Python 상관관계 분석

Correlation Analysis¶

In [ ]:

import warnings
warnings.filterwarnings('ignore')

Load Data¶

• 키, 몸무게 데이터

In [2]:

import pandas as pd

url = 'https://raw.githubusercontent.com/rusita-ai/pyData/master/PII.csv'
DF = pd.read_csv(url)

DF.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 17 entries, 0 to 16
Data columns (total 8 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   Name       17 non-null     object 
 1   Gender     17 non-null     object 
 2   Age        17 non-null     int64  
 3   Grade      17 non-null     int64  
 4   Picture    17 non-null     object 
 5   BloodType  17 non-null     object 
 6   Height     17 non-null     float64
 7   Weight     17 non-null     float64
dtypes: float64(2), int64(2), object(4)
memory usage: 1.2+ KB

In [3]:

DF.head()

Out[3]:

	Name	Gender	Age	Grade	Picture	BloodType	Height	Weight
0	송태섭	남자	21	3	무	B	179.1	63.9
1	최유정	여자	23	1	유	A	177.1	54.9
2	이한나	여자	20	1	무	A	167.9	50.2
3	김소혜	여자	23	3	무	O	176.1	53.5
4	서태웅	남자	24	4	무	B	176.1	79.8

I. Covariance¶

1) 공분산¶

In [4]:

import numpy as np

np.cov(DF.Height, DF.Weight)[0][1]

Out[4]:

63.83036764705884

2) Pearson 상관계수¶

• 공분산을 두 변수의 표준편차의 곱으로 나눈 값

In [5]:

np.cov(DF.Height, DF.Weight)[0][1] / ((np.std(DF.Height, ddof = 1) * np.std(DF.Weight, ddof = 1)))

Out[5]:

0.6848075756314843

II. scipy¶

In [6]:

from scipy import stats

1) Karl Pearson 상관계수¶

• 기본적으로 등간척도/비율척도 변수에만 적용가능

In [10]:

stats.pearsonr(DF.Height, DF.Weight)[0]

Out[10]:

0.6848075756314843

2) spearman 상관계수¶

• 서열척도 변수가 포함되어도 적용가능
• 등간척도/비율척도 두 변수 간의 관계가 비선형적 일 때 적용

In [8]:

stats.spearmanr(DF.Height, DF.Weight)[0]

Out[8]:

0.6507060771796446

3) kendall tau¶

• spearman 상관계수와 같은 경우 적용가능
• 표본이 작을 때 spearman 상관계수보다 신뢰할 수 있음

In [11]:

stats.kendalltau(DF.Height, DF.Weight)[0]

Out[11]:

0.5278846884821402

III. pandas¶

1) Pearson 상관계수¶

• method('pearson', 'spearman', 'kendall')

In [12]:

DF.corr(method = 'pearson') # default

Out[12]:

	Age	Grade	Height	Weight
Age	1.000000	0.495118	0.349681	0.452384
Grade	0.495118	1.000000	0.312777	0.574785
Height	0.349681	0.312777	1.000000	0.684808
Weight	0.452384	0.574785	0.684808	1.000000

In [13]:

DF.corr(method = 'spearman')

Out[13]:

	Age	Grade	Height	Weight
Age	1.000000	0.469285	0.303355	0.442665
Grade	0.469285	1.000000	0.303913	0.575186
Height	0.303355	0.303913	1.000000	0.650706
Weight	0.442665	0.575186	0.650706	1.000000

In [14]:

DF.corr(method = 'kendall')

Out[14]:

	Age	Grade	Height	Weight
Age	1.000000	0.414786	0.221565	0.337703
Grade	0.414786	1.000000	0.232970	0.442621
Height	0.221565	0.232970	1.000000	0.527885
Weight	0.337703	0.442621	0.527885	1.000000

2) Heat Map¶

In [15]:

import matplotlib.pyplot as plt
import seaborn as sns

plt.figure(figsize = (9, 7))
sns.heatmap(DF.corr(),
            cbar = True,
            annot = True,
            annot_kws={'size' : 20},
            fmt = '.2f',
            square = True,
            cmap = 'Blues')
plt.show()

IV. numpy¶

In [16]:

import numpy as np

1) Pearson 상관계수¶

In [17]:

np.corrcoef(DF.Height, DF.Weight)[0][1]

Out[17]:

0.6848075756314843

V. Visualization¶

In [18]:

plt.figure(figsize = (7, 5))
sns.scatterplot(x = DF.Height,
                y = DF.Weight,
                s = 100)
plt.axvline(DF.Height.mean(),
            color = 'r',
            linestyle = 'dashed',
            linewidth = 2)
plt.axhline(DF.Weight.mean(),
            color = 'b',
            linestyle = 'dashed',
            linewidth = 2)
plt.show()

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End Of Document¶

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