线性回归

简单理解

  • 就是用一条直线较为精确地描述数据之间的关系, 这样当出现新的数据的时候, 就能够预测出一个简单的值。

  • 一些概念:

    • 回归平均值(regression to the mean)

    • 因变量(dependent variable): y=a1x1+a2x2+a3x3......+anxn 中的y, 即需要预测的值

    • 自变量(independent variables): y=a1x1+a2x2+a3x3......+anxn 中的x1, x2 ... xn, 即预测变量

    • 广义线性回归(GLM, Generalized Linear Model), 如逻辑回归, 泊松分布等......

      1574991065311

最小二乘法

  • 法国数学家，阿德里安-馬里·勒讓德（1752－1833）提出让总的误差的平方最小的y 就是真值，这是基于，如果误差是随机的，应该围绕真值上下波动。

    1574991347122

    1574991355643

    1574991408805

梯度下降算法

  • 先确定向下一步的步伐大小, 即Learning Rate

  • 任意给定一个初始值

  • 确定一个向下的方向, 并向下走预先规定的步伐, 并更新当下降的高度小于某个定义的值, 则停止下降。

  • 需要注意的是导数=0取得的解不一定是最优解, 很可能是某个局部最优解。

    1574991900124

损失函数 (Cost Function)

  • 损失函数分为经验风险损失函数和结构风险损失函数，经验风险损失函数反映的是预测结果和实际结果之间的差别

  • 结构风险损失函数则是经验风险损失函数加上正则项(L0、L1（Lasso）、L2（Ridge）)

  • 常用损失函数

    • 0-1损失函数 (gold standard 标准式)

      • 预测值和目标值不相等为1，否则为0

        img

      • 该损失函数不考虑预测值和真实值的误差程度，也就是说只要预测错误，预测错误差一点和差很多是一样的。

      • 感知机就是用的这种损失函数，但是由于相等这个条件太过严格，我们可以放宽条件，即满足 |Y−f(X)|<T时认为相等

        img

      • 这种损失函数用在实际场景中比较少，更多的是用俩衡量其他损失函数的效果。

    • 绝对值损失函数

      img

    • 平方损失函数(squared loss)

      • 实际结果和观测结果之间差距的平方和，一般用在线性回归中，可以理解为最小二乘法

      img

    • 对数损失函数(Logarithmic loss)

      • 主要在逻辑回归中使用，样本预测值和实际值的误差符合高斯分布，使用极大似然估计的方法，取对数得到损失函数

        img

      • 损失函数L(Y,P(Y|X))L(Y,P(Y|X))是指样本X在分类Y的情况下，使概率P(Y|X)达到最大值。

      • 经典的对数损失函数包括entropy(信息熵)和softmax，一般在做分类问题的时候使用

        • 回归时多用绝对值损失
        • 拉普拉斯分布时，μ值为中位数）和平方损失（高斯分布时，μ值为均值）

    • 指数损失函数(Exp-Loss)

      • 在boosting算法中比较常见，比如Adaboosting中，标准形式是：

        img

    • 铰链损失函数(Hinge Loss)

      • 铰链损失函数主要用在SVM中，Hinge Loss的标准形式为：

      img

      • y为预测值, 在-1到+1之间，t为目标值（-1或+1）

      • 其含义为，y的值在-1和+1之间就可以了，并不鼓励|y|>1, 即并不鼓励分类器过度自信，让某个正确分类的样本的距离分割线超过1并不会有任何奖励，从而使分类器可以更专注于整体的分类误差。

多元线性回归

  • 大多数现实世界的分析不止一个自变量，大多数情况下，很有可能使用多元线性回归。

    1574992823579

相关系数

  • 两个变量之间的相关系数是一个数，它表示两个变量服从一条直线的关系有多麽紧密
  • 相关系数就是指Pearson相关系数，它是数学家Pearson提出来的，相关系数的范围是-1~+1之间，两端的值表示一个完美的线性关系

Keras实现Demo

import numpy as np
np.random.seed(1337)  
from keras.models import Sequential
from keras.layers import Dense
import matplotlib.pyplot as plt
 
# 生成数据
X = np.linspace(-1, 1, 200) #在返回（-1, 1）范围内的等差序列
np.random.shuffle(X)    # 打乱顺序
Y = 0.5 * X + 2 + np.random.normal(0, 0.05, (200, )) #生成Y并添加噪声
# plot
plt.scatter(X, Y)
plt.show()
 
X_train, Y_train = X[:160], Y[:160]     # 前160组数据为训练数据集
X_test, Y_test = X[160:], Y[160:]      #后40组数据为测试数据集
 
# 构建神经网络模型
model = Sequential()
model.add(Dense(input_dim=1, units=1))
 
# 选定loss函数和优化器
model.compile(loss='mse', optimizer='sgd')
 
# 训练过程
print('Training -----------')
for step in range(501):
    cost = model.train_on_batch(X_train, Y_train)
    if step % 50 == 0:
        print("After %d trainings, the cost: %f" % (step, cost))
 
# 测试过程
print('\nTesting ------------')
cost = model.evaluate(X_test, Y_test, batch_size=40)
print('test cost:', cost)
W, b = model.layers[0].get_weights()
print('Weights=', W, '\nbiases=', b)
 
# 将训练结果绘出
Y_pred = model.predict(X_test)
plt.scatter(X_test, Y_test)
plt.plot(X_test, Y_pred)
plt.show()

SparkMrLib实现Demo

  • lpsa.data

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4.3851468,1.25591974271076 0.577607033774471 0.555266033439982 -1.02470580167082 1.89254797819741 1.07357183940747 0.342627053981254 1.26288870310799
4.6844434,2.09650591351268 0.625488598331018 -2.66832330782754 -1.02470580167082 1.89254797819741 1.67954222367555 0.342627053981254 0.553770299626224
5.477509,1.30028987435881 0.338383613253713 0.555266033439982 1.00481276295349 1.89254797819741 1.24263233939889 0.342627053981254 1.97200710658975

  • 代码:

    import org.apache.spark.ml.feature.LabeledPoint
import org.apache.spark.ml.linalg.Vectors
import org.apache.spark.ml.regression.{LinearRegression, LinearRegressionModel, LinearRegressionSummary}
import org.apache.spark.sql.{Dataset, Encoders, SparkSession}


object LinearRegression1 {

    def main(args: Array[String]) {
        val spark = SparkSession
            .builder
            .master("local")
            .appName("LinearRegression")
            .getOrCreate()
        //scala. 隐式转换
        import spark.implicits._
        //读取样本数据
        val data_path1 = "lpsa.data"

        val data1: Dataset[String] = spark.read.textFile(data_path1)


        val data2: Dataset[LabeledPoint] = data1.map { line =>
            val parts = line.split(',')

            val features: Array[Double] = parts(1).split(' ').map(_.toDouble)

            LabeledPoint(parts(0).toDouble, Vectors.dense(features));
        }

//        //1 为随机种子
        val train2TestData: Array[Dataset[LabeledPoint]] = data2.randomSplit(Array(0.8, 0.2), 1)


