1. Copyright © 2010 Pearson Education, Inc. 17-1 Chapter Seventeen Correlation and Regression

2. Copyright © 2010 Pearson Education, Inc. 17-2 1) Chapter Outline 1) Overview 2) Correlation 3) Regression Analysis

3. Copyright © 2010 Pearson Education, Inc. 17-3 2) Correlation Coefficient The correlation coefficient, r, summarizes the strength of association between two metric (interval or ratio scaled) variables, say X and Y. In other words, you can have a correlation coefficient for Likert scale items, not dichotomous items. It is an index used to determine whether a linear (straight-line) relationship exists between X and Y. As it was originally proposed by Karl Pearson, it is known as the Pearson correlation coefficient.

4. Copyright © 2010 Pearson Education, Inc. 17-4 Linear relationships For example: How much does weight (Y) go up as height (X) goes up by one unit? Height and weight are positively correlated.

5. Copyright © 2010 Pearson Education, Inc. 17-5 Product Moment Correlation R can be calculated from a sample of n observations: sum X = average of all x’s Y = average of all y’s Don’t worry, we can do this in SPSS…

6. Copyright © 2010 Pearson Education, Inc. 17-6 Product Moment Correlation r varies between -1.0 and +1.0. The correlation coefficient between two variables will be the same regardless of their underlying units of measurement. For example, comparing a 5 point scale to a 7 point scale is okay. Note: correlation does not equal causation! e.g. ice cream does not cause a sunburn.

7. Copyright © 2010 Pearson Education, Inc. 17-7 Explaining Attitude Toward the City of Residence

8. Copyright © 2010 Pearson Education, Inc. 17-8 Interpretation of the Correlation Coefficient The correlation coefficient ranges from −1 to 1. A value of 1 implies that all data points lie on a line for which Y increases as X increases. A value of −1 implies that all data points lie on a line for which Y decreases as X increases. A value of 0 implies that there is no linear correlation between the variables.

9. Copyright © 2010 Pearson Education, Inc. 17-9 Positive and Negative Correlation

10. Copyright © 2010 Pearson Education, Inc. 17-10 CorrelationNegativePositive None−0.09 to 0.00.0 to 0.09 Small−0.3 to −0.10.1 to 0.3 Medium−0.5 to −0.30.3 to 0.5 Strong−1.0 to −0.50.5 to 1.0 Interpretation of the Correlation Coefficient As a rule of thumb, correlation values can be interpreted in the following manner:

11. Copyright © 2010 Pearson Education, Inc. 17-11 SPSS Windows: Correlations 1. Select ANALYZE from the SPSS menu bar. 2. Click CORRELATE and then BIVARIATE. 3. Move “variable x” into the VARIABLES box. Then move “variable y” into the VARIABLES box. 4. Check PEARSON under CORRELATION COEFFICIENTS. 5. Check ONE-TAILED under TEST OF SIGNIFICANCE. 6. Check FLAG SIGNIFICANT CORRELATIONS. 7. Click OK.

12. Copyright © 2010 Pearson Education, Inc. 17-12 SPSS Example: Correlation Correlations AgeInternetUsage InternetShoppi ng AgePearson Correlation 1-.740-.622 Sig. (1- tailed).000.002 N20 InternetUsagePearson Correlation -.7401.767 Sig. (1- tailed).000 N20 InternetShoppingPearson Correlation -.622.7671 Sig. (1- tailed).002.000 N20

13. Copyright © 2010 Pearson Education, Inc. 17-13 3) Linear Relationships and Regression Analysis Regression analysis is a predictive analysis technique in which one or more variables are used to predict the level of another by use of the straight-line formula, y=a+bx.

14. Copyright © 2010 Pearson Education, Inc. 17-14 Bivariate Linear Regression Analysis Bivariate regression analysis is a type of regression in which only two variables are used in the regression, predictive model. One variable is termed the dependent variable (y), the other is termed the independent variable (x). The independent variable is used to predict the dependent variable, and it is the x in the regression formula.

15. Copyright © 2010 Pearson Education, Inc. 17-15 Bivariate Linear Regression Analysis With bivariate analysis, one variable is used to predict another variable. The straight-line equation is the basis of regression analysis.

16. Copyright © 2010 Pearson Education, Inc. 17-16 Bivariate Linear Regression Analysis

17. Copyright © 2010 Pearson Education, Inc. 17-17 Bivariate Linear Regression Analysis: Basic Procedure Independent variable: used to predict the independent variable (x in the regression straight-line equation) Dependent variable: that which is predicted (y in the regression straight-line equation) Least squares criterion: used in regression analysis; guarantees that the “best” straight-line slope and intercept will be calculated. The regression model, intercept, and slope must always be tested for statistical significance (p <.05).

18. Copyright © 2010 Pearson Education, Inc. 17-18 Regression Analysis "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation. It aims to find the best line!

19. Copyright © 2010 Pearson Education, Inc. 17-19 Multiple Regression Analysis Multiple regression analysis uses the same concepts as bivariate regression analysis, but uses more than one independent variable. With multiple regression, you can develop a conceptual model:

20. Copyright © 2010 Pearson Education, Inc. 17-20 Example of Multiple Regression

21. Copyright © 2010 Pearson Education, Inc. 17-21 Multiple Regression Analysis In SPSS: Analyze  Regression  Linear Look at: R – square (for fit) Beta Sig. Example: What variables would influence an employee to accept a new product?

22. Copyright © 2010 Pearson Education, Inc. 17-22 Multiple Regression Analysis Peer support, individual motivation, usefulness of the product, and ease of use all influence an employees acceptance of a product. Work experience is not influential. Above.3 = good model fit!

23. Copyright © 2010 Pearson Education, Inc. 17-23 Thank you! Questions??