Using the data in the table, first plot the data and comment on the appearance of the demand pattern. Then develop a forecast for periods 51-70 that fits the data

Question

Time Output Time Output Time Output Time Output
1 12.5 14 16.4 27 -19.2 40 11.3
2 14.8 15 11.7 28 10.6 41 11.1
3 15.3 16 11.1 29 16.8 42 52.5
4 15 17 11.9 30 22.5 43 11.3
5 11.5 18 11.3 31 15.5 44 -19.3
6 11.6 19 13.7 32 11.7 45 12
7 12.8 20 16.3 33 11.9 46 15.5
8 51.9 21 13.1 34 13 47 20.5
9 11 22 10.8 35 11.9 48 16.5
10 -19.7 23 10.3 36 13.5 49 12.5
11 11.9 24 11 37 16.5 50 10.5
12 17.8 25 51.4 38 14
13 20.3 26 11.6 39 11

What will be an ideal response?

Answer 1

Answer: Data are highly seasonal as the graph and data table indicate.

Peaks near 50 occur at points 8, 25 and 42, and this seasonality is reflected in the other significant features of the graph, e.g., lows near -20 at points 10, 27 and 44. The data are rearranged in this table into three 17 observation rows with a seasonal average and seasonal relative appended to the right. The overall average for the data is 13.828; the column labeled "Seasonal" is each average divided by the 13.828 figure.

Time Output Time Output Time Output Average Seasonal
1 12.5 18 11.3 35 11.9 11.9 0.861
2 14.8 19 13.7 36 13.5 14.0 1.012
3 15.3 20 16.3 37 16.5 16.0 1.159
4 15 21 13.1 38 14 14.0 1.015
5 11.5 22 10.8 39 11 11.1 0.803
6 11.6 23 10.3 40 11.3 11.1 0.800
7 12.8 24 11 41 11.1 11.6 0.841
8 51.9 25 51.4 42 52.5 51.9 3.756
9 11 26 11.6 43 11.3 11.3 0.817
10 -19.7 27 -19.2 44 -19.3 -19.4 -1.403
11 11.9 28 10.6 45 12 11.5 0.832
12 17.8 29 16.8 46 15.5 16.7 1.208
13 20.3 30 22.5 47 20.5 21.1 1.526
14 16.4 31 15.5 48 16.5 16.1 1.167
15 11.7 32 11.7 49 12.5 12.0 0.865
16 11.1 33 11.9 50 10.5 11.2 0.808
17 11.9 34 13 Overall 13.828 12.45 0.934

Dividing each entry in the table by the seasonal relative and using linear regression with independent variables ranging from 1-50 yields the regression equation
Output = 14.03752-0.00899 ∗ Time
Reseasoning the forecasted values by the seasonal relatives gives the results in the table and the graph below.

Time Regression Adjusted by Factor Seasonally Adjusted
51 13.58 .86 11.69
52 13.57 1.01 13.74
53 13.56 1.16 15.72
54 13.55 1.01 13.75
55 13.54 0.82 10.87
56 13.53 0.80 10.83
57 13.53 0.84 11.38
58 13.52 3.76 50.76
59 13.51 0.82 11.04
60 13.50 -1.4 -18.94
61 13.49 0.83 11.22
62 13.48 1.21 16.28
63 13.47 1.52 20.56
64 13.46 1.17 15.71
65 13.45 0.87 11.64
66 13.44 0.81 10.86
67 13.44 0.93 12.54
68 13.43 0.86 11.55

The graph below is a plot of the original data for points 1-50 and the forecast points 51-72