AP Stats Regression Analysis 2 — Questions and Answers
Question 1: A residual plot shows a curved (non-linear) pattern. What does this indicate about the linear regression model?
- The linear model is appropriate
- The linear model is not appropriate; a transformation may be needed (Correct answer)
- The slope is not statistically significant
- The residuals have unequal variance only
Correct answer: The linear model is not appropriate; a transformation may be needed
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?
- All residuals are positive
- The sum of the residuals equals zero (Correct answer)
- Each residual equals the slope
- The largest residual determines r²
Correct answer: The sum of the residuals equals zero
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?
- 63
- 85
- 95 (Correct answer)
- 75
Correct answer: 95
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?
- Weak positive linear association
- Strong positive linear association
- Strong negative linear association (Correct answer)
- No linear association
Correct answer: Strong negative linear association
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?
- The slope will become negative
- The predictions may be unreliable because the linear pattern may not hold (Correct answer)
- The y-intercept changes automatically
- Residuals will always be larger inside the data range
Correct answer: The predictions may be unreliable because the linear pattern may not hold
Extrapolation is risky because the linear relationship observed within the data range may not extend outside it.
Question 6: Which value of r² indicates that the least-squares regression line explains the greatest proportion of variation in y?
- r² = 0.15
- r² = 0.45
- r² = 0.72 (Correct answer)
- r² = 0.08
Correct answer: r² = 0.72
r² = 0.72 means 72% of the variation in y is explained by x, which is the highest among the choices.
Question 7: A data point has a large positive residual. This means the actual y-value is __________ the predicted value.
- equal to
- less than
- greater than (Correct answer)
- the square of
Correct answer: greater than
Residual = observed − predicted, so a positive residual means the actual value exceeds the predicted value.
AP Stats Regression Analysis 2
A residual plot shows a curved (non-linear) pattern.
What does this indicate about the linear regression model?