Lecture 5 Hypothesis Testing in Multiple Linear Regression
The regression sums of squares due to X2 when X1 is already in the model is SSR(X2|X1) = SSR(X)−SSR(X1) with r degrees of freedom. This is also known as the extra sum of squares due to X2. SSR(X2|X1) is independent of MSE. We can test H 0: β2 = 0 with the statistic F 0 = SSR(X2|X1)/r MSE ∼ F r,n−p−1.
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