数据的回归分析_数据回归.ppt-优快云博客

本文介绍了使用Excel进行线性回归分析以研究父母与子女身高的关系，并探讨了线性回归是否成立的判断方法。接着，通过鸢尾花数据集展示了如何利用Anaconda创建虚拟环境，安装必要的Python包，并运用LinearSVC实现分类。通过调整C参数，观察决策边界的改变，强调了C值对分类边界的影响。

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一、Excel线性回归数据分析

这里使用excel的数据分析功能来分析父母身高与子女身高的关系
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如果没有则需要去文件–>选项–>加载项里面开启功能

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首先点击数据分析，选择回归，然后选择对应的X和Y值，最后选择所需输出的信息即可

这里由于没有处理掉多余项，所以相关性会极差并出现以下图片，但是也不妨碍大概分析

父子身高关系图：
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根据图中信息显示，子女的身高与父亲的身高大致呈正比关系，并由方程得出当父亲身高为75英寸时，子女身高大概为69.065英寸

母子身高关系图：
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根据图中信息显示，子女的身高与父亲的身高大致呈正比关系

其实由与没有对数据进行预处理，因此得出的回归方程并不成立，但是我们还是能大致看出“母高高一窝，父高高一个”的习俗说法还是成立的

二、判断线性回归是否成立

这里判断了4个例子的线性回归是否成立

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不难看出，除了第三个外，其余例子中的线性回归都不成立

三、鸢尾花Iris数据集

1、Anaconda创建虚拟环境及安装对应的包

创建虚拟环境
1.命令行创建
打开命令行
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输入下面命令

conda create -n sklearn python=3.6

tf1是自己为创建虚拟环境取的名字，后面python的版本可以根据自己需求进行选择。

2.界面创建
打开界面
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创建环境

安装包

pip install 包名
直接这样安装可以由于网络的原因，安装失败或者安装很慢
解决方式：
pip install -i https://pypi.tuna.tsinghua.edu.cn/simple 包名
此处安装的包包括numpy、pandas、sklearn、matplotlib

2、LinearSVC（C）方式实现分类

导入需要使用的包

#导入相应的包
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.preprocessing import StandardScaler
from sklearn.svm import LinearSVC

获取数据

# 获取所需数据集
iris=datasets.load_iris()
#每行的数据，一共四列，每一列映射为feature_names中对应的值
X=iris.data
#每行数据对应的分类结果值（也就是每行数据的label值）,取值为[0,1,2]
Y=iris.target
#通过Y=iris.target.size，可以得到一共150行数据,三个类别个50条数据，并且数据是按照0，1，2的顺序放的

对数据进行处理

#只取y<2的类别，也就是0 1并且只取前两个特征
X=X[:,:2]
#获取0 1类别的数据
Y1=Y[Y<2]
y1=len(Y1)
#获取0类别的数据
Y2=Y[Y<1]
y2=len(Y2)
X=X[:y1,:2]

未经标准化的原始数据点的绘制

#绘制出类别0和类别1
plt.scatter(X[0:y2,0],X[0:y2,1],color='red')
plt.scatter(X[y2+1:y1,0],X[y2+1:y1,1],color='blue')
plt.show()

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数据归一化处理

#标准化
standardScaler=StandardScaler()
standardScaler.fit(X)
#计算训练数据的均值和方差
X_standard=standardScaler.transform(X)
#用scaler中的均值和方差来转换X,使X标准化
svc=LinearSVC(C=1e9)
svc.fit(X_standard,Y1)

