I have a question about how to interpret or use the result of an OLS regression w a log transformed DV. Due to non-normal distribution of the Dependent variable, I used a log10 transformation to coax it into normality. I'm looking at a state by state dataset, each row is a state IE N=51. Data are industry data.
EQ: Ylog10(market_size)= B0 + Bx1(consumption) + Bx2(price) + Bx3(income) + Bx4(govt intervention) + Bx5(climate) + Bx6(socioeconomic proxy).
With a non-transformed Y, I can get a state total by multiplying the value of each variable by its coefficient, and summing them for each state.
Because log transformed data are percentage change rather than raw number, can I do the same thing with the logged result?
If not, is there something else I can do with the logged coefficients to see where states rank in terms of their values for the variables above? If I multiply the value for each state datapoint by the coefficient and sum them, does it matter that they're percentage change and not raw numbers?
The ranking of states differs in a few noticeable ways if I use raw numbers vs logged results.
Any help would be very much appreciated. Thank you.
EDIT: Gung linked a thread I had previously read before asking my question, it is/was helpful but did not fully answer my question. I know that in an OLS regression with a log transformed DV with non-transformed IVs, the IV coefficients reflect percent changes in the DV.
Maybe an example is better:
Values for CA:
consumption=50 price=10 income=12 govt intervention=2 climate=0 socioeconomic proxy=5
Non-transformed coefficients: consumption 1.3 price 3258 income 42 intervention 18 climate 1 socioecon 5968
Transformed coefficients: consumption 0.0 price 0.0005 income 0.04 intervention 0.00001 climate 1 socioecon .2
'Value' for CA non-transformed (50*1.3)+(10*3258)+(12*42)+(2*18)+(0*1)+(5*5968)=63205
'Value' for CA transformed (50*0.0)+(10*.0005)+(12*.04)+(2*.00001)+(0*1)+(5*.2)=1.48502
With the above example - are the two values for CA valid? Specifically, is the 2nd value with the log transformed data as valid as the non-transformed value?
Thank you again.