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Additive model and multiplicative model

As you can see on Multiplicative model of Errorsl page,
proportional regression
is an additive model.

proportional regression
proportional regression
are multiplicative models.

There is a difference between addition and multiplication, so the phenomena that can be handled are quite different, but there is a relationship between the formulas.

Derive an additive model from a multiplicative model E

If you logarithmic both sides of the multiplicative model E, you can convert it to an additive model.
proportional regression

The additive model has a better outlook than the multiplicative model.

Incidentally, the relationship between the multiplicative model and the additive model is similar to the relationship between equal variance and proportional variance, but the difference between equal variance and proportional variance does not mean that the outlook will be improved by conversion.

Here, we have transformed the multiplicative model E, but the same is true for the multiplicative model exp(E).

Derive the multiplicative model exp(E) from the additive model

Let's also try to transform the additive model.
proportional regression
With this transformation, we can see that the additive model can be transformed into the multiplicative model exp(E).

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