[python] 공분산이란? cov

summary

print('-'*100)
print(sp.cov(x, y, ddof=0))
print(sp.cov(x, y, ddof=1))

 

 

 

공분산 공식

 

공분산 data 형태

분산 처럼 N-1을 취한 형태

공분산

과소하는 경우 N으로 나눠져있다.

cov_sample = sum((x-mu_x)*(y-mu_y))/N
print('{0:.3f}'.format(cov_sample))       #6.906

 

공분산

과소하는 경우 해결 N-1을 곱함

cov = sum((x-mu_x)*(y-mu_y))/(N-1)
print('{0:.3f}'.format(cov))        # 7.673

 

full code

github

from pandas import DataFrame
import pandas as pd
import scipy as sp
import numpy as np


datas:DataFrame = pd.DataFrame({'x':[18.5,18.7,19.1,19.7,21.5,21.7,21.8,22.0,23.4,23.8],
                                'y':[34, 39, 41, 38, 45, 41, 52, 44, 44, 49]})


print(datas.info())
print(datas.describe())

print(datas)

x = datas['x']
y = datas['y']

print(x)
print(y)

N = len(datas)

mu_x = sp.mean(x)
mu_y = sp.mean(y)

print(mu_x)
print(mu_y)

cov_sample = sum((x-mu_x)*(y-mu_y))/N
print('{0:.3f}'.format(cov_sample))

cov = sum((x-mu_x)*(y-mu_y))/(N-1)
print('{0:.3f}'.format(cov))

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분산-공분산 행렬

분산-공분산 행렬

 

snippets

print('-'*100)
print(sp.cov(x, y, ddof=0))
print(sp.cov(x, y, ddof=1))

 

출력 결과

아래와 같이 분산-공분산 행렬을 얻을 수 있다.

[[ 3.2816  6.906 ]
 [ 6.906  25.21  ]]
[[ 3.64622222  7.67333333]
 [ 7.67333333 28.01111111]]

 

full code

github

from pandas import DataFrame
import pandas as pd
import scipy as sp
import numpy as np


datas:DataFrame = pd.DataFrame({'x':[18.5,18.7,19.1,19.7,21.5,21.7,21.8,22.0,23.4,23.8],
                                'y':[34, 39, 41, 38, 45, 41, 52, 44, 44, 49]})


print(datas.info())
print(datas.describe())

print(datas)

x = datas['x']
y = datas['y']

print(x)
print(y)

N = len(datas)

mu_x = sp.mean(x)
mu_y = sp.mean(y)

print(mu_x)
print(mu_y)

cov_sample = sum((x-mu_x)*(y-mu_y))/N
print('{0:.3f}'.format(cov_sample))

cov = sum((x-mu_x)*(y-mu_y))/(N-1)
print('{0:.3f}'.format(cov))

print('-'*100)
print(sp.cov(x, y, ddof=0))
print(sp.cov(x, y, ddof=1))