Regression on Python (part 2)

# IMPORT PACKAGES

import pandas as pd
import numpy as np
! pip install ipywidgets
from IPython.display import display
from IPython.html import widgets
from IPython.display import display
from ipywidgets import interact, interactive, fixed, interact_manual


# IMPORT DATA

path = 'https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/module_5_auto.csv'
df = pd.read_csv(path)
df=df._get_numeric_data()


# FUNCTIONS FOR PLOTTING

def DistributionPlot(RedFunction, BlueFunction, RedName, BlueName, Title):
    width = 12
    height = 10
    plt.figure(figsize=(width, height))
    ax1 = sns.distplot(RedFunction, hist=False, color="r", label=RedName)
    ax2 = sns.distplot(BlueFunction, hist=False, color="b", label=BlueName, ax=ax1)
    plt.title(Title)
    plt.xlabel('Price (in dollars)')
    plt.ylabel('Proportion of Cars')
    plt.show()
    plt.close()

def PollyPlot(xtrain, xtest, y_train, y_test, lr,poly_transform):
    width = 12
    height = 10
    plt.figure(figsize=(width, height))
    #training data
    #testing data
    # lr:  linear regression object
    #poly_transform:  polynomial transformation object
    xmax=max([xtrain.values.max(), xtest.values.max()])
    xmin=min([xtrain.values.min(), xtest.values.min()])
    x=np.arange(xmin, xmax, 0.1)
    plt.plot(xtrain, y_train, 'ro', label='Training Data')
    plt.plot(xtest, y_test, 'go', label='Test Data')
    plt.plot(x, lr.predict(poly_transform.fit_transform(x.reshape(-1, 1))), label='Predicted Function')
    plt.ylim([-10000, 60000])
    plt.ylabel('Price')
    plt.legend()


# TRAINING AND TESTING

y_data = df['price']
x_data=df.drop('price',axis=1)


# SPLIT DATA INTO TRAINING AND TESTING

from sklearn.model_selection import train_test_split
x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.15, random_state=1)
print("number of test samples :", x_test.shape[0])
print("number of training samples:",x_train.shape[0])


# LINEAR REGRESSION

from sklearn.linear_model import LinearRegression
lre=LinearRegression()
lre.fit(x_train[['horsepower']], y_train)
lre.score(x_test[['horsepower']], y_test)     # R^2 in test
lre.score(x_train[['horsepower']], y_train)     # R^2 in train, generally higher


# CROSS-VALIDATION SCORE

from sklearn.model_selection import cross_val_score

Rcross = cross_val_score(lre, x_data[['horsepower']], y_data, cv=4)    # 4 folds
Rcross    # R^2 for each fold

from sklearn.model_selection import cross_val_predict
yhat = cross_val_predict(lre,x_data[['horsepower']], y_data,cv=4)    # predict the value
yhat[0:5]


# OVERFITTING, UNDERFITTING AND MODEL SELECTION

# multiple regression model
lr = LinearRegression()
lr.fit(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_train)

# prediction using training data
yhat_train = lr.predict(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])
yhat_train[0:5]

# prediction using test data
yhat_test = lr.predict(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])
yhat_test[0:5]

# packages for plotting
import matplotlib.pyplot as plt
import seaborn as sns

# distribution for training and test prediction vs actual values
Title = 'Distribution  Plot of  Predicted Value Using Training Data vs Training Data Distribution'
DistributionPlot(y_train, yhat_train, "Actual Values (Train)", "Predicted Values (Train)", Title)
Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'
DistributionPlot(y_test,yhat_test,"Actual Values (Test)","Predicted Values (Test)",Title)

# overfitting with polynomial regression
from sklearn.preprocessing import PolynomialFeatures
x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.45, random_state=0)
pr = PolynomialFeatures(degree=5)
x_train_pr = pr.fit_transform(x_train[['horsepower']])
x_test_pr = pr.fit_transform(x_test[['horsepower']])
pr
poly = LinearRegression()
poly.fit(x_train_pr, y_train)
yhat = poly.predict(x_test_pr)
yhat[0:5]
print("Predicted values:", yhat[0:4])
print("True values:", y_test[0:4].values)
PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train, y_test, poly,pr)
poly.score(x_train_pr, y_train)   # R^2 of training
poly.score(x_test_pr, y_test)    # R^2 of testing
# A very low R^2 on testing is a sign of overfitting

Rsqu_test = []
order = [1, 2, 3, 4]
for n in order:
        pr = PolynomialFeatures(degree=n)
        x_train_pr = pr.fit_transform(x_train[['horsepower']])
        x_test_pr = pr.fit_transform(x_test[['horsepower']])   
        lr.fit(x_train_pr, y_train)
        Rsqu_test.append(lr.score(x_test_pr, y_test))
plt.plot(order, Rsqu_test)
plt.xlabel('order')
plt.ylabel('R^2')
plt.title('R^2 Using Test Data')
plt.text(3, 0.75, 'Maximum R^2 ')   
# We see the R^2 gradually increases until an order three polynomial is used. Then the R^2 dramatically decreases at four. We choose the order before the decrease.

# interactive graph for polynomial regression
def f(order, test_data):
    x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=test_data, random_state=0)
    pr = PolynomialFeatures(degree=order)
    x_train_pr = pr.fit_transform(x_train[['horsepower']])
    x_test_pr = pr.fit_transform(x_test[['horsepower']])
    poly = LinearRegression()
    poly.fit(x_train_pr,y_train)
    PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train,y_test, poly, pr)
interact(f, order=(0, 6, 1), test_data=(0.05, 0.95, 0.05))


# RIDGE REGRESSION

pr=PolynomialFeatures(degree=2)
x_train_pr=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])
x_test_pr=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])
from sklearn.linear_model import Ridge
RigeModel=Ridge(alpha=0.1)    # Ridge model
RigeModel.fit(x_train_pr, y_train)     # fit the model
yhat = RigeModel.predict(x_test_pr)     # predict
print('predicted:', yhat[0:4])
print('test set :', y_test[0:4].values)
# We select the value of Alfa that minimizes the test error
Rsqu_test = []
Rsqu_train = []
dummy1 = []
ALFA = 10 * np.array(range(0,1000))
for alfa in ALFA:
    RigeModel = Ridge(alpha=alfa)
    RigeModel.fit(x_train_pr, y_train)
    Rsqu_test.append(RigeModel.score(x_test_pr, y_test))
    Rsqu_train.append(RigeModel.score(x_train_pr, y_train))
# We can plot out the value of R^2 for different Alphas
width = 12
height = 10
plt.figure(figsize=(width, height))
plt.plot(ALFA,Rsqu_test, label='validation data  ')
plt.plot(ALFA,Rsqu_train, 'r', label='training Data ')
plt.xlabel('alpha')
plt.ylabel('R^2')
plt.legend()
# The red line in figure 6 represents the R^2 of the test data, as Alpha increases the R^2 decreases; therefore as Alfa increases the model performs worse on the test data. The blue line represents the R^2 on the validation data, as the value for Alfa increases the R^2 decreases.


# GRID SEARCH

from sklearn.model_selection import GridSearchCV
parameters1= [{'alpha': [0.001,0.1,1, 10, 100, 1000, 10000, 100000, 100000]}]
RR=Ridge()    # Ridge region object
Grid1 = GridSearchCV(RR, parameters1,cv=4)    # grid search object
Grid1.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_data)    # fit the model
# The object finds the best parameter values on the validation data. We can obtain the estimator with the best parameters and assign it to the variable BestRR as follows
BestRR=Grid1.best_estimator_
# test our model
BestRR.score(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_test)

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