Page 174 - Applied Statistics with R

174 CHAPTER 9. MULTIPLE LINEAR REGRESSION

# SSE
sum(resid(full_mpg_model) ^ 2)

## [1] 4556.646

# SST
sum(resid(null_mpg_model) ^ 2)

## [1] 23761.67

# Degrees of Freedom: Regression
length(coef(full_mpg_model)) - length(coef(null_mpg_model))

## [1] 2

# Degrees of Freedom: Error
length(resid(full_mpg_model)) - length(coef(full_mpg_model))

## [1] 387

# Degrees of Freedom: Total
length(resid(null_mpg_model)) - length(coef(null_mpg_model))

## [1] 389

9.4 Nested Models

The significance of regression test is actually a special case of testing what we
will call nested models. More generally we can compare two models, where
one model is “nested” inside the other, meaning one model contains a subset of
the predictors from only the larger model.
Consider the following full model,

= + + + ⋯ + ( −1) ( −1) +
0
1 1
2 2

This model has − 1 predictors, for a total of -parameters. We will denote
the fitted values of this model as ̂ .

1
Let the null model be