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Can the relative magnitude of standardized coefficients indicate variable importance?

Comparing the standardized coefficients (resulting from linear regression) across different samples can be problematic (because the sample variances can be influenced by measurement error).
But can the standardized coefficients of two different variables be compared in one sample - to ascertain which variable has a 'larger effect' ?
~~Is it be a reasonable way to infer the larger effect - even if an imperfect one?~~

Comparing the standardized coefficients (resulting from linear regression) across different samples can be problematic (because the sample variances can be influenced by measurement error).
But can the standardized coefficients of two different variables be compared in one sample - to ascertain which variable has a 'larger effect' ?
Is it a reasonable way to infer the larger effect - even if an imperfect one?

statistics regression

statistics regression