## Logistic regression

As previously discussed, our classification problem is best modeled with the probabilities that are bound by `0`

and `1`

. We can do this for all of our observations with a number of different functions, but here we will focus on the logistic function. The logistic function used in logistic regression is as follows:

If you have ever placed a friendly wager on horse races or the World Cup, you may understand the concept better as odds. The logistic function can be turned to odds with the formulation of *Probability (Y) / 1 - Probability (Y)*. For instance, if the probability of Brazil winning the World Cup is 20 percent, then the odds are *0.2 / 1 - 0.2*, which is equal to *0.25*, translating to odds of one in four.

To translate the odds back to probability, take the odds and divide by one plus the odds. The World Cup example is thus *0.25 / 1 + 0.25*, which is equal to 20 percent. Additionally, let's consider the odds ratio. Assume that the odds of Germany winning the Cup are *0.18*....