Chapter 7 Relationships Among Variables What Correlational Research Investigates Understanding the Nature of Correlation Positive Correlation Negative Correlation Correlation and Causation Pearson Product Moment Correlation What the Coefficient of Correlation Means Interpreting Reliability of r Interpreting Meaningfulness of r

Regression Using Correlation for Prediction Working With Regression Equations Procedures for Multiple Regression Forward-Selection Multiple Regression Backward-Selection Multiple Regression Maximum R-Squared Method Stepwise Regression Procedure Multiple Regression Prediction Equations

Regression Equations Y = a + bX b = r(s y /s x ) a = M y – bM x Y = a + b X + b X b X Formula for straight line Calculating beta (slope) Calculating intercept (a) Standard error of the estimate Multiple regression

Multiple Regression What multiple regression does: – Linear combination of Xs ® Y – Relationship of each X ® Y – Relationship among Xs R’s relationship to r Test of R: F test Prediction–formula for a straight line: Y = a + b 1 X b i X i

Approaches to multiple regression: – Forward selection – Backward selection – Stepwise selection Max R selection Shrinkage Number of predictors Number of subjects Cross-validation