파이썬으로 하는 선형대수학 (4. 공분산과 상관계수)

4.1 평균, 분산, 표준편차 (numpy와 pandas의 ddof 디폴트값 차이)

def myfunc(data) :
  mean = np.sum(data)/len(data)
  var = np.sum([np.power(i - mean,2) for i in data])/len(data)
  std = var**0.5
  return mean, var, std

data0 = np.array([243, 278, 184, 249, 207])
data_panda = pd.DataFrame(data0)
x,y,z = myfunc(data0)
print('평균 : ',x,
      '\nnumpy : ',data0.mean(),
      '\npandas : ',data_panda.mean(),
      '\n\n분산 : ',y,
      '\nnumpy : ',data0.var(),
      '\npandas(default) : ',data_panda.var(),
      '\npandas(ddof=0) : ',data_panda.var(ddof=0),
      '\n\n표준편차 : ',z,
      '\nnumpy : ',data0.std(),
      '\npandas(default) : ',data_panda.std(),
      '\npandas(ddof=0) : ',data_panda.std(ddof=0))

 

4.2 Scattering으로 시각화

import pandas as pd
data1 = [216,32,50,302,40]
data2 = [320,420,60,50,20]
data = pd.DataFrame({'data1':data1, 'data2':data2})
plt.scatter(data.data1, data.data2)
plt.show()

4.3 공분산과 상관계수 구하기

mean_1 = np.sum(data1)/len(data1)
mean_2 = np.sum(data2)/len(data2)

var_1 = np.sum([np.power(i - mean_1,2) for i in data1])/(len(data1)-1)
var_2 = np.sum([np.power(i - mean_2,2) for i in data2])/(len(data2)-1)

std_1 = var_1**0.5
std_2 = var_2**0.5

covar = sum((data1-mean_1)*(data2-mean_2))/(len(data1)-1)
corre = covar / (std_1*std_2)

###
print(covar)
data.cov(ddof=1)
###
print(corre)
data.corr()

공분산 (왼쪽) 상관계수 (오른쪽)

4.4 공분산과 상관계수 구하기 2

import seaborn as sns
tips = sns.load_dataset('tips')
tips.head()
fig, axes = plt.subplots(1, 3, figsize=(10,5))
axes[0].scatter(tips.total_bill,tips.total_bill, c = 'blue', alpha = 0.3)
axes[0].set_title("Total_bill & total_bil",fontsize=20)
axes[1].scatter(tips.total_bill,tips.tip, c = 'red', alpha = 0.3)
axes[1].set_title("Total_bill & tip",fontsize=20)
axes[2].scatter(tips.total_bill,tips['size'], c = 'blue', alpha = 0.3)
axes[2].set_title("Total_bill & size",fontsize=20)
plt.show()
tips.cov()