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LINEAR REGRESSION: What it Is and How it WorksPowerPoint Presentation

LINEAR REGRESSION: What it Is and How it Works

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LINEAR REGRESSION: What it Is and How it Works

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LINEAR REGRESSION:What it Is and How it Works

- What is BivariateLinear Regression?
- The Regression Equation
- How It’s Based on r
- Assumptions

- 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

- Quantitative data (or dichotomous)
- Independent observations
- Predict for same population that was sampled

- Linear relationship
- Examine scatterplot

- Homoscedasticity – equal spread of residuals at different values of predictor
- Examine ZRESID vs ZPRED plot

- 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.