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Unit 5 · Regression Analysis Flashcards Cheat Sheet Essentials Visual Review MC Practice FRQ Practice

AP Statistics Unit 5 Essentials

The must-know terms and core concepts for Unit 5: Regression Analysis. Every vocabulary word and idea you need to master.

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Key Concept 1
Describe a two-variable relationship before you model it
With two quantitative variables, always start with a scatterplot and describe its direction, form, strength, and unusual features. The correlation r then summarizes the strength and direction of the linear relationship on a −1 to 1 scale. But r has limits: it has no units, is not resistant to outliers, only captures linear patterns, and never proves causation — a strong relationship can be driven by a lurking variable.
Scatterplots Correlation Association
Key Concept 2
The least-squares line models the relationship and makes predictions
The least-squares regression line ŷ = a + bx is the line that minimizes the sum of squared residuals; its slope is b = r·(s_y/s_x) and it passes through (x̄, ȳ). The most-tested skill is interpreting the slope and y-intercept in context — the predicted change in y per unit of x, and the predicted y when x = 0 — and using the equation to predict, while avoiding extrapolation beyond the range of the data.
Regression Line Slope & Intercept Prediction
Key Concept 3
Assess the fit with residuals, r², and a look for influential points
A residual (observed − predicted) measures the model's error at each point, and a residual plot is the key diagnostic: random scatter around zero supports a linear model, while a curved or fanning pattern warns that it does not fit. r² reports the proportion of the variation in y explained by the line, the residual standard deviation s gives the typical prediction error, and influential (high-leverage) points can distort the entire model.
Residuals r-squared Influential Points
Explanatory variable
The predictor variable, plotted on the x-axis.
Two Variables
Response variable
The outcome variable being predicted, plotted on the y-axis.
Two Variables
Scatterplot
A graph of paired (x, y) values used to display a relationship between two quantitative variables.
Two Variables
Direction, form, strength
The features used to describe a scatterplot, along with any unusual points.
Two Variables
Correlation (r)
A number from −1 to 1 measuring the strength and direction of a linear relationship.
Correlation
Properties of r
No units, symmetric in x and y, only measures linear association, and not resistant to outliers.
Correlation
Lurking variable
A variable, not among those studied, that influences the relationship and can create a misleading correlation.
Correlation
Causation
A cause-and-effect link, which correlation alone cannot establish.
Correlation
Least-squares regression line
The line ŷ = a + bx that minimizes the sum of the squared residuals.
Regression
Slope (b)
The predicted change in y for each one-unit increase in x; b = r·(s_y/s_x).
Regression
y-intercept (a)
The predicted value of y when x = 0.
Regression
Predicted value (ŷ)
The value of y estimated by the regression line for a given x.
Regression
Point of averages
(x̄, ȳ), through which every least-squares line passes.
Regression
Extrapolation
Using the model to predict for x-values outside the range of the data; unreliable.
Prediction
Residual
The difference between an observed and predicted value, y − ŷ.
Residuals
Residual plot
A plot of residuals versus x (or ŷ); no pattern supports a linear model.
Residuals
Standard deviation of residuals (s)
The typical size of a residual, in the units of y.
Residuals
Coefficient of determination (r²)
The proportion of the variation in y explained by the linear model, from 0 to 1.
Assessing Fit
Outlier (regression)
A point that lies far from the overall linear pattern, often with a large residual.
Assessing Fit
High-leverage point
A point with an x-value far from the mean of x, which can strongly affect the line.
Assessing Fit
Influential point
A point whose removal would substantially change the slope, intercept, or correlation.
Assessing Fit
Computer regression output
A table listing the intercept and slope coefficients, r², and s for a fitted model.
Assessing Fit