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Thread: Regression analysis

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    Regression analysis




    Hi all.
    Could I use linear regression with not normal distributed variable?

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    Re: Regression analysis

    It depends on what you're doing. The Gauss-Markov theorem still holds even if the error terms of the regression model are not normally distributed

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    Re: Regression analysis

    You can but your confidence intervals will likely be in error. It is generally a better idea to transform the data to make it normal (other alternatives include various robust regressions and non-parametrics).
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Regression analysis

    Quote Originally Posted by noetsi View Post
    You can but your confidence intervals will likely be in error. It is generally a better idea to transform the data to make it normal (other alternatives include various robust regressions and non-parametrics).
    Although before jumping to conclusions it might not be bad for us to ask the OP what they mean by their question. As we have to say quite often - we don't care if the dependent or independent variables are normally distributed. It's the distribution of the error term that matters.
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    Re: Regression analysis

    Yes I assumed they meant the residuals were not normally distributed. Also it is commonly said that ANOVA (and thus regression I assume) are highly robust to the assumption of normality of the residuals. Of course what that means in practice is not very clear....
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Regression analysis

    Quote Originally Posted by noetsi View Post
    Yes I assumed they meant the residuals were not normally distributed.
    You're too optimistic. I've done enough consulting that when I see
    not normal distributed variable
    I don't assume they are talking about the residuals.
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    Re: Regression analysis


    Unfortunately in many articles, text, and online reports not only do they fail to distinguish this, they actually analyze the univariate distrtibutions for normality. This is even more common I think with skew and kurtosis. It is the individual variable that is analyzed not multivariate skew/kurtosis (in fairness some software don't analyze multivariate aka mardia's skew kurtosis so its not easy to do this).
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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