Some Effects of Errors of Measurement on Multiple Correlation

Abstract In many multiple correlation and regression studies the values of the variables are difficult to measure accurately. This paper attempts to discuss the effects of such errors of measurements on the squared multiple correlation coefficient. With independent errors and a multivariate normal model, the effect is very roughly that R 2 becomes reduced to about , where gy is the coefficient of reliability of y and is a weighted mean of the coefficients of reliability of the x's. If most intercorrelations among the true X's are detrimental to R 2, the value of R'2 may exceed by 10 percent to 20 percent. The situation in which errors are correlated with the true values and the effects of errors on the interpretation of regression coefficients are briefly discussed.