Homework SourseSales of HotBlast heaters have grown steadily during the pas
Sales of Hot-Blast heaters have grown steadily dur-ing the past five years, as shown in the following table:
Year
Sales
1
480
2
525
3
548
4
593
5
614
(a) Using exponential smoothing constants of 0.35, 0.65, and 0.95, develop forecasts for years 2 through 6. The sales manager had pre-dicted, before the business started, that year 1’s sales would be 440 air conditioners. Which smoothing constant gives the most accurate forecast?
(b) Use a three-year moving average forecasting model to forecast sales of heaters.
(c) Using linear trend analysis, develop a forecast-ing model for the sales of heaters.
(d) Which of the methods analyzed here would you use? Explain your answer.
| Year | Sales |
| 1 | 480 |
| 2 | 525 |
| 3 | 548 |
| 4 | 593 |
| 5 | 614 |
Solution
Sales of Hot-Blast heaters have grown steadily dur-ing the past five years, as shown in the following table
By using exponential smoothing constants we have to calculate forecasts.
The constant is nothing but the alpha.
we calculate forecasts for three different value.
i) alpha = 0.35
First enter the given data in MINITAB .
This will done in MINITAB the path for that is
STAT ->Time series ->double exponential smoothing -> variable sales ->weights to use in smoothing -> use 0.35 for level and trend ->generate forecasts number of forecasts 6.->ok
So the output is,
Double Exponential Smoothing for sales
Data sales
Length 5
Smoothing Constants
Alpha (level) 0.35
Gamma (trend) 0.35
Accuracy Measures
MAPE 1.2717
MAD 7.0537
MSD 52.4874
Time sales Smooth Predict Error
1 480 483.120 484.800 -4.80000
2 525 519.236 516.132 8.86800
3 548 551.467 553.334 -5.33413
4 593 587.743 584.912 8.08792
5 614 619.316 622.179 -8.17852
Forecasts
Period Forecast Lower Upper
6 652.750 635.469 670.031
7 686.184 667.779 704.588
8 719.617 699.975 739.260
9 753.051 732.076 774.027
10 786.485 764.100 808.870
11 819.919 796.060 843.778
year sales SMOO1 LEVE1 TREN1 FITS1 RESI1 FORE1 UPPE1 LOWE1
1 480 483.120 483.120 33.0120 484.800 -4.80000 652.750 670.031 635.469
2 525 519.236 519.236 34.0983 516.132 8.86800 686.184 704.588 667.779
3 548 551.467 551.467 33.4449 553.334 -5.33413 719.617 739.260 699.975
4 593 587.743 587.743 34.4357 584.912 8.08792 753.051 774.027 732.076
5 614 619.316 619.316 33.4338 622.179 -8.17852 786.485 808.870 764.100
819.919 843.778 796.060
For alpha = 0.65
Double Exponential Smoothing for sales
Data sales
Length 5
Smoothing Constants
Alpha (level) 0.65
Gamma (trend) 0.65
Accuracy Measures
MAPE 1.6980
MAD 9.4673
MSD 96.5605
Time sales Smooth Predict Error
1 480 481.680 484.800 -4.8000
2 525 520.888 513.252 11.7480
3 548 551.298 557.424 -9.4237
4 593 589.798 583.852 9.1477
5 614 618.276 626.217 -12.2172
Forecasts
Period Forecast Lower Upper
6 649.533 626.339 672.728
7 680.790 652.341 709.240
8 712.047 677.857 746.238
9 743.305 703.095 783.514
10 774.562 728.163 820.960
11 805.819 753.121 858.517
year sales SMOO1 LEVE1 TREN1 FITS1 RESI1 FORE1 UPPE1 LOWE1
1 480 481.680 481.680 31.5720 484.800 -4.8000 649.533 672.728 626.339
2 525 520.888 520.888 36.5355 513.252 11.7480 680.790 709.240 652.341
3 548 551.298 551.298 32.5540 557.424 -9.4237 712.047 746.238 677.857
4 593 589.798 589.798 36.4189 583.852 9.1477 743.305 783.514 703.095
5 614 618.276 618.276 31.2571 626.217 -12.2172 774.562 820.960 728.163
805.819 858.517 753.121
For alpha = 0.95
Double Exponential Smoothing for sales
Data sales
Length 5
Smoothing Constants
Alpha (level) 0.95
Gamma (trend) 0.95
Accuracy Measures
MAPE 2.782
MAD 15.688
MSD 278.402
Time sales Smooth Predict Error
1 480 480.240 484.800 -4.8000
2 525 524.225 509.508 15.4920
3 548 548.974 567.475 -19.4749
4 593 592.082 574.647 18.3528
5 614 615.016 634.319 -20.3192
Forecasts
Period Forecast Lower Upper
6 638.915 600.480 677.349
7 662.813 606.019 719.608
8 686.712 610.525 762.900
9 710.611 614.621 806.601
10 734.510 618.519 850.501
11 758.409 622.304 894.513
year sales SMOO1 LEVE1 TREN1 FITS1 RESI1 FORE1 UPPE1 LOWE1
1 480 480.240 480.240 29.2680 484.800 -4.8000 638.915 677.349 600.480
2 525 524.225 524.225 43.2495 509.508 15.4920 662.813 719.608 606.019
3 548 548.974 548.974 25.6734 567.475 -19.4749 686.712 762.900 610.525
4 593 592.082 592.082 42.2369 574.647 18.3528 710.611 806.601 614.621
5 614 615.016 615.016 23.8988 634.319 -20.3192 734.510 850.501 618.519
758.409 894.513 622.304
As alpha increases forecasts forecasts value decreases.
Moving Average for sales
Data sales
Length 5
NMissing 0
Moving Average
Length 3
Accuracy Measures
MAPE 7.15
MAD 42.22
MSD 1926.89
Time sales MA Predict Error
1 480 * * *
2 525 517.667 * *
3 548 555.333 517.667 30.3333
4 593 585.000 555.333 37.6667
5 614 * 555.333 58.6667
Forecasts
Period Forecast Lower Upper
6 555.333 469.298 641.369
7 555.333 469.298 641.369
8 555.333 469.298 641.369
9 555.333 469.298 641.369
10 555.333 469.298 641.369
11 555.333 469.298 641.369
469.298
Trend analysis :
Trend Analysis for sales
Data sales
Length 5
NMissing 0
Fitted Trend Equation
Yt = 451.2 + 33.6*t
Accuracy Measures
MAPE 1.0164
MAD 5.6000
MSD 32.8800
Time sales Trend Detrend
1 480 484.8 -4.8
2 525 518.4 6.6
3 548 552.0 -4.0
4 593 585.6 7.4
5 614 619.2 -5.2
Forecasts
Period Forecast
6 652.8
7 686.4
8 720.0
9 753.6
10 787.2
11 820.8
| year | sales | AVER1 | FITS1 | RESI1 | FORE1 | UPPE1 | LOWE1 |
| 1 | 480 | * | * | * | 555.333 | 641.369 | 469.298 |
| 2 | 525 | 517.667 | * | * | 555.333 | 641.369 | 469.298 |
| 3 | 548 | 555.333 | 517.667 | 30.3333 | 555.333 | 641.369 | 469.298 |
| 4 | 593 | 585 | 555.333 | 37.6667 | 555.333 | 641.369 | 469.298 |
| 5 | 614 | * | 555.333 | 58.6667 | 555.333 | 641.369 | 469.298 |
| 555.333 | 641.369 | 469.298 |
