Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
8th Edition
ISBN: 9781464158933
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 12, Problem 22E
(a)
To determine
To find: The fitted data and the residuals. Also, generate the
(a)
Expert Solution
Answer to Problem 22E
Solution: The residuals of the provided data is scattered symmetrically above and below the zero and there is no extreme outlier.
Explanation of Solution
Given: The data provided in the Facebook friends study as,
| Friends | Participant | Score |
| 102 | 1 | 3.8 |
| 102 | 2 | 3.6 |
| 102 | 3 | 3.2 |
| 102 | 4 | 2.4 |
| 102 | 5 | 4.8 |
| 102 | 6 | 3.0 |
| 102 | 7 | 4.2 |
| 102 | 8 | 3.6 |
| 102 | 9 | 3.2 |
| 102 | 10 | 3.0 |
| 102 | 11 | 4.8 |
| 102 | 12 | 3.4 |
| 102 | 13 | 4.8 |
| 102 | 14 | 3.0 |
| 102 | 15 | 4.6 |
| 102 | 16 | 2.8 |
| 102 | 17 | 6.0 |
| 102 | 18 | 2.8 |
| 102 | 19 | 5.2 |
| 102 | 20 | 3.2 |
| 102 | 21 | 4.2 |
| 102 | 22 | 2.2 |
| 102 | 23 | 5.0 |
| 102 | 24 | 4.8 |
| 302 | 25 | 5.0 |
| 302 | 26 | 5.2 |
| 302 | 27 | 5.6 |
| 302 | 28 | 2.6 |
| 302 | 29 | 3.8 |
| 302 | 30 | 4.8 |
| 302 | 31 | 5.6 |
| 302 | 32 | 4.8 |
| 302 | 33 | 6.4 |
| 302 | 34 | 4.8 |
| 302 | 35 | 4.4 |
| 302 | 36 | 6.0 |
| 302 | 37 | 3.8 |
| 302 | 38 | 4.8 |
| 302 | 39 | 4.6 |
| 302 | 40 | 6.0 |
| 302 | 41 | 5.0 |
| 302 | 42 | 3.0 |
| 302 | 43 | 4.4 |
| 302 | 44 | 5.4 |
| 302 | 45 | 5.4 |
| 302 | 46 | 4.6 |
| 302 | 47 | 5.6 |
| 302 | 48 | 5.8 |
| 302 | 49 | 4.2 |
| 302 | 50 | 4.8 |
| 302 | 51 | 5.0 |
| 302 | 52 | 5.2 |
| 302 | 53 | 4.2 |
| 302 | 54 | 5.0 |
| 302 | 55 | 5.8 |
| 302 | 56 | 5.6 |
| 302 | 57 | 3.8 |
| 502 | 58 | 4.6 |
| 502 | 59 | 4.0 |
| 502 | 60 | 4.8 |
| 502 | 61 | 3.0 |
| 502 | 62 | 2.0 |
| 502 | 63 | 5.8 |
| 502 | 64 | 5.6 |
| 502 | 65 | 4.4 |
| 502 | 66 | 4.4 |
| 502 | 67 | 5.6 |
| 502 | 68 | 4.6 |
| 502 | 69 | 5.6 |
| 502 | 70 | 3.0 |
| 502 | 71 | 5.6 |
| 502 | 72 | 3.6 |
| 502 | 73 | 6.8 |
| 502 | 74 | 3.2 |
| 502 | 75 | 4.8 |
| 502 | 76 | 4.6 |
| 502 | 77 | 5.4 |
| 502 | 78 | 4.8 |
| 502 | 79 | 4.8 |
| 502 | 80 | 5.4 |
| 502 | 81 | 3.6 |
| 502 | 82 | 4.8 |
| 502 | 83 | 3.8 |
| 702 | 84 | 3.2 |
| 702 | 85 | 3.6 |
| 702 | 86 | 5.8 |
| 702 | 87 | 1.2 |
| 702 | 88 | 3.8 |
| 702 | 89 | 5.4 |
| 702 | 90 | 3.6 |
| 702 | 91 | 3.4 |
| 702 | 92 | 5.0 |
| 702 | 93 | 5.2 |
| 702 | 94 | 3.6 |
| 702 | 95 | 2.6 |
| 702 | 96 | 7.0 |
| 702 | 97 | 4.4 |
| 702 | 98 | 4.8 |
| 702 | 99 | 5.2 |
| 702 | 100 | 5.4 |
| 702 | 101 | 3.6 |
| 702 | 102 | 1.0 |
| 702 | 103 | 5.0 |
| 702 | 104 | 5.0 |
| 702 | 105 | 6.0 |
| 702 | 106 | 4.2 |
| 702 | 107 | 5.8 |
| 702 | 108 | 3.2 |
| 702 | 109 | 5.4 |
| 702 | 110 | 6.4 |
| 702 | 111 | 4.4 |
| 702 | 112 | 3.0 |
| 702 | 113 | 6.0 |
| 902 | 114 | 4.2 |
| 902 | 115 | 4.6 |
| 902 | 116 | 3.0 |
