Chapter 13.4, Problem 42E

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

 

1. a. Carry out the model utility test.
2. b. Calculate and interpret a 95% confidence interval for β₂, the population regression coefficient of x₂.
3. c. When x₁ = 1300 and x₂ = 7, the estimated standard deviation of $\hat{Y}$ is $S_{\hat{Y}}=.353$. Calculate a 95% confidence interval for true average temperature difference when furnace temperature is 1300 and die close time is 7.
4. 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.