Month 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 Jan 95 104 101 88 132 12
ID: 3276524 • Letter: M
Question
Month
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
Jan
95
104
101
88
132
125
111
127
119
147
Feb
94
100
96
110
109
118
123
129
147
146
Mar
98
99
82
129
101
121
121
132
164
133
Apr
96
88
84
113
111
140
139
108
135
148
May
95
89
85
114
140
141
119
115
124
141
Jun
115
108
124
169
179
201
156
149
168
191
Jul
107
109
134
131
145
152
154
155
159
178
Aug
104
101
109
139
140
138
136
129
137
156
Sep
96
106
121
120
120
137
105
117
149
119
Oct
112
102
111
115
129
138
132
166
159
138
Nov
98
78
101
116
118
144
123
152
175
175
Dec
102
111
112
128
139
148
164
173
195
188
Question:
Develop multiplicative seasonal indices for the linear trend model developed in question 3. Use these indices to adjust predictions from the linear trend model from question 3 above for seasonal effects. Plot the predictions from this model on the graph with the original data. How well does this technique fit the data? Make forecasts for the next 12 months of 1997 using this technique.
Which forecasting method of those that you tried do you have the most confidence for making accurate forecasts for 1997?Use MAPE (mean absolute percent error) as your criterion to justify your decision.
Month
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
Jan
95
104
101
88
132
125
111
127
119
147
Feb
94
100
96
110
109
118
123
129
147
146
Mar
98
99
82
129
101
121
121
132
164
133
Apr
96
88
84
113
111
140
139
108
135
148
May
95
89
85
114
140
141
119
115
124
141
Jun
115
108
124
169
179
201
156
149
168
191
Jul
107
109
134
131
145
152
154
155
159
178
Aug
104
101
109
139
140
138
136
129
137
156
Sep
96
106
121
120
120
137
105
117
149
119
Oct
112
102
111
115
129
138
132
166
159
138
Nov
98
78
101
116
118
144
123
152
175
175
Dec
102
111
112
128
139
148
164
173
195
188
Explanation / Answer
Year Quarter Period Sales MA CMA Ratio Avg_Ratio SI DeS Forecast Error Absolute error Squared error Absolute % error 1987 1 1 95 0.954414403 99.53747518 95.77 -0.77 0.77 0.5929 1% 1987 2 2 94 0.899587601 104.492325 96.32 -2.32 2.32 5.3824 2% 1987 3 3 98 95.75 95.75 1.023498695 1.158882928 84.56419339 96.87 1.13 1.13 1.2769 1% 1987 4 4 96 95.75 98.375 0.975857687 1.049817447 91.44446998 97.42 -1.42 1.42 2.0164 1% 1987 5 5 95 101 102.125 0.930232558 0.96983705 97.95459971 97.97 -2.97 2.97 8.8209 3% 1987 6 6 115 103.25 104.25 1.103117506 0.935571224 122.9195565 98.52 16.48 16.48 271.5904 14% 1987 7 7 107 105.25 105.375 1.015421115 1.017869237 105.121558 99.07 7.93 7.93 62.8849 7% 1987 8 8 104 105.5 105.125 0.989298454 0.953997 109.0150179 99.62 4.38 4.38 19.1844 4% 1987 9 9 96 104.75 103.625 0.92641737 1.114939665 86.10331391 100.17 -4.17 4.17 17.3889 4% 1987 10 10 112 102.5 102.25 1.095354523 0.947641451 118.1881606 100.72 11.28 11.28 127.2384 10% 1987 11 11 98 102 103 0.951456311 0.987699955 99.22041561 101.27 -3.27 3.27 10.6929 3% 1987 12 12 102 104 102.5 0.995121951 1.009742039 101.0158992 101.82 0.18 0.18 0.0324 0% 1988 1 13 104 101 101.125 1.028430161 0.951721188 0.954414403 108.9673413 102.37 1.63 1.63 2.6569 2% 1988 2 14 100 101.25 99.5 1.005025126 0.897049099 0.899587601 111.1620479 102.92 -2.92 2.92 8.5264 3% 1988 3 15 99 97.75 95.875 1.032594524 1.155612732 1.158882928 85.42709332 103.47 -4.47 4.47 19.9809 5% 1988 4 16 88 94 95 