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Normal assumption with least squares regression

  1. Nov 6, 2007 #1
    My google search just turns up results telling me that one of the assumptions I have to make is that each Y is normal. My question is why do I have to assume its normal. Why does it follow that it has to be normal as opposed to some other distribution? Hope that makes sense.

    Edit: I thought about this some more. Is it just as simple as the standard errors for the parameters are computed assuming each Y is normal? If you write it out you can easily see that B1 for example is a linear function of Y1...Yn and thus will be normal.
     
    Last edited: Nov 6, 2007
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  3. Nov 7, 2007 #2

    EnumaElish

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    You do not need normality for least squares estimation. That includes the estimation of standard errors. The LS parameter estimates and the standard deviations are sample-based statistics; they do not require making assumptions about a distribution.

    You do need normality when you are testing hypotheses based on the parameter estimates and the standard deviations. Since hypothesis testing means looking up probability values from a "probability table," you need to know which table to look at, and that means you have to make an assumption about the distribution.
     
  4. Nov 7, 2007 #3
    Ok, so I guess my question is why do I have to assume that it's normal. Why can't I assume it's gamma or anything else. I was under the impression that if I wanted to use anything other than normal, I had to use GLMs (which I'll admit I know nothing about).
     
    Last edited: Nov 7, 2007
  5. Nov 7, 2007 #4

    EnumaElish

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    My advice is not to make distributional assumptions whenever you don't have to.

    However, that would imply you cannot use ordinary LS results to test hypotheses.

    If you wish to assume a non-normal distribution, then my advice is to use maximum likelihood estimation: http://en.wikipedia.org/wiki/Maximum_likelihood
     
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