An investigation of a die-casting process resulted in the accompanying data on x1= furn...

An investigation of a die-casting process resulted in the accompanying data on x₁= furnace temperature , x₂ = die close time, and y = temperature difference on the die surface (“A Multiple-Objective Decision-Making Approach for Assessing Simultaneous Improvement in Die Life and Casting Quality in a Die Casting Process,” Quality Engineering, 1994: 371–383).

Minitab output from fitting the multiple regression model with predictors x₁ and x₂ is given here.

a. Carry out the model utility test.

b. Calculate and interpret a 95% confidence interval for β₂, the population regression coefficient of x₂.

c. When x₁ = 1300 and x₂ = 7 , the estimated standard deviation of . Calculate a 95% confidence interval for true average temperature difference when furnace temperature is 1300 and die close time is 7.

d. Calculate a 95% prediction interval for the temperature difference resulting from a single experimental run with a furnace temperature of 1300 and a die close time of 7.