Review AP Statistics Unit 5 to build your skills in describing and modeling relationships between two quantitative variables. This unit covers scatterplots, correlation, the least-squares regression line, residuals, and r-squared from topics 5.1 through 5.5.
Use the topic guides, key terms, and practice questions available on this page to work through every concept before your exam.
What is AP Statistics Unit 5?
Unit 5 teaches you how to analyze the relationship between two quantitative variables. You start by reading and describing scatterplots, then use the correlation coefficient to quantify linear association, fit a least-squares regression line to make predictions, and use residuals and residual plots to judge whether a linear model is appropriate.
Every scatterplot description must address four things: form (linear or non-linear), direction (positive or negative), strength (strong, moderate, or weak), and unusual features such as outliers or clusters. The explanatory variable always goes on the x-axis; the response variable goes on the y-axis.
The correlation coefficient r measures the strength and direction of a linear association on a scale from -1 to 1. The least-squares regression line y-hat = a + bx uses that relationship to produce predicted values. The slope b is the predicted change in y for each one-unit increase in x, and r-squared tells you what proportion of variation in y the model explains.
A residual equals the observed y minus the predicted y-hat. Positive residuals mean the model underpredicted; negative residuals mean it overpredicted. A residual plot with no clear pattern confirms that a linear model is appropriate. Curvature in the residual plot signals that a different model may fit better.
Every skill in this unit follows the same sequence: look at the scatterplot to decide if a linear model makes sense, quantify the association with r, fit the LSRL to make predictions, and then check residuals to confirm the model is appropriate. Skipping any step, especially the residual check, is a common source of lost points on the exam.
Construct scatterplots with the explanatory variable on the x-axis and the response variable on the y-axis. Describe the association using form, direction, strength, and unusual features.
Interpret the correlation coefficient r as a measure of the strength and direction of a linear association. Remember that r is unit-free and that correlation does not imply causation.
Use y-hat = a + bx to calculate predicted response values. Interpret slope and y-intercept in context, and distinguish between reliable interpolation and less reliable extrapolation.
Calculate residuals using y - y-hat, interpret their sign, and use residual plots to determine whether a linear model is appropriate for the data.
Identify properties of the LSRL, interpret slope and y-intercept in context, and use r-squared to describe the proportion of variation in the response variable explained by the model.
A scatterplot displays bivariate quantitative data as ordered pairs. The explanatory variable is on the x-axis and the response variable is on the y-axis. To describe a scatterplot completely, address form, direction, strength, and unusual features every time.
Given a scatterplot of study hours (x) and test scores (y), can you write a complete four-part description including form, direction, strength, and any unusual features?
| Feature | What to look for | Example language |
|---|---|---|
| Form | Do points follow a line or a curve? | The association appears linear. |
| Direction | Does y increase or decrease as x increases? | There is a positive association. |
| Strength | How tightly do points cluster around the pattern? | The association is moderately strong. |
| Unusual features | Any outliers or clusters? | There is one outlier at approximately (12, 95). |
The correlation coefficient r summarizes the strength and direction of the linear association between two quantitative variables. It is always between -1 and 1, has no units, and does not change if you switch the units of either variable.
If r = -0.91 for the relationship between hours of TV watched and GPA, what does that value tell you about direction, strength, and causation?
| r value | Interpretation |
|---|---|
| r = 1 | Perfect positive linear association |
| r = 0.85 | Strong positive linear association |
| r = 0 | No linear association |
| r = -0.72 | Moderate negative linear association |
| r = -1 | Perfect negative linear association |
When a scatterplot shows a linear form, you can model the relationship with y-hat = a + bx. Plug an x-value into the equation to get a predicted response. Predictions are more reliable when x is within the range of the data used to build the model.
Given y-hat = 12.3 + 4.2x where x is study hours and y is exam score, predict the score for 5 hours of study and interpret the slope in context.
| Prediction type | x-value location | Reliability |
|---|---|---|
| Interpolation | Within observed x range | Generally reliable |
| Extrapolation | Outside observed x range | Less reliable; use with caution |
A residual measures how far an observed value is from the model's prediction. Residual = y - y-hat. Residual plots are used to check whether a linear model is appropriate for the data.
A student's predicted score is 78 but the actual score is 83. Calculate the residual and explain what it means in context.
| Residual sign | Model behavior | Meaning |
|---|---|---|
| Positive (y > y-hat) | Underpredicts | Actual value is above the regression line |
| Negative (y < y-hat) | Overpredicts | Actual value is below the regression line |
| Zero | Exact prediction | Point falls exactly on the regression line |
The least-squares regression line (LSRL) is the specific linear model that minimizes the sum of squared residuals. It always passes through the point (x-bar, y-bar). The coefficient of determination r-squared describes how well the model fits the data.
