线性回归和逻辑回归的基本区别是: 线性回归用于预测一个连续的或数值，但当我们寻找预测一个值，是分类逻辑回归进入画面。

二元分类采用逻辑回归。

Linear regression output as probabilities It's tempting to use the linear regression output as probabilities but it's a mistake because the output can be negative, and greater than 1 whereas probability can not. As regression might actually produce probabilities that could be less than 0, or even bigger than 1, logistic regression was introduced. Source: http://gerardnico.com/wiki/data_mining/simple_logistic_regression Outcome In linear regression, the outcome (dependent variable) is continuous. It can have any one of an infinite number of possible values. In logistic regression, the outcome (dependent variable) has only a limited number of possible values. The dependent variable Logistic regression is used when the response variable is categorical in nature. For instance, yes/no, true/false, red/green/blue, 1st/2nd/3rd/4th, etc. Linear regression is used when your response variable is continuous. For instance, weight, height, number of hours, etc. Equation Linear regression gives an equation which is of the form Y = mX + C, means equation with degree 1. However, logistic regression gives an equation which is of the form Y = eX + e-X Coefficient interpretation In linear regression, the coefficient interpretation of independent variables are quite straightforward (i.e. holding all other variables constant, with a unit increase in this variable, the dependent variable is expected to increase/decrease by xxx). However, in logistic regression, depends on the family (binomial, Poisson, etc.) and link (log, logit, inverse-log, etc.) you use, the interpretation is different. Error minimization technique Linear regression uses ordinary least squares method to minimise the errors and arrive at a best possible fit, while logistic regression uses maximum likelihood method to arrive at the solution. Linear regression is usually solved by minimizing the least squares error of the model to the data, therefore large errors are penalized quadratically. Logistic regression is just the opposite. Using the logistic loss function causes large errors to be penalized to an asymptotically constant. Consider linear regression on categorical {0, 1} outcomes to see why this is a problem. If your model predicts the outcome is 38, when the truth is 1, you've lost nothing. Linear regression would try to reduce that 38, logistic wouldn't (as much)2.

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。

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)

| 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).                                              |

简单地说，如果在线性回归模型中有更多的测试用例到达，这些测试用例远离预测y=1和y=0的阈值(例如=0.5)。在这种情况下，假设就会改变，变得更糟。因此，线性回归模型不适用于分类问题。

另一个问题是，如果分类是y=0和y=1, h(x)可以是> 1或< 0。因此，我们使用Logistic回归0<=h(x)<=1。