最小二乘法构建线性回归方程

首先需要下载一个数据分析的插件：

点击左上角文件->选项->加载项->分析工具库->转到-数据分析库->确定

下载好插件之后就可以开始使用Excel做数据分析了

点击数据->数据分析

回归->确定

最后得到的结果：

根据最小二乘法公式手动构建一元线性回归模型

#不掉包实现一元线性回归
import pandas as pd
def read_file(raw):#根据行数来读取文件
    df = pd.read_excel('..\source\weights_heights(身高-体重数据集).xls',sheet_name ='weights_heights')
    height=df.iloc[0:raw,1:2].values
    weight=df.iloc[0:raw,2:3].values
    return height,weight

def array_to_list(array):#将数组转化为列表
    array=array.tolist()
    for i in range(0,len(array)):
        array[i]=array[i][0]
    return array

def unary_linear_regression(x,y):#一元线性回归，x,y都是列表类型
    xi_multiply_yi=0
    xi_square=0;
    x_average=0;
    y_average=0;
    f=x
    for i in range(0,len(x)):
        xi_multiply_yi+=x[i]*y[i]
        x_average+=x[i]
        y_average+=y[i]
        xi_square+=x[i]*x[i]
    x_average=x_average/len(x)
    y_average=y_average/len(x)
    b=(xi_multiply_yi-len(x)*x_average*y_average)/(xi_square-len(x)*x_average*x_average)
    a=y_average-b*x_average
    for i in range(0,len(x)):
        f[i]=b*x[i]+a
    R_square=get_coefficient_of_determination(f,y,y_average)
    print('R_square='+str(R_square)+'n'+'a='+str(a)+'  b='+str(b))
    
def get_coefficient_of_determination(f,y,y_average):#传输计算出的值f和x,y的真实值还有平均值y_average，获取决定系数，也就是R²
    res=0
    tot=0
    for i in range(0,len(y)):
        res+=(y[i]-f[i])*(y[i]-f[i])
        tot+=(y[i]-y_average)*(y[i]-y_average)
    R_square=1-res/tot 
    return R_square

raw=[20,200,2000,20000]
for i in raw:
    print('数据组数为'+str(i)+":")
    height,weight=read_file(i)
    height=array_to_list(height)
    weight=array_to_list(weight)
    unary_linear_regression(height,weight)

结果如下：

#调包实现一元线性回归
from sklearn import linear_model
from sklearn.metrics import r2_score
import numpy as np
import pandas as pd
def read_file(raw):#根据行数来读取文件
    df = pd.read_excel('..\source\weights_heights(身高-体重数据集).xls',sheet_name ='weights_heights')
    height=df.iloc[0:raw,1:2].values
    weight=df.iloc[0:raw,2:3].values
    return height,weight

raw=[20,200,2000,20000]#要读取的行数
for i in raw:
    print('数据组数为'+str(i)+":")
    height,weight=read_file(i)
    weight_predict=weight
    lm = linear_model.LinearRegression()
    lm.fit(height,weight)
    b=lm.coef_
    a=lm.intercept_
    weight_predict=lm.predict(height)#计算有方程推测出来的值
    R_square=r2_score(weight,weight_predict)#计算方差
    print('b='+str(b[0][0])+' a='+str(a[0]))
    print('R_square='+str(R_square))
    

结果如下：