0.926315789 1.046855018 1.049817447 83.82409748 104.02 -16.02 16.02 256.6404 18% 1988 5 17 89 96 97.25 0.915167095 0.967100314 0.96983705 91.76799342 104.57 -15.57 15.57 242.4249 17% 1988 6 18 108 98.5 100.125 1.078651685 0.932931181 0.935571224 115.4374966 105.12 2.88 2.88 8.2944 3% 1988 7 19 109 101.75 103.875 1.049338147 1.014996961 1.017869237 107.0864469 105.67 3.33 3.33 11.0889 3% 1988 8 20 101 106 105.25 0.959619952 0.951304962 0.953997 105.8703539 106.22 -5.22 5.22 27.2484 5% 1988 9 21 106 104.5 100.625 1.053416149 1.111793471 1.114939665 95.07240911 106.77 -0.77 0.77 0.5929 1% 1988 10 22 102 96.75 98 1.040816327 0.944967348 0.947641451 107.6356463 107.32 -5.32 5.32 28.3024 5% 1988 11 23 78 99.25 98.625 0.790874525 0.984912812 0.987699955 78.9713512 107.87 -29.87 29.87 892.2169 38% 1988 12 24 111 98 97.25 1.141388175 1.006892697 1.009742039 109.9290668 108.42 2.58 2.58 6.6564 2% 1989 1 25 101 96.5 97 1.041237113 0.954414403 105.8240526 108.97 -7.97 7.97 63.5209 8% 1989 2 26 96 97.5 94.125 1.019920319 0.899587601 106.715566 109.52 -13.52 13.52 182.7904 14% 1989 3 27 82 90.75 88.75 0.923943662 1.158882928 70.75779447 110.07 -28.07 28.07 787.9249 34% 1989 4 28 84 86.75 90.25 0.930747922 1.049817447 80.01391123 110.62 -26.62 26.62 708.6244 32% 1989 5 29 85 93.75 100.25 0.847880299 0.96983705 87.64358922 111.17 -26.17 26.17 684.8689 31% 1989 6 30 124 106.75 109.875 1.128555176 0.935571224 132.5393479 111.72 12.28 12.28 150.7984 10% 1989 7 31 134 113 117.5 1.140425532 1.017869237 131.6475586 112.27 21.73 21.73 472.1929 16% 1989 8 32 109 122 120.375 0.905503634 0.953997 114.2561245 112.82 -3.82 3.82 14.5924 4% 1989 9 33 121 118.75 114.625 1.05561614 1.114939665 108.5260519 113.37 7.63 7.63 58.2169 6% 1989 10 34 111 110.5 110.875 1.001127396 0.947641451 117.1329092 113.92 -2.92 2.92 8.5264 3% 1989 11 35 101 111.25 107.125 0.942823804 0.987699955 102.2577753 114.47 -13.47 13.47 181.4409 13% 1989 12 36 112 103 102.875 1.088699878 1.009742039 110.9194187 115.02 -3.02 3.02 9.1204 3% 1990 1 37 88 102.75 106.25 0.828235294 0.954414403 92.20313491 115.57 -27.57 27.57 760.1049 31% 1990 2 38 110 109.75 109.875 1.001137656 0.899587601 122.2782527 116.12 -6.12 6.12 37.4544 6% 1990 3 39 129 110 113.25 1.139072848 1.158882928 111.3140913 116.67 12.33 12.33 152.0289 10% 1990 4 40 113 116.5 123.875 0.912209889 1.049817447 107.6377615 117.22 -4.22 4.22 17.8084 4% 1990 5 41 114 131.25 131.5 0.866920152 0.96983705 117.5455197 117.77 -3.77 3.77 14.2129 3% 1990 6 42 169 131.75 135 1.251851852 0.935571224 180.6383048 118.32 50.68 50.68 2568.4624 30% 1990 7 43 131 138.25 139 0.942446043 1.017869237 128.7002252 118.87 12.13 12.13 147.1369 9% 1990 8 44 139 139.75 133 1.045112782 0.953997 145.7027643 119.42 19.58 19.58 383.3764 14% 1990 9 45 120 126.25 124.375 0.964824121 1.114939665 107.6291424 119.97 0.03 0.03 0.0009 0% 1990 10 46 115 122.5 121.125 0.949432405 0.947641451 121.3539149 120.52 -5.52 5.52 30.4704 5% 1990 11 47 116 119.75 121.25 0.956701031 0.987699955 117.4445736 121.07 -5.07 5.07 25.7049 4% 1990 12 48 128 122.75 122 1.049180328 1.009742039 126.76505 121.62 6.38 6.38 40.7044 5% 1991 1 49 132 121.25 119.375 1.105759162 0.954414403 138.3047024 122.17 9.83 9.83 96.6289 7% 1991 2 50 109 117.5 115.375 0.944745395 0.899587601 121.1666322 122.72 -13.72 13.72 188.2384 13% 1991 3 51 101 113.25 114.25 0.884026258 