At a bottling plant, the least-squares regression line for predicting milliliters of fill volume from an explanatory variable has slope 1.2. The standard deviation of the explanatory variable is 2.5 and the standard deviation of milliliters of fill volume is 15. What is the correlation between the two variables?
scatterplots, correlation and least-squares regression
Review scatterplots, correlation and least-squares regression for AP Statistics and try 2 free AP-style practice questions. 18 questions on this topic in AP Statistics · Unit 5 · Regression Analysis.
2 topics32 multiple-choice8 free-response
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Using data from 22 professional cyclists, an analyst fits a least-squares regression model predicting finishing time in a race, in minutes, from average power output, in watts: , with . Which of the following correctly interprets the slope and the value of in context?
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.
16 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."