From 4d7f80e63a0012fff72e3285fd071138a40c7c25 Mon Sep 17 00:00:00 2001
From: wizardforcel <562826179@qq.com>
Date: Sun, 4 Mar 2018 19:56:11 +0800
Subject: [PATCH] tex

---
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diff --git a/13.md b/13.md
index a2774e5..ef52bae 100644
--- a/13.md
+++ b/13.md
@@ -604,17 +604,17 @@ regression_line(0.6)
 
 在回归中，我们使用一个变量（我们称`x`）的值来预测另一个变量的值（我们称之为`y`）。 当变量`x`和`y`以标准单位测量时，基于`x`预测`y`的回归线斜率为`r`并通过原点。 因此，回归线的方程可写为：
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bestimate%20of%20%7Dy%20%7E%3D%7E%20r%20%5Ccdot%20x%20%7E%7E%7E%20%5Cmbox%7Bwhen%20both%20variables%20are%20measured%20in%20standard%20units%7D)
+![](img/tex-13-1.gif)
 
 在数据的原始单位下，就变成了：
 
-![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmbox%7Bestimate%20of%7D%7Ey%20%7E-%7E%5Cmbox%7Baverage%20of%7D%7Ey%7D%7B%5Cmbox%7BSD%20of%7D%7Ey%7D%20%7E%3D%7E%20r%20%5Ctimes%20%5Cfrac%7B%5Cmbox%7Bthe%20given%7D%7Ex%20%7E-%7E%5Cmbox%7Baverage%20of%7D%7Ex%7D%7B%5Cmbox%7BSD%20of%7D%7Ex%7D)
+![](img/tex-13-2.gif)
 
 原始单位的回归线的斜率和截距可以从上图中导出。
 
-![](http://latex.codecogs.com/gif.latex?%5Cmathbf%7B%5Cmbox%7Bslope%20of%20the%20regression%20line%7D%7D%20%7E%3D%7E%20r%20%5Ccdot%20%5Cfrac%7B%5Cmbox%7BSD%20of%20%7Dy%7D%7B%5Cmbox%7BSD%20of%20%7Dx%7D)
+![](img/tex-13-3.gif)
 
-![](http://latex.codecogs.com/gif.latex?%5Cmathbf%7B%5Cmbox%7Bintercept%20of%20the%20regression%20line%7D%7D%20%7E%3D%7E%20%5Cmbox%7Baverage%20of%20%7Dy%20%7E-%7E%20%5Cmbox%7Bslope%7D%20%5Ccdot%20%5Cmbox%7Baverage%20of%20%7Dx)
+![](img/tex-13-4.gif)
 
 下面的三个函数计算相关性，斜率和截距。 它们都有三个参数：表的名称，包含`x`的列的标签以及包含`y`的列的标签。
 
@@ -651,7 +651,7 @@ galton_slope, galton_intercept
 
 回归直线的方程是：
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bestimate%20of%20child%27s%20height%7D%20%7E%3D%7E%200.64%20%5Ccdot%20%5Cmbox%7Bmidparent%20height%7D%20%7E&plus;%7E%2022.64)
+![](img/tex-13-5.gif)
 
 这也成为回归方程。回归方程的主要用途是根据`x`预测`y`。
 
@@ -769,13 +769,13 @@ slope(baby, 'Maternal Height', 'Maternal Pregnancy Weight')
 
