# Regression with uncertain data

1. May 9, 2013

### mrburns404

So I have this set of statistical data, which is not completely relevant to what I want to model, and I would like to compensate for that somehow since I do not have the more precise data.

I have about 500 observations of average wages in certain areas which are modeled as dependent on several other parameters (taxes in the area, education of people living in the area, age, etc). The problem is, for each one of those areas I know in percent (from about 5% up to 50%) amount of people travelling to other areas to work there (and ofc getting paid by that area's standard), while still living in home area (and ofc contributing to parameters in home area).

Any ideas how to deal with this kind of problem? I was thinking about weighted regressions but I got kinda stuck since they use standard deviations which is different from what I have.

PS I am working with regressions in Excel but any help would be appreciated.

2. May 9, 2013

### Office_Shredder

Staff Emeritus
Can you confirm whether this description of your problem is correct?

Ideally your model would be that a person's wages are a function of where they work, or possibly a function of where they work and where they live, but you only have data on where they live. You know what percentage of people work in different areas than where they live, but you don't know who they are or where they are working.

For example you have regions A, B and C. You know the wages of people living in region A, and you also know 10% of people living in A work in B or C, but you don't know who they are or how many work in B and how many in C?

3. May 9, 2013

### mrburns404

Yes, that seems pretty accurate.

Ideally a model without those "travelling" people would be enough if there were statistical data over people who live and work in same area. So I am trying to somehow reduce the data which include everyone AND the "uncertainty coefficient" for each area expressed in % of people travelling to work (more travels = less reliable data) to this ideal model.

I am still getting meaningful results but the regression is very weak, R squared is ~0.3 or so.

Last edited: May 9, 2013