Multivariable linear regression - multiply beta coefficients and 95% CIs by a given value

[_maldini_]

I'm performing a multivariable linear regression using PROC REG or PROC GENMOD. I want to multiply beta coefficients and 95% CIs by a given value (e.g., 10). Is there a statement (UNITS?) I can use or do I have to use a DATA step to do this? 

[ballardw]

What exactly would it mean to multiply a CI by a given value? Do you mean the upper and lower confidence limits? What would the meaning of that result actually be?

I think you may want to provide some explanation as to what you are attempting as this brief request sounds pretty dubious as to how the result would be interpreted.

Adjusting the ALPHA= option the regression proc would yield a different set of confidence limits in a meaningful sense. Alpha= 0.1 would have 90% confidence limits and would be narrower than the default alpha=.05, or 0.01 with 99% CI would be wider. But that wouldn't effect the betas.

If I understand what you request the mechanics would be to get the values from the regression output into a data set, such as use of the OUTEST= option in proc reg, and then use a data step to modify them.

[_maldini_]

Yes, multiplying the confidence limits. As an example, say I wanted standardized betas and confidence limits per the standard deviation. Or, say my independent variable was in years and I wanted to report it in decades (...a 1 unit change would be a decade, instead of a year). 

[ballardw · Accepted solution]

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@_maldini_ wrote:

Yes, multiplying the confidence limits. As an example, say I wanted standardized betas and confidence limits per the standard deviation. Or, say my independent variable was in years and I wanted to report it in decades (...a 1 unit change would be a decade, instead of a year). 

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For your "decade" description you would need to change the input data to the regression procedure so that the appropriate variable(s) have the desired unit and rerun the regression for this to make any sort of sense.

[Rick_SAS]

There is no UNITS statement. You would have to use the DATA step.

It sounds like you already understand how the beta coefficients (and the CIs) are related to linear changes of scale. But if you want a review of the formulas, you can look at the section "Linear transformations of random variables" in the article "Standardized regression coefficients." That section has formulas that describe how the regression coefficients change if you perform an affine change of the dependent variable or an independent variable.