Question

In: Statistics and Probability

The sale records of a retail store are given in the Excel worksheet "Retail" Week Value...

The sale records of a retail store are given in the Excel worksheet "Retail"

Week	Value
1	10.37
2	5.90
3	8.70
4	6.80
5	7.00
6	9.87
7	10.95
8	10.77
9	11.15
10	8.85
11	13.22
12	6.02
13	6.55
14	9.12
15	11.77
16	10.05
17	10.72
18	9.40
19	9.07
20	12.82
21	4.92
22	10.95
23	13.92
24	15.62
25	6.65
26	13.77
27	8.77
28	9.70
29	8.40
30	10.35
31	8.65
32	6.30
33	6.40
34	9.45
35	9.77
36	5.42
37	10.67
38	7.32
39	7.20
40	7.05
41	9.97
42	7.72
43	10.87
44	7.47
45	13.05
46	9.40
47	12.07
48	10.40
49	6.12
50	12.87
51	12.05
52	12.10
53
54
55

1. Using the moving average method with p = 3 most recent data, the forecast value at time t = 53 is:

a/ 12.34

b/ 10.50

c/ 11.15

d/ 11.32

2. Using the moving average method with p = 3 most recent data, the M A P E is

a/ 9.52%

b/ 39.23%

c/ 26.92%

d/ 40.45%

3. Using the exponential smoothing with alpha = 4, the smoothed SALE at time t = 10 is

a/ 8.87

b/ 9.81

c/ 12.92

d/ 13.15

4. Using the exponential smoothing with alpha = 4, the forecasted SALE at time t = 53 is

a/ 11.49

b/ 14.50

c/ 11.05

d/ 15.53

5. The value of M A D for using exponential smoothing with alpha = 4 to forecast is

a/ 3.66

b/ 2.29

c/ 4.34

d/ 8.76

Expert Solution

Week	Value	Total for p =3	Moving avg
1	10.37
2	5.9
3	8.7
4	6.8	24.97	8.323
5	7	21.4	7.133
6	9.87	22.5	7.500
7	10.95	23.67	7.890
8	10.77	27.82	9.273
9	11.15	31.59	10.530
10	8.85	32.87	10.957
11	13.22	30.77	10.257
12	6.02	33.22	11.073
13	6.55	28.09	9.363
14	9.12	25.79	8.597
15	11.77	21.69	7.230
16	10.05	27.44	9.147
17	10.72	30.94	10.313
18	9.4	32.54	10.847
19	9.07	30.17	10.057
20	12.82	29.19	9.730
21	4.92	31.29	10.430
22	10.95	26.81	8.937
23	13.92	28.69	9.563
24	15.62	29.79	9.930
25	6.65	40.49	13.497
26	13.77	36.19	12.063
27	8.77	36.04	12.013
28	9.7	29.19	9.730
29	8.4	32.24	10.747
30	10.35	26.87	8.957
31	8.65	28.45	9.483
32	6.3	27.4	9.133
33	6.4	25.3	8.433
34	9.45	21.35	7.117
35	9.77	22.15	7.383
36	5.42	25.62	8.540
37	10.67	24.64	8.213
38	7.32	25.86	8.620
39	7.2	23.41	7.803
40	7.05	25.19	8.397
41	9.97	21.57	7.190
42	7.72	24.22	8.073
43	10.87	24.74	8.247
44	7.47	28.56	9.520
45	13.05	26.06	8.687
46	9.4	31.39	10.463
47	12.07	29.92	9.973
48	10.4	34.52	11.507
49	6.12	31.87	10.623
50	12.87	28.59	9.530
51	12.05	29.39	9.797
52	12.1	31.04	10.347
53		37.02	12.340

For moving avg the forecast is calculate by taking sum of preceding 'n' years and then dividing by 'n' where p = n

1. Using the moving average method with p = 3 most recent data, the forecast value at time t = 53 is:

a/ 12.34

b/ 10.50

c/ 11.15

d/ 11.32

Week	Value	Forecast	Absolute error \|value - forecast\|	Percentage error =AE / value
1	10.37
2	5.9
3	8.7
4	6.8	8.323	1.523	22.40%
5	7	7.133	0.133	1.90%
6	9.87	7.500	2.370	24.01%
7	10.95	7.890	3.060	27.95%
8	10.77	9.273	1.497	13.90%
9	11.15	10.530	0.620	5.56%
10	8.85	10.957	2.107	23.80%
11	13.22	10.257	2.963	22.42%
12	6.02	11.073	5.053	83.94%
13	6.55	9.363	2.813	42.95%
14	9.12	8.597	0.523	5.74%
15	11.77	7.230	4.540	38.57%
16	10.05	9.147	0.903	8.99%
17	10.72	10.313	0.407	3.79%
18	9.4	10.847	1.447	15.39%
19	9.07	10.057	0.987	10.88%
20	12.82	9.730	3.090	24.10%
21	4.92	10.430	5.510	111.99%
22	10.95	8.937	2.013	18.39%
23	13.92	9.563	4.357	31.30%
24	15.62	9.930	5.690	36.43%
25	6.65	13.497	6.847	102.96%
26	13.77	12.063	1.707	12.39%
27	8.77	12.013	3.243	36.98%
28	9.7	9.730	0.030	0.31%
29	8.4	10.747	2.347	27.94%
30	10.35	8.957	1.393	13.46%
31	8.65	9.483	0.833	9.63%
32	6.3	9.133	2.833	44.97%
33	6.4	8.433	2.033	31.77%
34	9.45	7.117	2.333	24.69%
35	9.77	7.383	2.387	24.43%
36	5.42	8.540	3.120	57.56%
37	10.67	8.213	2.457	23.02%
38	7.32	8.620	1.300	17.76%
39	7.2	7.803	0.603	8.38%
40	7.05	8.397	1.347	19.10%
41	9.97	7.190	2.780	27.88%
42	7.72	8.073	0.353	4.58%
43	10.87	8.247	2.623	24.13%
44	7.47	9.520	2.050	27.44%
45	13.05	8.687	4.363	33.44%
46	9.4	10.463	1.063	11.31%
47	12.07	9.973	2.097	17.37%
48	10.4	11.507	1.107	10.64%
49	6.12	10.623	4.503	73.58%
50	12.87	9.530	3.340	25.95%
51	12.05	9.797	2.253	18.70%
52	12.1	10.347	1.753	14.49%
Total				1319.30%
MAPE				26.92%

