An investigation of a die-casting process resulted in the accompanying data on ,

, and 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).

x1 1250 1300 1350 1250 1300 x2 67676 y 80 95 101 85 92 x1 1250 1300 1350 1350 x2 8878 y 87 96 106 108 Minitab output from fitting the multiple regression model with predictors x1 and x2 is given here.

The regression equation is Predictor Coef Stdev t-ratio p Constant 199.56 11.64 17.14 0.000 furntemp 0.210000 0.008642 24.30 0.000 clostime 3.0000 0.4321 6.94 0.000 Analysis of Variance SOURCE DF SS MS F p Regression 2 715.50 357.75 319.31 0.000 Error 6 6.72 1.12 Total 8 722.22

a. Carry out the model utility test.

b. Calculate and interpret a 95% confidence interv

c. When and , the estimated standard deviation of is . 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.