AP Statistics Flashcards: Analyzing Departures from Linearity
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
What is the primary purpose of transforming variables in a regression analysis?
The primary purpose of transforming variables is to create a data set that is more linear, making it more appropriate for a linear regression model.
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What is the primary purpose of transforming variables in a regression analysis?
The primary purpose of transforming variables is to create a data set that is more linear, making it more appropriate for a linear regression model.
What is the 'test' to determine if a point is influential?
To test if a point is influential, you can compare the regression model with the point included to the model with the point removed to see if it changes substantially.
How does the r-squared value indicate a better model fit after a data transformation?
An r-squared value that is closer to 1 after a transformation suggests that the new, more linear model is a more appropriate fit for the data.
Define an influential point.
An influential point is a point that, if removed from the data set, would cause a substantial change to the regression model (e.g., slope, y-intercept, r-squared).
What are two key indicators that a data transformation has resulted in a more appropriate model?
A more appropriate model is indicated by a residual plot with increased randomness and an r-squared value that is closer to 1.
How can an influential point affect a regression model?
An influential point can substantially change the regression model's slope, y-intercept, and/or correlation (r) and coefficient of determination (r-squared).
What is the defining characteristic of an outlier's residual?
An outlier has a large residual, meaning its actual y-value is far from the y-value predicted by the least-squares regression line.
How do you identify a high-leverage point by looking at the x-values?
You can identify a high-leverage point by finding an observation with an x-value that is far from the mean of the other x-values.
What is a high-leverage point?
A high-leverage point is an observation that has a substantially larger or smaller x-value than the other observations in the data set.
After a data transformation, what change in the residual plot suggests the new model is more appropriate?
A more appropriate model is suggested by increased randomness and a lack of a clear pattern in the residual plot after the transformation.
What is an outlier in regression?
An outlier is a data point that does not follow the general trend of the data and is characterized by having a large residual.
What is the relationship between high-leverage points and influential points?
Points with high leverage have the potential to be influential points, but they are only influential if their removal substantially changes the regression model.
How do you calculate a predicted response using a regression line for a transformed data set?
First, apply the same transformation to the given x-value, then substitute that transformed value into the least-squares regression line to find the predicted response.
What is the first step in identifying influential points in a regression analysis?
The first step is often to create a scatterplot to visually inspect for any unusual points, such as outliers or high-leverage points, that might be influential.