scikit-learn的线性回归模型 利用pandas处理数据
作为有监督学习,分类问题是预测类别结果,而回归问题是预测一个连续的结果。
In [1]:
import pandas as pd
In [2]:
# read csv file directly from a URL and save the results
data = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)
# display the first 5 rows
data.head()
Out[2]:
上面显示的结果类似一个电子表格,这个结构称为Pandas的数据帧(data frame)。
pandas的两个主要数据结构:Series和DataFrame:
- Series类似于一维数组,它有一组数据以及一组与之相关的数据标签(即索引)组成。
- DataFrame是一个表格型的数据结构,它含有一组有序的列,每列可以是不同的值类型。DataFrame既有行索引也有列索引,它可以被看做由Series组成的字典。
In [3]:
# display the last 5 rows
data.tail()
Out[3]:
In [4]:
# check the shape of the DataFrame(rows, colums)
data.shape
Out[4]:
特征:
- TV:对于一个给定市场中单一产品,用于电视上的广告费用(以千为单位)
- Radio:在广播媒体上投资的广告费用
- Newspaper:用于报纸媒体的广告费用
响应:
- Sales:对应产品的销量
在这个案例中,我们通过不同的广告投入,预测产品销量。因为响应变量是一个连续的值,所以这个问题是一个回归问题。数据集一共有200个观测值,每一组观测对应一个市场的情况。
In [5]:
import seaborn as sns
%matplotlib inline
In [6]:
# visualize the relationship between the features and the response using scatterplots
sns.pairplot(data, x_vars=['TV','Radio','Newspaper'], y_vars='Sales', size=7, aspect=0.8)
Out[6]:
seaborn的pairplot函数绘制X的每一维度和对应Y的散点图。通过设置size和aspect参数来调节显示的大小和比例。可以从图中看出,TV特征和销量是有比较强的线性关系的,而Radio和Sales线性关系弱一些,Newspaper和Sales线性关系更弱。通过加入一个参数kind='reg',seaborn可以添加一条最佳拟合直线和95%的置信带。
In [7]:
sns.pairplot(data, x_vars=['TV','Radio','Newspaper'], y_vars='Sales', size=7, aspect=0.8, kind='reg')
Out[7]:
线性模型表达式: 其中
- y是响应
在这个案例中:
In [8]:
# create a python list of feature names
feature_cols = ['TV', 'Radio', 'Newspaper']
# use the list to select a subset of the original DataFrame
X = data[feature_cols]
# equivalent command to do this in one line
X = data[['TV', 'Radio', 'Newspaper']]
# print the first 5 rows
X.head()
Out[8]:
In [9]:
# check the type and shape of X
print type(X)
print X.shape
In [10]:
# select a Series from the DataFrame
y = data['Sales']
# equivalent command that works if there are no spaces in the column name
y = data.Sales
# print the first 5 values
y.head()
Out[10]:
In [11]:
print type(y)
print y.shape
In [12]:
from sklearn.cross_validation import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)
In [14]:
# default split is 75% for training and 25% for testing
print X_train.shape
print y_train.shape
print X_test.shape
print y_test.shape
In [15]:
from sklearn.linear_model import LinearRegression
linreg = LinearRegression()
linreg.fit(X_train, y_train)
Out[15]:
In [16]:
print linreg.intercept_
print linreg.coef_
In [17]:
# pair the feature names with the coefficients
zip(feature_cols, linreg.coef_)
Out[17]:
如何解释各个特征对应的系数的意义?
- 对于给定了Radio和Newspaper的广告投入,如果在TV广告上每多投入1个单位,对应销量将增加0.0466个单位
- 更明确一点,加入其它两个媒体投入固定,在TV广告上没增加1000美元(因为单位是1000美元),销量将增加46.6(因为单位是1000)
In [18]:
y_pred = linreg.predict(X_test)
下面介绍三种常用的针对回归问题的评价测度
In [21]:
# define true and predicted response values
true = [100, 50, 30, 20]
pred = [90, 50, 50, 30]
(1)平均绝对误差(Mean Absolute Error, MAE)
(2)均方误差(Mean Squared Error, MSE)
(3)均方根误差(Root Mean Squared Error, RMSE)
In [24]:
from sklearn import metrics
import numpy as np
# calculate MAE by hand
print "MAE by hand:",(10 + 0 + 20 + 10)/4.
# calculate MAE using scikit-learn
print "MAE:",metrics.mean_absolute_error(true, pred)
# calculate MSE by hand
print "MSE by hand:",(10**2 + 0**2 + 20**2 + 10**2)/4.
# calculate MSE using scikit-learn
print "MSE:",metrics.mean_squared_error(true, pred)
# calculate RMSE by hand
print "RMSE by hand:",np.sqrt((10**2 + 0**2 + 20**2 + 10**2)/4.)
# calculate RMSE using scikit-learn
print "RMSE:",np.sqrt(metrics.mean_squared_error(true, pred))
In [26]:
print np.sqrt(metrics.mean_squared_error(y_test, y_pred))
In [27]:
feature_cols = ['TV', 'Radio']
X = data[feature_cols]
y = data.Sales
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)
linreg.fit(X_train, y_train)
y_pred = linreg.predict(X_test)
print np.sqrt(metrics.mean_squared_error(y_test, y_pred))
我们将Newspaper这个特征移除之后,得到RMSE变小了,说明Newspaper特征不适合作为预测销量的特征,于是,我们得到了新的模型。我们还可以通过不同的特征组合得到新的模型,看看最终的误差是如何的