A regression analysis using an intercept and one independent variable gave The variance–covariance matrix for  was (a) Compute the 95% confidence interval estimate of 1 . The estimate of σ 2 used to...

A regression analysis using an intercept and one independent variable gave

The variance–covariance matrix for
 was

(a) Compute the 95% confidence interval estimate of

₁. The estimate of σ²
used to compute s²(
₁) was s²
= 1.6360, the residual mean square from the model using only X₀
and X₁. The data had n = 34 observations.

(b) Compute
 for X1 = 4. Compute the variance of
 if it is being used to estimate the mean of Y when X₁
= 4. Compute the variance of
 if it is being used to predict a future observation at X₁
= 4.