In a simple linear regression model suppose we know that the intercept parameter is zero, so the model is yi b2xi ei. The

In a simple linear regression model suppose we know that the intercept parameter is zero, so the model is yi ¼ b2xi þ ei. The least squares estimator of b2 is developed in Exercise 2.4.

(a) What is the least squares predictor of y in this case?

(b) When an intercept is not present in a model, R2 is often defined to be R2 u ¼ 1 SSE=
y2 i , where SSE is the usual sum of squared residuals. Compute R2 u for the data in Exercise 2.4.

(c) Compare the value of R2 u in part

(b) to the generalized R2 ¼ r2 y^y, where ^y is the predictor based on the restricted model in part (a).

(d) Compute SST ¼
ðyi yÞ

2 and SSR ¼
ð^yi yÞ

2

, where ^y is the predictor based on the restricted model in part (a). Does the sum of squares decomposition SST ¼ SSR þ SSE hold in this case?