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430 CHAPTER 17. LOGISTIC REGRESSION
working with logistic regression is very similar. Many of the things we did with
ordinary linear regression can be done with logistic regression in a very similar
fashion. For example,
• Testing for a single parameter
• Testing for a set of parameters
• Formula specification in R
• Interpreting parameters and estimates
• Confidence intervals for parameters
• Confidence intervals for mean response
• Variable selection
After some introduction to the new tests, we’ll demonstrate each of these using
an example.
17.3.1 Testing with GLMs
Like ordinary linear regression, we’ll want to be able to perform hypothesis
testing. We’ll again want both single parameter, and multiple parameter tests.
17.3.2 Wald Test
In ordinary linear regression, we performed the test of
∶ = 0 vs ∶ ≠ 0
0
1
using a -test.
For the logistic regression model,
(x)
log ( ) = + + … + −1 −1
0
1 1
1 − (x)
we can again perform a test of
∶ = 0 vs ∶ ≠ 0
1
0
however, the test statistic and its distribution are no longer . We see that the
test statistic takes the same form
̂
−
= approx (0, 1)
∼
̂
SE[ ]
