Multiplying regression coefficients by a constant

Question

Lots on this on CV already but most tend to be about multiplying predictors by constants before performing the regression.

I feel like I should know this already but I'm wondering if it's kosher to multiply the regression coefficients by a constant after the regression has been run.

For example. I have performed a Gaussian linear regression where score on an anxiety scale (higher score equates to worse anxiety) was regressed on the number of days in the last 28 days participants used cannabis.

If my regression coefficient for this is 0.31 (95% CI: 0.22, 0.41) this means that every extra day of cannabis use in the previous 28 days is associated with an estimated increase of 0.31 on the anxiety scale.

But just say instead of expressing it in days of use in the last 28-day period, I wanted to express it in terms of days per week. Could I simply multiply the regression coefficient and CI by 4? So every extra day per week of cannabis use was associated with a 1.24-point increase in anxiety score (95% CI: 0.88, 1.62)? Would this yield the same result as if I transformed the predictor itself prior to running the regression?

Answer 1

I actually ran some of my own data to answer my own question. Really I was just being lazy. So for anyone out there who wants to know, yes you can simply multiply the point estimate and lower and upper bounds of the regression coefficients after you have run the analysis.

So multiplying the regression coefficient by 4 after analysis results in the same coefficient as creating a new predictor where the values of the original predictor are divided by 4 prior to running the analysis.

This also works with the log-odds coefficients from logistic regressions, with an important caveat: make sure you multiply the log-odds coefficients (and upper and lower bounds of confidence intervals of the log-dds coefficients) by the constant before you exponentiate it to odds-ratios, not after.