Questions: Week Value Forecast ------------ 1 16 2 15 3 17 4 16 16 5 12 16 6 14 15

Solution Steps

To find the Mean Squared Error (MSE), we first need to calculate the forecast errors. The forecast errors are given by:

\[ \text{Error}_i = \text{Actual}_i - \text{Forecast}_i \]

For the given data, the actual values for weeks 4 to 6 are \(16\), \(12\), and \(14\), and the corresponding forecast values are \(16\), \(16\), and \(15\). Thus, the errors are:

\[ \begin{align_} \text{Error}_1 & = 16 - 16 = 0 \\ \text{Error}_2 & = 12 - 16 = -4 \\ \text{Error}_3 & = 14 - 15 = -1 \\ \end{align_} \]

Next, we square each of the forecast errors:

\[ \begin{align_} \text{Error}_1^2 & = 0^2 = 0 \\ \text{Error}_2^2 & = (-4)^2 = 16 \\ \text{Error}_3^2 & = (-1)^2 = 1 \\ \end{align_} \]

The MSE is calculated by taking the average of the squared errors:

\[ \text{MSE} = \frac{1}{n} \sum_{i=1}^{n} \text{Error}_i^2 \]

Where \(n\) is the number of forecasted values. In this case, \(n = 3\):

\[ \text{MSE} = \frac{1}{3} (0 + 16 + 1) = \frac{17}{3} \approx 5.67 \]

Final Answer