# Bivariate Regression

**Topics:**Regression analysis, Linear regression, Errors and residuals in statistics

**Pages:**30 (4412 words)

**Published:**April 28, 2013

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SPSS for Windows® Intermediate & Advanced Applied Statistics Zayed University Office of Research SPSS for Windows® Workshop Series Presented by Dr. Maher Khelifa Associate Professor Department of Humanities and Social Sciences College of Arts and Sciences

© Dr. Maher Khelifa

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Bi-variate Linear Regression

(Simple Linear Regression)

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

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Many statistical indices summarize information about particular

phenomena under study.

For example, the Pearson (r) summarizes the magnitude of a linear

relationship between pairs of variables.

However, one major scientific research objective is to “explain”,

“predict”, or “control” phenomena.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

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To explain, predict, and control phenomena, we must not view

variables in isolation.

How variables do or do not relate to other variables provide us with

valuable clues which allow us to:

Explain Predict, and Control

The examination of these relationships leads to the formation of

networks of variables that provide the basis for the development of theories about a phenomenon.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

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Linear regression analyses are statistical procedures which allow us to

move from description to explanation, prediction, and possibly control.

Bivariate linear regression analysis is the simplest linear regression

procedure.

The procedure is called simple linear regression because the

model:

explores the predictive or explanatory relationship for only 2 variables, and Examines only linear relationships.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

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Simple linear regression focuses on explaining/ predicting one of the

variables on the basis of information on the other variable.

The regression model thus examines changes in one variable as a

function of changes or differences in values of the other variable.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

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The regression model labels variables according to their role:

Dependent Variable (Criterion Variable): The variable whose variation we want to explain or predict. Independent Variable (Predictor Variable): Variable used to predict systematic changes in the dependent/criterion variable.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

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To summarize:

The regression analysis aims to determine how, and to what extent, the criterion variable varies as a function of changes in the predictor variable. The criterion variable in a study is easily identifiable. It is the variable of primary interest, the one we want to explain or predict.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

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Several points should be remembered in conceptualizing simple linear

regression:

Data must be collected on two variables under investigation. The dependent and independent variables should be quantitative (categorical variables need to recoded to binary variables). The criterion variable is designated as Y and the predictor variable as X. The data analyzed are the same as in correlational analysis. The test still examines covariability and variability but with different assumptions and intentions.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

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The relationship between X & Y explored by the linear regression is described

by the general linear model.

The model applies to both experimental and non-experimental settings. The model has both explanatory and predictive capabilities. The word linear indicates that the model produces a straight line.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

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The mathematical equation for the...

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