multivariate regression. (multiple regression)
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What if more than 1 variable influence the one you are interested in ?
Example:
predicting a price for a car based on its many attributes(body style, brand, mileage, etc.)
例如有多个因素都会影响车辆的价格，车型，品牌，公里数，车门数。still use least squares.
We just end up with coefficients for each factor.
For example,
prices = a + b(mileage) + c(doors)
These coefficients imply how important each factor is (if the data is all normalized)
Get rid of ones that don’t matter.
Can still measure fit with r-squared.
Need to assume the different factors are not themselves dependent on each other.这些统计学的概念弄的我头大，好在敲代码不那么难：
回归评价指标MSE、RMSE、MAE、R-Squared -
直接上代码了.
使用pandas 来读一个excel. 有可能碰到ImportError#statsmodel package #ImportError: Install xlrd >= 0.9.0 for Excel support , need xlrd. apt-get install python3-xlrd import pandas as pd df=pd.read_excel("http://cdn.sundog-soft.com/Udemy/DataScience/cars.xls") df.head()第一种版本:
import statsmodels.api as sm from sklearn.preprocessing import StandardScaler scale= StandardScaler() X=df[['Mileage','Cylinder', 'Doors', 'Model_ord']] y=df[['Price']] X[['Mileage', 'Cylinder', 'Doors']]=scale.fit_transform(X[['Mileage', 'Cylinder', 'Doors']].as_matrix()) print(X) est=sm.OLS(y, X).fit() est.summary()第二种版本：
df['Model_ord'] = pd.Categorical(df.Model).codes X=df[['Mileage','Cylinder', 'Doors', 'Model_ord']] y=df[['Price']] X1=sm.add_constant(X) est=sm.OLS(y, X1).fit() est.summary()当然得到的结果都是一样的
""" OLS Regression Results ============================================================================== Dep. Variable: Price R-squared: 0.425 Model: OLS Adj. R-squared: 0.422 Method: Least Squares F-statistic: 147.4 Date: Sun, 08 Jul 2018 Prob (F-statistic): 2.10e-94 Time: 20:51:27 Log-Likelihood: -8313.9 No. Observations: 804 AIC: 1.664e+04 Df Residuals: 799 BIC: 1.666e+04 Df Model: 4 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 1.037e+04 1669.695 6.211 0.000 7093.297 1.36e+04 Mileage -0.1608 0.032 -4.966 0.000 -0.224 -0.097 Cylinder 4726.1696 204.906 23.065 0.000 4323.952 5128.387 Doors -1742.6007 312.188 -5.582 0.000 -2355.406 -1129.795 Model_ord -309.4669 32.666 -9.474 0.000 -373.587 -245.346 ============================================================================== Omnibus: 193.097 Durbin-Watson: 0.081 Prob(Omnibus): 0.000 Jarque-Bera (JB): 440.016 Skew: 1.288 Prob(JB): 2.83e-96 Kurtosis: 5.549 Cond. No. 1.37e+05 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. [2] The condition number is large, 1.37e+05. This might indicate that there are strong multicollinearity or other numerical problems. """注意这里的R-squared ，1是完美，0是极差，0.425, 算是不那么差。如果把使用的columns 减少一个，
例如：使用三列，这个R-squared 就会变得很比较糟， 0.042.`X=df[['Mileage','Cylinder', 'Doors' ]]` In [13]: df['Model_ord'] = pd.Categorical(df.Model).codes ...: X=df[['Mileage', 'Doors', 'Model_ord']] ...: y=df[['Price']] ...: X1=sm.add_constant(X) ...: est=sm.OLS(y, X1).fit() ...: ...: est.summary() ...: Out[13]: <class 'statsmodels.iolib.summary.Summary'> """ OLS Regression Results ============================================================================== Dep. Variable: Price R-squared: 0.042 Model: OLS Adj. R-squared: 0.038 Method: Least Squares F-statistic: 11.57 Date: Sun, 08 Jul 2018 Prob (F-statistic): 1.98e-07 Time: 20:52:16 Log-Likelihood: -8519.1 No. Observations: 804 AIC: 1.705e+04 Df Residuals: 800 BIC: 1.706e+04 Df Model: 3 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 3.125e+04 1809.549 17.272 0.000 2.77e+04 3.48e+04 Mileage -0.1765 0.042 -4.227 0.000 -0.259 -0.095 Doors -1652.9303 402.649 -4.105 0.000 -2443.303 -862.558 Model_ord -39.0387 39.326 -0.993 0.321 -116.234 38.157 ============================================================================== Omnibus: 206.410 Durbin-Watson: 0.080 Prob(Omnibus): 0.000 Jarque-Bera (JB): 470.872 Skew: 1.379 Prob(JB): 5.64e-103 Kurtosis: 5.541 Cond. No. 1.15e+05 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. [2] The condition number is large, 1.15e+05. This might indicate that there are strong multicollinearity or other numerical problems. """ -
最后
#The table of coefficients above give us the values to plug into an equation of form B0 + B1 mileage + B2 model_ord + B3 * doors #In this example it's pretty clear that the number of cylinders is more important than anything based on the coefficient. #Could we have figured that out outliers? y.groupby(df.Doors).mean() #surpringly , more doors does not mean a higher price, so it's not surprising that it's pretty useless as a predictor here.