Pandas cov()函数结果解释

Pandas cov()函数结果解释

df = pd.DataFrame([(1, 2), (0, 3), (2, 0), (1, 1)],columns=['dogs', 'cats'])    
print(df.cov())

结果：

              dogs      cats
    dogs  0.666667 -1.000000
    cats -1.000000  1.666667  

计算过程：

E[dogs]=(1+0+2+1)/4=1
E[cats]=(2+3+0+1)/4=1.5
cov(dogs,cats)
=E[(dog-E[dogs])(cat-E[cats])]
=[(1-1)(2-1.5)+(0-1)(3-1.5)+(2-1)(0-1.5)+(1-1)(1-1.5)]/(4-1)
=-1

即（dogs,cats）索引处的值

cov()为协方差函数，协方差表示的是两个变量的总体误差

$var(X)=S^2=\frac{{\sum }_{i=1}^n(X_i-\overline{X})(X_i-\overline{X})}{n-1}$

$cov(X,Y)=\frac{{\sum }_{i=1}^n(X_i-\overline{X})(Y_i-\overline{Y})}{n-1}$ (即上述结果所用公式)

$cov(X,Y)=E[(X-E(X))(Y-E[Y])]$
$=E[XY]-2E[X]E[Y]+E[x]E[Y]$
$=E[XY]-E[X]E[Y]$