Bluebook SAT Test Two-Variable Data: Models and Scatterplots 4 — Questions and Answers
Question 1: Data on number of employees (x) and company revenue (y, millions) is modeled by y = 0.05x + 1.2. What does the slope represent?
- Revenue increases by $0.05 million for each additional employee (Correct answer)
- The company earns $1.2 million with no employees
- Revenue decreases by $0.05 million per employee
- There are 0.05 employees per million dollars
Correct answer: Revenue increases by $0.05 million for each additional employee
The slope is the rate of change of y per unit of x: each extra employee is associated with $0.05 million more revenue.
Question 2: A quadratic model best fits a dataset when the scatterplot looks like which of these?
- A U-shape or inverted U-shape (parabola) (Correct answer)
- A straight line sloping upward
- A curve that accelerates upward without reversing
- Randomly scattered points
Correct answer: A U-shape or inverted U-shape (parabola)
Quadratic models produce parabolic (U or inverted-U) curves, distinct from linear or exponential shapes.
Question 3: A linear model predicts that a car's value (y, dollars) decreases with age (x, years): y = −1200x + 18000. What was the car's initial value?
- $18,000 (Correct answer)
- $1,200
- $16,800
- $19,200
Correct answer: $18,000
Initial value is when x = 0: y = −1200(0) + 18000 = $18,000.
Question 4: Using the model y = −1200x + 18000, after how many years is the car's predicted value $9,600?
- 7 (Correct answer)
- 8
- 6
- 9
Correct answer: 7
9600 = −1200x + 18000 → −1200x = −8400 → x = 7.
Question 5: A researcher fits both a linear and an exponential model to the same dataset. The exponential model has smaller residuals overall. What does this indicate?
- The exponential model is a better fit for the data (Correct answer)
- The linear model is a better fit for the data
- Both models fit equally well
- The data has no pattern
Correct answer: The exponential model is a better fit for the data
Smaller residuals mean the model's predictions are closer to the actual data, indicating a better fit.
Question 6: A scatterplot of daily high temperature (x, °F) vs. electricity usage (y, kWh) shows points going upward from left to right. The correlation is r = 0.78. How would you describe this relationship?
- Moderate positive linear relationship (Correct answer)
- Strong negative linear relationship
- Weak positive linear relationship
- No linear relationship
Correct answer: Moderate positive linear relationship
r = 0.78 is positive and moderately strong (between 0.5 and 0.9).
Question 7: A line of best fit has the equation y = 0.8x + 3. Which point lies on this line?
- (5, 7) (Correct answer)
- (5, 8)
- (4, 7)
- (10, 11)
Correct answer: (5, 7)
y = 0.8(5) + 3 = 4 + 3 = 7, so (5, 7) lies on the line.
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 4
Data on number of employees (x) and company revenue (y, millions) is modeled by y = 0.05x + 1.2.
What does the slope represent?