Generalized Linear Model over Normal Distribution reduces to Linear Regression Model

Theorem

Let $Y$ be a random variable which obeys a normal distribution.

Let a generalized linear model for one variable for $Y$ be:

$\mu = \expect Y = \beta_0 + \beta_1 x$

whose variance is $\sigma^2$.

Then the generalized linear model reduces to the linear regression model.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): generalized linear models
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): generalized linear models