画出决策边界
相关函数的说明：

meshgrid() 返回了有两个向量定义的方形空间中的所有点的集合。x0是x值，x1是y的值
ravel() 将向量拉成一行
c_[] 将向量排列在一起
contourf() 等高线

def plot_decision_boundary(model, axis):
    x0, x1 = np.meshgrid(
        np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*100)).reshape(-1, 1),# 600个，影响列数
        np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*100)).reshape(-1, 1),# 600个，影响行数
    )
    # x0 和 x1 被拉成一列，然后拼接成360000行2列的矩阵，表示所有点
    X_new = np.c_[x0.ravel(), x1.ravel()]    # 变成 600 * 600行， 2列的矩阵
y_predict <span class="token operator">=</span> model<span class="token punctuation">.</span><span class="token function">predict</span><span class="token punctuation">(</span>X_new<span class="token punctuation">)</span>   # 二维点集才可以用来预测
zz <span class="token operator">=</span> y_predict<span class="token punctuation">.</span><span class="token function">reshape</span><span class="token punctuation">(</span>x0<span class="token punctuation">.</span>shape<span class="token punctuation">)</span>   # <span class="token punctuation">(</span><span class="token number">600</span><span class="token punctuation">,</span> <span class="token number">600</span><span class="token punctuation">)</span>
<span class="token keyword">from</span> matplotlib<span class="token punctuation">.</span>colors <span class="token keyword">import</span> ListedColormap
custom_cmap <span class="token operator">=</span> <span class="token function">ListedColormap</span><span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token string">'#EF9A9A'</span><span class="token punctuation">,</span><span class="token string">'#FFF59D'</span><span class="token punctuation">,</span><span class="token string">'#90CAF9'</span><span class="token punctuation">]</span><span class="token punctuation">)</span>    
plt<span class="token punctuation">.</span><span class="token function">contourf</span><span class="token punctuation">(</span>x0<span class="token punctuation">,</span> x1<span class="token punctuation">,</span> zz<span class="token punctuation">,</span> linewidth<span class="token operator">=</span><span class="token number">5</span><span class="token punctuation">,</span> cmap<span class="token operator">=</span>custom_cmap<span class="token punctuation">)</span>
    #<span class="token function">print</span><span class="token punctuation">(</span>X_new<span class="token punctuation">)</span>

plot_decision_boundary(svc, axis=[-3, 3, -3, 3])
plt.scatter(X_standard[0:y2,0], X_standard[0:y2,1],color=‘red’)
plt.scatter(X_standard[y2:y1,0], X_standard[y2:y1,1],color=‘blue’)
plt.show()

svc2=LinearSVC(C=0.01)
svc2.fit(X_standard,Y1)
print(svc2.coef_)
print(svc2.intercept_)
plot_decision_boundary(svc2, axis=[-3, 3, -3, 3])
plt.scatter(X_standard[0:y2,0], X_standard[0:y2,1],color='red')
plt.scatter(X_standard[y2:y1,0], X_standard[y2:y1,1],color='blue')
plt.show()

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通过两个绘制得到的图表可以很明显的看到决策边界的不同，表面C C 越小容错空间越大。
分类后的内容基础上添加上下边界

def plot_svc_decision_boundary(model, axis):
    x0, x1 = np.meshgrid(
        np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*100)).reshape(-1, 1),# 600个，影响列数
        np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*100)).reshape(-1, 1),# 600个，影响行数
    )
    # x0 和 x1 被拉成一列，然后拼接成360000行2列的矩阵，表示所有点
    X_new = np.c_[x0.ravel(), x1.ravel()]    # 变成 600 * 600行， 2列的矩阵
y_predict <span class="token operator">=</span> model<span class="token punctuation">.</span><span class="token function">predict</span><span class="token punctuation">(</span>X_new<span class="token punctuation">)</span>   # 二维点集才可以用来预测
zz <span class="token operator">=</span> y_predict<span class="token punctuation">.</span><span class="token function">reshape</span><span class="token punctuation">(</span>x0<span class="token punctuation">.</span>shape<span class="token punctuation">)</span>   # <span class="token punctuation">(</span><span class="token number">600</span><span class="token punctuation">,</span> <span class="token number">600</span><span class="token punctuation">)</span>

