An investigation of a die-casting process resulted in the accompanying data on x,= furnace temperature, x,= die close time, and y = temperature difference on the die surfacet. 1250 1300 1350 1250 1300 1250 1300 1350 1350 6 6 7 80 95 101 85 92 87 96 106 108 Minitab output from fitting the multiple regression model with predictorsx, and x, is given here. The regression equation is tempdiff = -200 + 0.210furntemp + 3.00clostime Fredictor Coef Stdev t-ratio Constant furntemp -199.56 11.64 -17.14 0.000 24.30 0.000 0.000 0.210000 0.000642 0.4321 clostime 3.0000 6.94 - 1.058 Analysis of£ Variance R-aq- 99.14 R-sg (adj) = 98.84 SOURCE Regression Error DF 0.000 5ר.357 1.12 2 715.50 319.31 6.72 Total 722.22 (a) Carry out the model utility test. State the appropriate hypotheses. Hi at least one , 0 O Hg: 8, - 8, 0 H at least one 8,-0 Hgi no P, = 0 Hi all P, = 0 State the appropriate test statistic to two decimal places. D19.31 State the conclusion in the problem context. O Reject H The model is useful. O Reject H The model is not useful. O Fail to reject H. The model is not useful. O Fail to reject H. The model is useful. (b) Calculate a 95% confidence interval for 8, the population regression coefficient of x. (Round your answers to three decimal places.) 1.943 (4.057 Interpret the confidence interval • Holding furnace temperature fixed, we estimate that the average change in temperature difference on the die surface will fall within this interval. O Holding both factors fixed, we estimate that the average change in temperature difference on the die surface will fall within this interval.
An investigation of a die-casting process resulted in the accompanying data on x,= furnace temperature, x,= die close time, and y = temperature difference on the die surfacet. 1250 1300 1350 1250 1300 1250 1300 1350 1350 6 6 7 80 95 101 85 92 87 96 106 108 Minitab output from fitting the multiple regression model with predictorsx, and x, is given here. The regression equation is tempdiff = -200 + 0.210furntemp + 3.00clostime Fredictor Coef Stdev t-ratio Constant furntemp -199.56 11.64 -17.14 0.000 24.30 0.000 0.000 0.210000 0.000642 0.4321 clostime 3.0000 6.94 - 1.058 Analysis of£ Variance R-aq- 99.14 R-sg (adj) = 98.84 SOURCE Regression Error DF 0.000 5ר.357 1.12 2 715.50 319.31 6.72 Total 722.22 (a) Carry out the model utility test. State the appropriate hypotheses. Hi at least one , 0 O Hg: 8, - 8, 0 H at least one 8,-0 Hgi no P, = 0 Hi all P, = 0 State the appropriate test statistic to two decimal places. D19.31 State the conclusion in the problem context. O Reject H The model is useful. O Reject H The model is not useful. O Fail to reject H. The model is not useful. O Fail to reject H. The model is useful. (b) Calculate a 95% confidence interval for 8, the population regression coefficient of x. (Round your answers to three decimal places.) 1.943 (4.057 Interpret the confidence interval • Holding furnace temperature fixed, we estimate that the average change in temperature difference on the die surface will fall within this interval. O Holding both factors fixed, we estimate that the average change in temperature difference on the die surface will fall within this interval.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:An investigation of a die-casting process resulted in the accompanying data on x, = furnace temperature, x, = die close time, and y = temperature difference on the die surfacet.
X1
1250
1300
1350
1250
1300
1250
1300
1350
1350
X2
6
7
6
7
6
8
80
95
101
85
92
87
96
106
108
Minitab output from fitting the multiple regression model with predictors x, and x, is given here.
The regression equation is
tempdiff = -200 + 0.210 furntemp + 3.00clostime
Predictor
Coef
Stdev
t-Iatio
P
Constant
-199.56
11.64
-17.14
0.000
0.008642
0.000
0.000
furntemp
0.210000
24.30
clostime
3.0000
0.4321
6.94
: = 1.058
R-sq - 99.18
R-=q(adj) - 98.8e
Analysis of£ Variance
SOURCE
DE
33
M3
0.000
715.50
6.72
Regression
319.31
2
357.75
Error
1.12
Total
722.22
(a) Carry out the model utility test.
State the appropriate hypotheses.
• Hg: B, = 82 = 0
H: at least one 8, = 0
O H,: 8, = 8, =0
H: at least one 8, = 0
O H,: B, = B2 = 0
Hyi no 8, = 0
O Hg: B 82 = 0
H: all 8, = 0
State the appropriate test statistic to two decimal places.
319.31
State the conclusion in the problem context.
O Reject H. The model is useful.
O Reject H The model is not useful.
O Fail to reject Hg: The model is not useful.
O Fail to reject Hg: The model is useful.
(b) Calculate a 95% confidence interval for 8,, the population regression coefficient of x- (Round your answers to three decimal places.)
1.943
4.057
Interpret the confidence interval.
O Holding furnace temperature fixed, we estimate that the average change in temperature difference on the die surface will fall within this interval.
O Holding both factors fixed, we estimate that the average change in temperature difference on the die surface will fall within this interval.
O Holding die close time fixed, we estimate that the average change in temperature difference on the die surface will fall within this interval.
O we estimate that the average change in temperature difference on the die surface will fall within this interval.
(c) When x, = 1250 and x, = 8, the estimated standard deviation of Y is s = 0.706. Calculate a 95% confidence interval for true average temperature difference when furnace temperature is 1250 and die close time is 8. (Round your answers to two decimal places.)
84.40
(d) Calculate a 95% prediction interval for the temperature difference resulting from a single experimental run with a furnace temperature of 1250 and a die close time of 8. (Round your answers to two decimal places.)
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