Question 3 of 7: Sales Forecast for iPad Tablets

Question 3: Sales Forecast for iPad Tablets (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Eight months of actual sales, September through April (see table); no other demand drivers (promotions, launch dates, pricing) are supplied.

Find. A justified point forecast for May sales, and a discussion of the forecast's reliability and how it could be improved.

Approach (part a). Test the series for a usable linear trend before trusting one, then compare a naive (last-value) forecast against a short moving average to pick the method that best matches the data's actual behaviour, rather than defaulting to whichever method is easiest to compute.

1. Check for a linear trend. Regressing sales $y$ against month index $t=1,\dots,8$ gives slope $\approx47.4$ units/month, intercept $\approx266.9$, but the coefficient of determination is $$R^2\approx\boxed{0.10},$$ meaning a straight line explains only about 10% of the month-to-month variation — the swings from 740 to 45 to 10 to 1023 are not a trend, they are volatility a linear model cannot capture. A naive trend-line forecast (which would give $\approx693$ units for May) is therefore not defensible as the primary method.
2. Compare candidate forecasts. Naive (last actual value, April) gives $F_{May}=\boxed{800}$; this reacts fully to the most recent month but ignores the two very low months (Jan, Feb) that came right before the March/April rebound — it would have forecast January from December's 740 and been off by a factor of 16. A 3-month moving average (Feb, Mar, Apr) smooths the recent volatility: $$F_{May}=\frac{10+1023+800}{3}=\boxed{611\ \text{units}}.$$
3. Select and justify. With $R^2\approx0.10$ there is no reliable trend or visible seasonal cycle in only eight points, and the series alternates between a near-zero month and a 700–1000-unit month, which looks like promotion- or launch-driven spikes rather than smooth demand. The 3-month moving average is the more defensible forecast because it damps the effect of any single unusual month (the Jan/Feb collapse or the March spike) while still tracking the recent (Mar–Apr) high-sales regime, giving $\boxed{F_{May}\approx611\ \text{units}}$ as the point forecast, bracketed by the naive estimate (800, an upper case if April's pace continues) and the pure trend line (693) as a plausibility check.

(b) Discussion and improvement. The forecast is weak: eight data points cannot establish seasonality (a real yearly cycle needs at least two full years of data to separate from noise), the two near-zero months (Jan 45, Feb 10) suggest a stock-out, a discontinued old model, or a lull ahead of a new-model launch rather than organic demand decay, and the March/April rebound (1023, 800) could equally be a one-time launch spike that will not repeat in May. To improve the forecast I would: (1) collect at least 24 months of history to test for a genuine annual seasonal pattern (back-to-school, holiday, or new-model-launch cycles are common for consumer electronics); (2) bring in causal information the retailer already has — Apple's announced launch calendar, planned promotions, and competitor pricing — since a launch-driven spike is a known event, not a random one, and should be modelled explicitly rather than smoothed away; (3) track forecast error (MAD or MSE) month over month and switch to exponential smoothing with a low smoothing constant once enough history exists, so the model adapts without over-reacting to a single outlier month; and (4) disaggregate "iPad sales" into old-model and new-model units, since combining them (as the table does) can hide a simple explanation — e.g. the March spike may be a new-model launch cannibalizing what would otherwise have been steady old-model demand.