Question

Calculate​ (a) MAD and​ (b) MSE for the following forecast versus actual sales​ figures: Forecast 98 112 126 140 Actual 91 116 123 140 ​a) MADequals nothing ​(round your response to one decimal​ place). ​b) MSEequals nothing ​(round your response to one decimal​ place).

Answer 1

(a) MAD = 278.4

(b) MSE = 18.5

Explanation:

The formula to compute the mean absolute deviation (MAD) and mean squared error (MSE) are:

`MAD=(1)/(n)\sum |Y_(i)-\bar Y|\\MSE=(1)/(n)\sum (Y_(i)-Y_(e))^(2)`

(a)

Compute the mean absolute deviation as follows:

The mean of the actual values is:

`\bar Y=(1)/(n) \sum Y_(i)=(1)/(4) (91+116+123+140)=117.5`

The value of MAD is:

`MAD=(1)/(n)\sum |Y_(i)-\bar Y|\\=(1)/(n) (|91-117.5|+|116-117.5|+|123-117.5|+|140-117.5|)\\=278.375\\\approx278.4`

Thus, the value of MAD is 278.4.

(b)

Consider the table attached below.

Compute the mean squared error as follows:

`\\MSE=(1)/(n)\sum (Y_(i)-Y_(e))^(2)=(1)/(4)*74=18.5`

Thus, the value of MSE is 18.5.