[Solved] Can linear regression be used to solve this?

I would say it does not.

The lack of agreement with the earlier values for Jan-Sep is a bad sign.

The large negative value for Nov suggests that there’s something wrong. What do these numbers represent? Is a negative value physically possible?

It’s a mistake to treat a function like a black box.

I could look at this data in different ways:

1. One fit per month where year is the input value.
2. One fit per year, with 12 values total.
3. A 2D surface with month, year as parameters.

Which one are you doing? What order fit are you assuming?

You should be able to calculate SSE and figure out goodness of fit for different schemes.

I would urge you to plot the data and look at it before you try to fit anything. Understand the data better.