(2) Using the FLAG data set (first 10 observations given), fit a model that pred
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Question
(2) Using the FLAG data set (first 10 observations given), fit a model that predicts COST based on DOTEST. Use the complete data set in your analysis. Show the relevant output from Minitab in your answer. The first 10 observations are given for informational purposes.
CONTRACT
COST
DOTEST
STATUS
1
1379.43
1386.29
1
2
134.03
85.71
1
3
202.33
248.89
0
4
397.12
467.49
0
5
158.54
117.72
1
6
1128.11
1008.91
1
7
400.33
472.98
1
8
581.64
785.39
0
9
353.96
370.02
0
10
138.71
174.25
0
Calculate a confidence and prediction interval for DOTEST = 100. Interpret the confidence and prediction intervals given in the output. Do you see any problems with the interpretation ofthe prediction interval in terms of what we are trying to predict?Why are confidence intervals always more narrow than prediction intervals?
CONTRACT
COST
DOTEST
STATUS
1
1379.43
1386.29
1
2
134.03
85.71
1
3
202.33
248.89
0
4
397.12
467.49
0
5
158.54
117.72
1
6
1128.11
1008.91
1
7
400.33
472.98
1
8
581.64
785.39
0
9
353.96
370.02
0
10
138.71
174.25
0
Explanation / Answer
From following results regression equation is
COST = -22.2 + 0.9959 DOTEST
Corresponding to unit icnrease in DOTEST there is on an average an increase of 0.9959 in cost. Also slope is significant with p=0.000<0.05. DOTEST explained 95.98% of the variations in cost.
Regression Analysis: COST versus DOTEST
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 1616780 1616780 190.95 0.000
DOTEST 1 1616780 1616780 190.95 0.000
Error 8 67735 8467
Total 9 1684515
Model Summary
S R-sq R-sq(adj) R-sq(pred)
92.0158 95.98% 95.48% 93.78%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -22.2 47.0 -0.47 0.649
DOTEST 0.9959 0.0721 13.82 0.000 1.00
Regression Equation
COST = -22.2 + 0.9959 DOTEST
Prediction for COST
Regression Equation
COST = -22.2 + 0.9959 DOTEST
Variable Setting
DOTEST 100
Fit SE Fit 95% CI 95% PI
77.3519 41.5608 (-18.4876, 173.191) (-155.477, 310.181)
95% cofnidence interval is (-18.4876, 173.191) which means that when DOTEST =100, there is -18.49 to 173.19 average change amonsgt all DOTEST of 100.
95% prediction interval is (-155.477, 310.181) which means that when DOTEST =100, there is -155.477 to 310.181 for individual observation
Prediction interval is wider as there is more uncertaininty in predicting a single observation than mean
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