Question

Assume that January sales for the fourth year turn out to be $295,000. The decomposition method predicted sales of $298,424, while the multiple regression method forecasted sales of $286,736. Which interpretation best describes the forecast error for both methods?

The forecast error for the decomposition method was within ±3% but the multiple regression error was not within ±3%. Therefore, the decomposition method was better for this forecast.
The forecast error for the decomposition method was not within ±3% but the multiple regression error was within ±3%. Therefore, the multiple regression method was better for this forecast.
The forecast error for the decomposition method was not within ±3% and the multiple regression error was also not within ±3%. Therefore, both methods generated error high enough to be cautious about sales forecasts.
The forecast error for the decomposition method was within ±3% and the multiple regression error was also within ±3%. Therefore, both methods provide low error and similar forecast accuracy.

Answer 1

The forecast error for the decomposition method was within ±3% and the multiple regression error was also within ±3%. Therefore, both methods provide low error and similar forecast accuracy.

Explanation:

January sales for the fourth year as stated is $295,000.

While predicted sales of decomposition method and forecasted sales of multiple regression method were $298,424 and $286,736 respectively.

Our assumption is that for the accuracy to be valid, there is need for it needs to be within ±3% area of the actual results .

Therefore:

295000 × 0.03 = 8850

295000 + 8850 = 303850 ( expected predicted sales of decomposition by ±3%)

295000 - 8850 = 286150 (expected forecasted sales for multiple regression by ±3%)

We could see that both the results are within this ±3% area and decomposition was slightly more accurate. The forecast error for the decomposition method was within ±3% and the multiple regression error was also within ±3%. Therefore, both methods provide low error and similar forecast accuracy.

That's it!