I am making a linear regression model and my dependent variable is highly seasonal. Now, I want to add months as independent variables like follows (it is incomplete):

First of all, is it a correct way of adding seasonality? Also Someone said we should not include all the twelve months in the model but he could not remember why. Is that so? Why?

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#### Best Answer

First, you can't add all the months because you have to have one month as a reference for the other months.

Second, if you have data more finely divided than month (e.g. weekly or daily) that would be good. If you only have month, then, you can make do. Is all your data from the same location? If not, things get more complicated.

Let's assume it is all from one place. Then, using dummy variables like this, you can only get a rough idea of seasonality with months. But you can examine the coefficients of the dummy variables and get a sort of idea. What else might be tried?

If "seasonality" is really "temperature" then you could try to find the average temperature for the month (or smaller time period) and use that. That would make it continuous (and July in one year would not be identical to July in another year). You could use a spline of temperature or, if you have a more specific idea of the effect, you could implement that. But splines are pretty flexible.

You could code month as numeric and then graph the results (maybe a different line for each year). That might give you ideas as to the right model. Maybe some trig function of month (probably transformed somehow). Or maybe a spline.

There are probably other good approaches, too.

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