量化线性关系

Python 线性建模入门

Jason Vestuto

Data Scientist

预可视化

3 个面板图,3 个散点图,相关性由强到零,从左到右

Python 线性建模入门

单变量统计回顾

# Mean
mean = sum(x)/len(x)
# Deviation, sometimes called "centering"
dx = x - np.mean(x)
# Variance
variance = np.mean(dx*dx)
# Standard Deviation
stdev = np.sqrt(variance)
Python 线性建模入门

协方差

# Deviations of two variables
dx = x - np.mean(x)
dy = y - np.mean(y)
# Co-vary means to vary together
deviation_products = dx*dy
# Covariance as the mean
covariance = np.mean(dx*dy)
Python 线性建模入门

相关系数

# Divide deviations by standard deviation 
zx = dx/np.std(x)
zy = dy/np.std(y)
# Mean of the normalize deviations
correlation = np.mean(zx*zy)
Python 线性建模入门

标准化:之前

高斯分布图:钟形曲线,中心、高度与宽度各不相同

Python 线性建模入门

标准化:之后

高斯分布图:钟形曲线,均以零为中心,且高度与宽度相同

Python 线性建模入门

大小与方向

  • 相关系数范围:-1 到 +1

6 个面板图,2 行 3 列散点图,相关性由强到弱从左到右

  • 两部分:大小(1 到 0)与符号(+ 或 -)
Python 线性建模入门

¡Vamos a practicar!

Python 线性建模入门

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