linear regression: evaluating regression models overview assumptions for linear regression...

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  • Slide 1
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  • LINEAR REGRESSION: Evaluating Regression Models
  • Slide 3
  • Overview Assumptions for Linear Regression Evaluating a Regression Model
  • Slide 4
  • Assumptions for Bivariate Linear Regression Quantitative data (or dichotomous) Independent observations Predict for same population that was sampled
  • Slide 5
  • Assumptions for Bivariate Linear Regression Linear relationship Examine scatterplot Homoscedasticity equal spread of residuals at different values of predictor Examine ZRESID vs ZPRED plot
  • Slide 6
  • Checking for Homoscedasticity
  • Slide 7
  • Assumptions for Bivariate Linear Regression Independent errors Durbin Watson should be close to 2 Normality of errors Examine frequency distribution of residuals
  • Slide 8
  • Checking for Normality of Errors
  • Slide 9
  • Influential Cases Influential cases have greater impact on the slope and y-intercept Select casewise diagnostics and look for cases with large residuals
  • Slide 10
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  • Standard Error of the Estimate Index of how far off predictions are expected to be Larger r means smaller standard error Standard deviation of y scores around predicted y scores
  • Slide 12
  • Sums of Squares Total SS total squared differences of Y scores from the mean of Y Model SS total squared differences of predicted Y scores from the mean of Y Residual SS total squared differences of Y scores from predicted Y scores
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  • Coefficient of Determination r 2 is the proportion of variance in Y explained by X Adjusted r 2 corrects for the fact that the r 2 often overestimates the true relationship. Adjusted r 2 will be lower when there are fewer subjects.
  • Slide 17
  • Goodness of Fit Dividing the Model SS by the Total SS produces r 2 The ANOVA F-test determines whether the regression equation accounted for a significant proportion of variance in Y F is the Model Mean Square divided by the Residual Mean Square
  • Slide 18
  • Coefficients The Constant B under unstandardized is the y-intercept b 0 The B listed for the X variable is the slope b 1 The t test is the coefficient divided by its standard error The standardized slope is the same as the correlation
  • Slide 19
  • Example of Reporting a Regression Analysis The linear regression for predicting quiz enjoyment from level of statistics anxiety did not account of a significant portion of variance, F(1, 24) = 1.75, p =.20, r 2 =.07.
  • Slide 20
  • Take-Home Points The validity of a regression procedure depends on multiple assumptions. A regression model can be evaluated based on whether and how well it predicts an outcome variable.