APEX AP Stats 3.3.8 Uses of the Regression Line Study Guide

What is the purpose of a least-squares regression line?

To predict the y values in relation to the x values.

What is a residual in regression analysis?

The difference between the observed (y) values and the predicted (y) values.

What does a residual plot indicate?

It determines if the least-squares regression line is useful.

What is the regression coefficient?

The slope of the linear regression line.

Define interpolation in the context of regression.

Predicting a value of y using a value of x that falls within the min and max values of x observed in the original data.

What is extrapolation in regression analysis?

Predicting a value of y using a value of x that falls outside the range of x-values observed in the original data.

Why is extrapolation less reliable than interpolation?

It ventures into unknown territory, making predictions more uncertain as you go farther out of the observed range.

y - y-hat =

0

What is (y-y-hat=0) aka?

y=0

What does it mean if the point is above y=0?

positive residuals

What does it mean if the point is below y=0?

negative residual

What does it mean if there is no observable pattern in a residual plot?

It indicates a strong correlation.

What does an observable pattern in a residual plot suggest?

It suggests a non-linear correlation.

What should be done if the residual plot shows a slight curving pattern?

Consider changing the data to fit the least-squares regression line for that range of x.

What is indicated if the least-squares regression line is not useful for making predictions?

The data may be better modeled by a quadratic or exponential equation.

What are observed (y) values?

The actual values collected from the data.

What are predicted (y) values?

The values estimated by the regression model based on the x values.

What is the significance of the highest point in a residual plot?

It represents the individual with the highest positive residual.

What does the lowest point in a residual plot represent?

It represents the individual with the lowest negative residual.

What does the term 'non-linear regression models' refer to?

Models that do not assume a linear relationship between variables.

What is the relationship between residuals and the usefulness of a regression line?

Residuals help assess whether the regression line is a good fit for the data.