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=== Relative importance of variables in multiple regression: standardized regression coefficients === Standardization of variables prior to [[multiple regression analysis]] is sometimes used as an aid to interpretation.<ref name="AfifiMayClark2012">{{Citation |last1= Afifi |first1= Abdelmonem |last2= May |first2= Susanne K. |last3= Clark |first3= Virginia A. |title= Practical Multivariate Analysis |edition= Fifth |year=2012 |publisher= Chapman & Hall/CRC |isbn= 978-1439816806}}</ref> (page 95) state the following. "The standardized regression slope is the slope in the regression equation if X and Y are standardized β¦ Standardization of X and Y is done by subtracting the respective means from each set of observations and dividing by the respective standard deviations β¦ In multiple regression, where several X variables are used, the standardized regression coefficients quantify the relative contribution of each X variable." However, Kutner et al.<ref name="KutnerNachtsheim2004">{{Citation |last1= Kutner |first1= Michael |last2= Nachtsheim |first2= Christopher |last3= Neter |first3= John |title= Applied Linear Regression Models |edition= Fourth |year=204 |publisher= McGraw Hill|isbn= 978-0073014661 }}</ref> (p 278) give the following caveat: "β¦ one must be cautious about interpreting any regression coefficients, whether standardized or not. The reason is that when the predictor variables are correlated among themselves, β¦ the regression coefficients are affected by the other predictor variables in the model β¦ The magnitudes of the standardized regression coefficients are affected not only by the presence of correlations among the predictor variables but also by the spacings of the observations on each of these variables. Sometimes these spacings may be quite arbitrary. Hence, it is ordinarily not wise to interpret the magnitudes of standardized regression coefficients as reflecting the comparative importance of the predictor variables."
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