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LINEAR REGRESSION: Evaluating Regression Models

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Overview Standard Error of the Estimate Goodness of Fit Coefficient of Determination Regression Coefficients

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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

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Goodness of Fit How well does the regression model fit with the observed data? An F-test is done to determine whether the model explains a significant amount of variance in y. Divide variability in y into parts, then compare the parts.

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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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F-test 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

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Coefficient of Determination r 2 is the proportion of variance in Y explained by X Model SS divided by Total SS 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.

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Regression 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

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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.

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Take-Home Point A regression model can be evaluated based on whether and how well it predicts an outcome variable.

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