简单的线性回归

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1、《麦子学院》

说到线性回归，都不陌生就不多讲了

如图所示，这条线如何求出的，线的方程式为

根据这两个公式求出方程带入即可

展示一下用Python的简单应用：

# coding=utf-8import numpy as np#numpy中有自带的求均值meandef fit(x, y):    up = 0    down = 0;    n = len(x)    for i in range(0, n):        up += (x[i]-np.mean(x))*(y[i]-np.mean(y))        down += (x[i]-np.mean(x))**2    b1 = up/float(down)    b0 = np.mean(y)-b1*float(np.mean(x))    print b0    print b1    return b0, b1def predicet(b0, b1, p):    return b1*p+b0x = [0, 1, 2, 3, 4, 5]y = [0, 20, 60, 68, 77, 110]b0, b1 = fit(x,y)p = 3.5print predicet(b0, b1, p)

2、

《机器学习实战》线性回归

1、线性回归的用处

2、线性回归的定义

3、公式定理

4、代码

5、数据

1、线性回归一般用于预测，比如销量预测，制造缺陷预测，商品的社会劳动时间预测商品的价值等等

2、线性回归一般可以用线性回归函数来进行表示，线性回归意味着可以将输入项分别乘以一个常量，再将结果加起来得到输出，例如房价=w0*离市中心距离+w1，需要说明的就是还存在另一种非线性回归，例如船只寿命=w0*出行次数+w1*造价+额外受损。

3、一般的，得到数据后，经过对数据的处理储存在矩阵X中，回归系数存在向量w中，表示为

一个通常的方法找到最小的误差w，这里的误差指的是真实值Y和预测值之间的差值，我们采用平方误差的方法，即：

用矩阵表示可以写作：

，对w求导可得到

令其等于零，解出w如下

^w表示w的一个最佳估计。

注意的一点就是，求矩阵的逆，首先来判断是否存在。

代码：

# coding=utf-8 from numpy import *import numpy as npimport pylab as pl#处理数据def loadDataSet(fileName):    numFeat = len(open(fileName).readline().split('\t')) - 1     dataMat = []; labelMat = []    fr = open(fileName)    for line in fr.readlines():        lineArr =[]        curLine = line.strip().split('\t')        for i in range(numFeat):            lineArr.append(float(curLine[i]))        dataMat.append(lineArr)        labelMat.append(float(curLine[-1]))    return dataMat,labelMat#求wdef standRegres(xArr,yArr):    xMat = mat(xArr);     yMat = mat(yArr).T    xTx = xMat.T*xMat    if linalg.det(xTx) == 0.0:        print "This matrix is singular, cannot do inverse"        return    ws = xTx.I * (xMat.T*yMat)    print "ws:",ws    return ws  def show(ws, xArr, yArr):    ws = array(ws)    xArr = array(xArr)    yArr = array(yArr)        x = linspace(0,1)    y = ws[0] + ws[1]*x    pl.figure(figsize = (6,5))    pl.plot(x, y, label="$y=ax+b$", linewidth=2.0, color = "red", linestyle = "-")    pl.plot(xArr[:, 1], yArr, '.', color = 'g')    pl.legend()    pl.show()def main():    xArr,yArr = loadDataSet(r"C:\Users\l\Desktop\ex0.txt")    ws = standRegres(xArr,yArr)    show(ws,xArr, yArr)    if __name__ == '__main__':    main();

