Exercise 7-9: Smartphones
Deseasonalized Analysis (to estimate initial values)
Year Quarter Period Sales
Deseasonalized
Level
Level from
Regression
Seasonal
Factor
Seasonal
Factor
Estimate
Regression – Deseasonalized Level vs. Period
0
1I 1513 0.50
II 2932 0.79 Regression Statistics
III 3 1,509 1,236.5 1,195.3 1.26 1.21 Multiple R 0.9973
IV 4 1,902 1,287.9 1,286.5 1.48 1.50 R Square 0.99461
2I 5693 1,360.3 1,377.7 0.50 Adjusted R Square 0.99407
II 6 1,163 1,474.6 1,469.0 0.79 Standard Error 25.3922
III 7 1,857 1,564.6 1,560.2 1.19 Observations 12
IV 8 2,469 1,618.3 1,651.4 1.50
3I 9846 1,704.5 1,742.7 0.49 ANOVA
II 10 1,439 1,832.5 1,833.9 0.78 df SS MS F
Significance F
III 11 2,271 1,936.8 1,925.1 1.18 Regression 1 1190345 1190344.87 1846.17 1.119E-12
IV 12 3,079 2,003.8 2,016.4 1.53 Residual 10 6447.64 644.7644322
4I 13 1,070 2,107.0 2,107.6 0.51 Total 11 1196793
II 14 1,751 2,238.0 2,198.9 0.80
III 15 2,785
Coefficients
Standard Error
t Stat P-value Lower 95%
Upper 95.0%
IV 16 3,613 Intercept 921.54 19.48 47.31 0.00 878.14 964.95 878.14 964.95
X Variable 1 91.24 2.12 42.97 0.00 86.51 95.97 86.51 95.97
1I 1513 1,013.6 91.32 0.50 505 -8 8-8 63 8 1.5 1.5 -1.00
II 2932 1,108.6 91.68 0.79 874 -58 58 -66 1,722 33 6.2 3.9 -2.00
III 3 1,509 1,202.5 91.91 1.21 1,453 -56 56 -122 2,184 41 3.7 3.8 -3.00
III 7 1,857 1,565.4 91.48 1.22 1,908 51 51 -15 1,575 33 2.8 2.5 -0.47
IV 8 2,469 1,656.5 91.45 1.50 2,478 9 9 -6 1,389 30 0.4 2.3 -0.21
III 11 2,271 1,923.2 90.75 1.21 2,336 65 65 110 1,513 32 2.8 2.4 3.42
IV 12 3,079 2,016.2 90.98 1.49 3,011 -68 68 42 1,774 35 2.2 2.4 1.20
4I 13 1,070 2,109.3 91.19 0.50 1,049 -21 21 21 1,673 34 2.0 2.3 0.61
II 14 1,751 2,200.6 91.20 0.79 1,749 -2 219 1,554 32 0.1 2.2 0.60
III 15 2,785 2,292.5 91.27 1.21 2,768 -17 17 3 1,469 31 0.6 2.1 0.09
IV 16 3,613 2,385.1 91.40 1.50 3,575 -38 38 -35 1,466 31 1.0 2.0 -1.12
5I 17 1,232 Estimate of SD of forecast error: 39.16
II 18 1,969
III 19 2,991
IV 20 3,714
Exercise 7-9: Smartphones
Deseasonalized Analysis (to estimate initial values)
Year Quarter Period Sales
Deseasonalized
Level
Level from
Regression
Seasonal
Factor
Seasonal
Factor
Estimate
Regression – Deseasonalized Level vs. Period
0
1I 1513 0.50
II 2932 0.79 Regression Statistics
III 3 1,509 1,236.5 1,195.3 1.26 1.21 Multiple R 0.9973
IV 4 1,902 1,287.9 1,286.5 1.48 1.50 R Square 0.99461
2I 5693 1,360.3 1,377.7 0.50 Adjusted R Square 0.99407
II 6 1,163 1,474.6 1,469.0 0.79 Standard Error 25.3922
III 7 1,857 1,564.6 1,560.2 1.19 Observations 12
IV 8 2,469 1,618.3 1,651.4 1.50
3I 9846 1,704.5 1,742.7 0.49 ANOVA
II 10 1,439 1,832.5 1,833.9 0.78 df SS MS F
Significance F
III 11 2,271 1,936.8 1,925.1 1.18 Regression 1 1190345 1190344.87 1846.17 1.119E-12
IV 12 3,079 2,003.8 2,016.4 1.53 Residual 10 6447.64 644.7644322
