逻辑回归用于预测分类输出，如是/否，低/中/高等。你基本上有2种类型的逻辑回归二元逻辑回归(是/否，批准/不批准)或多类逻辑回归(低/中/高，0-9等数字)

另一方面，线性回归是因变量(y)是连续的。 Y = mx + c是一个简单的线性回归方程(m =斜率，c是Y截距)。多元线性回归有不止一个自变量(x1,x2,x3，…)等)

逻辑回归用于预测分类输出，如是/否，低/中/高等。你基本上有2种类型的逻辑回归二元逻辑回归(是/否，批准/不批准)或多类逻辑回归(低/中/高，0-9等数字)

另一方面，线性回归是因变量(y)是连续的。 Y = mx + c是一个简单的线性回归方程(m =斜率，c是Y截距)。多元线性回归有不止一个自变量(x1,x2,x3，…)等)

非常同意以上的评论。 除此之外，还有一些不同之处

在线性回归中，残差被假设为正态分布。 在逻辑回归中，残差需要是独立的，但不是正态分布。

线性回归假设解释变量值的恒定变化导致响应变量的恒定变化。 如果响应变量的值代表概率(在逻辑回归中)，则此假设不成立。

广义线性模型(GLM)不假设因变量和自变量之间存在线性关系。但在logit模型中，它假设link函数与自变量之间是线性关系。

只是补充一下之前的答案。

线性回归

Is meant to resolve the problem of predicting/estimating the output value for a given element X (say f(x)). The result of the prediction is a continuous function where the values may be positive or negative. In this case you normally have an input dataset with lots of examples and the output value for each one of them. The goal is to be able to fit a model to this data set so you are able to predict that output for new different/never seen elements. Following is the classical example of fitting a line to set of points, but in general linear regression could be used to fit more complex models (using higher polynomial degrees):

解决问题

线性回归有两种不同的求解方法:

法方程(直接解题方法) 梯度下降(迭代法)

逻辑回归

是为了解决分类问题，给定一个元素，你必须把它分成N个类别。典型的例子是，例如，给定一封邮件，将其分类为垃圾邮件，或者给定一辆车辆，查找它属于哪个类别(汽车、卡车、货车等)。基本上输出是一组有限的离散值。

解决问题

逻辑回归问题只能通过梯度下降来解决。一般来说，公式与线性回归非常相似，唯一的区别是使用不同的假设函数。在线性回归中，假设的形式为:

h(x) = theta_0 + theta_1*x_1 + theta_2*x_2 .. 

其中是我们试图拟合的模型[1,x_1, x_2， ..]为输入向量。在逻辑回归中，假设函数是不同的:

g(x) = 1 / (1 + e^-x)

This function has a nice property, basically it maps any value to the range [0,1] which is appropiate to handle propababilities during the classificatin. For example in case of a binary classification g(X) could be interpreted as the probability to belong to the positive class. In this case normally you have different classes that are separated with a decision boundary which basically a curve that decides the separation between the different classes. Following is an example of dataset separated in two classes.

You can also use the below code to generate the linear regression curve q_df = details_df # q_df = pd.get_dummies(q_df) q_df = pd.get_dummies(q_df, columns=[ "1", "2", "3", "4", "5", "6", "7", "8", "9" ]) q_1_df = q_df["1"] q_df = q_df.drop(["2", "3", "4", "5"], axis=1) (import statsmodels.api as sm) x = sm.add_constant(q_df) train_x, test_x, train_y, test_y = sklearn.model_selection.train_test_split( x, q3_rechange_delay_df, test_size=0.2, random_state=123 ) lmod = sm.OLS(train_y, train_x).fit() lmod.summary() lmod.predict()[:10] lmod.get_prediction().summary_frame()[:10] sm.qqplot(lmod.resid,line="q") plt.title("Q-Q plot of Standardized Residuals") plt.show()

简而言之: 线性回归给出连续的输出。即在一个值范围内的任何值。 逻辑回归给出离散的输出。即Yes/No, 0/1类型的输出。

| Basis                                                           | Linear                                                                         | Logistic                                                                                                            |
|-----------------------------------------------------------------|--------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------|
| Basic                                                           | The data is modelled using a straight line.                                    | The probability of some obtained event is represented as a linear function of a combination of predictor variables. |
| Linear relationship between dependent and independent variables | Is required                                                                    | Not required                                                                                                        |
| The independent variable                                        | Could be correlated with each other. (Specially in multiple linear regression) | Should not be correlated with each other (no multicollinearity exist).                                              |