Python編程作業【第十四周】（jupyter homework）

Anscombe’s quartet

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Anscombe’s quartet comprises of four datasets, and is rather famous. Why? You’ll find out in this exercise.

%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")

anascombe = pd.read_csv('data/anscombe.csv') ##pd represents pandas
print(anascombe['x'].head())
anascombe.head()

Part 1

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For each of the four datasets…
- Compute the mean and variance of both x and y
- Compute the correlation coefficient between x and y
- Compute the linear regression line: y=β0+β1x+ϵ$y={\beta }_0+{\beta }_{1}x+ϵ$ (hint: use statsmodels and look at the Statsmodels notebook)

mean = anascombe.groupby('dataset')['x', 'y'].mean()
print("Mean is as follows: \n", mean)
variance = anascombe.groupby('dataset')['x', 'y'].var()
print("\nvariance is as follows: \n", variance)
correlation_coe = anascombe.groupby('dataset')['x', 'y'].corr()
print('\ncorrelation coefficient is as follows\n', correlation_coe)
print('\n')
# group according to dataset
for gp in anascombe.groupby('dataset'):
    print('Dataset', gp[0], ':')
    result = smf.ols('y ~ x', gp[1]).fit()
    print(result.params, '\n')

Result

Mean is as follows:
x y
dataset
I 9.0 7.500909
II 9.0 7.500909
III 9.0 7.500000
IV 9.0 7.500909
variance is as follows:
x y
dataset
I 11.0 4.127269
II 11.0 4.127629
III 11.0 4.122620
IV 11.0 4.123249
correlation coefficient is as follows
x y
dataset
I x 1.000000 0.816421
y 0.816421 1.000000
II x 1.000000 0.816237
y 0.816237 1.000000
III x 1.000000 0.816287
y 0.816287 1.000000
IV x 1.000000 0.816521
y 0.816521 1.000000
Dataset I :
Intercept 3.000091
x 0.500091
dtype: float64
Dataset II :
Intercept 3.000909
x 0.500000
dtype: float64
Dataset III :
Intercept 3.002455
x 0.499727
dtype: float64
Dataset IV :
Intercept 3.001727
x 0.499909
dtype: float64

Part 2

Using Seaborn, visualize all four datasets.

hint: use sns.FacetGrid combined with plt.scatter

graph = sns.FacetGrid(anascombe, col="dataset",  hue="y")
graph = graph.map(plt.scatter, "x", "y", edgecolor="R")