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[QUOTE="statdad, post: 6863147, member: 136993"] "Does each pair represent the realization of a bivariate random variable with Gaussian joint distribution?" Not classically, no. First of all, the assumption of a Gaussian distribution is not part of those required for regression, and when it's made it doesn't apply to the response but to the error distribution. If you assume both response and predictor are random the regression model is typically viewed as saying the conditional expected value of Y given x. "In the regression analysis, are both and random variables or only the variable is random?" As noted above, traditionally only Y is considered random. "A random variable has its possible values and associated probabilities. Two random variables and are said to be jointly normal if aX + bY has a normal distribution." You're missing a bit here: you need to add the statement "for all real numbers, a, b". [/QUOTE]
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