Two-Variable Data • Topic 5 of 5

Regression Concepts

A regression line, or line of best fit, is the straight line y = mx + b that best summarises the trend in a scatterplot. Its slope m tells you how much y changes for each one-unit increase in x, and its intercept b is the predicted y when x = 0. The main use is prediction: substitute an x-value into the equation to estimate the matching y. Interpreting the slope in context — “each extra hour adds about m units” — is a frequent SAT task. Predictions are most reliable within the range of the data; extending far beyond it (extrapolation) is unreliable.

Points with a rising line of best fit and a prediction pointLine of best fitxyy = mx + bSubstitute x into the line to predict y.

✅ Solved examples

1. Line of best fit y = 5x + 10. Predict y at x = 6.
y = 5(6) + 10 = 40.
2. For y = 4x + 30 relating experience (years) to salary (thousands), what does the slope mean?
Salary rises about $4,000 per extra year of experience.
3. Line of best fit y = 2x + 7. Predict y at x = 9.
y = 2(9) + 7 = 25.
4. In y = 3x + 12, what is the predicted value when x = 0?
y = 12 (the intercept).

✏️ Practice — try these, take hints as needed

1. Line of best fit y = 6x + 5. Predict y at x = 4.
Substitute x = 4.
6(4) + 5.
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29.
2. Line of best fit y = 3x + 8. Predict y at x = 10.
3(10) + 8.
—
—
38.
3. For y = 7x + 20, what does the slope 7 represent per unit of x?
Slope = change in y per +1 x.
—
—
y increases by 7 for each unit increase in x.
4. In y = 5x + 15, what is the predicted y at x = 0?
The intercept.
—
—
15.
5. Line of best fit y = 2x + 1. Predict y at x = 12.
2(12) + 1.
—
—
25.

📝 Topic test — 8 questions

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