1.158882928 87.15289318 123.27 -22.27 22.27 495.9529 22% 1991 4 52 111 115.25 124 0.89516129 1.049817447 105.7326684 123.82 -12.82 12.82 164.3524 12% 1991 5 53 140 132.75 138.25 1.012658228 0.96983705 144.3541469 124.37 15.63 15.63 244.2969 11% 1991 6 54 179 143.75 147.375 1.214588634 0.935571224 191.3269619 124.92 54.08 54.08 2924.6464 30% 1991 7 55 145 151 148.5 0.976430976 1.017869237 142.4544477 125.47 19.53 19.53 381.4209 13% 1991 8 56 140 146 139.75 1.001788909 0.953997 146.7509856 126.02 13.98 13.98 195.4404 10% 1991 9 57 120 133.5 130.125 0.922190202 1.114939665 107.6291424 126.57 -6.57 6.57 43.1649 5% 1991 10 58 129 126.75 126.625 1.01875617 0.947641451 136.127435 127.12 1.88 1.88 3.5344 1% 1991 11 59 118 126.5 127.125 0.928220256 0.987699955 119.46948 127.67 -9.67 9.67 93.5089 8% 1991 12 60 139 127.75 126.375 1.099901088 1.009742039 137.6589214 128.22 10.78 10.78 116.2084 8% 1992 1 61 125 125 125.375 0.997008973 0.954414403 130.9703621 128.77 -3.77 3.77 14.2129 3% 1992 2 62 118 125.75 125.875 0.937437934 0.899587601 131.1712165 129.32 -11.32 11.32 128.1424 10% 1992 3 63 121 126 128 0.9453125 1.158882928 104.4108918 129.87 -8.87 8.87 78.6769 7% 1992 4 64 140 130 140.375 0.997328584 1.049817447 133.3565187 130.42 9.58 9.58 91.7764 7% 1992 5 65 141 150.75 154.625 0.911883589 0.96983705 145.385248 130.97 10.03 10.03 100.6009 7% 1992 6 66 201 158.5 158.25 1.27014218 0.935571224 214.8420075 131.52 69.48 69.48 4827.4704 35% 1992 7 67 152 158 157.5 0.965079365 1.017869237 149.331559 132.07 19.93 19.93 397.2049 13% 1992 8 68 138 157 149.125 0.925398156 0.953997 144.6545429 132.62 5.38 5.38 28.9444 4% 1992 9 69 137 141.25 140.25 0.976827094 1.114939665 122.8766042 133.17 3.83 3.83 14.6689 3% 1992 10 70 138 139.25 140.5 0.982206406 0.947641451 145.6246979 133.72 4.28 4.28 18.3184 3% 1992 11 71 144 141.75 138.5 1.039711191 0.987699955 145.7932638 134.27 9.73 9.73 94.6729 7% 1992 12 72 148 135.25 133.375 1.109653233 1.009742039 146.572089 134.82 13.18 13.18 173.7124 9% 1993 1 73 111 131.5 128.625 0.862973761 0.954414403 116.3016815 135.37 -24.37 24.37 593.8969 22% 1993 2 74 123 125.75 124.625 0.986960883 0.899587601 136.7293189 135.92 -12.92 12.92 166.9264 11% 1993 3 75 121 123.5 124.5 0.97188755 1.158882928 104.4108918 136.47 -15.47 15.47 239.3209 13% 1993 4 76 139 125.5 129.625 1.072324012 1.049817447 132.4039722 137.02 1.98 1.98 3.9204 1% 1993 5 77 119 133.75 137.875 0.863100635 0.96983705 122.7010249 137.57 -18.57 18.57 344.8449 16% 1993 6 78 156 142 141.625 1.101500441 0.935571224 166.7430506 138.12 17.88 17.88 319.6944 11% 1993 7 79 154 141.25 139.5 1.103942652 1.017869237 151.2964479 138.67 15.33 15.33 235.0089 10% 1993 8 80 136 137.75 134.75 1.009276438 0.953997 142.5581003 139.22 -3.22 3.22 10.3684 2% 1993 9 81 105 131.75 127.875 0.82111437 1.114939665 94.17549959 139.77 -34.77 34.77 1208.9529 33% 1993 10 82 132 124 127.5 1.035294118 0.947641451 139.2931893 140.32 -8.32 8.32 69.2224 6% 1993 11 83 123 131 133.75 0.919626168 0.987699955 124.5317461 140.87 -17.87 17.87 319.3369 15% 1993 12 84 164 136.5 136.125 1.204775023 1.009742039 162.4177203 141.42 22.58 22.58 509.8564 14% 1994 1 85 127 135.75 136.875 0.927853881 0.954414403 133.0658879 141.97 -14.97 14.97 224.1009 12% 1994 2 86 129 138 131 0.984732824 0.899587601 143.3990418 142.52 -13.52 13.52 182.7904 10% 1994 3 87 132 124 122.5 