Chapter 5 Multiple correlation and multiple regression

Chapter 5 Multiple correlation and Multiple regressionThe previous Chapter considered how to determine the relationship between two variablesand how to predict one from the other. The general solution was to consider the ratio ofthe covariance between two variables to the variance of the predictor variable ( regression )or the ratio of the covariance to the square root of the product the variances ( correlation ).This solution may be generalized to the problem of how to predict a single variable from theweighted linear sum of Multiple variables ( Multiple regression ) or to measure the strength ofthis relationship ( Multiple correlation ). As part of the problem of finding the weights, theconcepts ofpartial covarianceandpartial correlationwill be introduced.

130 5 Multiple correlation and multiple regression 5.2.1 Direct and indirect effects, suppression and other surprises If the predictor set x i,x j are uncorrelated, then each separate variable makes a unique con- tribution to the dependent variable, y, and R2,the amount of variance accounted for in y,is the sum of the individual r2.In that case, even though each predictor accounted for only

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