数据：

1.000000   0.067732   3.176513
1.000000   0.427810   3.816464
1.000000   0.995731   4.550095
1.000000   0.738336   4.256571
1.000000   0.981083   4.560815
1.000000   0.526171   3.929515
1.000000   0.378887   3.526170
1.000000   0.033859   3.156393
1.000000   0.132791   3.110301
1.000000   0.138306   3.149813
1.000000   0.247809   3.476346
1.000000   0.648270   4.119688
1.000000   0.731209   4.282233
1.000000   0.236833   3.486582
1.000000   0.969788   4.655492
1.000000   0.607492   3.965162
1.000000   0.358622   3.514900
1.000000   0.147846   3.125947
1.000000   0.637820   4.094115
1.000000   0.230372   3.476039
1.000000   0.070237   3.210610
1.000000   0.067154   3.190612
1.000000   0.925577   4.631504
1.000000   0.717733   4.295890
1.000000   0.015371   3.085028
1.000000   0.335070   3.448080
1.000000   0.040486   3.167440
1.000000   0.212575   3.364266
1.000000   0.617218   3.993482
1.000000   0.541196   3.891471
1.000000   0.045353   3.143259
1.000000   0.126762   3.114204
1.000000   0.556486   3.851484
1.000000   0.901144   4.621899
1.000000   0.958476   4.580768
1.000000   0.274561   3.620992
1.000000   0.394396   3.580501
1.000000   0.872480   4.618706
1.000000   0.409932   3.676867
1.000000   0.908969   4.641845
1.000000   0.166819   3.175939
1.000000   0.665016   4.264980
1.000000   0.263727   3.558448
1.000000   0.231214   3.436632
1.000000   0.552928   3.831052
1.000000   0.047744   3.182853
1.000000   0.365746   3.498906
1.000000   0.495002   3.946833
1.000000   0.493466   3.900583
1.000000   0.792101   4.238522
1.000000   0.769660   4.233080
1.000000   0.251821   3.521557
1.000000   0.181951   3.203344
1.000000   0.808177   4.278105
1.000000   0.334116   3.555705
1.000000   0.338630   3.502661
1.000000   0.452584   3.859776
1.000000   0.694770   4.275956
1.000000   0.590902   3.916191
1.000000   0.307928   3.587961
1.000000   0.148364   3.183004
1.000000   0.702180   4.225236
1.000000   0.721544   4.231083
1.000000   0.666886   4.240544
1.000000   0.124931   3.222372
1.000000   0.618286   4.021445
1.000000   0.381086   3.567479
1.000000   0.385643   3.562580
1.000000   0.777175   4.262059
1.000000   0.116089   3.208813
1.000000   0.115487   3.169825
1.000000   0.663510   4.193949
1.000000   0.254884   3.491678
1.000000   0.993888   4.533306
1.000000   0.295434   3.550108
1.000000   0.952523   4.636427
1.000000   0.307047   3.557078
1.000000   0.277261   3.552874
1.000000   0.279101   3.494159
1.000000   0.175724   3.206828
1.000000   0.156383   3.195266
1.000000   0.733165   4.221292
1.000000   0.848142   4.413372
1.000000   0.771184   4.184347
1.000000   0.429492   3.742878
1.000000   0.162176   3.201878
1.000000   0.917064   4.648964
1.000000   0.315044   3.510117
1.000000   0.201473   3.274434
1.000000   0.297038   3.579622
1.000000   0.336647   3.489244
1.000000   0.666109   4.237386
1.000000   0.583888   3.913749
1.000000   0.085031   3.228990
1.000000   0.687006   4.286286
1.000000   0.949655   4.628614
1.000000   0.189912   3.239536
1.000000   0.844027   4.457997
1.000000   0.333288   3.513384
1.000000   0.427035   3.729674
1.000000   0.466369   3.834274
1.000000   0.550659   3.811155
1.000000   0.278213   3.598316
1.000000   0.918769   4.692514
1.000000   0.886555   4.604859
1.000000   0.569488   3.864912
1.000000   0.066379   3.184236
1.000000   0.335751   3.500796
1.000000   0.426863   3.743365
1.000000   0.395746   3.622905
1.000000   0.694221   4.310796
1.000000   0.272760   3.583357
1.000000   0.503495   3.901852
1.000000   0.067119   3.233521
1.000000   0.038326   3.105266
1.000000   0.599122   3.865544
1.000000   0.947054   4.628625
1.000000   0.671279   4.231213
1.000000   0.434811   3.791149
1.000000   0.509381   3.968271
1.000000   0.749442   4.253910
1.000000   0.058014   3.194710
1.000000   0.482978   3.996503
1.000000   0.466776   3.904358
1.000000   0.357767   3.503976
1.000000   0.949123   4.557545
1.000000   0.417320   3.699876
1.000000   0.920461   4.613614
1.000000   0.156433   3.140401
1.000000   0.656662   4.206717
1.000000   0.616418   3.969524
1.000000   0.853428   4.476096
1.000000   0.133295   3.136528
1.000000   0.693007   4.279071
1.000000   0.178449   3.200603
1.000000   0.199526   3.299012
1.000000   0.073224   3.209873
1.000000   0.286515   3.632942
1.000000   0.182026   3.248361
1.000000   0.621523   3.995783
1.000000   0.344584   3.563262
1.000000   0.398556   3.649712
1.000000   0.480369   3.951845
1.000000   0.153350   3.145031
1.000000   0.171846   3.181577
1.000000   0.867082   4.637087
1.000000   0.223855   3.404964
1.000000   0.528301   3.873188
1.000000   0.890192   4.633648
1.000000   0.106352   3.154768
1.000000   0.917886   4.623637
1.000000   0.014855   3.078132
1.000000   0.567682   3.913596
1.000000   0.068854   3.221817
1.000000   0.603535   3.938071
1.000000   0.532050   3.880822
1.000000   0.651362   4.176436
1.000000   0.901225   4.648161
1.000000   0.204337   3.332312
1.000000   0.696081   4.240614
1.000000   0.963924   4.532224
1.000000   0.981390   4.557105
1.000000   0.987911   4.610072
1.000000   0.990947   4.636569
1.000000   0.736021   4.229813
1.000000   0.253574   3.500860
1.000000   0.674722   4.245514
1.000000   0.939368   4.605182
1.000000   0.235419   3.454340
1.000000   0.110521   3.180775
1.000000   0.218023   3.380820
1.000000   0.869778   4.565020
1.000000   0.196830   3.279973
1.000000   0.958178   4.554241
1.000000   0.972673   4.633520
1.000000   0.745797   4.281037
1.000000   0.445674   3.844426
1.000000   0.470557   3.891601
1.000000   0.549236   3.849728
1.000000   0.335691   3.492215
1.000000   0.884739   4.592374
1.000000   0.918916   4.632025
1.000000   0.441815   3.756750
1.000000   0.116598   3.133555
1.000000   0.359274   3.567919
1.000000   0.814811   4.363382
1.000000   0.387125   3.560165
1.000000   0.982243   4.564305
1.000000   0.780880   4.215055
1.000000   0.652565   4.174999
1.000000   0.870030   4.586640
1.000000   0.604755   3.960008
1.000000   0.255212   3.529963
1.000000   0.730546   4.213412
1.000000   0.493829   3.908685
1.000000   0.257017   3.585821
1.000000   0.833735   4.374394
1.000000   0.070095   3.213817
1.000000   0.527070   3.952681
1.000000   0.116163   3.129283

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