When required, perform all the tests at 5% level and give 95% confidence and prediction
intervals.
Problem A1. Consider the data transact.txt, and consider the model
E(T ime|T1, T 2) = β0+β1T1+β2T2
a. Fit the above model to the dat.
b. Is this model significantly different from the model E(T ime|T1, T 2) = β0?
c. Is the coefficient of T1significantly different from zero?
d. Is the coefficient of T1significantly different from 4?
e. Is 2β1+β2significantly different from 10?
f. Find a confidence interval for the value of the response at T1= 200 and T2= 500.
g. Find a prediction interval for the value of the response at T1= 200 and T2= 500.
Consider the model
E(T ime|T1, T 2) = β0+β1T1+β2T2+β3T2
1+β4T2
2.
Test this model against the model
E(T ime|T1, T 2) = β0+β1T1+β2T2.
Problem A2. The design matrix for the simple linear regression model is X= (1,x).
a. Show
X0X=n n¯x
n¯xPx2
i
b. Invert X0Xand use the formulas ˆ
β= (X0X)−1X0yand Var(ˆ
β) = σ2(X0X)−1to
obtain the parameter estimate and their corresponding variances.