<span class="token keyword">from</span> matplotlib<span class="token punctuation">.</span>colors <span class="token keyword">import</span> ListedColormap
custom_cmap <span class="token operator">=</span> <span class="token function">ListedColormap</span><span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token string">'#EF9A9A'</span><span class="token punctuation">,</span><span class="token string">'#FFF59D'</span><span class="token punctuation">,</span><span class="token string">'#90CAF9'</span><span class="token punctuation">]</span><span class="token punctuation">)</span>

plt<span class="token punctuation">.</span><span class="token function">contourf</span><span class="token punctuation">(</span>x0<span class="token punctuation">,</span> x1<span class="token punctuation">,</span> zz<span class="token punctuation">,</span> linewidth<span class="token operator">=</span><span class="token number">5</span><span class="token punctuation">,</span> cmap<span class="token operator">=</span>custom_cmap<span class="token punctuation">)</span>

w <span class="token operator">=</span> model<span class="token punctuation">.</span>coef_<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span>
b <span class="token operator">=</span> model<span class="token punctuation">.</span>intercept_<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span>

index_x <span class="token operator">=</span> np<span class="token punctuation">.</span><span class="token function">linspace</span><span class="token punctuation">(</span>axis<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">,</span> axis<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token number">100</span><span class="token punctuation">)</span>

f(x,y) = w[0]x1 + w[1]x2 + b

1 = w[0]x1 + w[1]x2 + b 上边界

-1 = w[0]x1 + w[1]x2 + b 下边界

y_up <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token number">1</span><span class="token operator">-</span>w<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token operator">*</span>index_x <span class="token operator">-</span> b<span class="token punctuation">)</span> <span class="token operator">/</span> w<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span>
y_down <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token operator">-</span><span class="token number">1</span><span class="token operator">-</span>w<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token operator">*</span>index_x <span class="token operator">-</span> b<span class="token punctuation">)</span> <span class="token operator">/</span> w<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span>

x_index_up <span class="token operator">=</span> index_x<span class="token punctuation">[</span><span class="token punctuation">(</span>y_up<span class="token operator">&lt;=</span>axis<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span><span class="token punctuation">)</span>  <span class="token operator">&amp;</span> <span class="token punctuation">(</span>y_up<span class="token operator">&gt;=</span>axis<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">]</span>
x_index_down <span class="token operator">=</span> index_x<span class="token punctuation">[</span><span class="token punctuation">(</span>y_down<span class="token operator">&lt;=</span>axis<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token operator">&amp;</span> <span class="token punctuation">(</span>y_down<span class="token operator">&gt;=</span>axis<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">]</span>

y_up <span class="token operator">=</span> y_up<span class="token punctuation">[</span><span class="token punctuation">(</span>y_up<span class="token operator">&lt;=</span>axis<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span><span class="token punctuation">)</span>  <span class="token operator">&amp;</span> <span class="token punctuation">(</span>y_up<span class="token operator">&gt;=</span>axis<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">]</span>
y_down <span class="token operator">=</span> y_down<span class="token punctuation">[</span><span class="token punctuation">(</span>y_down<span class="token operator">&lt;=</span>axis<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token operator">&amp;</span> <span class="token punctuation">(</span>y_down<span class="token operator">&gt;=</span>axis<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">]</span>

plt<span class="token punctuation">.</span><span class="token function">plot</span><span class="token punctuation">(</span>x_index_up<span class="token punctuation">,</span> y_up<span class="token punctuation">,</span> color<span class="token operator">=</span><span class="token string">"black"</span><span class="token punctuation">)</span>
plt<span class="token punctuation">.</span><span class="token function">plot</span><span class="token punctuation">(</span>x_index_down<span class="token punctuation">,</span> y_down<span class="token punctuation">,</span> color<span class="token operator">=</span><span class="token string">"black"</span><span class="token punctuation">)</span>

plot_svc_decision_boundary(svc, axis=[-3, 3, -3, 3])
plt.scatter(X_standard[0:y2,0], X_standard[0:y2,1],color=‘red’)
plt.scatter(X_standard[y2:y1,0], X_standard[y2:y1,1],color=‘blue’)
plt.show()

在这里插入图片描述
修改C的值

plot_svc_decision_boundary(svc2, axis=[-3, 3, -3, 3])
plt.scatter(X_standard[0:y2,0], X_standard[0:y2,1],color='red')
plt.scatter(X_standard[y2:y1,0], X_standard[y2:y1,1],color='blue')
plt.show()