Week 8 fit days_to_pay from account history. Here the target is sales, and the
single predictor is something the business actually controls: monthly marketing spend. That is the
structural forecasting move — forecast an output from a driver, instead of extrapolating the output's own
history. Summit Gear has 30 months of spend and sales to fit on. The AI can run the regression in one line; the
judgment that matters is whether you would trust the line at the spend level you are about to plan around.
Below is every month of Summit Gear's marketing spend and the sales that followed it — no line fitted yet. Say Summit Gear plans to spend $350,000 on marketing next month. Before you see any fitted line, write down your own forecast of what sales that spend would produce. There is no wrong guess here. The point is to have a number on the table before the model hands you one, so you have something to compare it against.
Type a number, then click the button. The tutor will not walk you through the fit until you have a guess down.
Same math as Week 8's ols_trainer, one predictor: least squares finds the one line through
sales = b₀ + b₁·spend that minimizes the sum of squared misses across all 30 months. This is
the exact fit from the Week 9 answer key — the numbers below are not illustrative, they are the actual fitted
coefficients on this dataset.
Drag the slider to set next month's planned marketing spend. The page reads the forecast straight off the fitted line. Summit Gear has only ever spent between $53,100 and $491,600 a month — that shaded band on the chart is the range the line was actually fit on. Push past either edge and the line is forecasting for months nobody has actually seen, so there is no real data behind the number.
A fitted line makes no promise past the range it was fit on. Inside $53,100–$491,600, the line is interpolating between real months — that is the safe use of a fit. Past either edge, it is extrapolating, and a straight line cannot know that a business's marketing returns bend. At a planned spend of $650,000, the fitted line forecasts $3,592,205. If returns diminish the way they often do at higher spend, the real number could land closer to $3,010,000 — a $582,205 overstatement built into one straight line extended past what has actually been observed.
Everything above assumes the line means what it looks like it means: spend moves sales. But a fitted association never proves the direction of the arrow. Ice cream sales and drownings rise and fall together every summer — heat drives both, and neither causes the other. The same shape of problem sits inside this chart: a strong sales month can just as easily talk a company into a bigger marketing budget the following month, sales driving spend rather than the other way around. Nothing in the slope, the intercept, or the R² rules that out. Before this forecast goes in front of a VP, ask what else could be moving spend and sales together, and whether the causal arrow could run backward.
One or two sentences: your VP wants to plan on $650,000 in marketing spend next quarter because "the regression says it pays off." What do you tell them? Name the extrapolation risk, the causality caveat, or both. Try it before asking the tutor to react — it will not write the sentence for you, but it will tell you what a strong answer includes.