        // 迭代次数
        val numIterations = 100

        val lir: LinearRegression = new LinearRegression()
            .setFeaturesCol("features")
            .setLabelCol("label")
            //收敛的值，越小结果越精确，但迭代次数也越大，花费更多时间
            .setTol(1E-6)
            //迭代次数
            .setMaxIter(numIterations)
            //是否需要截距，默认true
//            .setFitIntercept(false)

        val startTime = System.nanoTime()

        val model: LinearRegressionModel = lir.fit(train2TestData(0))
        //训练模型所消耗的时间
        val elapsedTime = (System.nanoTime() - startTime) / 1e9

        println("Training time: " + elapsedTime +" seconds")
        //权重.
        println("Weights: " + model.coefficients)
        //截距.
        println("Intercept:" +  model.intercept)

        //用测试集数据去评估模型，得到一个评估结果。
        val summary: LinearRegressionSummary = model.evaluate(train2TestData(1))
////
////        //打印测试结果
        summary.predictions.show()
//
//
//        //平均绝对误差，预测数据和原始数据对应点误差绝对值和的均值
        println("平均绝对值误差: " + summary.meanAbsoluteError)
////        //均方差，预测数据和原始数据对应点误差的平方和的均值
        println("均方差: " + summary.meanSquaredError)
////        //测试集的数据条目
        println(summary.numInstances)

        /**
          * 训练完之后，可以将模型进行保存..
          *  model.save("model/lir.model")
          *  模型训练完毕后，以后用的时候可以直接加载模型，无需再训练
          *  val model = LinearRegressionModel.load("model/lir.model")
          */

        spark.stop()


    }

}

  • 执行结果

    +---------+--------------------+------------------+
|    label|            features|        prediction|
+---------+--------------------+------------------+
|0.3715636|[-0.5078744753006...|1.6421433505218315|
|1.3480731|[0.10778590023681...|1.8821794069229758|
|1.7137979|[0.36627391851114...|2.7289870384929062|
|1.8484548|[-0.2627917281138...| 2.539418711837841|
|2.0476928|[-1.1539378999075...|0.8615391122353211|
|2.5533438|[0.26634132994993...| 2.788666352465077|
|2.7180005|[-0.0704736333296...|2.9210948847330584|
|2.8063861|[-0.6852776524309...|  2.02853043658855|
|2.8419982|[-0.7573102775567...|2.1731148778913285|
|2.9626924|[-1.5240614015806...|0.8988821228525923|
|3.2752562|[1.39927182372944...|3.1449164943520214|
|3.5876769|[0.18015632325519...|  2.65539506621454|
+---------+--------------------+------------------+

