scatterplots, correlation and least-squares regression

Review scatterplots, correlation and least-squares regression for AP Statistics and try 2 free AP-style practice questions. 20 questions on this topic in AP Statistics · Unit 2 · Exploring Two-Variable Data.

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Question 1

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?

Question 2

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: $\hat{y} = 280 - 0.35x$ , with $r^{2} = 0.83$ . Which of the following correctly interprets the slope and the value of $r^{2}$ in context?

18 more questions on this topic

Full practice for AP Statistics · Unit 2 · Exploring Two-Variable Data: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.

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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

94% sure

Reason: 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

91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned

88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned

82% sure

Reason: With inelastic demand, a price increase raises total revenue.

Evidence: "Revenue goes down."

Scatterplots, correlation and least-squares regression: AP Statistics Practice Questions | S&D Academy