Bluebook SAT Test Two-Variable Data: Models and Scatterplots 6

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?

Accepted Answer

2.5 inches

Answer

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?

Accepted Answer

y = 4x + 12

Answer

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?

Accepted Answer

Quadratic

Answer

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?

Accepted Answer

The chosen model is not an appropriate fit; a different model should be tried

Answer

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?

Accepted Answer

There is a moderate positive linear relationship between x and y

Answer

r = 0.60 indicates a moderate positive linear relationship; r is not the slope.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Two-Variable Data: Models and Scatterplots 6