To calculate the Mean Squared Error (MSE), we first need to find the squared errors for each week. The squared error is calculated as follows:
\[ \text{Squared Error} = (\text{Actual} - \text{Forecast})^2 \]
Let's calculate the squared errors for each week:
-
Week 1:
- Actual = 7
- Forecast = 4.00
- Squared Error = \((7 - 4)^2 = (3)^2 = 9\)
-
Week 2:
- Actual = 15
- Forecast = 4.00
- Squared Error = \((15 - 4)^2 = (11)^2 = 121\)
-
Week 3:
- Actual = 14
- Forecast = 16.00
- Squared Error = \((14 - 16)^2 = (-2)^2 = 4\)
-
Week 4:
- Actual = 13
- Forecast = 17.00
- Squared Error = \((13 - 17)^2 = (-4)^2 = 16\)
Now, we can sum up the squared errors:
\[ \text{Total Squared Error} = 9 + 121 + 4 + 16 = 150 \]
Now, we calculate the Mean Squared Error (MSE) by dividing the total squared error by the number of observations:
\[ \text{MSE} = \frac{\text{Total Squared Error}}{n} = \frac{150}{4} = 37.5 \]
Thus, the value of MSE is 37.5.