To calculate the Mean Squared Error (MSE), we first need to determine the squared errors for each week. The squared error is calculated as:
\[ \text{Squared Error} = (\text{Actual} - \text{Forecast})^2 \]
Let's calculate the squared errors for each week:
-
Week 1:
- Actual = 7, Forecast = 7.00
- Squared Error = (7 - 7.00)² = 0² = 0
-
Week 2:
- Actual = 15, Forecast = 13.00
- Squared Error = (15 - 13.00)² = 2² = 4
-
Week 3:
- Actual = 14, Forecast = 17.00
- Squared Error = (14 - 17.00)² = (-3)² = 9
-
Week 4:
- Actual = 13, Forecast = 18.00
- Squared Error = (13 - 18.00)² = (-5)² = 25
Now we sum the squared errors:
\[ \text{Total Squared Errors} = 0 + 4 + 9 + 25 = 38 \]
Next, we calculate the MSE by dividing the total squared errors by the number of observations (weeks):
\[ \text{MSE} = \frac{\text{Total Squared Errors}}{\text{Number of Observations}} = \frac{38}{4} = 9.5 \]
Thus, the value of the Mean Squared Error (MSE) is 9.5.