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I have a multiple regression model(original model) that has been estimated already, and the details on the mean and standard deviations of the regressors, and the standard errors of coefficients from the original model are provided. This model has 4 explanatory variables along with an intercept.

In general, what is the procedure to calculate standardized coefficients using the values of estimated coefficients in the original model, (which is linear in parameters and the regressors) and all the other details I just mentioned that have been provided to me?

The purpose of doing this being that I've been asked to compare the magnitudes of the influence of some explanatory variables on the dependent variable.

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You can simply compute:

$$ \hat{\beta}_{i,std} = \hat{\beta}_i*\frac{sd(x_i)}{sd(y)} $$

Where $\hat{\beta}_i$ is the original coefficient of covariate $X_i$, and $sd(\cdot)$ refers to sample standard deviations.

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