4I 13 1,070 2,107.0 2,107.6 0.51 Total 11 1196793
II 14 1,751 2,238.0 2,198.9 0.80
III 15 2,785
Coefficients
Standard Error
t Stat P-value Lower 95%
Upper 95.0%
IV 16 3,613 Intercept 921.54 19.48 47.31 0.00 878.14 964.95 878.14 964.95
X Variable 1 91.24 2.12 42.97 0.00 86.51 95.97 86.51 95.97
1I 1513 1,012.8 91.27 0.50 505 -8 8-8 63 8 2 2 -1.00
II 2932 1,104.3 91.45 0.79 873 -59 59 -67 1,758 33 6 4 -2.00
III 3 1,509 1,195.9 91.57 1.21 1,448 -61 61 -128 2,421 43 4 4 –3.00
III 7 1,857 1,561.9 91.48 1.21 1,891 34 34 -70 1,333 28 2 2 –2.47
III 11 2,271 1,927.2 91.19 1.21 2,334 63 63 42 1,285 28 3 2 1.49
IV 12 3,079 2,018.5 91.27 1.50 3,028 -51 51 -9 1,396 30 2 2 –0.31
4I 13 1,070 2,109.9 91.35 0.50 1,052 -18 18 -27 1,313 29 2 2 -0.93
II 14 1,751 2,201.2 91.38 0.79 1,741 -10 10 -37 1,226 28 1 2 -1.34
III 15 2,785 2,292.6 91.40 1.21 2,776 -9 9 -46 1,150 26 0 2 –1.75
IV 16 3,613 2,384.1 91.46 1.50 3,576 -37 37 -83 1,162 27 1 2 -3.06
5I 17 1,235 Estimate of SD of forecast error: 33.82
II 18 1,958
III 19 2,997
IV 20 3,714
Exercise 7-9: Smartphones
Deseasonalized Analysis (to estimate initial values)
Year Quarter Period Sales
Deseasonalized
Level
Level from
Regression
Seasonal
Factor
Seasonal
Factor
Estimate
Regression – Deseasonalized Level vs. Period
0
1I 1513 0.50
II 2932 0.79 Regression Statistics
III 3 1,509 1,236.5 1,195.3 1.26 1.21 Multiple R 0.9973
IV 4 1,902 1,287.9 1,286.5 1.48 1.50 R Square 0.99461
2I 5693 1,360.3 1,377.7 0.50 Adjusted R Square 0.99407
II 6 1,163 1,474.6 1,469.0 0.79 Standard Error 25.3922
III 7 1,857 1,564.6 1,560.2 1.19 Observations 12
IV 8 2,469 1,618.3 1,651.4 1.50
3I 9846 1,704.5 1,742.7 0.49 ANOVA
II 10 1,439 1,832.5 1,833.9 0.78 df SS MS F
Significance F
III 11 2,271 1,936.8 1,925.1 1.18 Regression 1 1190345 1190344.87 1846.17 1.119E-12
IV 12 3,079 2,003.8 2,016.4 1.53 Residual 10 6447.64 644.7644322
4I 13 1,070 2,107.0 2,107.6 0.51 Total 11 1196793
II 14 1,751 2,238.0 2,198.9 0.80
III 15 2,785
Coefficients
Standard Error
t Stat P-value Lower 95%
Upper 95.0%
IV 16 3,613 Intercept 921.54 19.48 47.31 0.00 878.14 964.95 878.14 964.95
X Variable 1 91.24 2.12 42.97 0.00 86.51 95.97 86.51 95.97
II 2932 1,104.3 91.48 0.79 873 -59 59 -67 1,758 33 6 4 -2.00
III 3 1,509 1,196.0 91.62 1.21 1,448 -61 61 -128 2,417 43 4 4 –3.00
III 7 1,857 1,562.2 91.51 1.21 1,892 35 35 -69 1,336 28 2 2 –2.43
III 11 2,271 1,927.5 91.17 1.21 2,334 63 63 44 1,294 28 3 2 1.56
IV 12 3,079 2,018.8 91.26 1.50 3,028 -51 51 -7 1,400 30 2 2 –0.22
4I 13 1,070 2,110.2 91.36 0.50 1,052 -18 18 -24 1,316 29 2 2 -0.83
II 14 1,751 2,201.6 91.39 0.79 1,741 -10 10 -34 1,229 28 1 2 -1.23
III 15 2,785 2,293.0 91.41 1.21 2,776 -9 9 -43 1,152 26 0 2 –1.61
IV 16 3,613 2,384.5 91.48 1.50 3,577 -36 36 -79 1,161 27 1 2 -2.91