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--- a/必备数学基础.md
+++ b/必备数学基础.md
@@ -828,3 +828,65 @@ Sigmoid没有负数，都是大于0的，当梯度更新的时候，要么全为
 - 同分布：他俩都是来同一银行，即我们假定的银行
 - 高斯分布：银行可能会多给，也可能会少给，但是绝大多数情况下浮动不会太大，极小情况下浮动大，符合正常情况
 
+#### 最小二乘法推导与求解
+
+- 预测值与误差![1604821754843](assets/1604821754843.png)
+
+- 由于误差服从高斯分布![1604821811796](assets/1604821811796.png)
+
+- 将（1）式代入（2）式：![1604821879046](assets/1604821879046.png)
+
+  > 什么样的θ和x相乘后，得到最相近或者相同的y
+
+- 似然函数：![1604821982496](assets/1604821982496.png)
+
+  解释：什么样的参数和我们的数据组合后恰好是真实值
+
+- 对数似然：![1604822042028](assets/1604822042028.png)
+
+  解释：乘法难解，加法就容易了，对数里乘法可以转换成加法
+
+- 展开化简：![1604822227025](assets/1604822227025.png)
+
+  ![1604822258878](assets/1604822258878.png)
+
+- 目标：让似然函数越大越好
+
+  ![1604822356847](assets/1604822356847.png)
+
+  最小二乘法
+
+**参数的最小二乘法估计**
+
+对于回归直线，关键在于求解参数，常用高斯提出的最小二乘法，它使因变量的观察值y与估计值之间的离差平方和达到最小来求解。
+
+![1604822532101](assets/1604822532101.png)
+
+![1604822559643](assets/1604822559643.png)
+
+展开得：
+
+![1604822595998](assets/1604822595998.png)
+
+求偏导可得：
+
+![1604822649659](assets/1604822649659.png)
+
+求解：
+
+![1604822675575](assets/1604822675575.png)
+
+实例：70年代世界制造业总产量与世界制成品总出口量的变化关系如表：
+
+| 年度 | 总产量年增长率(%) x | 总出口量年增长率(%) y |
+| ---- | ------------------- | --------------------- |
+| 1970 | 4.0                 | 8.5                   |
+| 1971 | 4.0                 | 8.0                   |
+| 1972 | 8.5                 | 10.5                  |
+| 1973 | 9.5                 | 15.5                  |
+| 1974 | 3.0                 | 8.5                   |
+| 1975 | -1.0                | -4.5                  |
+| 1976 | 8.0                 | 13.5                  |
+| 1977 |                     |                       |
+|      |                     |                       |
+