平均绝对值误差: 0.8090483779032781
均方差: 0.9257651846620174
12

  • house_data.csv

    0.00632,18,2.31,0,0.538,6.575,65.2,4.09,1,296,15.3,396.9,4.98,24
0.02731,0,7.07,0,0.469,6.421,78.9,4.9671,2,242,17.8,396.9,9.14,21.6
0.02729,0,7.07,0,0.469,7.185,61.1,4.9671,2,242,17.8,392.83,4.03,34.7
0.03237,0,2.18,0,0.458,6.998,45.8,6.0622,3,222,18.7,394.63,2.94,33.4
0.06905,0,2.18,0,0.458,7.147,54.2,6.0622,3,222,18.7,396.9,5.33,36.2
0.02985,0,2.18,0,0.458,6.43,58.7,6.0622,3,222,18.7,394.12,5.21,28.7
0.08829,12.5,7.87,0,0.524,6.012,66.6,5.5605,5,311,15.2,395.6,12.43,22.9
0.14455,12.5,7.87,0,0.524,6.172,96.1,5.9505,5,311,15.2,396.9,19.15,27.1
0.21124,12.5,7.87,0,0.524,5.631,100,6.0821,5,311,15.2,386.63,29.93,16.5
0.17004,12.5,7.87,0,0.524,6.004,85.9,6.5921,5,311,15.2,386.71,17.1,18.9
0.22489,12.5,7.87,0,0.524,6.377,94.3,6.3467,5,311,15.2,392.52,20.45,15
0.11747,12.5,7.87,0,0.524,6.009,82.9,6.2267,5,311,15.2,396.9,13.27,18.9
0.09378,12.5,7.87,0,0.524,5.889,39,5.4509,5,311,15.2,390.5,15.71,21.7
0.62976,0,8.14,0,0.538,5.949,61.8,4.7075,4,307,21,396.9,8.26,20.4
0.63796,0,8.14,0,0.538,6.096,84.5,4.4619,4,307,21,380.02,10.26,18.2
0.62739,0,8.14,0,0.538,5.834,56.5,4.4986,4,307,21,395.62,8.47,19.9
1.05393,0,8.14,0,0.538,5.935,29.3,4.4986,4,307,21,386.85,6.58,23.1
0.7842,0,8.14,0,0.538,5.99,81.7,4.2579,4,307,21,386.75,14.67,17.5
0.80271,0,8.14,0,0.538,5.456,36.6,3.7965,4,307,21,288.99,11.69,20.2
0.7258,0,8.14,0,0.538,5.727,69.5,3.7965,4,307,21,390.95,11.28,18.2
1.25179,0,8.14,0,0.538,5.57,98.1,3.7979,4,307,21,376.57,21.02,13.6
0.85204,0,8.14,0,0.538,5.965,89.2,4.0123,4,307,21,392.53,13.83,19.6
1.23247,0,8.14,0,0.538,6.142,91.7,3.9769,4,307,21,396.9,18.72,15.2
0.98843,0,8.14,0,0.538,5.813,100,4.0952,4,307,21,394.54,19.88,14.5
0.75026,0,8.14,0,0.538,5.924,94.1,4.3996,4,307,21,394.33,16.3,15.6
0.84054,0,8.14,0,0.538,5.599,85.7,4.4546,4,307,21,303.42,16.51,13.9
0.67191,0,8.14,0,0.538,5.813,90.3,4.682,4,307,21,376.88,14.81,16.6
0.95577,0,8.14,0,0.538,6.047,88.8,4.4534,4,307,21,306.38,17.28,14.8
0.77299,0,8.14,0,0.538,6.495,94.4,4.4547,4,307,21,387.94,12.8,18.4
1.00245,0,8.14,0,0.538,6.674,87.3,4.239,4,307,21,380.23,11.98,21
1.13081,0,8.14,0,0.538,5.713,94.1,4.233,4,307,21,360.17,22.6,12.7
1.35472,0,8.14,0,0.538,6.072,100,4.175,4,307,21,376.73,13.04,14.5
1.38799,0,8.14,0,0.538,5.95,82,3.99,4,307,21,232.6,27.71,13.2
1.15172,0,8.14,0,0.538,5.701,95,3.7872,4,307,21,358.77,18.35,13.1
1.61282,0,8.14,0,0.538,6.096,96.9,3.7598,4,307,21,248.31,20.34,13.5
0.06417,0,5.96,0,0.499,5.933,68.2,3.3603,5,279,19.2,396.9,9.68,18.9
0.09744,0,5.96,0,0.499,5.841,61.4,3.3779,5,279,19.2,377.56,11.41,20
0.08014,0,5.96,0,0.499,5.85,41.5,3.9342,5,279,19.2,396.9,8.77,21
0.17505,0,5.96,0,0.499,5.966,30.2,3.8473,5,279,19.2,393.43,10.13,24.7
0.02763,75,2.95,0,0.428,6.595,21.8,5.4011,3,252,18.3,395.63,4.32,30.8
0.03359,75,2.95,0,0.428,7.024,15.8,5.4011,3,252,18.3,395.62,1.98,34.9
0.12744,0,6.91,0,0.448,6.77,2.9,5.7209,3,233,17.9,385.41,4.84,26.6
0.1415,0,6.91,0,0.448,6.169,6.6,5.7209,3,233,17.9,383.37,5.81,25.3
0.15936,0,6.91,0,0.448,6.211,6.5,5.7209,3,233,17.9,394.46,7.44,24.7
0.12269,0,6.91,0,0.448,6.069,40,5.7209,3,233,17.9,389.39,9.55,21.2
0.17142,0,6.91,0,0.448,5.682,33.8,5.1004,3,233,17.9,396.9,10.21,19.3
0.18836,0,6.91,0,0.448,5.786,33.3,5.1004,3,233,17.9,396.9,14.15,20
0.22927,0,6.91,0,0.448,6.03,85.5,5.6894,3,233,17.9,392.74,18.8,16.6
0.25387,0,6.91,0,0.448,5.399,95.3,5.87,3,233,17.9,396.9,30.81,14.4
0.21977,0,6.91,0,0.448,5.602,62,6.0877,3,233,17.9,396.9,16.2,19.4
0.08873,21,5.64,0,0.439,5.963,45.7,6.8147,4,243,16.8,395.56,13.45,19.7
0.04337,21,5.64,0,0.439,6.115,63,6.8147,4,243,16.8,393.97,9.43,20.5
0.0536,21,5.64,0,0.439,6.511,21.1,6.8147,4,243,16.8,396.9,5.28,25
0.04981,21,5.64,0,0.439,5.998,21.4,6.8147,4,243,16.8,396.9,8.43,23.4
0.0136,75,4,0,0.41,5.888,47.6,7.3197,3,469,21.1,396.9,14.8,18.9
0.01311,90,1.22,0,0.403,7.249,21.9,8.6966,5,226,17.9,395.93,4.81,35.4
0.02055,85,0.74,0,0.41,6.383,35.7,9.1876,2,313,17.3,396.9,5.77,24.7
0.01432,100,1.32,0,0.411,6.816,40.5,8.3248,5,256,15.1,392.9,3.95,31.6
0.15445,25,5.13,0,0.453,6.145,29.2,7.8148,8,284,19.7,390.68,6.86,23.3
0.10328,25,5.13,0,0.453,5.927,47.2,6.932,8,284,19.7,396.9,9.22,19.6
0.14932,25,5.13,0,0.453,5.741,66.2,7.2254,8,284,19.7,395.11,13.15,18.7
0.17171,25,5.13,0,0.453,5.966,93.4,6.8185,8,284,19.7,378.08,14.44,16
0.11027,25,5.13,0,0.453,6.456,67.8,7.2255,8,284,19.7,396.9,6.73,22.2
0.1265,25,5.13,0,0.453,6.762,43.4,7.9809,8,284,19.7,395.58,9.5,25
0.01951,17.5,1.38,0,0.4161,7.104,59.5,9.2229,3,216,18.6,393.24,8.05,33
0.03584,80,3.37,0,0.398,6.29,17.8,6.6115,4,337,16.1,396.9,4.67,23.5
0.04379,80,3.37,0,0.398,5.787,31.1,6.6115,4,337,16.1,396.9,10.24,19.4
0.05789,12.5,6.07,0,0.409,5.878,21.4,6.498,4,345,18.9,396.21,8.1,22
0.13554,12.5,6.07,0,0.409,5.594,36.8,6.498,4,345,18.9,396.9,13.09,17.4
