Exercise 35 of Section 3.5 gave data on x_{1} wire feed rate, x_{2} welding speed, and y deposition rate of a welding process. Minitab output from fitting the multiple regression model with x_{1} and x_{2} as predictors is given here.

a. Carry out the model utility test.

b. Calculate and interpret a 95% confidence interval for _{2}, the population regression coefficient of x_{2.}

c. When x_{1} 11.5 and x_{2} 40, the estimated standard deviation of is s .02438. Calculate a 95% confidence interval for true average deposition rate for the given values of x_{1} and x_{2}.

d. Calculate a 95% prediction interval for the deposition rate resulting from a single experimental run with x_{1} 11.5 and x_{2} 40.

Exercise 35

Fill in all the columns in the design matrix for the 2^{5}^{2} design of Example 10.12.

Example 10.12

_{ }