[R] Confidence intervals of log transformed data

From: tom soyer <tom.soyer_at_gmail.com>
Date: Wed, 16 Apr 2008 11:19:27 -0500


 I have a general statistics question on calculating confidence interval of log transformed data.

I log transformed both x and y, regressed the transformed y on transformed x: lm(log(y)~log(x)), and I get the following relationship:

log(y) = alpha + beta * log(x) with se as the standard error of residuals

My question is how do I calculate the confidence interval in the original scale of x and y? Should I use

exp(alpha + beta * log(x) +- 2 * se), or, exp(alpha + beta * log(x)) +- exp(2 * se)



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