The line will fit anything you give it.

A regression line is obedient, not wise. It will run past the edge of your data, and it will happily draw one trend through two groups that both point the other way.

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Revision time against test mark — bivariate data: two measurements for each student. Revision time is the explanatory variable, so it goes on the $x$-axis; the mark responds to it.

The pattern is clearly positive.

In Year 1 the equation is always handed to you:

Each extra hour is worth about 6.9 more marks. The intercept claims 27 marks for no revision — but nobody revised under an hour.

At 3.5 hours the line says 52 marks. That is interpolation, inside the 1–7 hour range, and reasonably reliable.

At 10 hours it says 97, and at 11 hours 103.5 — through the ceiling of a paper marked out of 100. Nothing in the data ever promised the pattern would continue.

Here both groups rise: $+3.5$ for $A$, $+3.4$ for $B$. Fit one line to all ten points and it falls, at $-0.68$.

The single line is mostly measuring the gap between the groups, not the pattern inside them. Always look at the scatter, never only at the line.

Even a faultless correlation proves nothing about cause. Homework hours and children's heights rise together — because age drives both.

Three explanations, every time: one really affects the other, a third variable affects both, or it is coincidence.

A line summarises whatever you feed it.

Describing correlation, interpreting $a$ and $b$ in context, interpolation against extrapolation, judging causal claims, and twelve graded exam questions with full worked solutions are waiting.

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