Question: The multiple linear regression model y = 0 + 1x1 + 2x2 + 3x3 is fitted to a data set of n = 30 observations.

The multiple linear regression model
y = β0 + β1x1 + β2x2 + β3x3
is fitted to a data set of n = 30 observations. The total sum of squares is SST = 108.9, and the error sum of squares is SSE = 12.4.
(a) What is the coefficient of determination R2?
(b) Write out the analysis of variance table.
(c) What is the estimate of the error variance a2'?
(d) What is the p-value for the null hypothesis
H0: βl = β2 = β3 = 0
(e) If β^1 = 16.5 and s.c.( β^1) = 2.6, construct a two-sided 95% confidence interval for β1.

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