Track 9 · Correlation and Regression · Lesson 5 of 15

Interpreting coefficients

Interpret a regression slope and intercept in the units of the data, rescale them, and recognise when a prediction is an extrapolation.

30 minAdvanced8 graded exercisesMembers

An estate agent fits a line to recent sales and announces that “each square metre is worth 4,751 SAR”. Is that what the slope says? What does the intercept mean, and can the same line price a 1,500 m² mansion? Reading coefficients correctly — with units, with care about cause, and within the range of the data — is most of the value of a regression.

A fitted simple regression line $\hat{y} = b_0 + b_1 x$ has two numbers, and each has units:

The slope $b_1$ is in units of $y$ per unit of $x$ . It is the difference in the average (predicted) response between observations whose $x$ differs by one unit.
The intercept $b_0$ is in units of $y$ . It is the predicted response when $x = 0$ — which is meaningful only if $x = 0$ is a sensible value that lies within the data.

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It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:

Interpret a slope as an average difference in the response per unit of the predictor, with units
Decide whether an intercept has a real-world meaning
Rescale coefficients when units change
Recognise extrapolation in x, in time and in the type of unit
Explain how “holding other predictors fixed” changes what a slope means

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