0.12816,12.5,6.07,0,0.409,5.885,33,6.498,4,345,18.9,396.9,8.79,20.9
0.08826,0,10.81,0,0.413,6.417,6.6,5.2873,4,305,19.2,383.73,6.72,24.2
0.15876,0,10.81,0,0.413,5.961,17.5,5.2873,4,305,19.2,376.94,9.88,21.7
0.09164,0,10.81,0,0.413,6.065,7.8,5.2873,4,305,19.2,390.91,5.52,22.8
0.19539,0,10.81,0,0.413,6.245,6.2,5.2873,4,305,19.2,377.17,7.54,23.4
0.07896,0,12.83,0,0.437,6.273,6,4.2515,5,398,18.7,394.92,6.78,24.1
0.09512,0,12.83,0,0.437,6.286,45,4.5026,5,398,18.7,383.23,8.94,21.4
0.10153,0,12.83,0,0.437,6.279,74.5,4.0522,5,398,18.7,373.66,11.97,20
0.08707,0,12.83,0,0.437,6.14,45.8,4.0905,5,398,18.7,386.96,10.27,20.8
0.05646,0,12.83,0,0.437,6.232,53.7,5.0141,5,398,18.7,386.4,12.34,21.2
0.08387,0,12.83,0,0.437,5.874,36.6,4.5026,5,398,18.7,396.06,9.1,20.3
0.04113,25,4.86,0,0.426,6.727,33.5,5.4007,4,281,19,396.9,5.29,28
0.04462,25,4.86,0,0.426,6.619,70.4,5.4007,4,281,19,395.63,7.22,23.9
0.03659,25,4.86,0,0.426,6.302,32.2,5.4007,4,281,19,396.9,6.72,24.8
0.03551,25,4.86,0,0.426,6.167,46.7,5.4007,4,281,19,390.64,7.51,22.9
0.05059,0,4.49,0,0.449,6.389,48,4.7794,3,247,18.5,396.9,9.62,23.9
0.05735,0,4.49,0,0.449,6.63,56.1,4.4377,3,247,18.5,392.3,6.53,26.6
0.05188,0,4.49,0,0.449,6.015,45.1,4.4272,3,247,18.5,395.99,12.86,22.5
0.07151,0,4.49,0,0.449,6.121,56.8,3.7476,3,247,18.5,395.15,8.44,22.2
0.0566,0,3.41,0,0.489,7.007,86.3,3.4217,2,270,17.8,396.9,5.5,23.6
0.05302,0,3.41,0,0.489,7.079,63.1,3.4145,2,270,17.8,396.06,5.7,28.7
0.04684,0,3.41,0,0.489,6.417,66.1,3.0923,2,270,17.8,392.18,8.81,22.6
0.03932,0,3.41,0,0.489,6.405,73.9,3.0921,2,270,17.8,393.55,8.2,22
0.04203,28,15.04,0,0.464,6.442,53.6,3.6659,4,270,18.2,395.01,8.16,22.9
0.02875,28,15.04,0,0.464,6.211,28.9,3.6659,4,270,18.2,396.33,6.21,25
0.04294,28,15.04,0,0.464,6.249,77.3,3.615,4,270,18.2,396.9,10.59,20.6
0.12204,0,2.89,0,0.445,6.625,57.8,3.4952,2,276,18,357.98,6.65,28.4
0.11504,0,2.89,0,0.445,6.163,69.6,3.4952,2,276,18,391.83,11.34,21.4
0.12083,0,2.89,0,0.445,8.069,76,3.4952,2,276,18,396.9,4.21,38.7
0.08187,0,2.89,0,0.445,7.82,36.9,3.4952,2,276,18,393.53,3.57,43.8
0.0686,0,2.89,0,0.445,7.416,62.5,3.4952,2,276,18,396.9,6.19,33.2
0.14866,0,8.56,0,0.52,6.727,79.9,2.7778,5,384,20.9,394.76,9.42,27.5
0.11432,0,8.56,0,0.52,6.781,71.3,2.8561,5,384,20.9,395.58,7.67,26.5
0.22876,0,8.56,0,0.52,6.405,85.4,2.7147,5,384,20.9,70.8,10.63,18.6
0.21161,0,8.56,0,0.52,6.137,87.4,2.7147,5,384,20.9,394.47,13.44,19.3
0.1396,0,8.56,0,0.52,6.167,90,2.421,5,384,20.9,392.69,12.33,20.1
0.13262,0,8.56,0,0.52,5.851,96.7,2.1069,5,384,20.9,394.05,16.47,19.5
0.1712,0,8.56,0,0.52,5.836,91.9,2.211,5,384,20.9,395.67,18.66,19.5
0.13117,0,8.56,0,0.52,6.127,85.2,2.1224,5,384,20.9,387.69,14.09,20.4
0.12802,0,8.56,0,0.52,6.474,97.1,2.4329,5,384,20.9,395.24,12.27,19.8
0.26363,0,8.56,0,0.52,6.229,91.2,2.5451,5,384,20.9,391.23,15.55,19.4
0.10793,0,8.56,0,0.52,6.195,54.4,2.7778,5,384,20.9,393.49,13,21.7
0.10084,0,10.01,0,0.547,6.715,81.6,2.6775,6,432,17.8,395.59,10.16,22.8
0.12329,0,10.01,0,0.547,5.913,92.9,2.3534,6,432,17.8,394.95,16.21,18.8
0.22212,0,10.01,0,0.547,6.092,95.4,2.548,6,432,17.8,396.9,17.09,18.7
0.14231,0,10.01,0,0.547,6.254,84.2,2.2565,6,432,17.8,388.74,10.45,18.5
0.17134,0,10.01,0,0.547,5.928,88.2,2.4631,6,432,17.8,344.91,15.76,18.3
0.13158,0,10.01,0,0.547,6.176,72.5,2.7301,6,432,17.8,393.3,12.04,21.2
0.15098,0,10.01,0,0.547,6.021,82.6,2.7474,6,432,17.8,394.51,10.3,19.2
0.13058,0,10.01,0,0.547,5.872,73.1,2.4775,6,432,17.8,338.63,15.37,20.4
0.14476,0,10.01,0,0.547,5.731,65.2,2.7592,6,432,17.8,391.5,13.61,19.3
0.06899,0,25.65,0,0.581,5.87,69.7,2.2577,2,188,19.1,389.15,14.37,22
0.07165,0,25.65,0,0.581,6.004,84.1,2.1974,2,188,19.1,377.67,14.27,20.3
0.09299,0,25.65,0,0.581,5.961,92.9,2.0869,2,188,19.1,378.09,17.93,20.5
0.15038,0,25.65,0,0.581,5.856,97,1.9444,2,188,19.1,370.31,25.41,17.3
0.09849,0,25.65,0,0.581,5.879,95.8,2.0063,2,188,19.1,379.38,17.58,18.8
0.16902,0,25.65,0,0.581,5.986,88.4,1.9929,2,188,19.1,385.02,14.81,21.4
0.38735,0,25.65,0,0.581,5.613,95.6,1.7572,2,188,19.1,359.29,27.26,15.7
0.25915,0,21.89,0,0.624,5.693,96,1.7883,4,437,21.2,392.11,17.19,16.2
0.32543,0,21.89,0,0.624,6.431,98.8,1.8125,4,437,21.2,396.9,15.39,18
0.88125,0,21.89,0,0.624,5.637,94.7,1.9799,4,437,21.2,396.9,18.34,14.3
0.34006,0,21.89,0,0.624,6.458,98.9,2.1185,4,437,21.2,395.04,12.6,19.2
1.19294,0,21.89,0,0.624,6.326,97.7,2.271,4,437,21.2,396.9,12.26,19.6
0.59005,0,21.89,0,0.624,6.372,97.9,2.3274,4,437,21.2,385.76,11.12,23
0.32982,0,21.89,0,0.624,5.822,95.4,2.4699,4,437,21.2,388.69,15.03,18.4
0.97617,0,21.89,0,0.624,5.757,98.4,2.346,4,437,21.2,262.76,17.31,15.6
0.55778,0,21.89,0,0.624,6.335,98.2,2.1107,4,437,21.2,394.67,16.96,18.1
0.32264,0,21.89,0,0.624,5.942,93.5,1.9669,4,437,21.2,378.25,16.9,17.4
0.35233,0,21.89,0,0.624,6.454,98.4,1.8498,4,437,21.2,394.08,14.59,17.1
0.2498,0,21.89,0,0.624,5.857,98.2,1.6686,4,437,21.2,392.04,21.32,13.3
