1. ## Interpreting log-linear coefficients

Hi there,

I am fairly new to regression and have been set the task of modelling a data set in the form ln(y) = bx1 +bx2 +bx3 +bx4 +bx5 + e.

In the regression output the coefficient value of b range from -0.081 to 0.61. I understand, that for b1=0.61, that a 1 unit increase in x1 will result in a 0.61 increase in ln(y). Using exp(0.61)=1.84, I have interpreted this as a 84% increase in y. For negative coefficients, there seems to be some indication of a different process - can anyone shed any light on this for me?

At the moment, for x3=-0.081, I have used exp(-0.081)=0.92, indicating a 8% decrease in y for every unit change in x. Is this correct?

Am I approaching this regression output in the correct way? Any advise would really be helpful and much appreciated.

Many Thanks,

2. ## Re: Interpreting log-linear coefficients

Uhm, tricky question of which i can't figure out the answer. I also looked at this source, where the same question was raised:
I think the answer is complicated. If I had such a task, it would be more easier if you make your model completely multiplicative, that is:
Ln(y)= b1 Ln x1 + b2 Ln x2 etc. or y= x1^b1 * x2^b2 etc. However, that was not your task if i'm right. Hope you find the answer in the link.

4. ## Re: Interpreting log-linear coefficients

Thanks Eyecatcher. The link was helpful. I think I will focus on the effect each independent has upon the ln(y).

5. ## Re: Interpreting log-linear coefficients

ln(y) = a + bx + e
y = e^(a+bx+e)

dy/dx = b*e^(a+bx+e) = b*y
elasticity = (dy/y)/(dx/x) = b*y*(x/y) = b*x

Same with multiple independent variables.

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