 为了计算回归线的方程，我们需要斜率和截距。
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bslope%7D%20%7E%3D%7E%20%5Cfrac%7Br%20%5Ccdot%20%5Cmbox%7BSD%20of%20%7Dy%7D%7B%5Cmbox%7BSD%20of%20%7Dx%7D%20%7E%3D%7E%20%5Cfrac%7B0.5%20%5Ccdot%202%20%5Cmbox%7B%20inches%7D%7D%7B5%20%5Cmbox%7B%20pounds%7D%7D%20%7E%3D%7E%200.2%20%7E%5Cmbox%7Binches%20per%20pound%7D)
+![](img/tex-13-6.gif)
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bintercept%7D%20%7E%3D%7E%20%5Cmbox%7Baverage%20of%20%7Dy%20-%20%5Cmbox%7Bslope%7D%5Ccdot%20%5Cmbox%7Baverage%20of%20%7D%20x%20%7E%3D%7E%2014%20%5Cmbox%7B%20inches%7D%20%7E-%7E%200.2%20%5Cmbox%7B%20inches%20per%20pound%7D%20%5Ccdot%2050%20%5Cmbox%7B%20pounds%7D%20%7E%3D%7E%204%20%5Cmbox%7B%20inches%7D)
+![](img/tex-13-7.gif)
 
 回归线的方程允许我们，根据给定重量（磅）计算估计高度（英寸）：
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bestimated%20height%7D%20%7E%3D%7E%200.2%20%5Ccdot%20%5Cmbox%7Bgiven%20weight%7D%20%7E&plus;%7E%204)
+![](img/tex-13-8.gif)
 
 线的斜率衡量随着重量的单位增长的估计高度的增长。 斜率是正值，重要的是要注意，这并不表示我们认为，如果体重增加巴塞特猎狗就会变得更高。 斜率反映了两组狗的平均身高的差异，这两组狗的体重相差 1 磅。 具体来说，考虑一组重量为`w`磅，以及另一组重量为`w + 1`磅的狗。 我们估计，第二组的均值高出 0.2 英寸。 对于样本中的所有`w`值都是如此。
 
@@ -956,7 +956,7 @@ Root mean squared error: 2701.69078531
 
 首先注意，使均方根误差最小的直线，也是使平方误差最小的直线。 平方根对最小值没有任何影响。 所以我们会为自己节省一个计算步骤，并将平均方差 MSE 减到最小。
 
-我们试图根据《小女人》的句子数（`x`）来预测字符数量（`y`）。 如果我们使用 ![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bprediction%7D%20%7E%3D%7E%20ax%20&plus;%20b) 直线，它将有一个 MSE，它取决于斜率`a`和截距`b`。 函数`lw_mse`以斜率和截距为参数，并返回相应的 MSE。
+我们试图根据《小女人》的句子数（`x`）来预测字符数量（`y`）。 如果我们使用 ![](img/tex-13-9.gif) 直线，它将有一个 MSE，它取决于斜率`a`和截距`b`。 函数`lw_mse`以斜率和截距为参数，并返回相应的 MSE。
 
 ```py
 def lw_mse(any_slope, any_intercept):
@@ -1090,11 +1090,11 @@ array([ 0.09834382,  5.95962911])
 
 无论散点图的形状如何，都有一条独特的线，可以使估计的均方误差最小。 它被称为回归线，其斜率和截距由下式给出：
 
-![](http://latex.codecogs.com/gif.latex?%5Cmathbf%7B%5Cmbox%7Bslope%20of%20the%20regression%20line%7D%7D%20%7E%3D%7E%20r%20%5Ccdot%20%5Cfrac%7B%5Cmbox%7BSD%20of%20%7Dy%7D%7B%5Cmbox%7BSD%20of%20%7Dx%7D)
+![](img/tex-13-10.gif)
 
 > 译者注：也就是`cov(x, y)/var(x)`。
 
-![](http://latex.codecogs.com/gif.latex?%5Cmathbf%7B%5Cmbox%7Bintercept%20of%20the%20regression%20line%7D%7D%20%7E%3D%7E%20%5Cmbox%7Baverage%20of%20%7Dy%20%7E-%7E%20%5Cmbox%7Bslope%7D%20%5Ccdot%20%5Cmbox%7Baverage%20of%20%7Dx)
+![](img/tex-13-11.gif)
 
 ```py
 fitted = fit(shotput, 'Weight Lifted', 'Shot Put Distance')
@@ -1160,13 +1160,13 @@ shotput.with_column('Best Quadratic Curve', shotput_fit).scatter(0)
 