| 902 | 117 | 2.6 |
| 902 | 118 | 5.2 |
| 902 | 119 | 5.2 |
| 902 | 120 | 1.6 |
| 902 | 121 | 5.0 |
| 902 | 122 | 4.4 |
| 902 | 123 | 5.0 |
| 902 | 124 | 3.6 |
| 902 | 125 | 4.2 |
| 902 | 126 | 5.0 |
| 902 | 127 | 3.4 |
| 902 | 128 | 3.6 |
| 902 | 129 | 5.0 |
| 902 | 130 | 3.2 |
| 902 | 131 | 2.4 |
| 902 | 132 | 4.8 |
| 902 | 133 | 3.6 |
| 902 | 134 | 4.2 |
Calculation:
Use Minitab to find the residuals, of the provided data as below:
Step1: Enter the provided data in the worksheet.
Step2: Select stat >ANOVA>one-way analysis of variance.
Step3: Select Score in the Response and Friends in the Factor.
Step4: Click on Graphs and select the Residual verses fitand then press OK.
Step5: Select Store residual and Store fit.
Step6: Press OK.
Theobtained output of fitted data and the residual stored in the data file as below:
| Friends | Participant | Score | RESI1 | FITS1 |
| 102 | 1 | 3.8 | -0.01667 | 3.816667 |
| 102 | 2 | 3.6 | -0.21667 | 3.816667 |
| 102 | 3 | 3.2 | -0.61667 | 3.816667 |
| 102 | 4 | 2.4 | -1.41667 | 3.816667 |
| 102 | 5 | 4.8 | 0.983333 | 3.816667 |
| 102 | 6 | 3.0 | -0.81667 | 3.816667 |
| 102 | 7 | 4.2 | 0.383333 | 3.816667 |
| 102 | 8 | 3.6 | -0.21667 | 3.816667 |
| 102 | 9 | 3.2 | -0.61667 | 3.816667 |
| 102 | 10 | 3.0 | -0.81667 | 3.816667 |
| 102 | 11 | 4.8 | 0.983333 | 3.816667 |
| 102 | 12 | 3.4 | -0.41667 | 3.816667 |
| 102 | 13 | 4.8 | 0.983333 | 3.816667 |
| 102 | 14 | 3.0 | -0.81667 | 3.816667 |
| 102 | 15 | 4.6 | 0.783333 | 3.816667 |
| 102 | 16 | 2.8 | -1.01667 | 3.816667 |
| 102 | 17 | 6.0 | 2.183333 | 3.816667 |
| 102 | 18 | 2.8 | -1.01667 | 3.816667 |
| 102 | 19 | 5.2 | 1.383333 | 3.816667 |
| 102 | 20 | 3.2 | -0.61667 | 3.816667 |
| 102 | 21 | 4.2 | 0.383333 | 3.816667 |
| 102 | 22 | 2.2 | -1.61667 | 3.816667 |
| 102 | 23 | 5.0 | 1.183333 | 3.816667 |
| 102 | 24 | 4.8 | 0.983333 | 3.816667 |
| 302 | 25 | 5.0 | 0.121212 | 4.878788 |
| 302 | 26 | 5.2 | 0.321212 | 4.878788 |
| 302 | 27 | 5.6 | 0.721212 | 4.878788 |
| 302 | 28 | 2.6 | -2.27879 | 4.878788 |
| 302 | 29 | 3.8 | -1.07879 | 4.878788 |
| 302 | 30 | 4.8 | -0.07879 | 4.878788 |
| 302 | 31 | 5.6 | 0.721212 | 4.878788 |
| 302 | 32 | 4.8 | -0.07879 | 4.878788 |
| 302 | 33 | 6.4 | 1.521212 | 4.878788 |
| 302 | 34 | 4.8 | -0.07879 | 4.878788 |
| 302 | 35 | 4.4 | -0.47879 | 4.878788 |
| 302 | 36 | 6.0 | 1.121212 | 4.878788 |
| 302 | 37 | 3.8 | -1.07879 | 4.878788 |
| 302 | 38 | 4.8 | -0.07879 | 4.878788 |
| 302 | 39 | 4.6 | -0.27879 | 4.878788 |
| 302 | 40 | 6.0 | 1.121212 | 4.878788 |
| 302 | 41 | 5.0 | 0.121212 | 4.878788 |
| 302 | 42 | 3.0 | -1.87879 | 4.878788 |
| 302 | 43 | 4.4 | -0.47879 | 4.878788 |
| 302 | 44 | 5.4 | 0.521212 | 4.878788 |
| 302 | 45 | 5.4 | 0.521212 | 4.878788 |
| 302 | 46 | 4.6 | -0.27879 | 4.878788 |