0.54452,0,21.89,0,0.624,6.151,97.9,1.6687,4,437,21.2,396.9,18.46,17.8
0.2909,0,21.89,0,0.624,6.174,93.6,1.6119,4,437,21.2,388.08,24.16,14
1.62864,0,21.89,0,0.624,5.019,100,1.4394,4,437,21.2,396.9,34.41,14.4
3.32105,0,19.58,1,0.871,5.403,100,1.3216,5,403,14.7,396.9,26.82,13.4
4.0974,0,19.58,0,0.871,5.468,100,1.4118,5,403,14.7,396.9,26.42,15.6
2.77974,0,19.58,0,0.871,4.903,97.8,1.3459,5,403,14.7,396.9,29.29,11.8
2.37934,0,19.58,0,0.871,6.13,100,1.4191,5,403,14.7,172.91,27.8,13.8
2.15505,0,19.58,0,0.871,5.628,100,1.5166,5,403,14.7,169.27,16.65,15.6
2.36862,0,19.58,0,0.871,4.926,95.7,1.4608,5,403,14.7,391.71,29.53,14.6
2.33099,0,19.58,0,0.871,5.186,93.8,1.5296,5,403,14.7,356.99,28.32,17.8
2.73397,0,19.58,0,0.871,5.597,94.9,1.5257,5,403,14.7,351.85,21.45,15.4
1.6566,0,19.58,0,0.871,6.122,97.3,1.618,5,403,14.7,372.8,14.1,21.5
1.49632,0,19.58,0,0.871,5.404,100,1.5916,5,403,14.7,341.6,13.28,19.6
1.12658,0,19.58,1,0.871,5.012,88,1.6102,5,403,14.7,343.28,12.12,15.3
2.14918,0,19.58,0,0.871,5.709,98.5,1.6232,5,403,14.7,261.95,15.79,19.4
1.41385,0,19.58,1,0.871,6.129,96,1.7494,5,403,14.7,321.02,15.12,17
3.53501,0,19.58,1,0.871,6.152,82.6,1.7455,5,403,14.7,88.01,15.02,15.6
2.44668,0,19.58,0,0.871,5.272,94,1.7364,5,403,14.7,88.63,16.14,13.1
1.22358,0,19.58,0,0.605,6.943,97.4,1.8773,5,403,14.7,363.43,4.59,41.3
1.34284,0,19.58,0,0.605,6.066,100,1.7573,5,403,14.7,353.89,6.43,24.3
1.42502,0,19.58,0,0.871,6.51,100,1.7659,5,403,14.7,364.31,7.39,23.3
1.27346,0,19.58,1,0.605,6.25,92.6,1.7984,5,403,14.7,338.92,5.5,27
1.46336,0,19.58,0,0.605,7.489,90.8,1.9709,5,403,14.7,374.43,1.73,50
1.83377,0,19.58,1,0.605,7.802,98.2,2.0407,5,403,14.7,389.61,1.92,50
1.51902,0,19.58,1,0.605,8.375,93.9,2.162,5,403,14.7,388.45,3.32,50
2.24236,0,19.58,0,0.605,5.854,91.8,2.422,5,403,14.7,395.11,11.64,22.7
2.924,0,19.58,0,0.605,6.101,93,2.2834,5,403,14.7,240.16,9.81,25
2.01019,0,19.58,0,0.605,7.929,96.2,2.0459,5,403,14.7,369.3,3.7,50
1.80028,0,19.58,0,0.605,5.877,79.2,2.4259,5,403,14.7,227.61,12.14,23.8
2.3004,0,19.58,0,0.605,6.319,96.1,2.1,5,403,14.7,297.09,11.1,23.8
2.44953,0,19.58,0,0.605,6.402,95.2,2.2625,5,403,14.7,330.04,11.32,22.3
1.20742,0,19.58,0,0.605,5.875,94.6,2.4259,5,403,14.7,292.29,14.43,17.4
2.3139,0,19.58,0,0.605,5.88,97.3,2.3887,5,403,14.7,348.13,12.03,19.1
0.13914,0,4.05,0,0.51,5.572,88.5,2.5961,5,296,16.6,396.9,14.69,23.1
0.09178,0,4.05,0,0.51,6.416,84.1,2.6463,5,296,16.6,395.5,9.04,23.6
0.08447,0,4.05,0,0.51,5.859,68.7,2.7019,5,296,16.6,393.23,9.64,22.6
0.06664,0,4.05,0,0.51,6.546,33.1,3.1323,5,296,16.6,390.96,5.33,29.4
0.07022,0,4.05,0,0.51,6.02,47.2,3.5549,5,296,16.6,393.23,10.11,23.2
0.05425,0,4.05,0,0.51,6.315,73.4,3.3175,5,296,16.6,395.6,6.29,24.6
0.06642,0,4.05,0,0.51,6.86,74.4,2.9153,5,296,16.6,391.27,6.92,29.9
0.0578,0,2.46,0,0.488,6.98,58.4,2.829,3,193,17.8,396.9,5.04,37.2
0.06588,0,2.46,0,0.488,7.765,83.3,2.741,3,193,17.8,395.56,7.56,39.8
0.06888,0,2.46,0,0.488,6.144,62.2,2.5979,3,193,17.8,396.9,9.45,36.2
0.09103,0,2.46,0,0.488,7.155,92.2,2.7006,3,193,17.8,394.12,4.82,37.9
0.10008,0,2.46,0,0.488,6.563,95.6,2.847,3,193,17.8,396.9,5.68,32.5
0.08308,0,2.46,0,0.488,5.604,89.8,2.9879,3,193,17.8,391,13.98,26.4
0.06047,0,2.46,0,0.488,6.153,68.8,3.2797,3,193,17.8,387.11,13.15,29.6
0.05602,0,2.46,0,0.488,7.831,53.6,3.1992,3,193,17.8,392.63,4.45,50
0.07875,45,3.44,0,0.437,6.782,41.1,3.7886,5,398,15.2,393.87,6.68,32
0.12579,45,3.44,0,0.437,6.556,29.1,4.5667,5,398,15.2,382.84,4.56,29.8
0.0837,45,3.44,0,0.437,7.185,38.9,4.5667,5,398,15.2,396.9,5.39,34.9
0.09068,45,3.44,0,0.437,6.951,21.5,6.4798,5,398,15.2,377.68,5.1,37
0.06911,45,3.44,0,0.437,6.739,30.8,6.4798,5,398,15.2,389.71,4.69,30.5
0.08664,45,3.44,0,0.437,7.178,26.3,6.4798,5,398,15.2,390.49,2.87,36.4
0.02187,60,2.93,0,0.401,6.8,9.9,6.2196,1,265,15.6,393.37,5.03,31.1
0.01439,60,2.93,0,0.401,6.604,18.8,6.2196,1,265,15.6,376.7,4.38,29.1
0.01381,80,0.46,0,0.422,7.875,32,5.6484,4,255,14.4,394.23,2.97,50
0.04011,80,1.52,0,0.404,7.287,34.1,7.309,2,329,12.6,396.9,4.08,33.3
0.04666,80,1.52,0,0.404,7.107,36.6,7.309,2,329,12.6,354.31,8.61,30.3
0.03768,80,1.52,0,0.404,7.274,38.3,7.309,2,329,12.6,392.2,6.62,34.6
0.0315,95,1.47,0,0.403,6.975,15.3,7.6534,3,402,17,396.9,4.56,34.9
0.01778,95,1.47,0,0.403,7.135,13.9,7.6534,3,402,17,384.3,4.45,32.9
0.03445,82.5,2.03,0,0.415,6.162,38.4,6.27,2,348,14.7,393.77,7.43,24.1
0.02177,82.5,2.03,0,0.415,7.61,15.7,6.27,2,348,14.7,395.38,3.11,42.3
0.0351,95,2.68,0,0.4161,7.853,33.2,5.118,4,224,14.7,392.78,3.81,48.5
0.02009,95,2.68,0,0.4161,8.034,31.9,5.118,4,224,14.7,390.55,2.88,50
0.13642,0,10.59,0,0.489,5.891,22.3,3.9454,4,277,18.6,396.9,10.87,22.6
0.22969,0,10.59,0,0.489,6.326,52.5,4.3549,4,277,18.6,394.87,10.97,24.4
0.25199,0,10.59,0,0.489,5.783,72.7,4.3549,4,277,18.6,389.43,18.06,22.5
