Bluebook SAT Test Two-Variable Data: Models and Scatterplots 12

Question 1

The linear model for shoe size (x) and height in inches (y) is y = 3x + 54. A person has shoe size 9. What height does the model predict?

Accepted Answer

81 inches

Answer

y = 3(9)+54 = 27+54 = 81 inches.

Question 2

A scatterplot shows points with a strong positive correlation. A second variable is added as an explanatory variable and the correlation drops significantly. What may have occurred?

Accepted Answer

A confounding variable may explain the original apparent relationship.

Answer

When adding a third variable removes a strong correlation, it suggests the original relationship was confounded — not necessarily causal.

Question 3

A data set on calories (x) and weight gain (y, lbs per week) is modeled by y = 0.005x − 1. According to the model, at how many calories does weight remain constant (y = 0)?

Accepted Answer

200 calories

Answer

Set 0 = 0.005x−1 → x = 1/0.005 = 200 calories.

Question 4

A scatterplot has the line y = 5x + 3. A point at (4, 24) lies above the line. What is the residual?

Accepted Answer

1

Answer

Predicted y = 5(4)+3 = 23; residual = 24−23 = 1.

Question 5

The exponential model y = 1000(0.9)^x models the value of an investment after x months. What type of change does this model represent?

Accepted Answer

Exponential decay

Answer

Since the base 0.9 < 1, each month the value is multiplied by 0.9, representing exponential decay.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Two-Variable Data: Models and Scatterplots 12