AP Statistics Flashcards: Least Squares Regression
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 19 cards to help you master important concepts.
A model predicts house price from square footage. If the slope is 150, what is the interpretation?
For each additional square foot of space, the predicted price of the house increases by $150.
Card 1 of 19
All Flashcards (19)
A model predicts house price from square footage. If the slope is 150, what is the interpretation?
For each additional square foot of space, the predicted price of the house increases by $150.
A regression model has an r-squared value of 0.81. What does this mean?
This means that 81% of the variation in the response variable can be explained by the linear model with the explanatory variable.
How do you interpret the y-intercept of a least-squares regression line?
The y-intercept is the predicted value of the response variable (y) when the explanatory variable (x) is equal to 0.
What specific point is every least-squares regression line guaranteed to pass through?
Every least-squares regression line passes through the point (x-bar, y-bar), which represents the mean of the explanatory and response variables.
If the mean study time (x-bar) is 5 hours and the mean test score (y-bar) is 82, what point must be on the regression line predicting score from study time?
The point (5 hours, 82 score) must be on the least-squares regression line.
What are the parameters that we estimate for a least-squares regression line model?
We estimate the true slope and y-intercept of the population regression line.
A model predicts a person's weight from their height. The y-intercept is -100 pounds. Why is this interpretation not logical?
This y-intercept is not logical because a height of 0 inches is impossible, and it results in a nonsensical predicted weight of -100 pounds.
Define the slope of the regression line.
The slope is the amount the predicted y-value changes for every one-unit increase in the x-value.
What is r-squared, the coefficient of determination?
r-squared is the proportion of the variation in the response variable (y) that is explained by the least-squares regression model with the explanatory variable (x).
What is the primary goal when we estimate the parameters for a least-squares regression line?
The goal is to find the line that best fits the data by minimizing the sum of the squared differences between the observed and predicted values.
A model predicts GPA based on hours of sleep, with a y-intercept of 1.5. Interpret this value.
For a student who gets 0 hours of sleep, the predicted GPA is 1.5.
What quantity does the least-squares regression model minimize?
The model minimizes the sum of the squared residuals (the squared differences between observed and predicted y-values).
What are the coefficients of a least-squares regression model?
The coefficients are the estimated slope and y-intercept of the regression line.
What is the coefficient of determination?
The coefficient of determination, or r-squared, is the proportion of variation in the response variable explained by the model.
What is the relationship between the coefficients of the model and the parameters of the model?
The coefficients (the calculated slope and y-intercept from the sample data) are the estimates for the true parameters of the population model.
How is the slope (b) of the regression line calculated using correlation and standard deviations?
The slope, b, is calculated with the formula b = r(sy/sx), where r is the correlation coefficient, sy is the standard deviation of y, and sx is the standard deviation of x.
Define the y-intercept of the regression line.
The y-intercept is the predicted y-value when the explanatory variable is 0.
How do you interpret the slope of a least-squares regression line?
The slope represents the predicted change in the y-value for every one-unit increase in the x-value.
Why might the y-intercept of a regression line not have a logical interpretation?
The y-intercept may not be logical if a value of 0 for the explanatory variable is not meaningful or is far outside the range of the collected data (extrapolation).