Part 1
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 (hint: use statsmodels and look at the Statsmodels notebook)
Part 2
Using Seaborn, visualize all four datasets.
hint: use sns.FacetGrid combined with plt.scatte
import pandas as pd
import seaborn as se
import matplotlib.pyplot as plt
import statsmodels.api as st
ans = se.load_dataset('anscombe')
df = ans.groupby('dataset')
mean_var = pd.concat([df.mean(), df.var()], keys=['mean', 'variance'])
corr = pd.concat([df.corr()], keys=['correlation'])
print(mean_var)
print(corr)
data_dict = dict(list(df))
array_x, array_y = {}, {}
for key, value in data_dict.items():
array_x[key] = value['x'].values
array_y[key] = value['y'].values
for key in array_x.keys():
x = st.add_constant(array_x[key])
y = array_y[key]
est = st.OLS(y, x).fit()
params = est.params
print(key, ': beta0 =', params[0], 'beta1 =', params[1])
se.set(style='whitegrid')
g = se.FacetGrid(ans, col="dataset", hue="dataset")
g.map(plt.scatter, 'x', 'y')
plt.show()