To calculate the weighted moving average for the 4th week using the specified weights of .20, .30, and .50, we will take the time series values for the 3 most recent weeks (Weeks 1, 2, and 3) and multiply them by their corresponding weights.
The time series values are:
- Week 1: 22.00
- Week 2: 24.00
- Week 3: 23.00
Now, we can compute the weighted moving average as follows:
Weighted Moving Average = (Weight of Week 1 * Value of Week 1) + (Weight of Week 2 * Value of Week 2) + (Weight of Week 3 * Value of Week 3)
Plugging in the values and weights:
Weighted Moving Average = (0.20 * 22.00) + (0.30 * 24.00) + (0.50 * 23.00)
Calculating each term:
- 0.20 * 22.00 = 4.40
- 0.30 * 24.00 = 7.20
- 0.50 * 23.00 = 11.50
Now add them together:
Weighted Moving Average = 4.40 + 7.20 + 11.50 = 23.10
Thus, the weighted moving average forecast for the 4th week is:
23.1