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

Answer:

$\bar{Y} = 17.2667$

$S_y^2 = 3.8626$

$MAD = 8.6778$

$SME = 535.3322$

Step-by-step explanation:

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

$\bar{Y} = \frac{1}{n} \sum{y_i} = 17.2667$

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

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

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

$MAD = \frac{1}{n}\sum|y_{predicted} - y_{real}| = 8.6778$

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

$SME = \frac{1}{n}\sum(y_{predicted} - y_{real})^2 = 535.3322$