How can I compare regression coefficients in the same multiple regression model

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I think this question has been answered in bits and pieces here and there, but I am still a bit unsure about what the best approach for this is: how to compare two coefficients from a multiple linear regression to see if the effect strengths are significantly different.

For example, I am interested in relating attitude (IV1) and behavioral control (IV2) to the medication adherence (DV). I found that standardized betas were 0.30 and 0.19 for attitude and behavioral control, respectively. Is it reasonable to say the attitude is the strongest predictor of medication adherence? If so, how can I test whether its effect is significantly different from those of the other predictors? I am using SPSS v19.

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关键词：coefficients coefficient regression regressio EFFICIENT multiple compare

• Just about any decent regression text warns that trying to get at the separate effects of predictors is difficult if not impossible. They act as a team, pulling together or against each other. Comparing relative strength is completely straightforward only if the predictors (you say dependent variables) are uncorrelated.
• You have done already the compariosn. Using standardized coefficients clearly adjusts for different measurement units and different variability. Beyond that what you seem to want is difficult to establish.
  

Nick Fox

In econometrics there's a concept of economic significance. In a nutshell it's a product of beta and the standard error of the variable. You compare these products.

You are already doing this. In a model y=Xβ+ε, the economic significance of a variable xi is std[xi]⋅βi. This product has the same unit of measure as y. The meaning is that one standard deviation of the variable causes this much change in y. There is no statistical test here to compare them. Since independent variables are correlated, you can't simply add up the significances to the total variance of y. So this economic significance metric is sort of qualitative.

z-test.

wald test