0.13587,0,10.59,1,0.489,6.064,59.1,4.2392,4,277,18.6,381.32,14.66,24.4
0.43571,0,10.59,1,0.489,5.344,100,3.875,4,277,18.6,396.9,23.09,20
0.17446,0,10.59,1,0.489,5.96,92.1,3.8771,4,277,18.6,393.25,17.27,21.7
0.37578,0,10.59,1,0.489,5.404,88.6,3.665,4,277,18.6,395.24,23.98,19.3
0.21719,0,10.59,1,0.489,5.807,53.8,3.6526,4,277,18.6,390.94,16.03,22.4
0.14052,0,10.59,0,0.489,6.375,32.3,3.9454,4,277,18.6,385.81,9.38,28.1
0.28955,0,10.59,0,0.489,5.412,9.8,3.5875,4,277,18.6,348.93,29.55,23.7
0.19802,0,10.59,0,0.489,6.182,42.4,3.9454,4,277,18.6,393.63,9.47,25
0.0456,0,13.89,1,0.55,5.888,56,3.1121,5,276,16.4,392.8,13.51,23.3
0.07013,0,13.89,0,0.55,6.642,85.1,3.4211,5,276,16.4,392.78,9.69,28.7
0.11069,0,13.89,1,0.55,5.951,93.8,2.8893,5,276,16.4,396.9,17.92,21.5
0.11425,0,13.89,1,0.55,6.373,92.4,3.3633,5,276,16.4,393.74,10.5,23
0.35809,0,6.2,1,0.507,6.951,88.5,2.8617,8,307,17.4,391.7,9.71,26.7
0.40771,0,6.2,1,0.507,6.164,91.3,3.048,8,307,17.4,395.24,21.46,21.7
0.62356,0,6.2,1,0.507,6.879,77.7,3.2721,8,307,17.4,390.39,9.93,27.5
0.6147,0,6.2,0,0.507,6.618,80.8,3.2721,8,307,17.4,396.9,7.6,30.1
0.31533,0,6.2,0,0.504,8.266,78.3,2.8944,8,307,17.4,385.05,4.14,44.8
0.52693,0,6.2,0,0.504,8.725,83,2.8944,8,307,17.4,382,4.63,50
0.38214,0,6.2,0,0.504,8.04,86.5,3.2157,8,307,17.4,387.38,3.13,37.6
0.41238,0,6.2,0,0.504,7.163,79.9,3.2157,8,307,17.4,372.08,6.36,31.6
0.29819,0,6.2,0,0.504,7.686,17,3.3751,8,307,17.4,377.51,3.92,46.7
0.44178,0,6.2,0,0.504,6.552,21.4,3.3751,8,307,17.4,380.34,3.76,31.5
0.537,0,6.2,0,0.504,5.981,68.1,3.6715,8,307,17.4,378.35,11.65,24.3
0.46296,0,6.2,0,0.504,7.412,76.9,3.6715,8,307,17.4,376.14,5.25,31.7
0.57529,0,6.2,0,0.507,8.337,73.3,3.8384,8,307,17.4,385.91,2.47,41.7
0.33147,0,6.2,0,0.507,8.247,70.4,3.6519,8,307,17.4,378.95,3.95,48.3
0.44791,0,6.2,1,0.507,6.726,66.5,3.6519,8,307,17.4,360.2,8.05,29
0.33045,0,6.2,0,0.507,6.086,61.5,3.6519,8,307,17.4,376.75,10.88,24
0.52058,0,6.2,1,0.507,6.631,76.5,4.148,8,307,17.4,388.45,9.54,25.1
0.51183,0,6.2,0,0.507,7.358,71.6,4.148,8,307,17.4,390.07,4.73,31.5
0.08244,30,4.93,0,0.428,6.481,18.5,6.1899,6,300,16.6,379.41,6.36,23.7
0.09252,30,4.93,0,0.428,6.606,42.2,6.1899,6,300,16.6,383.78,7.37,23.3
0.11329,30,4.93,0,0.428,6.897,54.3,6.3361,6,300,16.6,391.25,11.38,22
0.10612,30,4.93,0,0.428,6.095,65.1,6.3361,6,300,16.6,394.62,12.4,20.1
0.1029,30,4.93,0,0.428,6.358,52.9,7.0355,6,300,16.6,372.75,11.22,22.2
0.12757,30,4.93,0,0.428,6.393,7.8,7.0355,6,300,16.6,374.71,5.19,23.7
0.20608,22,5.86,0,0.431,5.593,76.5,7.9549,7,330,19.1,372.49,12.5,17.6
0.19133,22,5.86,0,0.431,5.605,70.2,7.9549,7,330,19.1,389.13,18.46,18.5
0.33983,22,5.86,0,0.431,6.108,34.9,8.0555,7,330,19.1,390.18,9.16,24.3
0.19657,22,5.86,0,0.431,6.226,79.2,8.0555,7,330,19.1,376.14,10.15,20.5
0.16439,22,5.86,0,0.431,6.433,49.1,7.8265,7,330,19.1,374.71,9.52,24.5
0.19073,22,5.86,0,0.431,6.718,17.5,7.8265,7,330,19.1,393.74,6.56,26.2
0.1403,22,5.86,0,0.431,6.487,13,7.3967,7,330,19.1,396.28,5.9,24.4
0.21409,22,5.86,0,0.431,6.438,8.9,7.3967,7,330,19.1,377.07,3.59,24.8
0.08221,22,5.86,0,0.431,6.957,6.8,8.9067,7,330,19.1,386.09,3.53,29.6
0.36894,22,5.86,0,0.431,8.259,8.4,8.9067,7,330,19.1,396.9,3.54,42.8
0.04819,80,3.64,0,0.392,6.108,32,9.2203,1,315,16.4,392.89,6.57,21.9
0.03548,80,3.64,0,0.392,5.876,19.1,9.2203,1,315,16.4,395.18,9.25,20.9
0.01538,90,3.75,0,0.394,7.454,34.2,6.3361,3,244,15.9,386.34,3.11,44
0.61154,20,3.97,0,0.647,8.704,86.9,1.801,5,264,13,389.7,5.12,50
0.66351,20,3.97,0,0.647,7.333,100,1.8946,5,264,13,383.29,7.79,36
0.65665,20,3.97,0,0.647,6.842,100,2.0107,5,264,13,391.93,6.9,30.1
0.54011,20,3.97,0,0.647,7.203,81.8,2.1121,5,264,13,392.8,9.59,33.8
0.53412,20,3.97,0,0.647,7.52,89.4,2.1398,5,264,13,388.37,7.26,43.1
0.52014,20,3.97,0,0.647,8.398,91.5,2.2885,5,264,13,386.86,5.91,48.8
0.82526,20,3.97,0,0.647,7.327,94.5,2.0788,5,264,13,393.42,11.25,31
0.55007,20,3.97,0,0.647,7.206,91.6,1.9301,5,264,13,387.89,8.1,36.5
0.76162,20,3.97,0,0.647,5.56,62.8,1.9865,5,264,13,392.4,10.45,22.8
0.7857,20,3.97,0,0.647,7.014,84.6,2.1329,5,264,13,384.07,14.79,30.7
0.57834,20,3.97,0,0.575,8.297,67,2.4216,5,264,13,384.54,7.44,50
0.5405,20,3.97,0,0.575,7.47,52.6,2.872,5,264,13,390.3,3.16,43.5
0.09065,20,6.96,1,0.464,5.92,61.5,3.9175,3,223,18.6,391.34,13.65,20.7
0.29916,20,6.96,0,0.464,5.856,42.1,4.429,3,223,18.6,388.65,13,21.1
0.16211,20,6.96,0,0.464,6.24,16.3,4.429,3,223,18.6,396.9,6.59,25.2
0.1146,20,6.96,0,0.464,6.538,58.7,3.9175,3,223,18.6,394.96,7.73,24.4
0.22188,20,6.96,1,0.464,7.691,51.8,4.3665,3,223,18.6,390.77,6.58,35.2
0.05644,40,6.41,1,0.447,6.758,32.9,4.0776,4,254,17.6,396.9,3.53,32.4
0.09604,40,6.41,0,0.447,6.854,42.8,4.2673,4,254,17.6,396.9,2.98,32
0.10469,40,6.41,1,0.447,7.267,49,4.7872,4,254,17.6,389.25,6.05,33.2
0.06127,40,6.41,1,0.447,6.826,27.6,4.8628,4,254,17.6,393.45,4.16,33.1
0.07978,40,6.41,0,0.447,6.482,32.1,4.1403,4,254,17.6,396.9,7.19,29.1
