A veterinary clinic records the age, in years, and annual visit cost, in dollars, for a random sample of 12 dogs. A scatterplot, shown below, shows a moderate positive linear trend for 11 of the dogs, but one dog, Dog R, has an age close to the average age in the sample yet an annual visit cost far above what the trend predicts. If Dog R is removed from the data set, which of the following is most likely true of the least-squares regression line?
AP Statistics · Unit 5 · Regression Analysis
32 AP-style multiple-choice questions and 8 free-response questions for AP Statistics · Unit 5 · Regression Analysis, sorted into 2 topics. Free sample questions for every topic.
2 topics32 multiple-choice8 free-response
Topic 1 of 2
residuals and influential points
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A wildlife reserve fits the least-squares model to predict the body mass of an animal, in kilograms, from its age in years. For one animal aged years the recorded body mass is 47 kilograms. Which of the following is the residual for that animal?
Sample free-response question
A forester measured trunk diameter (cm) and height (m) for a random sample of 40 trees of one species in a large forest. She plans to test whether there is a linear relationship.
(a) List the conditions for inference about the slope of a regression line.
(b) Explain how the forester would check the linear and equal-variance conditions.
(c) The residual plot fans out, with larger residuals for larger trees. Explain which condition this violates and why it matters.
(d) Explain how to check that the residuals are approximately normal.
(e) Explain why the 10% condition is met.
(f) If the slope test is significant, can the forester conclude that thicker trunks cause trees to be taller? Explain.
12 more questions on this topic
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Answer, then see why
The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?
Not quite. The answer is B.
Why the other options are wrong
AI grading for free-response
Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.
Question 13 / 4 pts
Part a1 / 1 pts
Point 1: Earned
Grader confidence 94% sureReason: Correctly identifies demand for gasoline as inelastic.
Evidence: "The price of gasoline rises and the quantity falls only a little."
Part b2 / 3 pts
Point 1: Earned
Grader confidence 91% sureReason: Graph shows relatively inelastic demand.
Evidence: Draws a steep demand curve.
Point 2: Earned
Grader confidence 88% sureReason: Correct new equilibrium price.
Evidence: Shifts supply left, P1 → P2.
Point 3: Not earned
Grader confidence 82% sureReason: With inelastic demand, a price increase raises total revenue.
Evidence: "Revenue goes down."