$\log(\text{odds}) = \text{logit}(P)=ln \big({{P}\over{1-P}}\big)$
$ln\big({{P}\over{1-P}}\big)=\beta_0+\beta_1x$
Consider this example: $0.7=\beta_o+\beta_1(x)+\beta_2(y)+\beta_3(z)$
How can this expression be interpreted?
Topic logarithmic logistic-regression
Category Data Science
Lets first understand what does odds ratio mean : Let’s say that the probability of success of some event is .8. Then the probability of failure is 1 – .8 = .2. The odds of success are defined as the ratio of the probability of success over the probability of failure.
In our example, the odds of success are .8/.2 = 4. That is to say that the odds of success are 4 to 1. If the probability of success is .5, i.e., 50-50 percent chance, then the odds of success is 1 to 1.
Why doe we take Log of Odds: One reason is that it is usually difficult to model a variable which has restricted range, such as probability. This transformation is an attempt to get around the restricted range problem. It maps probability ranging between 0 and 1 to log odds ranging from negative infinity to positive infinity.
Now Coming to interpratation:
If this equation gives 0.7 as log of odds it means that the values of x for which it was calculated increases the odds of success by that ratio
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