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In many statistics textbooks I read the following text: “A models based on ordinary linear regression equation models Y, the dependent variable, as a normal random variable, whose mean is linear function of the predictors, b0 + b1*X1 + ... , and whose variance is constant. While generalized linear models extend the linear model in two ways. First, assumption of linearity in the parameters is relaxed, by introducing the link function. Second, error distributions other than the normal can be modeled.”

My Stat teacher never bothered to explain these things to us. He started the regression lesson with the equation Y = b0 + b1 * X1, and an example based on the Weight and Height relation. He never talked about these assumptions about normality and the variance.

As a result for quite some time, I treated this equation was an identity, similar to Assets= Liability + Equity. I have never understood what difference those underlying assumptions make.

Can anybody please explain me why these assumptions are required for this model, and what happens to the result of this model if these assumptions are violated?

Thanks,

MG.