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This is not a homework question. I just want to understand an aspect of linear regression better. The book "Applied Linear Models" by Kutchner et al, states that a linear regression model is of the form

[tex] Y_i = B_0 + B_1 X_i + \epsilon_i [/tex]

where

[itex] Y_i [/itex] is the value of the response variable in the ith trial

[itex] B_0, B_1 [/itex] are parameters

[itex] X_i [/itex] is a known constant

[itex] \epsilon_i [/itex] is a random variable, normally distributed.

Therefore, [itex]Y_i [/itex] is also a random variable, normally distributed but [itex]X_i [/itex] is a constant.

This confused me a bit because I always associated linear regression with the bivariate normal distribution. That is, the underlying assumption of linear regression is the data [itex]\{(x_1,y_1), (x_2,y_2),...,(x_n,y_x) \} [/itex] is sampled from a bivariate normal distribution. In which case, both X and Y are random variables. But in the formulation above, X is a known constant, while [itex]\epsilon[/itex] and therefore [itex]Y[/itex] are the random variables.

So in summary, what is the connection (if any) is between linear regression as formulated by Kutner and the bivariate normal.

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# Linear regression and bivariate normal, is there a relationship?

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