Here we ahve forecast for oly 49 values therefore we divide total percentage error by 49.

MAPE = mean absolute percetage error.

2. Using the moving average method with p = 3 most recent data, the M A P E is

a/ 9.52%

b/ 39.23%

c/ 26.92%

d/ 40.45%

Week	Value	Forecast
1	10.37	10.37
2	5.9	10.37
3	8.7	8.58
4	6.8	8.63
5	7	7.90
6	9.87	7.54
7	10.95	8.47
8	10.77	9.46
9	11.15	9.99
10	8.85	10.45
11	13.22	9.81
12	6.02	11.17
13	6.55	9.11
14	9.12	8.09
15	11.77	8.50
16	10.05	9.81
17	10.72	9.91
18	9.4	10.23
19	9.07	9.90
20	12.82	9.57
21	4.92	10.87
22	10.95	8.49
23	13.92	9.47
24	15.62	11.25
25	6.65	13.00
26	13.77	10.46
27	8.77	11.78
28	9.7	10.58
29	8.4	10.23
30	10.35	9.50
31	8.65	9.84
32	6.3	9.36
33	6.4	8.14
34	9.45	7.44
35	9.77	8.25
36	5.42	8.86
37	10.67	7.48
38	7.32	8.76
39	7.2	8.18
40	7.05	7.79
41	9.97	7.49
42	7.72	8.48
43	10.87	8.18
44	7.47	9.26
45	13.05	8.54
46	9.4	10.34
47	12.07	9.97
48	10.4	10.81
49	6.12	10.64
50	12.87	8.83
51	12.05	10.45
52	12.1	11.09
53		11.49

Since we do not have a forecast for 1st time we equate the forecast to actual. So our forecast will be 1 period later.

Formula:

3. Using the exponential smoothing with alpha =0. 4, the smoothed SALE at time t = 10 is

a/ 8.87

b/ 9.81

c/ 12.92

d/ 13.15

4. Using the exponential smoothing with alpha = 4, the forecasted SALE at time t = 53 is

a/ 11.49

b/ 14.50

c/ 11.05

d/ 15.53

Week	Value	Forecast	Absolute error (deviation)
1	10.37	10.37	0.000
2	5.9	10.37	4.470
3	8.7	8.58	0.118
4	6.8	8.63	1.829
5	7	7.90	0.898
6	9.87	7.54	2.331
7	10.95	8.47	2.479
8	10.77	9.46	1.307
9	11.15	9.99	1.164
10	8.85	10.45	1.601
11	13.22	9.81	3.409
12	6.02	11.17	5.154
13	6.55	9.11	2.563
14	9.12	8.09	1.032
15	11.77	8.50	3.269
16	10.05	9.81	0.242
17	10.72	9.91	0.815
18	9.4	10.23	0.831
19	9.07	9.90	0.829
20	12.82	9.57	3.253
21	4.92	10.87	5.948
22	10.95	8.49	2.461
23	13.92	9.47	4.447
24	15.62	11.25	4.368
25	6.65	13.00	6.349
26	13.77	10.46	3.310
27	8.77	11.78	3.014
28	9.7	10.58	0.878
29	8.4	10.23	1.827
30	10.35	9.50	0.854
31	8.65	9.84	1.188
32	6.3	9.36	3.063
33	6.4	8.14	1.738
34	9.45	7.44	2.007
35	9.77	8.25	1.524
36	5.42	8.86	3.435
37	10.67	7.48	3.189
38	7.32	8.76	1.437
39	7.2	8.18	0.982
40	7.05	7.79	0.739
41	9.97	7.49	2.476
42	7.72	8.48	0.764
43	10.87	8.18	2.692
44	7.47	9.26	1.785
45	13.05	8.54	4.509
46	9.4	10.34	0.945
47	12.07	9.97	2.103
48	10.4	10.81	0.408
49	6.12	10.64	4.525
50	12.87	8.83	4.035
51	12.05	10.45	1.601
52	12.1	11.09	1.011
Total			117.207
MAD			2.298

MAD = mean aboslute deivation or error

Here since we are forecasting from time period 2 we have 51 pairs of actual and forecast.

5. The value of M A D for using exponential smoothing with alpha = 4 to forecast is

a/ 3.66

b/ 2.29

c/ 4.34

d/ 8.76

orchestra answered 1 year ago

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