7. Multiple Correlation and Multiple Regression

There are many times in environmental science research when you want to predict a criterion, Y, but you want to find out if you can develop a better prediction model by using several predictors to predict Y instead of a single predictor as we discussed in Chap. 6 of this book. The resulting statistical procedure is called “multiple correlation” because it uses two or more predictors, each weighed differently in an equation, to predict Y. The job of multiple correlation is to determine if using several predictors can do a better job of predicting Y than any single predictor by itself. The equation for multiple correlation is presented, explained, and a practical environmental science problem is used to present the Excel commands needed to find the multiple correlation and the multiple regression equation generated from the data set. Excel commands are also used to create a SUMMARY OUTPUT which gives the coefficients needed to write the multiple regression equation for the data. Finally, the Excel commands needed to find the correlation between all of the variables is explained so that you can create a “correlation matrix” for your data set. You will learn how to read this correlation matrix to determine the correlation between any two variables in your study. Three practice problems are given at the end of the chapter to test your Excel skills, and the answers to these problems appear in Appendix A of this book. An additional practice problem is presented in the Practice Test given in Appendix B along with its answer in Appendix C of this book.