# Additive model like multiplicative model

The "a+E" part of Proportional variance model can be interpreted as "the variation in which the mean value is a". If you think about it that way, a and E represent two things in one. The proportional variance model is a multiplicative model (a multiplicative model in a broad sense) in which "a + E" and X are multiplied.

## The proportional variance model is an additive model like multiplicative model

The graph above is an example of a proportional distribution model.

In the proportional variance model, the a part is the slope, and the E part is a number that determines the magnitude of the variation in the Y-axis direction.

The proportional distribution model can be expressed by the equation , but

it is convenient to interpret it as a model that combines the two effects of aX and EX, because it allows you to consider countermeasures separately.

A model that can be expressed as a multiplicative model in this way, but can be written like an additive model and interpreted like an additive model, is called an "additive model multiplicative model" here.

### Chance and systematic errors

Of the chance errors and systematic errors, the chance error is a distribution with a mean value of 0, and the systematic error is a deviation from the mean value.

The fact that the "a + E" part is considered to be "the variation in which the mean value is a" can be interpreted as "both chance error and systematic error are included".

## Proportional proportional variance model

If you write it in the form of, Proportional-proportional variance model is also a multiplicative model.

However, "1" is used for convenience in order to make it a form of a multiplicative model. It doesn't have any particular physical meaning. This is different from the proportional distribution model. Therefore, as a model formula, it feels unnatural.