4.3 Logistic Regression
It is for classification.
4.3.1 The Logistic Model
我们可以通过改变 Beta_1 的值来调整 sigmoid function的增长率。
Beta_0 的值能够将此函数向右和向左移动。
Odds:
Log odds 又叫作 logit
the logit function is indeed the inverse of the logistic function.
So, if a coefficient β1 is 0.0030 for a predictor variable X1 (like income), the interpretation in logistic regression is that for every one-unit increase in X1 (e.g., for every dollar increase in income), the log odds of the event occurring increases by 0.0030 on the log scale. This does not directly translate to a probability increase because the relationship between the log odds and the probability is nonlinear due to the logistic function.
“Increasing X by one unit changes the log
odds by beta1 (4.4). Equivalently, it multiplies the odds by e^beta1 (4.3).”
4.3.2 Estimating the Regression Coefficients
Estimating coefficients by Maximizing the Likelihood function
(In the linear regression setting, the least squares approach is in fact a special case of maximum likelihood.)
“However, in general, logistic regression and other models can be easily fit using statistical software such as R, and so we do not need to concern ourselves with the details of the maximum likelihood fitting procedure.”
4.3.3 Making Predictions
4.3.4 Multiple Logistic Regression
predicting a binary response using multiple
predictors. 受多因素影响
4.3.5 Multinomial Logistic Regression
more than two classes 分成好几个类别
–Book “An Introduction To Statistical Learning Textbook” 这是一本非常著名的教材《统计学习导论》，为什么中英文版本有出入？？？