AP Stats Regression Analysis 2

Question 1

A residual plot shows a curved (non-linear) pattern. What does this indicate about the linear regression model?

Accepted Answer

The linear model is not appropriate; a transformation may be needed

Answer

A curved pattern in a residual plot indicates that the linear model fails to capture the true relationship, suggesting a non-linear model or transformation is needed.

Question 2

In a least-squares regression, which of the following is always true about the residuals?

Accepted Answer

The sum of the residuals equals zero

Answer

By the least-squares criterion, the sum (and mean) of the residuals is always exactly zero.

Question 3

The regression equation for predicting exam score (y) from hours studied (x) is ŷ = 55 + 8x. What is the predicted score for a student who studies 5 hours?

Accepted Answer

95

Answer

Substituting x = 5: ŷ = 55 + 8(5) = 55 + 40 = 95.

Question 4

A regression line is fit to data with r = −0.92. Which statement best describes the relationship?

Accepted Answer

Strong negative linear association

Answer

r = −0.92 indicates a strong (|r| close to 1) negative linear association between the variables.

Question 5

When extrapolating beyond the range of the data using a regression model, what is the main concern?

Accepted Answer

The predictions may be unreliable because the linear pattern may not hold

Answer

Extrapolation is risky because the linear relationship observed within the data range may not extend outside it.

AP Practice Test

AP Practice Test

AP Stats Regression Analysis 2