onsider the following data:



Monthly Profit of a GymMonth

Jan-12

Feb-12

Mar-12

Apr-12

May-12

Jun-12

Jul-12

Aug-12

Sep-12

Profit ($)

5,3505,350

5,1035,103

4,8244,824

4,4374,437

5,0805,080

5,3585,358

5,8195,819

6,0916,091

5,8375,837

Step 4 of 5 :  

What are the MSE scores for the three-period weighted moving average forecast? Round any intermediate calculations, if necessary, to no less than six decimal places, and round your final answer to one decimal place.

Based on the calculations I previously performed for the three-period weighted moving average forecast, the Mean Squared Error (MSE) score was calculated as 262,313.7.

Here’s a brief recap:

- The forecast was computed using weights of 3, 2, and 1.
- The actual profits for the months April 2012 to September 2012 were compared against these forecasts.
- The MSE, which measures the average squared difference between the actual and forecasted values, was computed using the formula:

\[
\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} ( \text{Actual}_i - \text{Forecast}_i )^2
\]

The MSE score, rounded to one decimal place, is **262,313.7**.

Would you like further clarification on how this was calculated or any additional details?

Here are some related questions you might find interesting:
1. How does changing the weights affect the MSE?
2. What other error metrics could be used alongside MSE for evaluating forecast accuracy?
3. What is the significance of MSE in making business decisions?
4. How does the presence of outliers affect the MSE value?
5. Can you explain how MSE differs from the standard deviation?

**Tip:** MSE is sensitive to large errors due to the squaring of differences. This can make it particularly useful in scenarios where large errors are especially undesirable.

Learn how to calculate Mean Squared Error (MSE) for a three-period weighted moving average forecast in time series analysis. Understand the significance of MSE in evaluating forecast accuracy with detailed calculations and explanations.

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