Question

Drawing Conclusions Using the Slope of a Trend Line
What does a positive correlation tell you about the graph that compares advertising costs and sales. Would the owners of the company be happier if the slope was steeper or flatter? Explain.

Answer 1

A positive correlation between advertising costs (x‑axis) and sales (y‑axis) means the points trend upward: as the company spends more on advertising, sales tend to increase.

What the slope tells you
- The slope measures how much sales change for a given change in advertising. A steeper (larger) positive slope means sales rise more for each additional dollar spent on advertising; a flatter slope means sales rise less per dollar.

Would owners prefer a steeper or flatter slope?
- Generally owners prefer a steeper slope, because it means higher sales per dollar of advertising (better return on ad spend).
- Important caveat: owners care about profit, not just sales. A steeper slope is good only if the additional revenue it generates exceeds the additional advertising cost (and other costs). So compare marginal revenue from the extra sales to the marginal advertising cost. If marginal revenue > marginal cost, spending more is profitable.

Other points to consider
- Positive correlation does not prove advertising causes the sales increase; other factors could influence both.
- There may be diminishing returns: slope could flatten at higher spending levels, so the best ad budget is where marginal profit is maximized, not necessarily where spending is highest.