19. Regression

%matplotlib inline

import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn import datasets, linear_model
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.model_selection import train_test_split
import pandas as pd
sns.set_theme(font_scale=2,palette='colorblind')

tips_df = sns.load_dataset('tips')

tips_df.head()

	total_bill	tip	sex	smoker	day	time	size
0	16.99	1.01	Female	No	Sun	Dinner	2
1	10.34	1.66	Male	No	Sun	Dinner	3
2	21.01	3.50	Male	No	Sun	Dinner	3
3	23.68	3.31	Male	No	Sun	Dinner	2
4	24.59	3.61	Female	No	Sun	Dinner	4

Split the data to use 80% of the data to train a model to predict the tip from the total bill.

tips_X = tips_df['total_bill']
tips_y = tips_df['tip']

type(tips_X.values)

numpy.ndarray

tips_X.values.shape

(244,)

tips_X.values[:,np.newaxis].shape

(244, 1)

tips_X = tips_X.values[:,np.newaxis]
tips_X_train,tips_X_test, tips_y_train, tips_y_test = train_test_split(tips_X, tips_y,
                                                                       train_size=.8)

regr = linear_model.LinearRegression()

type(tips_X)

numpy.ndarray

regr.fit(tips_X_train,tips_y_train)

LinearRegression()

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regr.get_params()

{'copy_X': True, 'fit_intercept': True, 'n_jobs': None, 'positive': False}

regr.coef_

array([0.10513009])

regr.intercept_

0.8998806720394064

tips_y_pred = regr.predict(tips_X_test)

tips_y_pred[0]

2.7838119316826817

tips_X_test[0]*regr.coef_ + regr.intercept_

array([2.78381193])

plt.scatter(tips_X_test,tips_y_test, color='black')
plt.plot(tips_X_test,tips_y_pred, color='blue')

[<matplotlib.lines.Line2D at 0x7f8bc9a9df10>]

plt.plot(tips_X_test, tips_y_pred, color='blue', linewidth=3)

# draw vertical lines frome each data point to its predict value
[plt.plot([x,x],[yp,yt], color='red', linewidth=3)
                 for x, yp, yt in zip(tips_X_test, tips_y_pred,tips_y_test)];
plt.scatter(tips_X_test, tips_y_test,  color='black')

<matplotlib.collections.PathCollection at 0x7f8bc7961f10>

mean_squared_error(tips_y_test,tips_y_pred)

0.8443482832748362

tips_y_test.mean()

3.1446938775510205

mean_squared_error(tips_y_test,tips_y_pred)/tips_y_test.mean()

0.26849935674259834

r2_score(tips_y_test,tips_y_pred)

0.5218612850368313

x = 10*np.random.random(20)
y_pred = 3*x
ex_df = pd.DataFrame(data = x,columns = ['x'])
ex_df['y_pred'] = y_pred
n_levels = range(1,18,2)
noise = (np.random.random(20)-.5)*2
for n in n_levels:
    y_true = y_pred + n* noise
    ex_df['r2 = '+ str(np.round(r2_score(y_pred,y_true),3))] = y_true

f_x_list = [2*x,3.5*x,.5*x**2, .03*x**3, 10*np.sin(x)+x*3,3*np.log(x**2)]
for fx in f_x_list:
    y_true = fx + noise
    ex_df['r2 = '+ str(np.round(r2_score(y_pred,y_true),3))] = y_true    

xy_df = ex_df.melt(id_vars=['x','y_pred'],var_name='rscore',value_name='y')
# sns.lmplot(x='x',y='y', data = xy_df,col='rscore',col_wrap=3,)
g = sns.FacetGrid(data = xy_df,col='rscore',col_wrap=3,aspect=1.5,height=3)
g.map(plt.plot, 'x','y_pred',color='k')
g.map(sns.scatterplot, "x", "y",)

<seaborn.axisgrid.FacetGrid at 0x7f8bc791e490>

regr.score(tips_X_test,tips_y_test)

0.5218612850368313

tips_df.head()

	total_bill	tip	sex	smoker	day	time	size
0	16.99	1.01	Female	No	Sun	Dinner	2
1	10.34	1.66	Male	No	Sun	Dinner	3
2	21.01	3.50	Male	No	Sun	Dinner	3
3	23.68	3.31	Male	No	Sun	Dinner	2
4	24.59	3.61	Female	No	Sun	Dinner	4

tips_X2 = tips_df[['total_bill','size']]
tips_X2_train,tips_X2_test, tips_y2_train, tips_y2_test = train_test_split(tips_X2, tips_y,
                                                                       train_size=.8)

regr2 = linear_model.LinearRegression()
regr2.fit(tips_X2_train,tips_y2_train)

LinearRegression()

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regr2.coef_

array([0.09588457, 0.1885609 ])

regr2.score(tips_X2_test,tips_y2_test)

0.43943140371626077

sns.relplot(data=tips_df,x='total_bill',y='tip',
           hue='size')

<seaborn.axisgrid.FacetGrid at 0x7f8bc7916dc0>

from sklearn import datasets

# Load the diabetes dataset
diabetes_X, diabetes_y = datasets.load_diabetes(return_X_y=True)
X_train,X_test, y_train,y_test = train_test_split(diabetes_X, diabetes_y ,
                                                  test_size=20,random_state=0)

regr_db = linear_model.LinearRegression()
regr_db.fit(X_train, y_train)

LinearRegression()

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y_pred = regr_db.predict(X_test)
r2_score(y_test,y_pred)

0.5195333332288746

diabetes_X.shape

(442, 10)

lasso = linear_model.Lasso()
lasso.fit(X_train, y_train)
lasso.score(X_test,y_test)

0.42249260665177746

lasso = linear_model.Lasso(.5)
lasso.fit(X_train, y_train)
lasso.score(X_test,y_test)

0.527228369284263

lasso = linear_model.Lasso(.25)
lasso.fit(X_train, y_train)
lasso.score(X_test,y_test)

0.5501992246861973

lasso.coef_

array([  -0.        ,  -52.1429064 ,  503.60281992,  219.24141192,
         -0.        ,   -0.        , -147.83111493,    0.        ,
        441.7507385 ,    0.        ])

link to polynomial regression