Regression Worksheet with Answers – AP Statistics (Free PDF)

Problem 1 Describing a Scatterplot ★★★

The scatterplot shows weekly drill hours and free-throw percentage for 12 players.

Describe the direction, form, strength and any unusual features.

Problem 2 Explanatory and Response Variables ★★★

For each pair, choose the explanatory variable and the response variable. (a) A student’s hours of sleep and the quiz score the next day. (b) The outdoor temperature and the number of customers at a coffee kiosk.

Problem 3 Correlation Facts ★★★

Four values of r are −0.92, −0.15, 0.35 and 0.88. (a) Which describes the strongest linear relationship? (b) Which describes a weak negative relationship? (c) If the heights are converted from inches to centimeters, what happens to r between height and weight?

Problem 4 Slope and Intercept from Summary Statistics ★★★

For adult women, height has mean 64.5 inches and standard deviation 3.1 inches; weight has mean 152 pounds and standard deviation 18.4 pounds; the correlation is 0.78. Find the least-squares line for predicting weight from height.

Problem 5 Interpreting the Slope ★★★

The line for predicting weight (pounds) from height (inches) is ŷ = −146.61 + 4.63x. Interpret the slope in context.

Problem 6 Interpreting the Intercept ★★★

Interpret the y-intercept of ŷ = −146.61 + 4.63x and decide whether it is meaningful.

Problem 7 Making a Prediction ★★★

Use ŷ = −146.61 + 4.63x to predict the weight of a woman who is 70 inches tall.

Problem 8 Computing a Residual ★★★

A woman 70 inches tall weighs 190 pounds. Using ŷ = −146.61 + 4.63x, find her residual and interpret it.

Problem 9 Interpreting r Squared ★★★

For the height and weight data the correlation is r = 0.78. Find r² and interpret it.

Problem 10 A Regression from Raw Data ★★★

A company recorded years of experience and salary (thousands of dollars) for six employees: (1, 38), (3, 44), (4, 47), (6, 55), (8, 60), (10, 68). Find the correlation and the least-squares line, and predict the salary for 5 years of experience.

Problem 11 A Curved Residual Pattern ★★★

A line was fitted to data on the speed of a ball (x, seconds after release) and its height. The residual plot is shown.

Is a linear model appropriate? Explain.

Problem 12 A Random Residual Pattern ★★★

A line was fitted to data on a plant’s height (y) and weeks since planting (x). The residual plot is shown.

Is a linear model appropriate? Explain.

Problem 13 An Influential Point ★★★

Eight points follow a clear linear trend. A ninth point at (16, 14) is added. The solid line fits all nine points; the dashed line fits the first eight.

Compare the slopes and the correlations, and state whether the point at (16, 14) is influential.

Problem 14 Outlier or Influential ★★★

Three points are added to a scatterplot that has a strong positive linear pattern for x from 10 to 30. Point A is at x = 20 with a y-value far above the line. Point B is at x = 60, on the line extended. Point C is at x = 60 and far below the line. Which point is an outlier, which is most influential, and which has little effect on the slope?

Problem 15 Extrapolation ★★★

A streaming service finds that, for the 9 years from 2015 (x = 0) to 2023 (x = 8), subscribers (thousands) follow ŷ = 12.4 + 3.8x. A manager predicts the subscribers for 2035 (x = 20). Make the prediction and comment on its reliability.

Problem 16 Standard Deviation of the Residuals ★★★

For the experience and salary data (x = 1, 3, 4, 6, 8, 10; y = 38, 44, 47, 55, 60, 68) the line is ŷ = 34.27 + 3.33x. Find the residuals and the standard deviation of the residuals s = √(∑e²/(n − 2)). Interpret s.

Problem 17 Finding r from r Squared ★★★

A regression of fuel use on vehicle weight has r² = 0.64 and a negative slope. What is the correlation r? Could the correlation be +0.8?

Problem 18 Correlation and Causation ★★★

Over many summer months, a coastal town finds a strong positive correlation between ice cream sales and the number of swimmers rescued. A council member proposes limiting ice cream sales. Explain the flaw in this reasoning.

Problem 19 Reading Computer Output ★★★

A regression of cups sold on temperature for a juice stand gives the following output.

S = 2.4, R-sq = 96.0%. (a) Write the regression equation. (b) Interpret the slope. (c) Interpret R-sq. (d) Interpret S. (e) Find r.

Problem 20 Complete Regression Analysis ★★★

For used cars, age in years has mean 5.2 and standard deviation 2.1; price in thousands of dollars has mean 14.8 and standard deviation 4.5; the correlation is −0.91. (a) Find the line for predicting price from age. (b) Interpret the slope. (c) Predict the price of an 8-year-old car. (d) A particular 8-year-old car sold for $4,100. Find its residual. (e) What percent of the variation in price is explained by age?