Linear regression and logistic regression

Linear regression is a regression problem , Logistic regression is a classification problem .

Linear regression

Labels are consecutive floating-point numbers , For example, based on the area of the house 、 Location and other predicted house prices , Forecast weather based on historical weather and other related issues . The prediction formula is as follows ：
$$Y=X\ast W+b$$

Logical regression

For linearly separable cases , Two types of data can be distinguished by a straight line , such as ：

Suppose the label at the top left of this red line is 1, The label at the bottom right of the red line is 0, be $X_1$ And $X_3$ Belong to 1,$X_2$ Belong to 0 class .
But this way is not very intuitive , There's no better way ？ The answer is yes , Further normalization through logical functions

The above is a logic function , Role is to z Map to the value of , The mapping range is $[0,1]$:

• If z The value is greater than 0, After being processed by logic function , The scope is $[0.5,1]$
• If z The value is less than 0, After being processed by logic function , The scope is $[0,0.5]$

Now we can calculate the probability of each point leaving ：

You can see ,$X_1$ Point belongs to 1 The probability is greater than $X_1$ Point belongs to 0 Probability .