3. An experiment is planned in which three observations will be taken at each of four temperatures, 30◦, 50◦, 70◦, and 90◦. When the experiment is actually done, the results obtained are those given below. Find, assuming η = E(Y |X) = β0 + β1X, the least-squares estimates of β0 and β1, and hence the least-squares estimate of η. Construct 95% confidence intervals for β0, β1, and η0 = β0 + β1x0.

X (temperature) 30 30 30 50 50 50 70 70 70 90 90 90 Y (response) 40 45 31 34 28 35 21 29 25 16 21 23