Question

In: Statistics and Probability

1. A supervisor suggests that the old computer program for estimating delivery times be abandoned. Instead,...

1. A supervisor suggests that the old computer program for estimating delivery times be abandoned. Instead, schedulers could use an alternative such as MapQuest to estimate driving times. As a pilot study, 500 recent deliveries were randomly selected. The Excel data listed below contains the following variables:

Actual Times: actual time required to make delivery

Old Model Deviations: difference in actual delivery time and predicted delivery time using old computer prediction model

MapQuest: predicted delivery times for the randomly selected routes using MapQuest

Use the data to calculate the deviations for the MapQuest estimates (DMapQuest = actual delivery time – MapQuest predicted delivery time), then construct an appropriate graph for comparing the deviations for the Old Computer model and the MapQuest model. Interpret the results and indicate which prediction model should be used in the future. (Do NOT include the calculated deviations here. Do include the graph and interpretation.)

2. A driver reads your answer to part (1) and makes the following comment: MapQuest gives driving times for cars. Driving times for trucks will probably be longer because we can’t go as fast, especially in city traffic. Is there some way to adjust the MapQuest prediction to make it fit trucks better? Construct a fitted line plot (scatterplot with fitted linear regression line) using the MapQuest times as the predictor variable and the actual times as the response variable. Call the fitted values ‘Adjusted MapQuest’ times. Provide the fitted line plot, regression equation and R2 values associated with the ‘Adjusted MapQuest’ times. Interpret your results and indicate whether the driver’s suggestion is valid or invalid.

3. Use the regression equation given in part (2) to provide ‘Adjusted MapQuest’ times for the sample of 500 deliveries and calculate the Adjusted Deviations = Actual times - Adjusted MapQuest times. (You do NOT need to put those values here.) Construct an appropriate graph for comparing the deviations associated with the Old Computer Model, the MapQuest model and Adjusted MapQuest model and include it here. Interpret the graph and recommend the modeling tool (method of predicting delivery times) you feel is most accurate.

