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Update Multiple Regression.

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Marco Oesting 2023-10-09 22:11:52 +02:00
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material/3_wed/regression/MultipleRegressionBasics.qmd
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@ -252,38 +252,30 @@ $$
For the models above, these are:
+----------------+----------------+----------------+
+----------------+------------------+--------------------------+
| Type of Data | Distribution | Link Function |
| | Family | |
+================+================+================+
+================+==================+==========================+
| continuous | Normal | identity: |
| | | |
| | | $$ |
| | | g(x)=x |
| | | $$ |
+----------------+----------------+----------------+
+----------------+------------------+--------------------------+
| count | Poisson | log: |
| | | |
| | | \$\$ |
| | | |
| | | $$ |
| | | g(x) = \log(x) |
| | | \$\$ |
+----------------+----------------+----------------+
| | | $$ |
+----------------+------------------+--------------------------+
| binary | Bernoulli | logit: |
| | | |
| | | $$ |
| | | g |
| | | ( |
| | | x) = \log\left |
| | | ( |
| | | \ |
| | | f |
| | | ra |
| | | c |
| | | { |
| | | x}{1-x}\right) |
| | | g(x) = \log\left( |
| | | \frac{x}{1-x} |
| | | \right) |
| | | $$ |
+----------------+----------------+----------------+
+----------------+------------------+--------------------------+
In general, the parameter vector $\beta$ is estimated via maximizing the
likelihood, i.e.,