How to convert regression coefficients based on standard deviation of an independent variable?

[Matthew Williams]

Dear all,

I have a question regarding how to convert regression coefficients based on standard deviation (SD) of an independent variable. Let's consider a simple regression model where the outcome is age at marriage and an independent variable is the intensity of an education reform. From a paper I am reading, I know that the mean of the outcome is 18.76, SD of the intensity is 0.77 and the regression coefficient of the intensity is 0.82. That means a one-unit increase in the intensity is associated with increased age at marriage by approximately 0.82 years. However, the author of that paper also interpret that a one SD (i.e., 0.77 unit) increase in the intensity is associated with an approximately 0.63 year increase in age at marriage. My question is that how did the author come up with 0.63 year increase in age at marriage when interpreting the results based on SD of the intensity? Any advice is highly appreciated. Thank you.

P/s: I have tried to ask the author but unfortunately I have not heard from him/her.

[Andrew Musau]

Isn't he/she just multiplying the coefficient by the std. deviation?

. di 0.82*0.77
.6314

[Matthew Williams]

Thank you Andrew. May I know a reference of the formula in #2?

[Andrew Musau]

There is no formula, just simple logic. The SD is measured in units of the independent variable and the coefficient on the independent variable reflects a 1-unit change. So if I want to know a 1-SD change, I just multiply the SD with the coefficient.

[Matthew Williams]

Thank you Andrew for the useful advice. Greatly appreciated!