for a non-zero slope (\(\beta \neq 0\)). If the mean squared value for the regression is much larger than the mean squared value for the residual error, then the line fits the data better than the simple mean, and thus, the slope of the line is not zero.

aov(fev.dad.model) |> summary() |> pander()
Analysis of Variance Model
  Df Sum Sq Mean Sq F value Pr(>F)
FHEIGHT 1 16.05 16.05 50.5 4.677e-11
Residuals 148 47.05 0.3179 NA NA