1.07755102 1.158882928 113.9027911 143.07 -11.07 11.07 122.5449 8% 1994 4 88 108 121 123.5 0.874493927 1.049817447 102.8750287 143.62 -35.62 35.62 1268.7844 33% 1994 5 89 115 126 128.875 0.892337536 0.96983705 118.5766207 144.17 -29.17 29.17 850.8889 25% 1994 6 90 149 131.75 134.375 1.108837209 0.935571224 159.2609907 144.72 4.28 4.28 18.3184 3% 1994 7 91 155 137 137.25 1.129326047 1.017869237 152.2788924 145.27 9.73 9.73 94.6729 6% 1994 8 92 129 137.5 139.625 0.923903312 0.953997 135.220551 145.82 -16.82 16.82 282.9124 13% 1994 9 93 117 141.75 141.375 0.827586207 1.114939665 104.9384138 146.37 -29.37 29.37 862.5969 25% 1994 10 94 166 141 146.5 1.133105802 0.947641451 175.171738 146.92 19.08 19.08 364.0464 11% 1994 11 95 152 152 152.25 0.998357964 0.987699955 153.8928895 147.47 4.53 4.53 20.5209 3% 1994 12 96 173 152.5 150.125 1.152373022 1.009742039 171.3308878 148.02 24.98 24.98 624.0004 14% 1995 1 97 119 147.75 149.25 0.797319933 0.954414403 124.6837847 148.57 -29.57 29.57 874.3849 25% 1995 2 98 147 150.75 146 1.006849315 0.899587601 163.4082104 149.12 -2.12 2.12 4.4944 1% 1995 3 99 164 141.25 141.875 1.155947137 1.158882928 141.5155889 149.67 14.33 14.33 205.3489 9% 1995 4 100 135 142.5 145.125 0.930232558 1.049817447 128.5937859 150.22 -15.22 15.22 231.6484 11% 1995 5 101 124 147.75 147.125 0.842820731 0.96983705 127.8565302 150.77 -26.77 26.77 716.6329 22% 1995 6 102 168 146.5 146.75 1.144804089 0.935571224 179.5694391 151.32 16.68 16.68 278.2224 10% 1995 7 103 159 147 150.125 1.059117402 1.017869237 156.2086703 151.87 7.13 7.13 50.8369 4% 1995 8 104 137 153.25 152.125 0.900575185 0.953997 143.6063216 152.42 -15.42 15.42 237.7764 11% 1995 9 105 149 151 153 0.973856209 1.114939665 133.6395185 152.97 -3.97 3.97 15.7609 3% 1995 10 106 159 155 162.25 0.979969183 0.947641451 167.784978 153.52 5.48 5.48 30.0304 3% 1995 11 107 175 169.5 169.25 1.033973412 0.987699955 177.1793136 154.07 20.93 20.93 438.0649 12% 1995 12 108 195 169 167.375 1.165048544 1.009742039 193.1186308 154.62 40.38 40.38 1630.5444 21% 1996 1 109 147 165.75 160.5 0.91588785 0.954414403 154.0211458 155.17 -8.17 8.17 66.7489 6% 1996 2 110 146 155.25 149.375 0.977405858 0.899587601 162.2965899 155.72 -9.72 9.72 94.4784 7% 1996 3 111 133 143.5 142.75 0.931698774 1.158882928 114.765691 156.27 -23.27 23.27 541.4929 17% 1996 4 112 148 142 147.625 1.00254022 1.049817447 140.9768912 156.82 -8.82 8.82 77.7924 6% 1996 5 113 141 153.25 158.875 0.887490165 0.96983705 145.385248 157.37 -16.37 16.37 267.9769 12% 1996 6 114 191 164.5 165.5 1.15407855 0.935571224 204.1533504 157.92 33.08 33.08 1094.2864 17% 1996 7 115 178 166.5 163.75 1.087022901 1.017869237 174.8751151 158.47 19.53 19.53 381.4209 11% 1996 8 116 156 161 154.375 1.010526316 0.953997 163.5225268 159.02 -3.02 3.02 9.1204 2% 1996 9 117 119 147.75 147.375 0.807463953 1.114939665 106.7322329 159.57 -40.57 40.57 1645.9249 34% 1996 10 118 138 147 151 0.913907285 0.947641451 145.6246979 160.12 -22.12 22.12 489.2944 16% 1996 11 119 175 155 0.987699955 177.1793136 160.67 14.33 14.33 205.3489 8% 1996 12 120 188 1.009742039 186.1861671 161.22 26.78 26.78 717.1684 14% 1997 1 121 161.77 1997 2 122 162.32 1997 3 123 162.87 1997 4 124 163.42 1997 5 125 163.97 1997 6 126 164.52 1997 7 127 165.07 1997 8 128 165.62 1997 9 129 166.17 1997 10 130 166.72 1997 11 131 167.27 1997 12 132 167.82