0.21038,20,3.33,0,0.4429,6.812,32.2,4.1007,5,216,14.9,396.9,4.85,35.1
0.03578,20,3.33,0,0.4429,7.82,64.5,4.6947,5,216,14.9,387.31,3.76,45.4
0.03705,20,3.33,0,0.4429,6.968,37.2,5.2447,5,216,14.9,392.23,4.59,35.4
0.06129,20,3.33,1,0.4429,7.645,49.7,5.2119,5,216,14.9,377.07,3.01,46
0.01501,90,1.21,1,0.401,7.923,24.8,5.885,1,198,13.6,395.52,3.16,50
0.00906,90,2.97,0,0.4,7.088,20.8,7.3073,1,285,15.3,394.72,7.85,32.2
0.01096,55,2.25,0,0.389,6.453,31.9,7.3073,1,300,15.3,394.72,8.23,22
0.01965,80,1.76,0,0.385,6.23,31.5,9.0892,1,241,18.2,341.6,12.93,20.1
0.03871,52.5,5.32,0,0.405,6.209,31.3,7.3172,6,293,16.6,396.9,7.14,23.2
0.0459,52.5,5.32,0,0.405,6.315,45.6,7.3172,6,293,16.6,396.9,7.6,22.3
0.04297,52.5,5.32,0,0.405,6.565,22.9,7.3172,6,293,16.6,371.72,9.51,24.8
0.03502,80,4.95,0,0.411,6.861,27.9,5.1167,4,245,19.2,396.9,3.33,28.5
0.07886,80,4.95,0,0.411,7.148,27.7,5.1167,4,245,19.2,396.9,3.56,37.3
0.03615,80,4.95,0,0.411,6.63,23.4,5.1167,4,245,19.2,396.9,4.7,27.9
0.08265,0,13.92,0,0.437,6.127,18.4,5.5027,4,289,16,396.9,8.58,23.9
0.08199,0,13.92,0,0.437,6.009,42.3,5.5027,4,289,16,396.9,10.4,21.7
0.12932,0,13.92,0,0.437,6.678,31.1,5.9604,4,289,16,396.9,6.27,28.6
0.05372,0,13.92,0,0.437,6.549,51,5.9604,4,289,16,392.85,7.39,27.1
0.14103,0,13.92,0,0.437,5.79,58,6.32,4,289,16,396.9,15.84,20.3
0.06466,70,2.24,0,0.4,6.345,20.1,7.8278,5,358,14.8,368.24,4.97,22.5
0.05561,70,2.24,0,0.4,7.041,10,7.8278,5,358,14.8,371.58,4.74,29
0.04417,70,2.24,0,0.4,6.871,47.4,7.8278,5,358,14.8,390.86,6.07,24.8
0.03537,34,6.09,0,0.433,6.59,40.4,5.4917,7,329,16.1,395.75,9.5,22
0.09266,34,6.09,0,0.433,6.495,18.4,5.4917,7,329,16.1,383.61,8.67,26.4
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0.05515,33,2.18,0,0.472,7.236,41.1,4.022,7,222,18.4,393.68,6.93,36.1
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5.82115,0,18.1,0,0.713,6.513,89.9,2.8016,24,666,20.2,393.82,10.29,20.2
7.83932,0,18.1,0,0.655,6.209,65.4,2.9634,24,666,20.2,396.9,13.22,21.4
3.1636,0,18.1,0,0.655,5.759,48.2,3.0665,24,666,20.2,334.4,14.13,19.9
3.77498,0,18.1,0,0.655,5.952,84.7,2.8715,24,666,20.2,22.01,17.15,19
4.42228,0,18.1,0,0.584,6.003,94.5,2.5403,24,666,20.2,331.29,21.32,19.1
15.5757,0,18.1,0,0.58,5.926,71,2.9084,24,666,20.2,368.74,18.13,19.1
13.0751,0,18.1,0,0.58,5.713,56.7,2.8237,24,666,20.2,396.9,14.76,20.1
4.34879,0,18.1,0,0.58,6.167,84,3.0334,24,666,20.2,396.9,16.29,19.9
4.03841,0,18.1,0,0.532,6.229,90.7,3.0993,24,666,20.2,395.33,12.87,19.6
3.56868,0,18.1,0,0.58,6.437,75,2.8965,24,666,20.2,393.37,14.36,23.2
4.64689,0,18.1,0,0.614,6.98,67.6,2.5329,24,666,20.2,374.68,11.66,29.8
8.05579,0,18.1,0,0.584,5.427,95.4,2.4298,24,666,20.2,352.58,18.14,13.8
6.39312,0,18.1,0,0.584,6.162,97.4,2.206,24,666,20.2,302.76,24.1,13.3
4.87141,0,18.1,0,0.614,6.484,93.6,2.3053,24,666,20.2,396.21,18.68,16.7
15.0234,0,18.1,0,0.614,5.304,97.3,2.1007,24,666,20.2,349.48,24.91,12
10.233,0,18.1,0,0.614,6.185,96.7,2.1705,24,666,20.2,379.7,18.03,14.6
14.3337,0,18.1,0,0.614,6.229,88,1.9512,24,666,20.2,383.32,13.11,21.4
5.82401,0,18.1,0,0.532,6.242,64.7,3.4242,24,666,20.2,396.9,10.74,23
5.70818,0,18.1,0,0.532,6.75,74.9,3.3317,24,666,20.2,393.07,7.74,23.7
5.73116,0,18.1,0,0.532,7.061,77,3.4106,24,666,20.2,395.28,7.01,25
2.81838,0,18.1,0,0.532,5.762,40.3,4.0983,24,666,20.2,392.92,10.42,21.8
2.37857,0,18.1,0,0.583,5.871,41.9,3.724,24,666,20.2,370.73,13.34,20.6
3.67367,0,18.1,0,0.583,6.312,51.9,3.9917,24,666,20.2,388.62,10.58,21.2
5.69175,0,18.1,0,0.583,6.114,79.8,3.5459,24,666,20.2,392.68,14.98,19.1
4.83567,0,18.1,0,0.583,5.905,53.2,3.1523,24,666,20.2,388.22,11.45,20.6
0.15086,0,27.74,0,0.609,5.454,92.7,1.8209,4,711,20.1,395.09,18.06,15.2
0.18337,0,27.74,0,0.609,5.414,98.3,1.7554,4,711,20.1,344.05,23.97,7
0.20746,0,27.74,0,0.609,5.093,98,1.8226,4,711,20.1,318.43,29.68,8.1
0.10574,0,27.74,0,0.609,5.983,98.8,1.8681,4,711,20.1,390.11,18.07,13.6
0.11132,0,27.74,0,0.609,5.983,83.5,2.1099,4,711,20.1,396.9,13.35,20.1
0.17331,0,9.69,0,0.585,5.707,54,2.3817,6,391,19.2,396.9,12.01,21.8
0.27957,0,9.69,0,0.585,5.926,42.6,2.3817,6,391,19.2,396.9,13.59,24.5
0.17899,0,9.69,0,0.585,5.67,28.8,2.7986,6,391,19.2,393.29,17.6,23.1
0.2896,0,9.69,0,0.585,5.39,72.9,2.7986,6,391,19.2,396.9,21.14,19.7
0.26838,0,9.69,0,0.585,5.794,70.6,2.8927,6,391,19.2,396.9,14.1,18.3
0.23912,0,9.69,0,0.585,6.019,65.3,2.4091,6,391,19.2,396.9,12.92,21.2
0.17783,0,9.69,0,0.585,5.569,73.5,2.3999,6,391,19.2,395.77,15.1,17.5
0.22438,0,9.69,0,0.585,6.027,79.7,2.4982,6,391,19.2,396.9,14.33,16.8
0.06263,0,11.93,0,0.573,6.593,69.1,2.4786,1,273,21,391.99,9.67,22.4
0.04527,0,11.93,0,0.573,6.12,76.7,2.2875,1,273,21,396.9,9.08,20.6
0.06076,0,11.93,0,0.573,6.976,91,2.1675,1,273,21,396.9,5.64,23.9
0.10959,0,11.93,0,0.573,6.794,89.3,2.3889,1,273,21,393.45,6.48,22
0.04741,0,11.93,0,0.573,6.03,80.8,2.505,1,273,21,396.9,7.88,11.9

