LINEAR REGRESSION: Evaluating Regression Models

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

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

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.

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

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

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.

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

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.

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