SAT Math: Scatterplots and Linear Models Practice Questions
Use a fitted line to predict values, interpret its coefficients, and compare observed values with model predictions. Try each original question before checking its worked explanation. This focused practice is free and requires no account.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. A fitted model for a plant is h = 2.5t + 6, where h is height in centimeters and t is days after measurement begins. What height does the model predict at t = 8?
Explanation. Substitute 8 for t: h = 2.5(8) + 6 = 20 + 6 = 26 centimeters. The 6 is added once; it is the modeled starting height.
2. A line of best fit for a data set passes through (2, 9) and (10, 29). What is the slope of this line?
Explanation. Slope is change in y divided by change in x: (29 - 9)/(10 - 2) = 20/8 = 5/2. Use the coordinates on the fitted line, even if no observed data point lies exactly there.
3. For a scatterplot, the model is y = 4x + 7. An observed point is (5, 24). Using residual = observed y - predicted y, what is this point's residual?
Explanation. At x = 5, the model predicts 4(5) + 7 = 27. The residual is 24 - 27 = -3. A negative residual places the observed point below the fitted line.
4. The exact values of y at x = 0, 1, 2, 3 are 5, 9, 13, 17. Which model matches every value?
Explanation. Each increase of 1 in x adds 4 to y, and y is 5 when x is 0. Thus y = 4x + 5. The exponential option gives 16.2 at x = 2, and the remaining options already fail at x = 0 or 1.
5. A fitted line is s = 1.8h + 42, where s is a practice-test score and h is hours of study. What does 1.8 represent in this model?
Explanation. The coefficient of h is the slope. Increasing h by 1 raises the predicted value of s by 1.8 points. This describes a model prediction and does not establish that studying causes that exact gain.
6. A fitted linear model gives y = 12 at x = 3 and y = 24 at x = 7. What value of y does the same model give at x = 4?
Explanation. The slope is (24 - 12)/(7 - 3) = 3. Moving from x = 3 to x = 4 adds 3 to the predicted y, so y = 15. This is interpolation between the given inputs.
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FAQ
What is a residual?
A residual is the observed output minus the output predicted by the model. Its sign tells you which side of the fitted curve contains the observation.
Does a fitted line prove causation?
No. A fitted line describes an association. A causal conclusion requires an appropriate study design and supporting evidence.