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LINEAR REGRESSION: Evaluating Regression Models

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

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LINEAR REGRESSION: Evaluating Regression Models

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  1. LINEAR REGRESSION: Evaluating Regression Models

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

  3. 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

  4. 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.

  5. 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

  6. 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

  7. Review! In predicting number of days to recover from an appendectomy, the standard error of the estimate is 2 days. Write a sentence explaining what that means.

  8. Review! Why does the Model SS compare the predicted Y scores to the mean of the Y scores?

  9. Review! TRUE OR FALSE: If the F-test for the regression model is significant, it means that the model is a good fit for the data.

  10. Coefficient of Determination • r2 is the proportion of variance in Y explained by X • Model SS divided by Total SS • Adjusted r2 corrects for the fact that the r2 often overestimates the true relationship. Adjusted r2 will be lower when there are fewer subjects.

  11. Regression Coefficients • The Constant B under “unstandardized” is the y-intercept b0 • The B listed for the X variable is the slope b1 • The t test is the coefficient divided by its standard error • The standardized slope is the same as the correlation

  12. 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, r2 = .07.

  13. Review! The F-test for the regression model divides the variability for the Y scores into parts and then …. does what?

  14. Review! Suppose the coefficient of determination for predicting number of days it takes to recover is .36. This means that we can explain 36% of the _______ in _______ based on X.

  15. Review! TRUE OR FALSE: In a bivariate regression, if the t-test for the regression coefficient b1 is significant, then the F-test for the regression model will always be significant too.

  16. Choosing Stats A researcher would like to determine whether handedness (left or right) is related to a measure of relationship satisfaction.

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