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Suppose that we have data on 1000 people. Each of these people are either from California, Texas, or Hawaii. We have various lifestyle variables on each person (e.g. age, gender, etc.). We are interested in comparing the income of people in California versus the income of people in Texas using linear regression. Is it okay to drop data of those people who are from Hawaii? Would we not lose any information if we did this?

Wouldn't is depend on how many people are in each group?

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How would you propose to use the information about Hawaiians in your analysis of income differences between Californians and Texans? –  Nick Stauner Mar 10 at 3:00
    
@NickStauner: I wouldn't use it directly. It would just be informative to see how people in Hawaii stack up to those in Texas and California. –  guestom Mar 10 at 3:01
    
You would loose data. You should include the information on Hawaiians also, unless the relationship b/t the other variables and income differs by state. –  gung Mar 10 at 3:10
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Sounds like you've answered your own question...but informative how? There are certainly more analyses you can perform with more data from a third population, but that doesn't mean you want to do those analyses necessarily. You have to decide what questions you want to ask! If you're interested in predicting income from location, that's a bigger question than what income differences exist between California and Texas. Same thing if you're interested in whether the difference between California and Texas is similar to the difference of either state vs. Hawaii. –  Nick Stauner Mar 10 at 3:10
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I am unclear what is the issue or the problem you are addressing. Given that, I am not sure that linear regression is the proper methodology. Maybe an hypothesis testing framework using ANOVA to figure out if those groups are statistically different would be a better approach followed up with related Post Hoc test to measure the statistical difference for each paired combination of States. –  Gaetan Lion Mar 10 at 3:17
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1 Answer 1

It depends on your prior assumptions. If you're going to allow for completely independent models for each state, then it cannot help you to keep the Hawaii data. However you might have a model that looks like this Wealth = A * Age + G* Gender + C(State) then you would be losing information by ignoring Hawaii as the Hawaii data also helps you measure A and G which in turn will help you measure the three C(State) values.

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+1 nice answer. –  mok Mar 10 at 4:06
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