Bluebook SAT Test Two-Variable Data: Models and Scatterplots 7 — Questions and Answers
Question 1: A model for monthly sales (y) based on marketing spend (x, hundreds of dollars) is y = 12x + 80. How many units are sold when $500 is spent on marketing?
- 140 (Correct answer)
- 180
- 680
- 60
Correct answer: 140
x = 5 (hundreds): y = 12(5) + 80 = 60 + 80 = 140.
Question 2: The data points (1, 3), (2, 6), (3, 9), (4, 12) lie exactly on a line. What is the slope of the best-fit line?
- 3 (Correct answer)
- 1
- 6
- 0
Correct answer: 3
The y value increases by 3 for each unit increase in x, so slope = 3.
Question 3: A dataset has a line of best fit y = −0.5x + 100. When x = 0, what is y? When x = 100, what is y?
- y = 100 when x = 0; y = 50 when x = 100 (Correct answer)
- y = 0 when x = 0; y = 50 when x = 100
- y = 100 when x = 0; y = 0 when x = 100
- y = 50 when x = 0; y = 100 when x = 100
Correct answer: y = 100 when x = 0; y = 50 when x = 100
At x = 0: y = 100; at x = 100: y = −0.5(100) + 100 = −50 + 100 = 50.
Question 4: A researcher collects data and finds the second differences of y are approximately constant. What type of model fits best?
- Quadratic (Correct answer)
- Linear
- Exponential
- Logarithmic
Correct answer: Quadratic
Constant second differences are the hallmark of a quadratic (second-degree polynomial) model.
Question 5: The correlation coefficient between hours of TV watched and GPA is r = −0.73. What can you conclude?
- Students who watch more TV tend to have lower GPAs, and the relationship is moderately strong (Correct answer)
- Watching TV causes lower GPAs
- There is a weak positive relationship between TV hours and GPA
- GPA decreases by 0.73 points per hour of TV
Correct answer: Students who watch more TV tend to have lower GPAs, and the relationship is moderately strong
r = −0.73 indicates a moderately strong negative association; correlation doesn't establish causation.
Question 6: Using the model y = 1.5x² − 3x + 4, what is y when x = 4?
- 16 (Correct answer)
- 18
- 10
- 28
Correct answer: 16
y = 1.5(16) − 3(4) + 4 = 24 − 12 + 4 = 16.
Question 7: A line of best fit is drawn through a scatterplot. Most points are very close to the line, and r = 0.98. What does this tell you?
- A linear model explains most of the variation in the data (Correct answer)
- The data has no variation
- The slope is 0.98
- The y-intercept is 0.98
Correct answer: A linear model explains most of the variation in the data
r = 0.98 means r² = 0.96, so about 96% of variability in y is explained by the linear model.
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 7
A model for monthly sales (y) based on marketing spend (x, hundreds of dollars) is y = 12x + 80.
How many units are sold when $500 is spent on marketing?