67 lines
2.5 KiB
Markdown
67 lines
2.5 KiB
Markdown
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---
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title: Linear Regression
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localeTitle: 线性回归
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---
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## 线性回归
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线性回归有助于我们根据其他变量Y的得分预测变量X的得分。当绘制变量Y时，线性回归找到通过点的最佳拟合直线。最合适的线称为回归线。
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[在线线性回归模拟器](https://www.mladdict.com/linear-regression-simulator)
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在Python中：
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```py
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#Price of wheat/kg and the average price of bread
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wheat_and_bread = [[0.5,5],[0.6,5.5],[0.8,6],[1.1,6.8],[1.4,7]]
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def step_gradient(b_current, m_current, points, learningRate):
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b_gradient = 0
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m_gradient = 0
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N = float(len(points))
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for i in range(0, len(points)):
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x = points[i][0]
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y = points[i][1]
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b_gradient += -(2/N) * (y - ((m_current * x) + b_current))
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m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))
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new_b = b_current - (learningRate * b_gradient)
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new_m = m_current - (learningRate * m_gradient)
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return [new_b, new_m]
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def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):
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b = starting_b
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m = starting_m
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for i in range(num_iterations):
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b, m = step_gradient(b, m, points, learning_rate)
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return [b, m]
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gradient_descent_runner(wheat_and_bread, 1, 1, 0.01, 100)
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```
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代码示例来自[本文](http://blog.floydhub.com/coding-the-history-of-deep-learning/) 。它还解释了梯度下降和深度学习的其他基本概念。
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值得注意的是，并非所有线性回归都是通过梯度下降完成的。正规方程也可以用于找到线性回归系数，但是，这使用矩阵乘法，因此使用超过100,000或1,000,000个实例可能非常耗时。
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在Python中： 使用scikit库直接应用，因此即使在大型数据集上也可以轻松使用线性回归。
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```py
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import pandas as pd
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from sklearn.cross_validation import train_test_split
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from sklearn.linear_model import LinearRegression as lr
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train = pd.read_csv('../input/train.csv')
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test = pd.read_csv('../input/test.csv')
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X = train.iloc[:, 0:4].values
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y = train.iloc[:, 4].values
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X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)
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X_train
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model = lr()
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model.fit(X_train, y_train)
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print(model.score(X_train,y_train))
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y_pred_class = model.predict(X_test)
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model.score(X_train,y_train)
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print(model.coef_)
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print(model.intercept_)
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# calculate accuracy
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from sklearn import metrics
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print(metrics.accuracy_score(y_test, y_pred_class))
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```
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