Question

Observed and predicted values of a variable Y based on a sample of size n=9 and a forecasting model are given below. Compute sample mean, sample variance for Y. compute MSE and MAD for residuals.Y 10.2 15 16.1 15.3 17 18.3 19.4 20.1 24 y 79.5 15.5 15 16 17.7 18 20 22 21

Answer 1

`\bar{Y} = 17.2667`

`S_y^2 = 3.8626`

`MAD = 8.6778`

`SME = 535.3322`

Explanation:

The sample mean for a finite set of values is given by:

`\bar{Y} = (1)/(n) \sum{y_i} = 17.2667`

The standard deviation for a finite set of values is given by:

`S_y^2 = (1)/(n-1) \sum (y_i - \bar{y})^2 = 3.8626`

The MAD for a set of predicted values is given by:

`MAD = (1)/(n)\sum|y_(predicted) - y_(real)| = 8.6778`

The MSE for a set of predicted values is given by:

`SME = (1)/(n)\sum(y_(predicted) - y_(real))^2 = 535.3322`