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).

Exact question:

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.

  • $\begingroup$ You should find an answer to your question at the linked thread. Please read it. If you still have a question afterwards, come back here & edit your Q to state what you've learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. $\endgroup$ – gung - Reinstate Monica May 3 '15 at 20:16
  • $\begingroup$ You are mixing up coefficients and the dependent variable. One interpretation of the coefficients is, indeed, the rate of change (when the base of logs is the natural, rather than 10, and when the coefficient in question is small, so that you are not talking about $\exp(5)$ which is not a five-fold increase, of course). [ CTD ] $\endgroup$ – StasK May 4 '15 at 14:14
  • $\begingroup$ The logs of the dependent variable are just what they are -- the logs. You can make a change out of them if they are ordered in time and form a time series, so when you subtract $\ln y_t - \ln y_{t-1} = \ln( y_t/y_{t-1})$, you do get the log of the rate of change $r_t = (y_t - y_{t-1})/y_t$, to the extent that the approximation $\ln( 1 + r_t) \approx r_t$ is reasonable (I'd say $|r_t| < 0.1$). $\endgroup$ – StasK May 4 '15 at 14:15