To calculate the Mean Squared Error (MSE), we first need to compute the errors (the difference between the actual values and the forecast values), then square those errors, and finally take the average of the squared errors.
Given the data:
| Month | Actuals | Forecast | |-------|---------|----------| | 1 | 7 | 6.00 | | 2 | 5 | 3.00 | | 3 | 4 | 7.00 | | 4 | 3 | 3.00 |
-
Calculate the errors:
- Month 1: \( 7 - 6.00 = 1 \)
- Month 2: \( 5 - 3.00 = 2 \)
- Month 3: \( 4 - 7.00 = -3 \)
- Month 4: \( 3 - 3.00 = 0 \)
-
Square the errors:
- Month 1: \( 1^2 = 1 \)
- Month 2: \( 2^2 = 4 \)
- Month 3: \( (-3)^2 = 9 \)
- Month 4: \( 0^2 = 0 \)
-
Sum the squared errors: \[ 1 + 4 + 9 + 0 = 14 \]
-
Divide by the number of observations (n = 4): \[ \text{MSE} = \frac{14}{4} = 3.5 \]
Thus, the Mean Squared Error (MSE) is 3.5.