And we know that if we collect a lot of data, a lot more data in our sample,

the arithmetic mean will converge to something.

So the geometric mean is what this quantity,

the product of the data, rays to the one over nth power, what it converges to.

So, what, it turns out, when you take the log of the natural log

of the outcome in a linear regression then, your exponentiated

coefficients are interpretable with respect to geometric means.

So, for example, E to the Beta of zero is the estimated geometric mean hits on day

zero and I should reiterate the point from earlier on in the class.

This intercept doesn't mean that much because January first 1970 is not

a date that we care about in terms of number of web hits.

So probably to make the intercept more interpretable, what we should have done is

subtracted off the earliest date that we saw and started counting days from there.

From all of the remaining days in our data set and

then the intercept would be the e to the inner estimated intercept would be

the geometric mean hits on the first day of this data set.

Okay. So that's a small point but

it doesn't change the fitted model.

It doesn't change the slope or anything like that to shift around the intercept

however nonetheless, if you want an interpretable intercept as we know

from earlier on in the class, you have to do something like that.

E to the beta1 on the other hand is the estimated relative increase or

decrease in the geometric mean hits per day, okay?