What the slope of a least-squares line actually tells you
"Interpret the slope in context" turns up in almost every bivariate data question. It is a reliable mark if you use the same sentence every time.
The template
On average, [response variable] increases (or decreases) by [slope] [units] for each one [unit] increase in [explanatory variable].
An example
Using the practice dataset below, a calculator gives
\[ \text{height} = 22.9 + 0.859 \times \text{arm span}. \]So: on average, height increases by 0.859 cm for each 1 cm increase in arm span.
Where marks go missing
- No "on average". The line describes a trend, not every person.
- No units. Both variables have units. Use them.
- Variables swapped. The slope describes the change in the response for a change in the explanatory variable, never the other way around.
Download the dataset and try it yourself, then work through the free worked examples on the intercept, \(r\), \(r^2\) and extrapolation.
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Reading a least-squares line
Unit 3 · Bivariate data · Worked examples
Worked examples on interpreting slope, intercept and r, and on when not to extrapolate.
Open: Reading a least-squares line