Question

In: Statistics and Probability

Year   Percentage 2000   28 2001   32 2002   36 2003   40 2004   44 2005   51 2006   53...

Year   Percentage
2000   28
2001   32
2002   36
2003   40
2004   44
2005   51
2006   53
2007   57
2008   60
2009   66

Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment.

alpha= 0.3 and beta= 0.4. Then calculate MAD.

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Quarter   Price
Q1 2017   186.3
Q2 2017   190.9
Q3 2017   195.2
Q4 2017   195.2
Q1 2018   198.7
Q2 2018   201.2

Forecast the price index for Q3 2018 using a​ three-period simple moving average. Then calculate MAD.

Solutions

Expert Solution

1.

Alpha 0.3
Beta 0.4
Data Forecasts and Error Analysis
Period Demand Smoothed Forecast, Ft Smoothed Trend, Tt Forecast Including Trend, FITt Error Absolute Squared Abs Pct Err
Period 1 28 28 28 0 0 0 00.00%
Period 2 32 28 0 28 4 4 16 12.50%
Period 3 36 29.2 6.8 6.8 46.24 18.89%
Period 4 40 31.24 8.76 8.76 76.7376 21.90%
Period 5 44 33.868 10.132 10.132 102.6574 23.03%
Period 6 51 36.9076 14.0924 14.0924 198.5957 27.63%
Period 7 53 41.13532 11.86468 11.86468 140.7706 22.39%
Period 8 57 44.69472 12.30528 12.30528 151.4198 21.59%
Period 9 60 48.38631 11.61369 11.61369 134.8779 19.36%
Period 10 66 51.87041 14.12959 14.12959 199.6452 0.214085
Total 93.69763 93.69763 1066.944 188.69%
Average 9.369763 9.369763 106.6944 18.87%
Bias MAD MSE MAPE
SE 11.54851

2.

Data Forecasts and Error Analysis
Period Demand Forecast Error Absolute Squared Abs Pct Err
Period 1 186.3
Period 2 190.9
Period 3 195.2
Period 4 195.2 190.8 4.4 4.4 19.36 02.25%
Period 5 198.7 193.7667 4.933333 4.933333 24.33778 02.48%
Period 6 201.2 196.3667 4.833333 4.833333 23.36111 02.40%
Total 14.16667 14.16667 67.05889 07.14%
Average 4.722222 4.722222 22.35296 02.38%
Bias MAD MSE MAPE
SE 8.188949
Next period 198.366667

orchestra answered 1 year ago
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