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.

在线性回归中，结果是连续的，而在逻辑回归中，结果只有有限数量的可能值(离散的)。

例子: 在一种情况下，x的给定值是一个地块的平方英尺大小，然后预测y的比率是在线性回归下。

相反，如果你想根据面积预测地块是否会以超过30万卢比的价格出售，你将使用逻辑回归。可能的输出是Yes，该地块的售价将超过30万卢比，或者No。

简单地说，线性回归是一种回归算法，它输出一个可能连续和无限的值;逻辑回归被认为是一种二进制分类器算法，它输出输入属于标签(0或1)的“概率”。

在线性回归中，结果(因变量)是连续的。它可以有无限个可能值中的任意一个。在逻辑回归中，结果(因变量)只有有限数量的可能值。

例如，如果X包含以平方英尺为单位的房屋面积，而Y包含这些房屋的相应销售价格，您可以使用线性回归来预测销售价格作为房屋大小的函数。虽然可能的销售价格实际上可能没有任何值，但有很多可能的值，因此可以选择线性回归模型。

相反，如果你想根据房子的大小来预测房子是否会卖到20万美元以上，你会使用逻辑回归。可能的输出是Yes，房子将以超过20万美元的价格出售，或者No，房子不会。

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)

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。