Answer :
Answer:
(a) MAD = 278.4
(b) MSE = 18.5
Step-by-step explanation:
The formula to compute the mean absolute deviation (MAD) and mean squared error (MSE) are:
[tex]MAD=\frac{1}{n}\sum |Y_{i}-\bar Y|\\MSE=\frac{1}{n}\sum (Y_{i}-Y_{e})^{2}[/tex]
(a)
Compute the mean absolute deviation as follows:
The mean of the actual values is:
[tex]\bar Y=\frac{1}{n} \sum Y_{i}=\frac{1}{4} (91+116+123+140)=117.5[/tex]
The value of MAD is:
[tex]MAD=\frac{1}{n}\sum |Y_{i}-\bar Y|\\=\frac{1}{n} (|91-117.5|+|116-117.5|+|123-117.5|+|140-117.5|)\\=278.375\\\approx278.4[/tex]
Thus, the value of MAD is 278.4.
(b)
Consider the table attached below.
Compute the mean squared error as follows:
[tex]\\MSE=\frac{1}{n}\sum (Y_{i}-Y_{e})^{2}=\frac{1}{4}\times74=18.5[/tex]
Thus, the value of MSE is 18.5.
