Question

Consider the following data set:

Month Actual Sales Forecast 1 Forecast 2
1 777 771 769
2 789 785 787
3 794 790 792
4 780 784 798
5 768 770 774
6 779 768 770
7 760 761 759
8 785 771 775
9 786 784 788
10 791 788 788
a. Calculate MAD and MSE for each forecast (forecast 1 and forecast 2).
b. Calculate MAPE for each forecast (forecast 1 and forecast 2).

Answer 1

Kindly check explanation

Step-by-step explanation:

To obtain the mean absolute deviation(MAD) :

Subtract the forecasted values from the actual values and find its absolute equivalent.

Error (E) = (Actual - forecast)

e1 - - - |e1| - - - - e2 - - - |e2| - APE1 - - APE2

6 - - - - 6 - - - - - 8 - - - - 8 - - 0.772 - - - 1.030

4 - - - - 4 - - - - - 2 - - - - 2 - - 0.507 - - 0.253

4 - - - - 4 - - - - - 2 - - - - 2 - - 0.504 - - 0.252

(-4) - - - 4 - - - - - (-18) - - 18 - 0.513 - - 2.308

(-2) - - - 2 - - - - (-6) - - - 6 - - 0.260 - - 0.781

11 - - - - 11 - - - - 9 - - - - 9 - - 1.412 - - - 1.155

(-1) - - - 1 - - - - - 1 - - - - 1 - - - 0.132 - - 0.132

14 - - - 14 - - - - 10 - - - 10 - - 1.783 - - 1.274

2 - - - - 2 - - - - (-2) - - 2 - - - 0.254 - - 0.254

3 - - - - 3 - - - - - 3 - - - 3 - - 0.379 - - - 0.379

MAD for forecast 1:

(Sum of |e1|) / number of observation

(6 + 4 + 4 + 4 + 2 + 11 + 1 + 14 + 2 + 3) / 10

= 51 / 10

= 5.1

MAD for forecast 2:

(Sum of |e2|) / number of observation

(8 + 2 + 2 + 18 + 6 + 9 + 1 + 10 + 2 + 3) / 10

61 / 10

= 6.1

MAPE = (Sum of absolute percentage error) / number of observations

Forecast 1:

(0.772 + 0.507 + 0.504 + 0.513 + 0.260 + 1.412 + 0.132 + 1.783 + 0.254 + 0.379)% / 10

= 6.516% / 10 = 0.6516%

MAPE Forecast 2:

(1.030 + 0.253 + 0.252 + 2.308 + 0.781 + 1.155 + 0.132 + 1.274 + 0.254 + 0.379)% / 10

= 7.818% / 10

= 0.7818%