# Standardized Coefficients and Partial r

Ive looked over a few of the posts here on regression coefficients and partial regression coefficients but haven't seen an answer to this question, which maybe easily inferred from the other answers but being new to all of this I haven't been able to figure it out.

Basically, lets say you run a linear regression with a number of IV's and you are interested in two of them - X1 and X2.

X1 standardized beta = -.338 and partial r = -.314

X2 standardized beta = .452 and partial r = .238

Is this possible? Can the beta for X2 be larger than the beta for X1 but the reverse be true of their partial r's? If so, why?

• I wonder about the motivation behind this question, because I understand that standardized betas tell us about the relationship between the $X_i$ and the response variable, whereas the partial r's tell us about the relationships between the $X_i$ themselves. Given these are such different things, what would be the reason to suppose there must be such a strict inequality? – whuber Apr 10 '15 at 21:08
• with a number of IV's and you are interested in two of them simplejack42, It can easily happen so when there is more than two IVs. Why not? Just generate few datasets, do multiple regression, and find out yourself that the phenomenon does occure sometimes. – ttnphns Apr 11 '15 at 7:26
• @ttnphns Don't know if this matters, but seeing as you use SPSS, I'm interested in this in regard to SPSS linear regression output such that the partial r's for X1 and X2 are in regard to their relationship to Y rather than each other. I think that was clear in my original post but just wanted to clarify. Also, I have seen it occur, I guess a better phrasing, or my true intention with the question is - why would this occur and/or is this a problem? – simplejack42 Apr 11 '15 at 17:55