  • 代码:

    import org.apache.spark.ml.feature.LabeledPoint
import org.apache.spark.ml.linalg.Vectors
import org.apache.spark.ml.regression.{LinearRegression, LinearRegressionModel}
import org.apache.spark.sql.{Dataset, SparkSession}

import scala.collection.immutable


object LinearRegression2 {

    def main(args: Array[String]) {

        val spark = SparkSession
            .builder
            .master("local")
            .appName("LinearRegression")
            .getOrCreate()
        import spark.implicits._
        //读取样本数据
        val data_path1 = "house_data.csv"

        val data1: Dataset[String] = spark.read.textFile(data_path1)

        val data2: Dataset[LabeledPoint] = data1.map { line =>
            val parts = line.split(',')
            //取特征值..
            val features: immutable.Seq[String] =  for(i <- 0 until 12) yield parts(i)

            LabeledPoint(parts(13).toDouble, Vectors.dense(features.map(_.toDouble).toArray))
        }

        //1 为随机种子
        val train2TestData: Array[Dataset[LabeledPoint]] = data2.randomSplit(Array(0.8, 0.2), 2)

        // 迭代次数
        val numIterations = 10

        val lr = new LinearRegression()
            .setFeaturesCol("features")
            .setLabelCol("label")
            //收敛的值，越小结果越精确，但迭代次数也越大，花费更多时间
            .setTol(1E-6)
            //迭代次数
            .setMaxIter(numIterations)
            //是否需要截距，默认true
            .setFitIntercept(true)

        val startTime = System.nanoTime()

        val model: LinearRegressionModel = lr.fit(train2TestData(0))
        //训练模型所消耗的时间
        val elapsedTime = (System.nanoTime() - startTime) / 1e9

        println("Training time: " + elapsedTime +"seconds")
        //权重.
        println("Weights: " + model.coefficients)
        //截距.
        println("Intercept:" +  model.intercept)
        //用测试集数据去评估模型，得到一个评估结果。

        val summary = model.evaluate(train2TestData(1))

        //打印测试结果
        summary.predictions.show()

        //平均绝对误差，预测数据和原始数据对应点误差绝对值和的均值
        println("平均绝对值误差: " + summary.meanAbsoluteError)
        //均方差，预测数据和原始数据对应点误差的平方和的均值
        println("均方差: " + summary.meanSquaredError)
        //测试集的数据条目
        println(summary.numInstances)


        /**
          * 训练完之后，可以将模型进行保存..
          *  model.save("model/lir.model")
          *  模型训练完毕后，以后用的时候可以直接加载模型，无需再训练
          *  val model = LinearRegressionModel.load("model/lir.model")
          */


        spark.stop()


    }

}

  • 执行结果

    +-----+--------------------+-------------------+
|label|            features|         prediction|
+-----+--------------------+-------------------+
|  7.2|[14.2362,0.0,18.1...| 19.292308597104586|
|  8.1|[0.20746,0.0,27.7...| 7.5416548482414925|
|  8.8|[73.5341,0.0,18.1...|-1.4905770946035553|
| 10.4|[25.9406,0.0,18.1...|  7.108399199583843|
| 10.5|[24.3938,0.0,18.1...|  7.463918272363248|
| 11.3|[9.18702,0.0,18.1...|  15.51902740402609|
| 12.0|[15.0234,0.0,18.1...| 13.096727831614949|
| 12.1|[9.59571,0.0,18.1...| 20.150862207690054|
| 12.8|[9.39063,0.0,18.1...| 15.209771092515677|
| 13.1|[23.6482,0.0,18.1...|  18.46433759809537|
| 13.4|[3.32105,0.0,19.5...| 19.258501533378304|
| 13.4|[7.05042,0.0,18.1...| 14.344269743723242|
| 13.8|[2.37934,0.0,19.5...| 16.417589029617595|
| 14.1|[4.75237,0.0,18.1...| 15.531296234009563|
| 14.3|[0.88125,0.0,21.8...| 13.989579508751198|
| 14.6|[10.233,0.0,18.1,...|  19.59835602444984|
| 15.0|[51.1358,0.0,18.1...| 3.8196651665200996|
| 15.2|[1.23247,0.0,8.14...| 17.927575362206746|
| 16.1|[6.44405,0.0,18.1...|  18.70165812465354|
| 16.6|[0.22927,0.0,6.91...| 20.527508513580685|
+-----+--------------------+-------------------+
only showing top 20 rows

平均绝对值误差: 3.5772891666288342
均方差: 25.93492056582901
93
posted @ 2019-11-29 10:52  wellDoneGaben  阅读(359)  评论(0)  编辑  收藏  举报