AP Statistics Flashcards: Linear Regression Models
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
How do you calculate a predicted response value using a linear regression model?
To calculate a predicted response value (y-hat), you substitute the value of the explanatory variable (x) into the equation y-hat = a + bx.
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How do you calculate a predicted response value using a linear regression model?
To calculate a predicted response value (y-hat), you substitute the value of the explanatory variable (x) into the equation y-hat = a + bx.
A researcher uses a regression line to predict a student's test score based on hours studied. If they predict a score for a student who studied for 20 hours, but the original data only included students who studied between 1 and 10 hours, what is this an example of?
This is an example of extrapolation, and the resulting prediction is less reliable.
What is the relationship between the explanatory variable and the response variable in a simple linear regression model?
The explanatory variable (x) is used in the model's equation to predict the value of the response variable (y).
Define extrapolation.
Extrapolation is predicting a response for an x-value outside the interval used to determine the regression line.
Why is extrapolation considered less reliable?
It is considered less reliable because there is no guarantee the linear relationship holds for x-values outside the range of the original data.
In the equation y-hat = a + bx, what do the variables 'a' and 'b' represent?
In the linear regression equation, 'a' represents the y-intercept and 'b' represents the slope of the regression line.
What does 'y-hat' represent in a linear regression model?
The term 'y-hat' represents the predicted response value that is calculated from the linear regression model equation.
What is a simple linear regression model?
A simple linear regression model is an equation that uses an explanatory variable, x, to predict a response variable, y.
What is the primary goal when using the equation y-hat = a + bx?
The primary goal is to calculate a predicted response value (y-hat) based on a given value for the explanatory variable (x).
What is the formula for a predicted response value in a linear regression model?
The predicted response value is calculated as y-hat = a + bx, where 'a' is the y-intercept and 'b' is the slope.