Two-variable data & scatterplots
A scatterplot shows how two quantities move together. The questions ask you to read its direction, use a line (or curve) of best fit to predict, interpret what the line's slope means, and measure how far a real point sits from the prediction.
What College Board tests
Reading association (positive, negative, none) and its strength, using a line of best fit to estimate a value, interpreting the slope and intercept of that line in context, and computing a residual — the gap between an actual data point and the line's prediction.
The key ideas
Four worked examples in SAT format. Read the approach, try it yourself, then tap Show the full solution.
1 · Predict with the line of best fit
A scatterplot (not shown) relates study hours to test score , and its line of best fit has equation . Based on the line of best fit, what is the predicted test score for a student who studies 10 hours?
Approach A prediction from the best-fit line is just substitution. Put the given -value into the equation and compute .
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Answer: C
Why the other choices are wrong
A Uses a slope of 1 instead of 2.
B Computes but drops the intercept.
D Adds the intercept twice.
2 · Interpret the slope in context
A line of best fit for a city's data is , where is years since 2010 and is the number of charging stations. Which is the best interpretation of the slope, 3?
- There were 3 charging stations in 2010.
- The number of charging stations increased by about 3 each year.
- There were 3 charging stations total.
- It took 3 years to build the first station.
Approach The slope is the predicted change in per one-unit increase in . Here is years and is stations, so the slope is stations per year.
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Answer: B
So each additional year predicts about 3 more charging stations. To see the rate in action, multiply by a span of years and watch "year" cancel: over 4 years. (The 12 in the equation is the intercept — the predicted count in 2010, when .)
Why the other choices are wrong
A Describes the intercept (12), and even then uses the wrong number.
C Treats 3 as a total, not a yearly rate.
D Reads 3 as a duration rather than a rate of change.
3 · Identify the association
In a scatterplot, as the values on the horizontal axis increase, the values on the vertical axis tend to decrease, with the points falling roughly along a straight line. Which best describes the association?
- Strong positive linear association
- Strong negative linear association
- No association
- Strong positive exponential association
Approach Two questions: direction and shape. "As goes up, goes down" sets the direction; "roughly along a straight line" sets the shape.
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Answer: B
Down-and-to-the-right along a line is a strong negative linear association.
Why the other choices are wrong
A Positive would mean rises as rises — the opposite here.
C A clear downward trend is an association, not the absence of one.
D Wrong direction and wrong shape — it's linear and decreasing.
4 · Compute a residual
The scatterplot shows the relationship between hours studied and test score for several students, along with a line of best fit. For the highlighted data point at , what is the difference between the actual score and the score predicted by the line of best fit? (The equation of the line is .)
Approach This difference is the residual: actual minus predicted. Read the actual score off the highlighted point, use the line to predict at , then subtract.
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Answer: B
The highlighted point lies above the best-fit line; the short vertical gap between the actual score (25) and the line's prediction (23) is the residual of +2.
Why the other choices are wrong
A Reverses the subtraction (predicted − actual).
C Reports the intercept rather than the residual.
D Uses the predicted value's pieces; is not the residual.