设计思路

输出结果

train_boston_data.shape (1460, 81)

  Id  MSSubClass MSZoning  ...  SaleType  SaleCondition SalePrice

0   1          60       RL  ...        WD         Normal    208500

1   2          20       RL  ...        WD         Normal    181500

2   3          60       RL  ...        WD         Normal    223500

3   4          70       RL  ...        WD        Abnorml    140000

4   5          60       RL  ...        WD         Normal    250000

[5 rows x 81 columns]

train_t.head()    LotFrontage  GarageArea  SalePrice

0         65.0         548     208500

1         80.0         460     181500

2         68.0         608     223500

3         60.0         642     140000

4         84.0         836     250000

after scale,train_t.head()    LotFrontage  GarageArea  SalePrice

0     0.207668    0.386460   0.276159

1     0.255591    0.324401   0.240397

2     0.217252    0.428773   0.296026

3     0.191693    0.452750   0.185430

4     0.268371    0.589563   0.331126

  LotFrontage  GarageArea

0     0.207668    0.386460

1     0.255591    0.324401

2     0.217252    0.428773

3     0.191693    0.452750

4     0.268371    0.589563

                    Id  MSSubClass  LotFrontage  ...    MoSold    YrSold  SalePrice

Id             1.000000    0.011156    -0.010601  ...  0.021172  0.000712  -0.021917

MSSubClass     0.011156    1.000000    -0.386347  ... -0.013585 -0.021407  -0.084284

LotFrontage   -0.010601   -0.386347     1.000000  ...  0.011200  0.007450   0.351799

LotArea       -0.033226   -0.139781     0.426095  ...  0.001205 -0.014261   0.263843

OverallQual   -0.028365    0.032628     0.251646  ...  0.070815 -0.027347   0.790982

OverallCond    0.012609   -0.059316    -0.059213  ... -0.003511  0.043950  -0.077856

YearBuilt     -0.012713    0.027850     0.123349  ...  0.012398 -0.013618   0.522897

YearRemodAdd  -0.021998    0.040581     0.088866  ...  0.021490  0.035743   0.507101

MasVnrArea    -0.050298    0.022936     0.193458  ... -0.005965 -0.008201   0.477493

BsmtFinSF1    -0.005024   -0.069836     0.233633  ... -0.015727  0.014359   0.386420

BsmtFinSF2    -0.005968   -0.065649     0.049900  ... -0.015211  0.031706  -0.011378

BsmtUnfSF     -0.007940   -0.140759     0.132644  ...  0.034888 -0.041258   0.214479

TotalBsmtSF   -0.015415   -0.238518     0.392075  ...  0.013196 -0.014969   0.613581

1stFlrSF       0.010496   -0.251758     0.457181  ...  0.031372 -0.013604   0.605852

2ndFlrSF       0.005590    0.307886     0.080177  ...  0.035164 -0.028700   0.319334

LowQualFinSF  -0.044230    0.046474     0.038469  ... -0.022174 -0.028921  -0.025606

GrLivArea      0.008273    0.074853     0.402797  ...  0.050240 -0.036526   0.708624

BsmtFullBath   0.002289    0.003491     0.100949  ... -0.025361  0.067049   0.227122

BsmtHalfBath  -0.020155   -0.002333    -0.007234  ...  0.032873 -0.046524  -0.016844

FullBath       0.005587    0.131608     0.198769  ...  0.055872 -0.019669   0.560664

HalfBath       0.006784    0.177354     0.053532  ... -0.009050 -0.010269   0.284108

BedroomAbvGr   0.037719   -0.023438     0.263170  ...  0.046544 -0.036014   0.168213

KitchenAbvGr   0.002951    0.281721    -0.006069  ...  0.026589  0.031687  -0.135907

TotRmsAbvGrd   0.027239    0.040380     0.352096  ...  0.036907 -0.034516   0.533723

Fireplaces    -0.019772   -0.045569     0.266639  ...  0.046357 -0.024096   0.466929

GarageYrBlt    0.000072    0.085072     0.070250  ...  0.005337 -0.001014   0.486362

GarageCars     0.016570   -0.040110     0.285691  ...  0.040522 -0.039117   0.640409

GarageArea     0.017634   -0.098672     0.344997  ...  0.027974 -0.027378   0.623431

WoodDeckSF    -0.029643   -0.012579     0.088521  ...  0.021011  0.022270   0.324413

OpenPorchSF   -0.000477   -0.006100     0.151972  ...  0.071255 -0.057619   0.315856

EnclosedPorch  0.002889   -0.012037     0.010700  ... -0.028887 -0.009916  -0.128578

3SsnPorch     -0.046635   -0.043825     0.070029  ...  0.029474  0.018645   0.044584

ScreenPorch    0.001330   -0.026030     0.041383  ...  0.023217  0.010694   0.111447

PoolArea       0.057044    0.008283     0.206167  ... -0.033737 -0.059689   0.092404

MiscVal       -0.006242   -0.007683     0.003368  ... -0.006495  0.004906  -0.021190

MoSold         0.021172   -0.013585     0.011200  ...  1.000000 -0.145721   0.046432

YrSold         0.000712   -0.021407     0.007450  ... -0.145721  1.000000  -0.028923

SalePrice     -0.021917   -0.084284     0.351799  ...  0.046432 -0.028923   1.000000

[38 rows x 38 columns]

coef and intercept:  [0.21627565 0.41024884] 0.0543428481373919

cost after log： -3.850369422061899 -4.52343070892457

best w1 and w2 after GD： 0.10003438525600654 0.30004957896248946

核心代码

LiR = linear_model.LinearRegression()

LiR.fit(X_train, y_train)

print('coef and intercept: ',LiR.coef_,LiR.intercept_)

def CalCostByW(train_df,slope):

   w1_lists=[];w2_lists=[];cost_lists=[]

   for i in range (30):

       for j in range(30):

           w1= slope*i+0.1

           w2= slope*j+0.3

           w1_lists.append(w1); w2_lists.append(w2)

           cost_lists.append(cost(train_df,train_df.LotFrontage,train_df.GarageArea,w1,w2))

          # print (cost(train_df))

   return w1_lists,w2_lists,cost_lists

w1_lists,w2_lists,cost_lists=CalCostByW(train_t,0.01)