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).

x1 | 1250 1300 1350 1250 1300 x2 | 6 7 6 76 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 tempdiff
200 0.210 furntemp 3.00 clostime 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 s
1.058 R-sq
99.1% R-sq(adj)
98.8%

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 interval for 2, the population regression coefficient of x2