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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 @@ $$
For the models above, these are: For the models above, these are:
+----------------+----------------+----------------+ +----------------+------------------+--------------------------+
| Type of Data | Distribution | Link Function | | Type of Data | Distribution | Link Function |
| | Family | | | | Family | |
+================+================+================+ +================+==================+==========================+
| continuous | Normal | identity: | | continuous | Normal | identity: |
| | | | | | | |
| | | $$ | | | | $$ |
| | | g(x)=x | | | | g(x)=x |
| | | $$ | | | | $$ |
+----------------+----------------+----------------+ +----------------+------------------+--------------------------+
| count | Poisson | log: | | count | Poisson | log: |
| | | | | | | |
| | | \$\$ | | | | $$ |
| | | | | | | g(x) = \log(x) |
| | | g(x) = \log(x) | | | | $$ |
| | | \$\$ | +----------------+------------------+--------------------------+
+----------------+----------------+----------------+ | binary | Bernoulli | logit: |
| binary | Bernoulli | logit: | | | | |
| | | | | | | $$ |
| | | $$ | | | | g(x) = \log\left( |
| | | g | | | | \frac{x}{1-x} |
| | | ( | | | | \right) |
| | | x) = \log\left | | | | $$ |
| | | ( | +----------------+------------------+--------------------------+
| | | \ |
| | | f |
| | | ra |
| | | c |
| | | { |
| | | x}{1-x}\right) |
| | | $$ |
+----------------+----------------+----------------+
In general, the parameter vector $\beta$ is estimated via maximizing the In general, the parameter vector $\beta$ is estimated via maximizing the
likelihood, i.e., likelihood, i.e.,