| 302 | 47 | 5.6 | 0.721212 | 4.878788 |
| 302 | 48 | 5.8 | 0.921212 | 4.878788 |
| 302 | 49 | 4.2 | -0.67879 | 4.878788 |
| 302 | 50 | 4.8 | -0.07879 | 4.878788 |
| 302 | 51 | 5.0 | 0.121212 | 4.878788 |
| 302 | 52 | 5.2 | 0.321212 | 4.878788 |
| 302 | 53 | 4.2 | -0.67879 | 4.878788 |
| 302 | 54 | 5.0 | 0.121212 | 4.878788 |
| 302 | 55 | 5.8 | 0.921212 | 4.878788 |
| 302 | 56 | 5.6 | 0.721212 | 4.878788 |
| 302 | 57 | 3.8 | -1.07879 | 4.878788 |
| 502 | 58 | 4.6 | 0.038462 | 4.561538 |
| 502 | 59 | 4.0 | -0.56154 | 4.561538 |
| 502 | 60 | 4.8 | 0.238462 | 4.561538 |
| 502 | 61 | 3.0 | -1.56154 | 4.561538 |
| 502 | 62 | 2.0 | -2.56154 | 4.561538 |
| 502 | 63 | 5.8 | 1.238462 | 4.561538 |
| 502 | 64 | 5.6 | 1.038462 | 4.561538 |
| 502 | 65 | 4.4 | -0.16154 | 4.561538 |
| 502 | 66 | 4.4 | -0.16154 | 4.561538 |
| 502 | 67 | 5.6 | 1.038462 | 4.561538 |
| 502 | 68 | 4.6 | 0.038462 | 4.561538 |
| 502 | 69 | 5.6 | 1.038462 | 4.561538 |
| 502 | 70 | 3.0 | -1.56154 | 4.561538 |
| 502 | 71 | 5.6 | 1.038462 | 4.561538 |
| 502 | 72 | 3.6 | -0.96154 | 4.561538 |
| 502 | 73 | 6.8 | 2.238462 | 4.561538 |
| 502 | 74 | 3.2 | -1.36154 | 4.561538 |
| 502 | 75 | 4.8 | 0.238462 | 4.561538 |
| 502 | 76 | 4.6 | 0.038462 | 4.561538 |
| 502 | 77 | 5.4 | 0.838462 | 4.561538 |
| 502 | 78 | 4.8 | 0.238462 | 4.561538 |
| 502 | 79 | 4.8 | 0.238462 | 4.561538 |
| 502 | 80 | 5.4 | 0.838462 | 4.561538 |
| 502 | 81 | 3.6 | -0.96154 | 4.561538 |
| 502 | 82 | 4.8 | 0.238462 | 4.561538 |
| 502 | 83 | 3.8 | -0.76154 | 4.561538 |
| 702 | 84 | 3.2 | -1.20667 | 4.406667 |
| 702 | 85 | 3.6 | -0.80667 | 4.406667 |
| 702 | 86 | 5.8 | 1.393333 | 4.406667 |
| 702 | 87 | 1.2 | -3.20667 | 4.406667 |
| 702 | 88 | 3.8 | -0.60667 | 4.406667 |
| 702 | 89 | 5.4 | 0.993333 | 4.406667 |
| 702 | 90 | 3.6 | -0.80667 | 4.406667 |
| 702 | 91 | 3.4 | -1.00667 | 4.406667 |
| 702 | 92 | 5.0 | 0.593333 | 4.406667 |
| 702 | 93 | 5.2 | 0.793333 | 4.406667 |
| 702 | 94 | 3.6 | -0.80667 | 4.406667 |
| 702 | 95 | 2.6 | -1.80667 | 4.406667 |
| 702 | 96 | 7.0 | 2.593333 | 4.406667 |
| 702 | 97 | 4.4 | -0.00667 | 4.406667 |
| 702 | 98 | 4.8 | 0.393333 | 4.406667 |
| 702 | 99 | 5.2 | 0.793333 | 4.406667 |
| 702 | 100 | 5.4 | 0.993333 | 4.406667 |
| 702 | 101 | 3.6 | -0.80667 | 4.406667 |
| 702 | 102 | 1.0 | -3.40667 | 4.406667 |
| 702 | 103 | 5.0 | 0.593333 | 4.406667 |
| 702 | 104 | 5.0 | 0.593333 | 4.406667 |
| 702 | 105 | 6.0 | 1.593333 | 4.406667 |
| 702 | 106 | 4.2 | -0.20667 | 4.406667 |
| 702 | 107 | 5.8 | 1.393333 | 4.406667 |
| 702 | 108 | 3.2 | -1.20667 | 4.406667 |
| 702 | 109 | 5.4 | 0.993333 | 4.406667 |
| 702 | 110 | 6.4 | 1.993333 | 4.406667 |
| 702 | 111 | 4.4 | -0.00667 | 4.406667 |
| 702 | 112 | 3.0 | -1.40667 | 4.406667 |
| 702 | 113 | 6.0 | 1.593333 | 4.406667 |
