## 14.1 Logistic Regression

• Logistic Regression belongs to the class of generalised linear models (glms)generalised linear models (glms)

• Used to model data with a dichotomous response variable.

• Logistic regression models the conditional probability of the response variable rather than its value.

• A logit link function, defined as $$logit\,p=log[p/(1-p)]$$, is used to transform the output of a linear regression to be suitable for probabilities.

• A linear model for these transformed probabilities can be setup as

$$$logit\,p=\beta_{0}+\beta_{1}x_{1}+\beta_{2}x_{2}+\ldots\beta_{k}x_{x} \tag{14.1}$$$
• R provides the glm function for modelling generalised linear models including the logistic regression model
• We will use the caret package to model logistic regression later in this topic.
• See and for further details on logistic regression.

### References

Boehmke, Brad, and Brandon M Greenwell. 2019. Hands-on Machine Learning with r. CRC Press. https://bradleyboehmke.github.io/HOML/.
Hastie, Trevor, Robert Tibshirani, Gareth James, and Daniela Witten. 2013. An Introduction to Statistical Learning with Applications in r. Springer New York.