AP Statistics Practice Quiz: Residuals
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 15 questions to check your progress.
Question 1 of 15
All Questions (15)
A) The difference between the actual and predicted value.
B) The predicted value from a model.
C) The actual measured value in a dataset.
D) The slope of the regression line.
Correct Answer: A
Based on the provided content, 'A residual is the difference between the actual and predicted value: residual = y - y-hat.'
A) -5
B) 5
C) 85
D) 90
Correct Answer: B
The residual is calculated as the actual value minus the predicted value (y - y-hat). In this case, it is 90 - 85 = 5.
A) To calculate the correlation coefficient.
B) To determine the slope of the regression line.
C) To investigate the appropriateness of a selected model.
D) To display the original bivariate data.
Correct Answer: C
The provided content states, 'Residual plots can be used to investigate the appropriateness of a selected model.'
A) The model is inappropriate for the data.
B) There is no association between the variables.
C) A linear form of association is appropriate.
D) The data contains significant outliers.
Correct Answer: C
The content specifies that 'Apparent randomness in a residual plot for a linear model suggests a linear form of association.'
A) The actual response values (y).
B) The explanatory variable values or predicted response values.
C) The slope of the regression line.
D) The y-intercept of the regression line.
Correct Answer: B
The definition given is, 'A residual plot is a plot of residuals versus explanatory variable values or predicted response values.'
A) The actual response value.
B) The predicted response value.
C) The explanatory variable value.
D) The average of the response values.
Correct Answer: B
The content defines a residual as the difference between the actual value (y) and the predicted value (y-hat). Therefore, `y-hat` is the predicted value.
A) The linear model is a perfect fit for the data.
B) The association between the variables is likely not linear.
C) The data has a strong positive correlation.
D) The residuals are all equal to zero.
Correct Answer: B
Since 'apparent randomness... suggests a linear form of association,' the absence of randomness (i.e., a clear pattern) implies that a linear model is not appropriate, and the form of association is likely not linear.
A) It shows the exact value of the correlation coefficient.
B) It represents the differences between these two types of responses.
C) It calculates the slope of the best-fit line.
D) It shows only the predicted responses.
Correct Answer: B
The content states that one can 'Represent differences between measured and predicted responses using residual plots.'
A) A clear, U-shaped pattern.
B) A pattern where the residuals consistently increase.
C) Apparent randomness with no discernible pattern.
D) A straight line of points with a positive slope.
Correct Answer: C
The content explicitly states, 'Apparent randomness in a residual plot for a linear model suggests a linear form of association,' indicating this is the desired feature for an appropriate model.
A) The values of the explanatory variable.
B) The values of the predicted response (y-hat).
C) The differences between the actual and predicted values (y - y-hat).
D) The values of the actual response (y).
Correct Answer: C
A residual plot graphs the residuals. A residual is defined as 'the difference between the actual and predicted value: residual = y - y-hat.'
A) 22
B) -28
C) 28
D) -22
Correct Answer: C
The formula is residual = y - y-hat. We are given residual = -3 and y = 25. So, -3 = 25 - y-hat. Solving for y-hat gives y-hat = 25 - (-3) = 28.
A) By calculating the R-squared value from the plot.
B) By observing whether the plot shows a random scatter or a distinct pattern.
C) By finding the average of all the residuals.
D) By counting the number of points above and below the horizontal axis.
Correct Answer: B
The content notes that one can 'Describe the form of association of bivariate data using residual plots' and that 'Apparent randomness... suggests a linear form.' Therefore, observing the pattern (or lack thereof) is how the form of association is described.
A) A residual is the predicted value minus the actual value.
B) A residual plot graphs the actual values against the predicted values.
C) A residual is the difference between the actual and predicted value.
D) A random pattern in a residual plot indicates a non-linear model is needed.
Correct Answer: C
The content directly states, 'A residual is the difference between the actual and predicted value: residual = y - y-hat.' Option A reverses the subtraction. Option B is a different type of plot. Option D is the opposite of what the content says.
A) The linear model is appropriate because the points form a clear shape.
B) The linear model is likely inappropriate because the residuals are not randomly scattered.
C) The association between the variables is perfectly linear.
D) The sample size was too small to make a conclusion.
Correct Answer: B
The content states that 'Apparent randomness in a residual plot for a linear model suggests a linear form of association.' A distinct pattern, like a parabola, indicates the absence of randomness, suggesting a linear model is not appropriate.
A) It magnifies the deviations of the data from the model, making patterns easier to see.
B) It directly calculates the p-value for the slope of the regression line.
C) It proves that the relationship between the variables is causal.
D) It provides the exact equation for the line of best fit.
Correct Answer: A
Based on the content, residual plots are used to 'investigate the appropriateness of a selected model' by looking for patterns. A residual plot removes the overall linear trend, which effectively magnifies the remaining patterns (or lack thereof) in the errors, making it easier to assess the model's fit. This is the underlying reason why it's a useful investigation tool.