logistic_regression.md

logistic regression

1 Logistic regression

1. Multinomial logistic regreesion(also know as: polytomous LR, multiclass LR, softmax regression, multinomial logit, maximum entropy (MaxEnt) classifier, conditional maximum entropy model)
2. Ordered logit
3. Conditional logistic regression

2 Multinomial logistic regreesion

1. Independent variable.

3 Ordered logit

4 null hypothesis and alternative hypothesis

1. There is no relationship between two phenomean.
2. In statistics, it is often denoted H0.
3. The statement that is hoped or expedted to be true instead of the null hypothesis is the alternative hypothesis.
4. Terminology: simple hypothesis, composite hypothesis, exact hypothesis, inexact hypothesis, one-tailed hypothesis.
5. There must be enough samples to observe for a null hypothesis.

5 One- and itwo-tailed testes

1. a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set.
2. One-tailed tests are used for asymmetric distributions that have a single tail, such as the chi-squared distribution, which are common in measuring goodness-of-fit, or for one side of a distribution that has two tails, such as the normal distribution, which is common in estimating location; this corresponds to specifying a direction.

6 Student's t-distribution

7 p-value

1. The p-value is defined as the probability, under the assumption of hypothesis H, of obtaining a result equal to or more extreme than what was actually observed.
2. Note for p-n

8 type-I and type-II error

1. In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is incorrectly retaining a false null hypothesis (a "false negative").
2. In terms of false positives and false negatives, a positive result corresponds to rejecting the null hypothesis, while a negative result corresponds to failing to reject the null hypothesis.

9 Confidence interval(CI)

1. In statistics, a confidence interval (CI) is a type of interval estimate of a statistical parameter.
2. . It is an observed interval (i.e., it is calculated from the observations), in principle different from sample to sample, that frequently includes the value of an unobservable parameter of interest if the experiment is repeated.

9 odds and odds ratio

1. The odds of the dependent variable equaling a case (given some linear combination {\displaystyle x} x of the predictors) is equivalent to the exponential function of the linear regression expression