1 / 26

Regression

Regression. The basic problem Regression and Correlation Accuracy of prediction in regression Hypothesis testing Regression with multiple predictors. The Basic Problem. How do we predict one variable from another? How does one variable change as the other changes?

Sharon_Dale
Download Presentation

Regression

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Regression • The basic problem • Regression and Correlation • Accuracy of prediction in regression • Hypothesis testing • Regression with multiple predictors

  2. The Basic Problem • How do we predict one variable from another? • How does one variable change as the other changes? • Cause and effect (can only be inferred if it makes theoretical sense)

  3. An Example • Effect of Dow Jones Performance on Darts performance (to what degree can Dow Jones predict Dart performance)

  4. The Data

  5. Relationship can be represented by line of best fit

  6. Why use regression? • We may want to make a prediction. • More likely, we want to understand the relationship. • How fast does Darts rise with one unit rise in Dow Jones?

  7. Regression Line • Formula • = the predicted value of Y (Darts) • X = Dow value

  8. Regression Coefficients • “Coefficients” are a and b • b = slope (also called rate of change) • Change in predicted Y for one unit change in X • a = intercept • value of when X = 0

  9. Calculation • Slope • Intercept

  10. For Our Data • b = 11.13/5.43 = 2.04 • a = 14.52 - 2.04*5.95 = 2.37 • See SPSS printout on next slide

  11. SPSS Printout for one Predictor R2, Percentage of Variance

  12. SPSS printout cont. Error of prediction Is regression Significant? Intercept Slope

  13. Note: • The values we obtained are shown on printout. • The intercept is labeled “constant.” • Slope is labeled by name of predictor variable.

  14. Making a Prediction • Suppose that we want to predict Darts score for a new Dow Score of 200 • We predict that Darts will be at 23.65 when Dow is at 25 • Check with data: what is real value of Darts when Dow is 25

  15. Prediction Residual

  16. Errors of Prediction • Residual variance • The variability of predicted values • Standard error of estimate • The standard deviation of predicted values

  17. Standard Error of Estimate • A common measure of the accuracy of our predictions • We want it to be as small as possible.

  18. r 2 as % Predictable Variability • Define Sum of Squares

  19. Major Points • Predicting one dependent variable from multiple predictor variables • Example with Product Advisor Data • Multiple correlation • Regression equation • Predictions

  20. The Problem • In the product advisor study, we asked participants to rate the system on a number of aspects: e.g, usefulness, ease of use, trust, kind of product information, number of ratings etc. • Lets think of overall usefulness as our dependent variable. Which of the above factors can predict overall usefulness? • What percentage variance do they explain in the usefulness overall? • What factors play the more important role?

  21. Product Advisor Data

  22. Correlational Matrix

  23. Regression Results(using simple linear regression using method “enter” R2, Percentage of Variance

  24. Regression is significant Importance of each variable Is contribution significant?

  25. Regression Coefficients • Slopes and an intercept. • Each variable adjusted for all others in the model. • Just an extension of slope and intercept in simple regression • SPSS output on next slide

  26. Regression Equation • A separate coefficient for each variable • These are slopes • An intercept (here called b0 instead of a)

More Related