I have data containing several variables. I ran a regression model. Prior to running the model I have normalized the dependent variable Y and the independent variables X1 and X2.
After receiving the output I want to interpret the results. For example, if the coefficient of X1 is 0.15, I know that it means that for addition of one standard deviation of X1, there is an increase of 0.15 standard deviations in Y, but this is not clear.
I want to go back to the original units of Y and X for interpretation. How do I do that ? Can I simply take the "normalized coefficients", multiply by the standard deviation of Y and add the mean of Y?
Something about it doesn't make me comfortable.