Actual

Times

Old Model Deviation MapQuest
142 42 113
82 -18 79
142 42 101
151 51 112
154 54 127
124 24 90
134 34 89
135 35 113
123 23 94
150 50 111
121 21 105
111 11 101
142 42 109
118 18 102
159 59 119
98 -2 89
150 50 115
128 28 101
134 34 110
158 58 123
106 6 89
147 47 123
117 17 84
153 53 105
126 26 96
129 29 100
98 -2 76
139 39 111
119 19 95
98 -2 69
137 37 105
140 40 110
140 40 121
134 34 99
131 31 100
98 -2 76
123 23 116
108 8 96
112 12 85
143 43 116
133 33 92
127 27 99
124 24 95
102 2 82
106 6 87
158 58 110
122 22 93
117 17 93
179 79 142
124 24 91
127 27 114
109 9 90
121 21 96
119 19 92
125 25 107
121 21 106
138 38 112
129 29 111
137 37 112
121 21 99
156 56 110
142 42 113
112 12 89
105 5 85
142 42 114
142 42 118
137 37 107
94 -6 79
132 32 115
112 12 98
97 -3 85
140 40 112
126 26 106
131 31 98
93 -7 81
161 61 115
113 13 87
108 8 81
117 17 102
147 47 108
113 13 98
92 -8 83
136 36 106
118 18 88
120 20 84
82 -18 68
139 39 111
121 21 101
157 57 129
150 50 110
133 33 95
118 18 107
115 15 93
144 44 110
124 24 110
110 10 77
145 45 112
172 72 123
111 11 88
134 34 106
131 31 103
118 18 116
122 22 100
118 18 93
132 32 108
109 9 100
100 0 83
111 11 97
109 9 82
141 41 102
124 24 108
85 -15 67
126 26 97
140 40 114
121 21 102
148 48 118
110 10 92
164 64 127
136 36 106
138 38 107
142 42 100
112 12 96
129 29 94
151 51 112
122 22 97
100 0 73
124 24 98
141 41 115
126 26 106
120 20 92
105 5 97
144 44 92
136 36 107
99 -1 94
97 -3 102
93 -7 86
132 32 97
130 30 108
89 -11 76
107 7 82
128 28 91
108 8 98
134 34 101
122 22 93
135 35 105
118 18 95
121 21 98
98 -2 78
104 4 82
117 17 83
135 35 112
175 75 131
120 20 113
94 -6 81
106 6 95
132 32 110
116 16 98
137 37 99
81 -19 73
122 22 93
101 1 85
126 26 111
148 48 116
136 36 109
90 -10 85
135 35 102
138 38 111
158 58 125
118 18 94
120 20 91
165 65 123
116 16 104
117 17 90
137 37 99
123 23 110
144 44 109
159 59 126
114 14 104
101 1 93
114 14 98
101 1 81
122 22 87
168 68 133
111 11 104
147 47 122
130 30 106
131 31 105
117 17 102
113 13 102
125 25 98
123 23 96
126 26 113
92 -8 78
136 36 106
124 24 95
153 53 131
91 -9 87
135 35 102
129 29 94
123 23 97
150 50 115
145 45 105
103 3 86
127 27 104
122 22 92
119 19 92
117 17 97
136 36 107
85 -15 70
106 6 84
111 11 89
166 66 119
124 24 112
163 63 122
154 54 104
134 34 93
100 0 83
109 9 82
125 25 105
72 -28 79
93 -7 86
148 48 110
70 -30 70
125 25 93
163 63 119
111 11 94
111 11 84
124 24 111
117 17 98
148 48 109
152 52 118
112 12 94
115 15 82
89 -11 87
124 24 88
126 26 104
133 33 103
131 31 107
178 78 134
69 -31 63
129 29 100
119 19 96
106 6 95
163 63 132
160 60 135
107 7 96
118 18 87
130 30 111
123 23 102
133 33 112
139 39 123
115 15 104
101 1 89
152 52 123
117 17 105
110 10 86
130 30 98
138 38 117
111 11 85
123 23 98
99 -1 87
149 49 107
130 30 95
161 61 121
157 57 123
86 -14 76
108 8 98
128 28 92
112 12 88
149 49 104
127 27 96
93 -7 82
136 36 105
119 19 93
118 18 90
114 14 89
146 46 105
106 6 83
94 -6 74
129 29 112
133 33 97
156 56 125
151 51 122
108 8 87
84 -16 74
127 27 91
150 50 103
137 37 107
112 12 97
124 24 103
101 1 77
125 25 98
122 22 92
117 17 91
136 36 110
110 10 86
123 23 116
129 29 102
128 28 105
126 26 105
141 41 104
113 13 99
127 27 98
137 37 96
112 12 93
159 59 124
148 48 108
111 11 90
133 33 113
118 18 104
157 57 108
118 18 98
147 47 125
118 18 94
125 25 109
110 10 85
105 5 97
75 -25 74
130 30 100
127 27 110
93 -7 70
123 23 99
114 14 94
159 59 129
113 13 108
89 -11 78
131 31 102
154 54 138
90 -10 74
98 -2 87
139 39 114
136 36 107
103 3 76
114 14 96
126 26 98
147 47 117
101 1 74
133 33 92
143 43 109
110 10 95
98 -2 89
121 21 88
113 13 91
149 49 123
128 28 97
133 33 103
116 16 94
176 76 124
117 17 99
118 18 99
92 -8 89
96 -4 77
126 26 90
81 -19 72
139 39 108
107 7 93
76 -24 64
133 33 107
109 9 79
137 37 111
127 27 101
136 36 103
134 34 95
100 0 83
103 3 88
106 6 75
125 25 101
120 20 101
127 27 94
129 29 99
148 48 110
108 8 92
123 23 106
136 36 118
162 62 116
113 13 81
136 36 108
119 19 96
135 35 113
144 44 91
166 66 124
143 43 114
90 -10 74
146 46 111
167 67 124
128 28 107
125 25 96
112 12 93
151 51 122
73 -27 76
125 25 104
116 16 94
116 16 101
103 3 100
104 4 86
133 33 104
166 66 119
125 25 107
148 48 108
147 47 117
85 -15 78
123 23 95
98 -2 91
145 45 120
148 48 115
101 1 80
131 31 110
115 15 90
99 -1 84
146 46 120
129 29 107
91 -9 77
116 16 92
126 26 92
90 -10 69
125 25 92
143 43 101
114 14 94
144 44 107
76 -24 82
124 24 97
151 51 123
133 33 101
103 3 91
103 3 97
124 24 108
96 -4 77
132 32 107
142 42 108
136 36 110
124 24 104
146 46 123
97 -3 83
99 -1 90
118 18 81
117 17 101
135 35 116
151 51 123
124 24 88
115 15 92
142 42 111
92 -8 90
117 17 88
148 48 116
146 46 114
167 67 122
114 14 91
149 49 109
123 23 102
111 11 100
106 6 92
126 26 103
148 48 117
108 8 83
108 8 85
166 66 137
140 40 103
119 19 85
126 26 94
132 32 92
141 41 118
157 57 127
142 42 112
145 45 100
81 -19 77
119 19 112
153 53 112
97 -3 78
123 23 91
121 21 91
121 21 89
120 20 106
104 4 83
97 -3 70
159 59 122
106 6 83
180 80 134
144 44 108
152 52 120
120 20 98
126 26 102
101 1 89
131 31 109
94 -6 86
106 6 79
124 24 95
145 45 118
168 68 111
123 23 95
130 30 95
113 13 94
137 37 110
90 -10 90
93 -7 79
147 47 112
146 46 108
125 25 97
128 28 99
132 32 97
119 19 77

Solutions

Expert Solution

1. If you observe the following graph it is evident that dmapquest values are varying less. Hence MapQuest can be used to predict the delivery times in the future.2.The regression equation is actual time = - 0.98 + 1.26*mapquest with R2 = 0.76.

Below I m producing the anlysis from regression.

Predictor Coef SE Coef T P
Constant -0.977 3.200 -0.31 0.760
mapquest 1.26021 0.03177 39.66 0.000

You can observe that the regression coefficient is significant approving the driver's claim and need of adjustment.

Now in the following graph one can observe that the variation in the 'adjusted deviation' is minimum and its varying around zero unlike 'old model deviation' and 'dmapquest'.

Hence, reaching to the concluson MapQuest can be used to used to predict the delivery time with adjustment provided by regression equation given above.


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