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"markdown", + "metadata": {}, + "source": [ + "## 皮尔逊相关系数" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 连续变量的相关分析\n", + "
    \n", + "
  • 连续变量即数据变量,它的取值之间可以比较大小,可以用加减法计算出差异的大小。\n", + "
  • 如“年龄”、“收入”、“成绩\"等变量当两个变量都是正态连续变量,而且两者之间呈线性关系时,通常用 Pearson相关系数来衡量。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Pearson.相关系数\n", + "**协方差:**\n", + "协方差是一个反映两个随机变量相关程度的指标,如果一个变量跟随着另一个变量同时变大或者变小,那么这两个变量的协方差就是正值\n", + "$$\n", + "cov(X, Y) = \\frac{\\sum_n^i=1(X_i-\\overline{X})(Y_i-\\overline{Y})}{n-1}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "虽然协方差能反映两个随机变量的相关程度(协方差大于0的时候表示两者正相关,小于0的时候表示两者负相关),但是协方差值的大小并不能很好地度量两个随机变量的关联程度\n", + "

    在二维空间中分布着一些数据,我们想知道数据点坐标X轴和Y轴的相关程度,如果X与Y的相关程度较小但是数据分布的比较离散,这样会导致求出的协方差值较大,用这个值来度量相关程度是不合理的\n", + "\n", + "为了更好的度量两个随机变量的相关程度, 引入Pearson相关系数,其在协方差的基础上除了两个随机变量的标准差" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Pearson相关系数**\n", + "$$\n", + "PX,Y = \\frac{cov(X,Y)}{σXσY} = \\frac{E[(X-μX)(Y-μY)]}{σXσY} \n", + "$$\n", + "pearson是一个介于-1和1之间的值,当两个变量的线性关系增强时,相关系数趋于1或-1;当一个变量增大,另一个变量也增大时,表明它们之间是正相关的,相关系数大于0;如果一个变量增大,另一个变量却减小,表明它们之间是负相关的,相关系数小于0;如果相关系数等于0,表明它们之间不存在线性相关关系\n", + "\n", + "\n", + "np.corrcoef(a)可结算行与行之间的相关系数,np.corrcoe" + ] + }, + { + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [] } ],