Two-Variable Data: Models and Scatterplots Flashcards

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?

Answer: 81 inches

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

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?

Answer: A confounding variable may explain the original apparent relationship.

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

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)?

Answer: 200 calories

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

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

Answer: 1

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

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?

Answer: Exponential decay

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

A linear model predicts test scores (y) from hours of sleep (x): y = 6x + 40. What is the predicted score for a student who slept 7 hours?

Answer: 82

y = 6(7)+40 = 42+40 = 82.

A dataset with x = {2, 4, 6, 8} and y = {5, 5, 5, 5} is plotted. What is the slope of the best-fit line?

Answer: 0

Since y is constant (5) for all values of x, there is no change in y, so the slope is 0.