【Udacity】线性回归方程 Regression

快来打我* 2022-01-11 07:47 255阅读 0赞

*  Concept in English
 *  Coding Portion
 *  评估回归的性能指标——R平方指标
 *  比较分类和回归

Continuous supervised learning 连续变量监督学习

Regression 回归

Continuous：有一定次序，且可以比较大小

### 一、Concept in English ###

**Slope：** 斜率

**Intercept：** 截距

**coefficient**:系数

### 二、Coding Portion ###

Google: sklearn regression

import numpy
    import matplotlib.pyplot as plt
    
    from ages_net_worths import ageNetWorthData
    
    ages_train, ages_test, net_worths_train, net_worths_test = ageNetWorthData()
    
    
    
    from sklearn.linear_model import LinearRegression
    
    reg = LinearRegression()
    reg.fit(ages_train, net_worths_train)
    
    ### get Katie's net worth (she's 27)
    ### sklearn predictions are returned in an array, so you'll want to index into
    ### the output to get what you want, e.g. net_worth = predict([[27]])[0][0] (not
    ### exact syntax, the point is the [0] at the end). In addition, make sure the
    ### argument to your prediction function is in the expected format - if you get
    ### a warning about needing a 2d array for your data, a list of lists will be
    ### interpreted by sklearn as such (e.g. [[27]]).
    km_net_worth = 1.0 ### fill in the line of code to get the right value
    km_net_worth = reg.predict([[27]])[0][0]
    ### get the slope
    ### again, you'll get a 2-D array, so stick the [0][0] at the end
    slope = 0. ### fill in the line of code to get the right value
    slope = reg.coef_[0][0]
    #print reg.coef_
    
    ### get the intercept
    ### here you get a 1-D array, so stick [0] on the end to access
    ### the info we want
    intercept = 0. ### fill in the line of code to get the right value
    intercept = reg.intercept_[0]
    
    ### get the score on test data
    test_score = 0. ### fill in the line of code to get the right value
    test_score = reg.score(ages_test,net_worths_test)
    
    ### get the score on the training data
    training_score = 0. ### fill in the line of code to get the right value
    training_score = reg.score(ages_train,net_worths_train)
    
    
    ### print all the value
    def submitFit():
        # all of the values in the returned dictionary are expected to be
        # numbers for the purpose of the grader.
        return {"networth":km_net_worth,
                "slope":slope,
                "intercept":intercept,
                "stats on test":test_score,
                "stats on training": training_score}

### 三、评估回归的性能指标 ###

评估拟合程度

#### 3.1 最小化误差平方和 ####

SSE sum of Squared Errors

*  相关算法实现

1.Ordinary Least Squares(OLS,普通最小二乘法)

2.Gradient Descent (梯度下降算法)

![1143923-20171011193542543-1602470746.jpg][]

**不足:** 添加的数据越多，误差平方的和必然增加，但并不代表拟合程度不好

![1143923-20171011193602762-153142619.jpg][]

**解决方案：** R平方指标

#### 3.2 R平方指标 ####

r平方越高，性能越好(MAX = 1)

**定义：** 有多少输出的改变能用输入的改变解释

![1143923-20171011193618840-1447062417.jpg][]

**优点：** 与训练点的数量无关

*  Sklearn中的R平方

print "r-squared score:",reg.score(x,y)

**R平方有可能小于0！**  
The coefficient R^2 is defined as (1 - u/v), where u is the regression sum of squares ((y\_true - y\_pred) \*\* 2).sum() and v is the residual sum of squares ((y\_true - y\_true.mean()) \*\* 2).sum(). Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.

### 四、比较分类和回归 ###

![1143923-20171011193631012-1549917760.jpg][]

<table> 
 <thead> 
  <tr> 
   <th>特性</th> 
   <th style="text-align:center;">监督分类</th> 
   <th style="text-align:right;">回归</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td>输出类型</td> 
   <td style="text-align:center;">标签(离散)</td> 
   <td style="text-align:right;">值(连续)</td> 
  </tr> 
  <tr> 
   <td>寻找的结果(可视化)</td> 
   <td style="text-align:center;">决策边界</td> 
   <td style="text-align:right;">最佳拟合曲线</td> 
  </tr> 
  <tr> 
   <td>评判模型的标准</td> 
   <td style="text-align:center;">准确度</td> 
   <td style="text-align:right;">误差平方和or R平方指标</td> 
  </tr> 
 </tbody> 
</table>

转载于:https://www.cnblogs.com/Neo007/p/7652498.html

[1143923-20171011193542543-1602470746.jpg]: /images/20220111/87daa46f2fe3496c86ec9e140aeb2ba7.png
[1143923-20171011193602762-153142619.jpg]: /images/20220111/dc5033b0c51949c4970cd55d477cd1f4.png
[1143923-20171011193618840-1447062417.jpg]: /images/20220111/a58ccd59cef245a5b093220cdef474c3.png
[1143923-20171011193631012-1549917760.jpg]: /images/20220111/a232139c48c841a0b7cdc07b3d7a727a.png