Bluebook SAT Test Two-Variable Data: Models and Scatterplots 4

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?

Accepted Answer

Revenue increases by $0.05 million for each additional employee

Answer

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?

Accepted Answer

A U-shape or inverted U-shape (parabola)

Answer

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?

Accepted Answer

$18,000

Answer

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?

Accepted Answer

7

Answer

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?

Accepted Answer

The exponential model is a better fit for the data

Answer

Smaller residuals mean the model's predictions are closer to the actual data, indicating a better fit.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Two-Variable Data: Models and Scatterplots 4