One of my college physics professors used to smile and say "I will now prove this by example" when he wanted to demonstrate a fact without proving it mathematically. It also derives how regression coefficients change after a linear transformation of the variables. This article uses SAS to demonstrate how parameter estimates for the original variables are related to parameter estimates for standardized variables. The SAS documentation for the STB option states, "a standardized regression coefficient is computed by dividing a parameter estimate by the ratio of the sample standard deviation of the dependent variable to the sample standard deviation of the regressor." Although correct, this definition does not provide an intuitive feeling for how to interpret the standardized regression estimates. A SAS programmer recently asked how to interpret the "standardized regression coefficients" as computed by the STB option on the MODEL statement in PROC REG and other SAS regression procedures.
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