Bluebook SAT Test Two-Variable Data: Models and Scatterplots 13

Question 1

A scatterplot of study hours (x) vs. exam score (y) shows the line y = 8x + 45. A student studies 0 hours. What does the y-intercept tell us about this student?

Accepted Answer

The model predicts a score of 45 even with no study time.

Answer

The y-intercept (45) is the model's predicted value of y when x = 0, representing the expected baseline score.

Question 2

The data (1, 3), (3, 7), (5, 11) appear to follow a pattern. Which model fits exactly?

Accepted Answer

y = 2x + 1

Answer

Slope = (7−3)/(3−1) = 2; using (1,3): 3=2(1)+b → b=1; equation y=2x+1 checks for all points.

Question 3

Two models are fit to a dataset: Model A (linear) has r² = 0.72; Model B (quadratic) has r² = 0.94. Which model is more appropriate?

Accepted Answer

Model B, because it explains more variability in the data.

Answer

A higher r² (0.94 vs 0.72) means Model B explains more of the variance in y and is a better fit.

Question 4

A linear model y = 2.5x + 15 predicts a student's GPA (y) from weekly hours of tutoring (x). What is the predicted GPA increase from 0 to 4 tutoring hours?

Accepted Answer

10 points

Answer

Change in y = slope × change in x = 2.5 × 4 = 10.

Question 5

A scatterplot shows data that follows a U-shaped pattern. Which model best fits this data?

Accepted Answer

Quadratic

Answer

A U-shaped pattern in a scatterplot is characteristic of a quadratic (parabolic) model.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Two-Variable Data: Models and Scatterplots 13