Bluebook SAT Test Two-Variable Data: Models and Scatterplots 6 — Questions and Answers
Question 1: The linear model for height (y, inches) based on age (x, years, ages 2–10) is y = 2.5x + 32. By how much does the model predict height increases per year?
- 2.5 inches (Correct answer)
- 32 inches
- 34.5 inches
- 30 inches
Correct answer: 2.5 inches
The slope 2.5 means the model predicts a 2.5-inch increase in height per year.
Question 2: A best-fit line passes through (0, 12) and (4, 28). What is the equation of this line?
- y = 4x + 12 (Correct answer)
- y = 12x + 4
- y = 4x − 12
- y = 3x + 12
Correct answer: y = 4x + 12
Slope = (28 − 12)/(4 − 0) = 4; y-intercept = 12, giving y = 4x + 12.
Question 3: A scatterplot shows the following points: (1, 2), (2, 8), (3, 18), (4, 32). Which model best fits these data?
- Quadratic (Correct answer)
- Linear
- Exponential
- Constant
Correct answer: Quadratic
The second differences are constant (Δ²y = 4), which is the signature of a quadratic model.
Question 4: What does a residual plot that shows a curved pattern (not random scatter) indicate?
- The chosen model is not an appropriate fit; a different model should be tried (Correct answer)
- The data has no pattern
- The model is a perfect fit
- The slope should be increased
Correct answer: The chosen model is not an appropriate fit; a different model should be tried
A curved pattern in residuals means the linear model fails to capture a non-linear trend in the data.
Question 5: A scatterplot of x and y shows r = 0.60. Which statement is most accurate?
- There is a moderate positive linear relationship between x and y (Correct answer)
- 60% of x values are positive
- x causes y with 60% certainty
- The slope of the best-fit line is 0.60
Correct answer: There is a moderate positive linear relationship between x and y
r = 0.60 indicates a moderate positive linear relationship; r is not the slope.
Question 6: A model y = 2x + 5 predicts production costs. An actual data point is (6, 22). By how much does the model overpredict or underpredict?
- The model overpredicts by 5 (Correct answer)
- The model underpredicts by 5
- The model overpredicts by 6
- The model matches exactly
Correct answer: The model overpredicts by 5
Predicted = 2(6) + 5 = 17; actual = 22; residual = 22 − 17 = 5 > 0, so the model underpredicts by 5.
Question 7: Two scatterplots: Plot A has r = 0.95 and Plot B has r = 0.40. Which plot shows points closer to the line of best fit?
- Plot A (Correct answer)
- Plot B
- Both are equally close
- Cannot be determined
Correct answer: Plot A
Higher |r| means points cluster more tightly around the line; r = 0.95 is much closer to 1 than r = 0.40.
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 6
The linear model for height (y, inches) based on age (x, years, ages 2–10) is y = 2.5x + 32.
By how much does the model predict height increases per year?