| 902 | 114 | 4.2 | 0.209524 | 3.990476 |
| 902 | 115 | 4.6 | 0.609524 | 3.990476 |
| 902 | 116 | 3.0 | -0.99048 | 3.990476 |
| 902 | 117 | 2.6 | -1.39048 | 3.990476 |
| 902 | 118 | 5.2 | 1.209524 | 3.990476 |
| 902 | 119 | 5.2 | 1.209524 | 3.990476 |
| 902 | 120 | 1.6 | -2.39048 | 3.990476 |
| 902 | 121 | 5.0 | 1.009524 | 3.990476 |
| 902 | 122 | 4.4 | 0.409524 | 3.990476 |
| 902 | 123 | 5.0 | 1.009524 | 3.990476 |
| 902 | 124 | 3.6 | -0.39048 | 3.990476 |
| 902 | 125 | 4.2 | 0.209524 | 3.990476 |
| 902 | 126 | 5.0 | 1.009524 | 3.990476 |
| 902 | 127 | 3.4 | -0.59048 | 3.990476 |
| 902 | 128 | 3.6 | -0.39048 | 3.990476 |
| 902 | 129 | 5.0 | 1.009524 | 3.990476 |
| 902 | 130 | 3.2 | -0.79048 | 3.990476 |
| 902 | 131 | 2.4 | -1.59048 | 3.990476 |
| 902 | 132 | 4.8 | 0.809524 | 3.990476 |
| 902 | 133 | 3.6 | -0.39048 | 3.990476 |
| 902 | 134 | 4.2 | 0.209524 | 3.990476 |
The scatterplot of the residuals versus the group variable is,
Interpretation: From the above graph, it is observed that the scatter plot of the residuals is symmetrically scattered below and above the zero and there are two outliers below the zero but these are not the extreme outliers.
(b)
To determine
Whether the spread of the residual of each group is relatively equal or not.
(b)
Expert Solution
Answer to Problem 22E
Solution: Yes, the spread of the residual of each group is relatively equal.
Explanation of Solution
From the scatterplot of the residuals versus the group variables in part (a), it is observed that the residuals are symmetrically scattered below and above the zero. It implies that the spread of the residual of each group is relatively equal.
(c)
To determine
To graph: The Normal quantile plot of the residuals obtained in part (a) and identify whether it is normal or not.
(c)
Expert Solution
Explanation of Solution
Graph:
Use Minitab to graph the Normal quantile plot as below:
Step1: Enter the provided data in the worksheet.
Step2: Select stat> ANOVA>one-way analysis of variance.
Step3: Select Score in the Response and Friends in the Factor.
Step4: Click on Graphs and select the Normal plot of residuals and then press OK.
Step5: Press OK.
The obtained graph is,
Interpretation: From the obtained graph, it is observed that the normal quantile plot is nearly fitted to the line. Hence, the residual is approximately normal.
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Chapter 12 Solutions
Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
Ch. 12.1 - Prob. 1UYKCh. 12.1 - Prob. 2UYKCh. 12.1 - Prob. 3UYKCh. 12.1 - Prob. 5UYKCh. 12.1 - Prob. 6UYKCh. 12.1 - Prob. 4UYKCh. 12.2 - Prob. 7UYKCh. 12.2 - Prob. 8UYKCh. 12 - Prob. 9ECh. 12 - Prob. 10E
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