1. Bivariate Correlation and Regression

2. For Quantitative variables measured on the Interval Level Which one is the First? –Correlation or Regression

3. Objectives Scattergram Superimpose a regression line Estimate and interpret a correlation Estimate and interpret the regression coefficients Estimate and interpret Spearman’s rho

4. Scattergram

5. Sunflower

6. Regression Line What is the relationship between income and education? We need to know : –How much income you could expect to make if you had no education? –And how much income you can expect for each additional year of education Intercept or Constant Slope

7. Regression Line Estimated income = 10000$ + 3000$(Educ) Y=b 0 +b 1 (x 1 ) Predictor Outcome Constant

9. Correlation Measure how close the observations are to the regression line It does not tell us how steep the relation is

10. Think The correlation between education and income –Women : r = 0.3 –Men : r = 0.5 –Does this mean that education has a bigger payoff for men than it does for women?

11. Correlation Vary from -1 to 1 –It tell us whether the regression line goes up or down What r=0 means?

12. Multiple Comparisons

13. With Alpha adjustment

14. Approach to Missing Values Exclude cases pairwise Exclude cases listwise

15. Linear Regression Variable Selection Methods Enter (Regression) Stepwise Remove Backward Elimination Forward Selection

16. Non-Linear Associations