A regression output shows r-squared = 0.74. Write a complete interpretation of this value in the context of hours of exercise (x) and resting heart rate (y).
| Statistic | What it measures | Range |
|---|---|---|
| r | Strength and direction of linear association | -1 to 1 |
| r-squared | Proportion of variation in y explained by x | 0 to 1 |
| Slope b | Predicted change in y per one-unit increase in x | Any real number |
| Residual | Difference between observed and predicted y | Any real number |
| Term | Definition |
|---|---|
| slope of a regression model | The predicted change in the response variable for each one-unit increase in the explanatory variable. Always interpret in context with units. |
r measures the strength and direction of the linear association; r-squared measures the proportion of variation in y explained by the model. Do not use them interchangeably. If r = 0.9, then r-squared = 0.81, not 0.9.
A strong r, even r = 0.99, does not mean one variable causes the other. Always say 'associated with' rather than 'causes' unless the study design supports a causal claim.
Leaving out one of the four components (form, direction, strength, unusual features) costs points. Even if there are no unusual features, state that explicitly.
Fitting a regression line without checking the residual plot is incomplete analysis. A curved residual plot means the linear model is not appropriate, regardless of how strong r appears.
Using the regression equation to predict y for an x-value outside the observed data range is extrapolation. Always note that the prediction is less reliable when extrapolating.
AP Statistics consistently asks you to interpret statistical values in context, not just state formulas. For Unit 5, that means writing slope interpretations that name both variables and include units, r-squared interpretations that reference the proportion of variation explained, and residual interpretations that state whether the model over- or underpredicted and by how much.
A common task pattern asks you to use a residual plot to decide whether a linear model is appropriate. You must describe what you see in the residual plot (random scatter or a curved pattern) and connect that observation to a conclusion about the model, not just say the plot looks good or bad.
Questions may present a strong correlation and ask you to evaluate a causal claim. You are expected to recognize that correlation alone does not establish causation and to identify that a lurking variable or the study design may explain the association.
For any scatterplot, write a description that addresses form, direction, strength, and unusual features. Do not skip any of the four components.
State the direction and strength of the linear association using r. Confirm that r is unit-free and that a strong r does not establish causation.
Plug an x-value into the regression equation to get a predicted response. Flag any prediction that requires extrapolation beyond the observed data range.
Compute residual = y - y-hat. State whether the model underpredicted or overpredicted and by how much, in context.
Identify whether the residual plot shows random scatter (linear model appropriate) or a curved pattern (linear model not appropriate).
For slope: predicted change in y per one-unit increase in x. For y-intercept: predicted y when x = 0 (note if not meaningful). For r-squared: proportion of variation in y explained by the linear relationship with x.
Read the 5.1 topic guide and practice writing four-part scatterplot descriptions. For each practice scatterplot, write out form, direction, strength, and unusual features before checking your answer.
Review the 5.2 topic guide. Practice interpreting r values in context, and write out why a given r does not imply causation. Use the comparison table in the review notes to anchor your interpretations.
Work through the 5.3 topic guide. Practice plugging x-values into y-hat = a + bx, writing slope and y-intercept interpretations in context, and identifying whether a prediction is interpolation or extrapolation.
Review the 5.4 topic guide. Calculate residuals from given data, interpret their sign in context, and practice reading residual plots to decide whether a linear model is appropriate.
Study the 5.5 topic guide. Focus on writing complete interpretations of slope, y-intercept, and r-squared in context. Use the AP Statistics score calculator to estimate how your overall performance maps to a score.
Open the individual guides for Unit 5 when you want a closer review of one topic.
Use AP-style practice after you review the notes so you can check what you understand.
Practice free-response reasoning and compare your answer with scoring guidance.
Watch past review streams filtered to Unit 5 when you want a video walkthrough.
Open the Fiveable one-page unit review, then explore visual cheatsheets for a quick refresher.
Estimate your broader AP score goal after you review the course and exam format.
Print the unit cheatsheets ($3) or full-length exam ($12) for Unit 5. Yours to keep, no subscription needed.
get printablesAP Stats Unit 5, Regression Analysis, contains 5 topics covering scatterplots; form, direction, strength, and unusual features; correlation; linear regression models; interpolation and extrapolation; residuals and residual plots; and least-squares regression. These are the Fall 2026 CED topics used for the May 2027 exam.
Unit 5 accounts for 10–20% of the multiple-choice section. That range is a section weight, not a promise that every practice form will use the same percentage, so review the full unit rather than trying to predict one exact question count.
By the end of Unit 5, you should be able to describe an association in context, interpret correlation and regression coefficients, calculate and interpret residuals, use residual plots to assess a linear model, and explain the meaning of the coefficient of determination. The exam rewards the method and the interpretation, so practice writing what a result means in the problem's context instead of stopping at a calculator output.
Common Unit 5 mistakes include claiming correlation proves causation, interpreting correlation as a slope, extrapolating without acknowledging the risk, reversing observed minus predicted when finding a residual, or describing r-squared without naming the response variable. Slow down long enough to identify the variables, population, and requested conclusion before calculating.
Start with the vocabulary and conditions, then mix short calculations with full-sentence interpretations. For each missed question, label whether the problem was choosing a method, doing the calculation, or interpreting the result. Finish with timed mixed practice so you have to recognize the method without a topic label.
Regression combines graphical analysis with contextual interpretation and can appear in multiple-choice sets or the multi-focus free-response questions.