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Boundless Statistics
Correlation and Regression
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Section 6

Multiple Regression

Book Version 1
By Boundless
Boundless Statistics
Statistics
by Boundless
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12 concepts
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Multiple Regression Models

Multiple regression is used to find an equation that best predicts the $Y$ variable as a linear function of the multiple $X$ variables.

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Estimating and Making Inferences About the Slope

The purpose of a multiple regression is to find an equation that best predicts the $Y$ variable as a linear function of the $X$ variables.

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Evaluating Model Utility

The results of multiple regression should be viewed with caution.

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Using the Model for Estimation and Prediction

Standard multiple regression involves several independent variables predicting the dependent variable.

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Interaction Models

In regression analysis, an interaction may arise when considering the relationship among three or more variables.

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Polynomial Regression

The goal of polynomial regression is to model a non-linear relationship between the independent and dependent variables.

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Qualitative Variable Models

Dummy, or qualitative variables, often act as independent variables in regression and affect the results of the dependent variables.

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Models with Both Quantitative and Qualitative Variables

A regression model that contains a mixture of quantitative and qualitative variables is called an Analysis of Covariance (ANCOVA) model.

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Comparing Nested Models

Multilevel (nested) models are appropriate for research designs where data for participants are organized at more than one level.

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Stepwise Regression

Stepwise regression is a method of regression modeling in which the choice of predictive variables is carried out by an automatic procedure.

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Checking the Model and Assumptions

There are a number of assumptions that must be made when using multiple regression models.

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Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

Some problems with multiple regression include multicollinearity, variable selection, and improper extrapolation assumptions.

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