Pearson’s Correlation and Bivariate Regression

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

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?

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

Bivariate Correlation

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

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

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

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

Bivariate Linear Regression (cont.) • Multiple correlation coefficient (R) • indicates strength but not direction • Coefficient of determination (R2) • Coefficient of alienation (residual or unexplained)

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

Pearson’s Correlation and Bivariate Regression