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Quizzes > Mathematics

AP Stats Chapter 3 Test: Correlation and Regression

20 quick questions in a correlation and regression quiz. Instant results.

Editorial: Review CompletedCreated By: Yousef SoftUpdated Aug 25, 2025
Difficulty: Moderate
Grade: Grade 12
Study OutcomesCheat Sheet
Paper art themed trivia quiz on Chapter 3 AP Statistics for high school students.

This AP Stats Chapter 3 quiz helps you practice correlation and linear regression, so you can read scatterplots and interpret r, slope, intercept, and residuals with confidence. See your answers right away and learn from any misses. For more practice, try a statistics quiz with answers or explore how studies work in a research methods quiz.

In a study relating hours studied (x) and exam score (y), which is the appropriate designation of variables for a regression analysis?
x is the explanatory variable; y is the response variable.
x is the response variable; y is the explanatory variable.
Both x and y are explanatory variables.
Both x and y are response variables.
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A scatterplot shows a linear pattern with points tightly clustered around an upward-sloping line. Which description best fits the association?
Strong, negative, linear association.
Weak, positive, nonlinear association.
Strong, positive, linear association.
No association.
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Correlation r measures the strength and direction of a linear relationship between two quantitative variables.
False
True
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Changing the units of x from meters to centimeters will change the correlation r between x and y.
False
True
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Given the least-squares regression line y-hat = 12 + 3.5x, what is the predicted y when x = 4?
26 + 3.5
26.5
26
26 + 14 = 40
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The y-intercept of a regression line is always meaningful in context.
True
False
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A residual is defined as observed y minus predicted y.
True
False
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In context of predicting weight (y, in kg) from height (x, in cm), interpret the slope b = 0.7 of the LSRL.
For each additional cm of height, actual weight increases by 0.7 kg.
For each additional cm of height, predicted weight increases by 0.7 kg.
For each 10 cm of height, predicted weight increases by 0.7 kg.
For each additional kg of weight, predicted height increases by 0.7 cm.
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A residual plot that shows a clear curved pattern indicates that a linear model is appropriate.
True
False
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If r^2 = 0.64 in a regression of y on x, what is the correct interpretation?
64% of the variation in y is explained by the linear relationship with x.
64% of the data points lie on the regression line.
y increases by 64% for each unit increase in x.
The correlation is 0.64 regardless of direction.
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Which regression line property is guaranteed for the least-squares regression of y on x?
The line passes through the origin (0,0).
The intercept equals the median of y.
The line passes through (x-bar, y-bar).
The slope equals the ratio of the standard deviations, s_y / s_x.
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The least-squares regression line minimizes the sum of the absolute values of the residuals.
False
True
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If every value of y is increased by 10, what happens to the slope and correlation in the regression of y on x?
Slope increases by 10; correlation increases by 10.
Slope unchanged; correlation increases by 10.
Slope unchanged; correlation unchanged.
Slope increases by 10; correlation unchanged.
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An outlier in the x-direction (a high-leverage point) will always decrease the slope of the regression line.
True
False
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Which point is most likely to be influential in a least-squares regression?
A point with an extreme x-value that lies far from the existing trend.
A point near the center of the x-values that lies exactly on the regression line.
Any point with a small residual.
A point with an average x-value and large positive residual.
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Given y-hat = a + bx with b = r * (s_y / s_x), which change to x will reverse the sign of the correlation?
Multiplying all x-values by -1.
Subtracting the mean from all x-values.
Adding 5 to all x-values.
Multiplying all x-values by 2.
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A data set follows an exponential model y = A * B^x with B > 1. Which transformation will linearize the relationship?
Plot log(y) versus log(x).
Plot log(y) versus x.
Plot 1/y versus x.
Plot y versus log(x).
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A data set follows a power model y = A * x^k. Which transformation will produce a linear relationship?
Plot y versus log(x).
Plot y versus 1/x.
Plot log(y) versus x.
Plot log(y) versus log(x).
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The regression of x on y is the same line as the regression of y on x.
False
True
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For the model log(y) = a + b x, what is the multiplicative change in y for a one-unit increase in x?
y is multiplied by 10^b (if log base 10) or e^b (if natural log).
y decreases by b percent.
y is multiplied by b^x.
y increases by b units.
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Study Outcomes

  1. Analyze statistical data sets to identify trends and outliers.
  2. Calculate and interpret summary statistics including mean, median, and standard deviation.
  3. Apply probability models to real-world scenarios.
  4. Evaluate the assumptions behind common statistical tests.
  5. Interpret graphical data representations to support statistical conclusions.

Chapter 3 AP Stats Practice Test Cheat Sheet

  1. Understanding Scatterplots - Think of scatterplots as the ultimate matchmaking app for numbers, showing how two variables pair up. They make it easy to spot tight friendships (positive relationships), shady breakups (negative relationships), and those loners (outliers).
  2. Correlation Coefficient (r) - This magic number between - 1 and 1 tells you how strongly two variables are BFFs or frenemies. A value near 1 means they're inseparable, while - 1 says they're total opposites; zero means they barely notice each other.
  3. Interpreting Regression Lines - Imagine drawing a straight line through a cloud of points to predict where future points might land - that's your regression line. The formula ŷ = a + bx uses 'a' for the starting height (y‑intercept) and 'b' for the slope, showing how much ŷ changes when x moves by one unit.
  4. Residuals and Residual Plots - Residuals are the "oops" distances between what you observed and what your line predicted. Plotting these leftovers helps you check if your model is behaving or if it's hiding a curve or pattern you missed.
  5. Influential Observations - Some data points pack a punch and can swing your regression line like a heavyweight boxer. Spotting these influencers is key because they can make your model look stronger or weaker than it really is.
  6. Explanatory vs. Response Variables - In any bivariate pairing, one variable plays detective (explanatory) and the other reacts (response). Pinning down who's who clarifies cause-and-effect vibes and keeps your conclusions on track.
  7. Coefficient of Determination (r²) - r² is your model's report card, revealing the percentage of response-variable drama explained by the explanatory star. A high r² means your line has impressive show-and-tell skills; a low r² hints you might need a new script.
  8. Limits of Correlation - Correlation is a powerful tool, but remember: it measures only straight-line BFF behavior and never guarantees a cause-and-effect party. Non-linear antics and third-party crashers (lurking variables) can fool you if you're not careful.
  9. Identifying Outliers in Bivariate Data - Outliers are the wild cards that can skew your correlation and regression vibe. Spotting them early lets you decide if they're meaningful exceptions or data-entry gremlins to ditch.
  10. Understanding Lurking Variables - Lurking variables sneak into your analysis, influencing both explanatory and response variables behind the scenes. Calling them out ensures your data drama isn't hijacked by unseen plot twists.
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