 假设数据科学家已经决定使用线性回归，基于预测变量估计响应变量的值。 为了了解这种估计方法的效果如何，数据科学家必须知道估计值距离实际值多远。 这些差异被称为残差。
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bresidual%7D%20%7E%3D%7E%20%5Cmbox%7Bobserved%20value%7D%20%7E-%7E%20%5Cmbox%7Bregression%20estimate%7D)
+![](img/tex-13-12.gif)
 
 残差就是剩下的东西 - 估计之后的剩余。
 
 残差是回归线和点的垂直距离。 散点图中的每个点都有残差。 残差是`y`的观测值与`y`的拟合值之间的差值，所以对于点`(x, y)`：
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bresidual%7D%20%7E%7E%20%3D%20%7E%7E%20y%20%7E-%7E%20%5Cmbox%7Bfitted%20value%20of%20%7Dy%20%7E%7E%20%3D%20%7E%7E%20y%20%7E-%7E%20%5Cmbox%7Bheight%20of%20regression%20line%20at%20%7Dx)
+![](img/tex-13-13.gif)
 
 `residual`函数计算残差。 该计算假设我们已经定义的所有相关函数：`standard_units`，`correlation`，`slope`，`intercept`和`fit`。
 
@@ -1379,9 +1379,9 @@ round(np.mean(dugong.column('Residual')), 10)
 
 ### 残差的标准差
 
-无论散点图的形状如何，残差的标准差是响应变量的标准差的一个比例。 比例是 ![](http://latex.codecogs.com/gif.latex?%5Csqrt%7B1-r%5E2%7D)。
+无论散点图的形状如何，残差的标准差是响应变量的标准差的一个比例。 比例是 ![](img/tex-13-14.gif)。
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7BSD%20of%20residuals%7D%20%7E%3D%7E%20%5Csqrt%7B1%20-%20r%5E2%7D%20%5Ccdot%20%5Cmbox%7BSD%20of%20%7Dy)
+![](img/tex-13-15.gif)
 
 我们将很快看到，它如何衡量回归估计的准确性。 但首先，让我们通过例子来确认。
 
@@ -1426,11 +1426,11 @@ np.std(hybrid.column('residual')), np.sqrt(1 - r**2)*np.std(hybrid.column('mpg')
 
 我们可以重写上面的结果，不管散点图的形状如何：
 
-![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmbox%7BSD%20of%20residuals%7D%7D%7B%5Cmbox%7BSD%20of%20%7Dy%7D%20%7E%3D%7E%20%5Csqrt%7B1-r%5E2%7D)
+![](img/tex-13-16.gif)
 
 互补的结果是，无论散点图的形状如何，拟合值的标准差是观察值`y`的标准差的一个比例。比例是`|r|`。
 
-![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmbox%7BSD%20of%20fitted%20values%7D%7D%7B%5Cmbox%7BSD%20of%20%7Dy%7D%20%7E%3D%7E%20%7Cr%7C)
+![](img/tex-13-17.gif)
 
 要查看比例在哪里出现，请注意拟合值全部位于回归线上，而`y`的观测值是散点图中所有点的高度，并且更加可变。
 
@@ -1471,8 +1471,8 @@ np.std(hybrid.column('fitted mpg'))/np.std(hybrid.column('mpg'))
 
 解释这个结果的更标准的方法是，回想一下：
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bvariance%7D%20%7E%3D%7E%20%5Cmbox%7Bmean%20squared%20deviation%20from%20average%7D%20%7E%3D%7E%20%5Cmbox%7BSD%7D%5E2)
+![](img/tex-13-18.gif)
 
 因此，对结果的两边取平方：
 
-![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmbox%7Bvariance%20of%20fitted%20values%7D%7D%7B%5Cmbox%7Bvariance%20of%20%7Dy%7D%20%7E%3D%7E%20r%5E2)
+![](img/tex-13-19.gif)
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-- 
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