82. An investigation of a die casting process resulted in the accompanying data on x1furnace 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, Qual. Engrg., 1994:371—383).

x1 1250 1300 1350 1250 1300 x2 6 7 6 7 6 y 80 95 101 85 92 x1 1250 1300 1350 1350 x2 8 8 7 8 y 87 96 106 108 MINITAB output from tting 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% con dence interval for b2, the population regression coef cient of x2.

c. When x1  1300 and x2  7, the estimated standard deviation of is . Calculate a 95%

con dence 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.

e. Use appropriate diagnostic plots to see if there is any reason to question the regression model assumptions.

sYˆ yˆ  .353