1. Pearson’s Correlation and Bivariate Regression Lab Exercise: Chapter 9 1

2. Example Questions: Do opposites really attract? Is there a negative correlation between the educational levels of spouses? One more year in school typically results in how much more annual income? Schooling accounts for how much of the differences in persons’ incomes? What annual income would we predict for someone with 16 years of schooling? 2

3. Interval/Ratio Measures of Association Pearson’s r – ranges from −1.00 to 1.00 – symmetric Analyze | Correlate | Bivariate – pairwise and listwise deletion of missing data 3

4. Bivariate Correlation 4

5. Scatterplot: Do opposites attract? * Check linearity, strength, direction, and homoscedasticity 5

6. Bivariate Linear Regression: Income on Schooling Equation for a straight line “Best-fitting” straight line 6

7. Bivariate Linear Regression (cont.) Analyze | Regression | Linear 7

8. Answering Questions with Statistics Chapter 9 8 Regression Output of INCOME86 on EDUC for 1980 GSS Young Adults

9. Bivariate Linear Regression (cont.) Unstandardized coefficients Regression equation Predicted value Ŷ: substitute value for X (16 yrs?) = $21,604.089 Regression residual: Y - Ŷ 9

10. Bivariate Linear Regression (cont.) Multiple correlation coefficient (R) – indicates strength but not direction Coefficient of determination (R 2 ) Coefficient of alienation (residual or unexplained)

11. Bivariate Linear Regression (cont.) Some limitations to remember – regression does not prove causality – for interval-ratio level variables Can be used with caution (requires special interpretation) for grouped interval ratio or ordinal variables with >5 categories – linear means only linear 11