Hi
I would like to comment on the measure of fit of a multiple linear regression model and i am using the 3 measures SER (standard error of regression) R2 and R2-adjusted. My Y variable is log-transformed and i am not sure how to interpret the SER. When i run the model the SER is 0.39.. Does this mean that the observations on average are 0.39 log Y of the regression line?
And does it even make sense to use SER when Y is log-transformed or should i just use R2 and R2-adjusted?
Thanks in advance
Measuring fit is far less important than measuring lack of fit! I presume you've run tests for the behaviour of residuals etc!
The SER gives the "typical distance" of observations from the regression model. This is meaningful also when the response is log-transformed. A difference in logarithms is the logarithm of a ratio! A 0.39 difference in log10(Y) means a 100.39 = 2.5 fold in Y. That is, a typical distance of an observalion (Y) is 2.5 times the value of the regression model (for Y) to the positive side and 1/2.5 = 0.4 times for the negative side.
Measuring fit is far less important than measuring lack of fit! I presume you've run tests for the behaviour of residuals etc!
Both Profs Wilhelm and Conroy are correct. I would look at it this way. Let z =log(y). The regression eqn is now, z=a+bx1+..... Interpret for this variable z as you would if its name was y. These are what you want, see for example:
https://www.amazon.com/Applied-Linear-Statistical-Models-2013/dp/1259064743/ref=sr_1_1?crid=12UCZLXZ3J96T&keywords=kutner+applied+linear+statistical+models&qid=1556311942&s=gateway&sprefix=Kutner+Applied+Linear%2Cstripbooks%2C205&sr=8-1
Best, D. Booth
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