Interpretation of linear-log regression model (Neep Help)


New Member
Dear All,

I had a problem with my data of growth in percentage regarding negative and positive values due to which I could not transform it into log and get rid of heteroskedasticity issue. However, I found out another way to get rid of negative values i.e. adding a constant with each variable (I guess, I did it right. Would you like to comment?)

I have run a linear-log regression model i.e.
y = a + b1log(x1) + b2log(x2) + e

The regression model has run and it has no problem of autocorrelation and heteroskedasticity. However, I am having problem in interpreting the results as the unit of data of all the variables is in percentage growth.

The method to interpret is;
A 1% increase in X is associated with an average b/100 units increase in Y.
But, how can I say it in my case as my data is already in percentage growth form?
Please suggest.

Bilal Ahmed


Omega Contributor
I get that the logged variables now become 1% increase.

Can you talk more about your outcome? It is a percentage? What is "b" just a values (proportion) of the hundred.

I don't have a great deepth in this area, but why wouldn't it be a 1% increase in x = a ???? percent increase in y?
If your model is:

y = a + b1log(x1) + b2log(x2) + e

so for the log transformed predictors, determine the change in y for a change in x on the log scale:

y(x1_2) - y(x1_1) = b1*(log(x1_2) - log(x1_1)) = b1*(log(x1_2/x1_1)

so, to interpret the change in y for, say, a 50% increase in the log transformed predictor:

change in y = b1*log(1.5)

But I guess if you are already working with percentage data, this could get confusing. Do you have to work with percentages? One of the advantages of using log transformations is that you don't have to convert your data to a percent before analysis.
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