AP Statistics Two Variable Quiz – Free PDF

Contents

This ap statistics two variable quiz asks 10 multiple-choice questions on regression analysis, and each answer comes with a short explanation.

Ten multiple-choice questions on regression: explanatory and response variables, describing scatterplots, correlation, slope, r squared, residuals, residual plots, extrapolation and influential points. Each has exactly one correct answer, and the explanation names the common mistake.

AP StatisticsCommon Core: AP Statistics Unit 5 (2026-27)

🎯 Regression Analysis – AP Statistics math quiz

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Question 1

A researcher predicts a student's final exam score from the number of hours the student studied. Which variable is the response variable?

A The final exam score

B The number of hours studied

C The student's name

D The correlation r

Question 2

Which description of the scatterplot is best?

Price and age of 10 used cars.

A Positive, linear and strong

B Negative, curved and weak

C Negative, linear and strong

D Positive, linear and weak

Question 3

Which correlation indicates the strongest linear relationship?

A r = -0.92

B r = 0.80

C r = 0.15

D r = -0.50

Question 4

The line is \(\hat{y}=-62.26+1.286x\), where x is the high temperature in °F and y is cups sold. What does the slope mean?

Least-squares line for lemonade sales: y-hat = -62.26 + 1.286x.

A Each additional degree is associated with about 1.286 more cups predicted

B When the temperature is 0 °F, 1.286 cups are sold

C 1.286% of the variation in cups is explained by temperature

D The temperature rises by 1.286 degrees for each cup sold

Question 5

A regression has \(r^{2}=0.49\). Which statement is correct?

A 49% of the data points lie on the line

B 49% of the variation in y is explained by the linear relationship with x

C The correlation is 0.49

D y is predicted correctly 49% of the time

Question 6

The line predicts \(\hat{y}=47\) for a point whose actual value is \(y=52\). What is the residual?

A -5

B 5

C 99

D 1.1

Question 7

What does this residual plot indicate?

Residual plot for a least-squares line.

A A linear model is appropriate because the residuals sum to zero

B A linear model is appropriate because the residuals vary randomly

C The correlation must be exactly 0

D A linear model is not appropriate because there is a curved pattern

Question 8

A line fit to ages 5 to 12 predicts a child's height. A student uses it to predict the height at age 40. This is an example of

A Interpolation, which is reliable

B A residual calculation

C Computing the correlation

D Extrapolation, which is unreliable

Question 9

What would most likely happen to the slope of the least-squares line if the circled point at (20, 14) were removed?

One point lies far to the right of the others.

A The slope would decrease

B The slope would increase

C The slope would stay the same

D The slope would change sign

Question 10

For a data set, \(r=0.6\), \(s_x=5\) and \(s_y=10\). What is the slope of the least-squares line?

A 0.3

B 3.0

C 1.2

D 0.6

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Describe a scatterplot by direction, form, strength and unusual points, in context.
The correlation r is between -1 and 1, has no units, and measures only linear association.
The least-squares line has slope b = r (s_y / s_x) and passes through (x-bar, y-bar).
A residual is y – y-hat; a residual plot with no pattern supports a linear model.
r squared is the percent of the variation in y explained by the linear relationship with x.