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 # Some Regression Topics
+
+## Poisson Regression
+
+Data $y_i$ are from a Poisson distribution with mean $\mu_i$ and $\ln{\mu_i}=\beta_1+\beta_2 x_i$.
+A likelihood function can be written and the parameters can be estimated using maximum likelihood.
+
+## The Generalized Linear Model (`GLM`)
+
+Data $y_i$ are from a distribution within the exponential family, with mean $\mu_i$ and $g(\mu_i)=\textbf{x}'_i\boldsymbol{\beta}$ for some link function, $g$.
+A likelihood function can now be written and the parameters can be estimated using maximum likelihood.
+
+### Details
+
+Data $y_i$ are from a distribution within the exponential family, with mean $\mu_i$ and $g(\mu_i)=\textbf{x}'_i\boldsymbol{\beta}$ for some link function, $g$.
+
+The exponential family includes distributions such as the Gaussian, binomial, Poisson, and gamma (and thus exponential and chi-squared)
+
+The link functions are typically
+
+- identity (with the Gaussian)
+
+- log (with the Poisson and the gamma)
+
+- logistic (with the binomial)
+
+A likelihood function can be set up for each of these models and the parameters can be estimated using maximum likelihood.
+
+The `glm` package in R has options to estimate parameters in these models.