y = 146.5x + 1958.7
For the fourth year, the total sales are obtained by plugging in x = 4 in the above equation.
[pic](in thousands of dollars)
The average monthly sales during the fourth year, therefore, is 2544.7/12 = 212.058 (in thousands of dollars).
The forecast for a particular month (say July) is calculated by multiplying the average monthly sales forecast by that month’s (July’s) seasonal index. For the month of July, it will be 0.831*212.058 = 176.22 (in thousands of dollars).
The monthly forecasts for the 12 months of the fourth year are as shown below:
Month (yr.4) |January |February |March |April |May |June |July |August |September |October |November |December | |S. Index |1.398 |1.293 |1.322 |1.023 |1.043 |0.798 |0.831 |0.865 |0.636 |0.725 |0.874 |1.192 | |Forecast |296.45755 |274.19143 |280.3411 |216.9357 |221.1768 |169.2226 |176.2205 |183.4305 |134.8691 |153.7423 |185.339 |252.7735 | |
Suppose the actual January sales for the fourth year turn out to be $295,000. The forecasted January sales are $296,458.
Error between actual and forecasted sales = $296,458 - $295,000 = $1458
Percentage Error = [pic]
This is an extremely small percentage error. Karen does not have to worry about this error and she can be assured that her forecast model is extremely…