Slope and intercept
The slope is the predicted change in y for each one-unit increase in x. The intercept is the predicted y when x is 0, which may be meaningless if x = 0 is far from your data.
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Analogy
The slope is the price per extra kilometre on a taxi fare. The intercept is the starting charge.
Example
Score = 50 + 5 x hours studiedSlope 5: each extra hour adds 5 pointsIntercept 50: predicted score at 0 hoursAt 4 hours: 50 + 20 = 70
In practice
Always state the slope with units so readers know what a change means.
Practice
Flashcards
- How do you interpret the slope?Predicted change in y for each one-unit increase in x.
Questions people ask
How do I interpret the slope in words?
Say: for each one-unit increase in x, y is predicted to change by the slope, on average. For a slope of 5, each extra hour of study goes with 5 more points. Say predicted or on average, not guaranteed, because individual points scatter around the line and some will miss it badly.
What if the intercept makes no sense?
Sometimes x = 0 is impossible or far outside the data, like a person with zero height. The intercept then just anchors the line and has no real-world meaning. Do not interpret it. Using centred x values can give an intercept that means something.