(1) Consider the GASTURBINE data set and corresponding output from Minitab. Note
ID: 3266286 • Letter: #
Question
(1) Consider the GASTURBINE data set and corresponding output from Minitab. Note that all tests should be performed at the = 0.05 level. Use the complete data set in your analysis. The first 10 observations are given for illustrative purposes. Complete parts a) through f) below.
ENGINE
SHAFTS
RPM
CPRATIO
INLET-TEMP
EXH-TEMP
AIRFLOW
POWER
HEATRATE
Traditional
1
27245
9.2
1134
602
7
1630
14622
Traditional
1
14000
12.2
950
446
15
2726
13196
Traditional
1
17384
14.8
1149
537
20
5247
11948
Traditional
1
11085
11.8
1024
478
27
6726
11289
Traditional
1
14045
13.2
1149
553
29
7726
11964
Traditional
1
6211
15.7
1172
517
176
52600
10526
Traditional
1
6210
17.4
1177
510
193
57500
10387
Traditional
1
3600
13.5
1146
503
315
89600
10592
Traditional
1
3000
15.1
1146
524
375
113700
10460
Traditional
1
3000
15
1171
525
514
164300
10086
Regression Analysis: HEATRATE versus RPM, CPRATIO, ...
The regression equation is
HEATRATE = 14314 + 0.0806 RPM - 6.8 CPRATIO - 9.51 INLET-TEMP + 14.2 EXH-TEMP
- 2.55 AIRFLOW + 0.00426 POWER
Predictor Coef SE Coef T P
Constant 14314 1112 12.87 0.000
RPM 0.08058 0.01611 5.00 0.000
CPRATIO -6.78 30.38 -0.22 0.824
INLET-TEMP -9.507 1.529 -6.22 0.000
EXH-TEMP 14.155 3.469 4.08 0.000
AIRFLOW -2.553 1.746 -1.46 0.149
POWER 0.004257 0.004217 1.01 0.317
S = 458.757 R-Sq = 92.5% R-Sq(adj) = 91.7%
Analysis of Variance
Source. DF SS MS F P
Regression 6 155269735 25878289 122.96 0.000
Residual Error 60 12627473 210458
Total 66 167897208
a) Write a first-order model in general form for the model that includes RPM, CPRATIO, INLET-TEMP, EXH-TEMP, AIRFLOW, and POWER to predict HEATRATE.
b) Write out the least squares prediction equation for the model that was fit in Minitab.
c) Calculate and give an interpretation of the coefficients based on a one-unit change in each xi.Calculate and give an interpretation of the effect on HEATRATE based on a 1-unit change in AIRFLOW together with a 200-unit change in POWER.
d) Interpret the overall model F-test. State the appropriate hypothesis test and associated numerator and denominator degrees of freedom used for this test as well as the critical value that the test statistic is compared to. State the conclusion you would make regarding the null hypothesis. Specifically, would you reject or fail to reject the null hypothesis, and what does this conclusion means about the model parameters? Does this tell us anything about the significance of the individual predictors? Why or why not?
e) Report and interpret the model R2.
f) Which predictors are significant in the model? Report the appropriate hypothesis test and formal conclusion you would make regarding RPM and CPRATIO. In your conclusion, state their p-values and test statistics. Would you suggest removing all non-significant predictors at once and refitting the model? Why or why not?
ENGINE
SHAFTS
RPM
CPRATIO
INLET-TEMP
EXH-TEMP
AIRFLOW
POWER
HEATRATE
Traditional
1
27245
9.2
1134
602
7
1630
14622
Traditional
1
14000
12.2
950
446
15
2726
13196
Traditional
1
17384
14.8
1149
537
20
5247
11948
Traditional
1
11085
11.8
1024
478
27
6726
11289
Traditional
1
14045
13.2
1149
553
29
7726
11964
Traditional
1
6211
15.7
1172
517
176
52600
10526
Traditional
1
6210
17.4
1177
510
193
57500
10387
Traditional
1
3600
13.5
1146
503
315
89600
10592
Traditional
1
3000
15.1
1146
524
375
113700
10460
Traditional
1
3000
15
1171
525
514
164300
10086
Explanation / Answer
a)
HEATRATE = b0+ b1 RPM +b2 CPRATIO + b3* INLET-TEMP + b4* EXH-TEMP + b5* AIRFLOW + b6* POWER
b)
HEATRATE = 14314 + 0.0806 RPM - 6.8 CPRATIO - 9.51 INLET-TEMP + 14.2 EXH-TEMP
- 2.55 AIRFLOW + 0.00426 POWER
c) any beta coefficient is interpreted as
if we change 1 unit in independent variable , dependent variable will change by beta coefficient of that variable
for eg , if we increase RPM by 1 unit , heat_rate will increase by 0.0806 unit
- 2.55 AIRFLOW + 0.00426 POWER
- 2.55 *1 + 0.00426 *200 = -1.698
hence heat_rate will decrease by 1.698 unit
d)
df1 = 6
df2 = 60
TS = 122.96
critical value = 2.25
since TS > critical value , we reject the null and conclude that overall model is significant.
it does not say about significance of individual variable.
e)
R^2 = 92.5%
it means that 92.5 % of variation in dependnet variable is explained by this model
f)
if p-value is less than 0.05 , the variable is significant
here RPM , INLET-TEMP ,EXh -TEMP are significant as their p-value =0.000 < 0.05
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Thanks and have a good day!
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