Machine learningLesson 2 of 4 in the course Supervised learning

Logistic Regression: Probabilities, Coefficients, and Model Fitting

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Logistic regression is a statistical method for modeling the probability of a categorical outcome, especially an outcome with two possible values. This lesson introduces the purpose of the model and the relationship between predictors, log-odds, and probability.

In binary logistic regression, the outcome or dependent variable is coded as 0 or 1. For example, an email might be labeled 1 if it is spam and 0 otherwise. The predictors, also called explanatory variables or features, describe each case. They may be continuous, such as hours studied, or binary, such as whether a condition is present.

All flashcards

What is the logit of a probability?
The natural logarithm of its odds: ln⁡(p1−p)\ln\left(\frac{p}{1-p}\right).
What does a logistic regression intercept represent?
The log-odds of class 1 when all predictors equal zero.
What is an odds ratio for a one-unit predictor increase?
The factor eβje^{\beta_j} by which the odds change, holding other predictors fixed.
What is complete separation in logistic regression?
A condition where predictors perfectly distinguish outcome classes, potentially causing coefficients to grow without bound.
What does a probit model use as its link?
A link based on the normal distribution rather than the logistic function.

Quiz questions

  1. In logistic regression, what does the logit of the outcome probability model as a linear function of the predictors?Answer: The log-odds of class 1.
  2. In logistic regression, how does eβje^{\beta_j} relate to a one-unit increase in predictor xjx_j?Answer: It is the multiplicative change in the odds, holding other predictors fixed.
  3. Which model is suited to an outcome with more than two unordered categories?Answer: Multinomial logistic regression.
  4. What does maximum likelihood estimation choose in logistic regression?Answer: Coefficients that make the observed outcomes most likely under the model.
  5. What is a key property of binary log loss?Answer: It assigns very high loss to confident predictions that are incorrect.

Based on the Wikipedia article Logistic regression, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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