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So basically I’ve been taught that in a linear regression model the parameters alpha and beta cannot be squared when defining the equation of our model, does this also apply for the error term (epsilon) or only for the parameters?

Paolo Totaro
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  • Can you give a real example where you would want to square the error term? What is the purpose? Do you mean that the errors cannot be negative? – kjetil b halvorsen Sep 09 '23 at 15:41
  • It’s a question I found online, no example provided :(. The question wanted to know if the following model was a linear regression model: Y = alpha + beta*X + epsilon^2 – Paolo Totaro Sep 09 '23 at 15:44
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    According to my answer at https://stats.stackexchange.com/a/148713/919, sort of. The problem is that because $E[\epsilon^2]\ne 0,$ it does double duty by modeling a systematic error as well as a random error. Under the usual iid conditions and supposing the error terms have a common second moment $\mu_2=E[\epsilon_i^2],$ we could rewrite the model as $Y = (\alpha+\mu_2)+\beta X + (\epsilon^2-\mu_2).$ That would be an ordinary regression setting with a non-Gaussian mean-zero conditional distribution. – whuber Sep 09 '23 at 17:21

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