高编课后作业------第十四周-Jupyter

上一篇博客应该是13周，上次打错了，已纠正。 用jupyter写完可以直接生成 markdown，然后复制过来就行了，挺方便的 %matplotlib inline import random import numpy as np import scipy as sp import pandas as pd import matplotlib.pyplot as plt import seaborn as sns import statsmodels.api as sm import statsmodels.formula.api as smf sns.set_context("talk") # Anscombe’s quartet Anscombe’s quartet comprises of four datasets, and is rather famous. Why? You’ll find out in this exercise. anascombe = pd.read_csv('C:/Users/sunyy/Desktop/cme193-ipython-notebooks-lecture-master/data/anscombe.csv') anascombe.head() .dataframe tbody tr th:only-of-type { vertical-align: middle; } .dataframe tbody tr th { vertical-align: top; } .dataframe thead th { text-align: right; } datasetxy0I10.08.041I8.06.952I13.07.583I9.08.814I11.08.33

计算均值

print(anascombe.groupby('dataset')['x'].mean()) print(anascombe.groupby('dataset')['y'].mean()) dataset I 9.0 II 9.0 III 9.0 IV 9.0 Name: x, dtype: float64 dataset I 7.500909 II 7.500909 III 7.500000 IV 7.500909 Name: y, dtype: float64

计算方差

print(anascombe.groupby('dataset')['x'].var()) print(anascombe.groupby('dataset')['y'].var()) dataset I 11.0 II 11.0 III 11.0 IV 11.0 Name: x, dtype: float64 dataset I 4.127269 II 4.127629 III 4.122620 IV 4.123249 Name: y, dtype: float64

相关系数不好直接用groupby分组算，所以先手动获取每组数据

Y1 = anascombe.y[0:10].values Y2 = anascombe.y[11:21].values Y3 = anascombe.y[22:32].values Y4 = anascombe.y[33:43].values X1 = anascombe.x[0:10].values X2 = anascombe.x[11:21].values X3 = anascombe.x[22:32].values X4 = anascombe.x[33:43].values

计算相关系数

cof = [0,0,0,0] cof[0] = sp.stats.pearsonr(X1, Y1)[0] #返回的第一个参数是相关系数 cof[1] = sp.stats.pearsonr(X2, Y2)[0] cof[2] = sp.stats.pearsonr(X3, Y3)[0] cof[3] = sp.stats.pearsonr(X4, Y4)[0] for co in cof: print(co) 0.7970815759062526 0.7773093020784241 0.7985632617088811 0.8146722146933596

线性回归

执行过程大概分成3步： X=sm.add_constant(X) #为模型增加常数项 est=sm.OLS(Y,X) est=est.fit() est.params params 里包括了 前2个系数 ，第三个是误差项 X1add=sm.add_constant(X1) #为模型增加常数项 est=sm.OLS(Y1,X1add) est=est.fit() print("For dataset I, β0 is " + str(est.params[0]) + " , β1 is" + str(est.params[1])) X2add=sm.add_constant(X2) #为模型增加常数项 est=sm.OLS(Y2,X2add) est=est.fit() print("For dataset II, β0 is " + str(est.params[0]) + " , β1 is" + str(est.params[1])) X3add=sm.add_constant(X3) #为模型增加常数项 est=sm.OLS(Y3,X3add) est=est.fit() print("For dataset III, β0 is " + str(est.params[0]) + " , β1 is" + str(est.params[1])) X4add=sm.add_constant(X4) #为模型增加常数项 est=sm.OLS(Y4,X4add) est=est.fit() print("For dataset IIII, β0 is " + str(est.params[0]) + " , β1 is" + str(est.params[1])) For dataset I, β0 is 2.9018181818181805 , β1 is0.5086363636363642 For dataset II, β0 is 3.417597402597403 , β1 is0.46376623376623394 For dataset III, β0 is 2.877099567099566 , β1 is0.5106277056277062 For dataset IIII, β0 is 3.023030303030302 , β1 is0.49878787878787884

官方的用法就是这样，也没有什么好解释的：

m = sns.FacetGrid(anascombe, col="dataset") m.map(plt.scatter, "x","y")