1 / 18

# LINEAR REGRESSION: What it Is and How it Works - PowerPoint PPT Presentation

LINEAR REGRESSION: What it Is and How it Works. Overview. What is Bivariate Linear Regression ? The Regression Equation How It’s Based on r Assumptions. What is Bivariate Linear Regression ?. Predict future scores on Y based on measured scores on X

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' LINEAR REGRESSION: What it Is and How it Works' - waneta

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### LINEAR REGRESSION:What it Is and How it Works

• What is BivariateLinear Regression?

• The Regression Equation

• How It’s Based on r

• Assumptions

What is BivariateLinear Regression?

• Predict future scores on Y based on measured scores on X

• Predictions are based on a correlation from a sample where both X and Y were measured

• Two variables: X and Y

• X - independent variable/predictor variable

• Y - dependent/outcome/criterion variable

• Based on the linear relationship (correlation) between X and Y

• The relationship can be described by the equation for a straight line

y = b1xi+ b0 + ei

y = predicted score on criterion variable

b0 = intercept

xi = measured score on predictor variable

b1 = slope

ei = residual (error score)

• Minimize squared error in prediction.

• Error (residual) = difference between predicted y and actual y

Replace x and y with zX and zY:

zY = b1zX + bo

and the y-intercept becomes 0:

zY = b1zX

and the slope becomes r:

zY = rzX

Assumptions for Bivariate Linear Regression

• Quantitative data (or dichotomous)

• Independent observations

• Predict for same population that was sampled

Assumptions for Bivariate Linear Regression

• Linear relationship

• Examine scatterplot

• Homoscedasticity – equal spread of residuals at different values of predictor

• Examine ZRESID vs ZPRED plot

Assumptions for Bivariate Linear Regression

• Independent errors

• Durbin Watson should be close to 2

• Normality of errors

• Examine frequency distribution of residuals

• Influential cases have greater impact on the slope and y-intercept

• Select casewise diagnostics and look for cases with large residuals

Participants are asked to pretend that they are jurors and, after watching a videotape of a defendant being questioned, indicate whether they think the defendant is guilty or not. The defendants are either African American or Caucasian. The researcher hypothesizes that participants will be more likely to think the African American defendants are guilty as compared to Caucasians.