AP Statistics Scatterplots and Correlation Worksheet (PDF)

Name the explanatory and response variables: (a) predicting a student’s final exam score from the number of absences; (b) predicting the price of a used car from its mileage.

Describe the association shown in the scatterplot of hours studied and test score.

Describe the direction and form: (a) outdoor temperature and heating costs; (b) hours of sleep and number of mistakes on a test; (c) a person’s age and height from age 1 to 60.

Which is the best estimate of r for the plot: -0.98, -0.5, 0, or 0.9? Explain.

Five students: (hours, score) = (1, 2), (2, 4), (3, 5), (4, 4), (5, 5). The means are 3 and 4; the standard deviations are 1.581 and 1.095. Find r from z-scores.

A study of 40 cities reports r = -0.72 between average winter temperature and heating costs. Interpret r in context.

The correlation between height in inches and weight in pounds is r = 0.62. What is r if height is measured in centimeters and weight in kilograms? Explain.

The correlation between x and y is 0.45. What is the correlation between y and x?

The scatterplot shows a clear arch. r is 0.000. Is there no relationship between the variables? Explain.

The original data (hours, score) had r = 0.934. One score is changed to (8, 40). The new r is 0.179. Explain the change.

The monthly number of ice cream sales and the number of sunburns are strongly positively correlated. Does eating ice cream cause sunburn? Name a lurking variable.

Maya says that because the points on a scatterplot rise steeply, r must be close to 1. Is she right?

Order from weakest to strongest linear association: r = 0.8, r = -0.3, r = -0.95, r = 0.1.

Five students’ weekly screen time (hours) and quiz scores are (2, 80), (4, 74), (6, 71), (8, 65), (10, 60). Describe the association and give r from a calculator.

A researcher wants to see whether the number of hours of exercise per week helps explain resting heart rate. Which variable goes on the horizontal axis? Would a positive or negative association be expected?

A scatterplot of height and weight for all students in a school shows two clusters of points, one for younger and one for older students, each with a weak trend. Explain how this could change r.

A calculator gives r = 0.87 and r squared = 0.757 for a data set. Describe the association, and state what the correlation tells you about causation.

A scatterplot of 10 points has r = 0.82. An 11th point is added far above the line at the right end. Will r likely increase or decrease? Explain.

A scatterplot of 50 cities shows average income (x) and average rent (y). Points rise in a straight pattern with moderate scatter. One city has very high income and rent. Write a description.

A coach records each runner’s weekly mileage and 5K time. Which variable is explanatory? Would you expect a positive or a negative association, and would r be closer to -1 or to 0 for runners of a similar level?