Regression: Transformed variables
I have a dilemma about a log-transformed regression
And so the transformation is
Assuming I have found the coefficient parameters for and , I am required to test the hypothesis that by building the 95% confidence interval using and .
I am unsure about transforming back or keeping the interval. Here is my thinking
1) I use the standard errors of the coefficients of and from the regression output and build a confidence interval:
where t - is the critical value
2) Take the exponential to get back to normal scale and if the confidence interval contains 1, then accept the null hypothesis
Would this be the correct procedure?
Some people have said to me that this distorts the standard errors of the coefficient.
I would also like to note that the original data (pre-transformed) has no scale and was just raw numbers
Thanks in advance for any feedback