Today I was asked when to use logs and when to use a linear growth model. My answer follows. Hopefully this is a meal for some.

The formula for continuous compounded growth is:

e^rt where e is Euler constant (2.72..) r is the rate t is time

If you are assuming a constant growth rate model then this is the correct model and not a linear model. In that case you would take the log (ln for financial work). The model then would be linearized by taking the logs. So you would regress:

ln next period sales = b * ln( last period sales) + a

Then to reverse ln( sales ) you would just take exp( ln(sales) ) to get the dollars or units. But the idea is to do the regression in log space because it is linear there and when you have your log answer convert back to the desired real world units.

the model could also be:

ln( sales ) = b * ln( t ) + a

The general rule is when you have arithmetic growth then a simple additive linear model is correct. when you have compound growth then the log linear model is the best.


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