The Wisconsin Breast Cancer dataset can be found here. The Multiple Linear Regression, Polynomial Regression, Support Vector Regression, Decision Tree Regression and Random Forest Regression models were tried on the dataset. The model performances were evaluated using the R2 coefficient and the best model was selected. R2 is a goodness of fit parameter usually between 0 and 1. The closer R2 is to 1, the better the model.
Multiple Linear Regression(MLR)
#Import the Libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd# Import the dataset
dataset = pd.read_csv('Breast_cancer_data.csv')
X = dataset.iloc[:, :-1].values
y = dataset.iloc[:, -1].values#Split dataset into training and test set
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)# Train the MLR model on the training set
from sklearn.linear_model import LinearRegression
regressor = LinearRegression()
regressor.fit(X_train, y_train)
Output:
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)#Predicting the test results
y_pred = regressor.predict(X_test)
np.set_printoptions(precision=2)
print(np.concatenate((y_pred.reshape(len(y_pred),1), y_test.reshape(len(y_test),1)),1))
output:
[[ 0.47 0. ]
[ 0.65 1. ]
[ 0.87 1. ]
[ 0.89 1. ]
[ 0.83 1. ]
[ 0.84 1. ]
[ 0.89 1. ]
[ 0.94 1. ]
[ 1.32 1. ]
[ 1.09 1. ]
[ 0.53 1. ]
[ 0.5 1. ]
[ 1.19 1. ]
[ 0.58 1. ]
[ 0.49 1. ]
[ 0.38 0. ]
[ 1.06 1. ]
[-0.01 0. ]
[ 0.03 0. ]
[-0.06 0. ]
[ 0.69 0. ]
[ 0.25 0. ]
[ 0.69 1. ]
[ 0.92 1. ]
[ 0.11 0. ]
[ 1.11 1. ]
[ 1.29 1. ]
[ 0.28 0. ]
[ 0.89 1. ]
[ 0.23 0. ]
[ 1. 1. ]
[ 0.35 0. ]
[ 0.7 1. ]
[ 0.31 0. ]
[ 1.31 1. ]
[ 0.49 0. ]
[ 0.87 1. ]
[ 0.39 0. ]
[ 0.69 1. ]
[ 0.33 0. ]
[ 0.42 0. ]
[ 1.37 1. ]
[ 0.5 0. ]
[ 1.11 1. ]
[ 0.73 1. ]
[-0.06 0. ]
[ 1.38 1. ]
[ 0.64 1. ]
[ 0.87 1. ]
[ 0.16 0. ]
[-0.17 0. ]
[ 0.24 0. ]
[ 0.25 0. ]
[ 0.99 1. ]
[ 0.83 1. ]
[ 1.02 1. ]
[ 0.94 1. ]
[ 0.73 1. ]
[ 0.93 1. ]
[-0.05 0. ]
[ 0.34 0. ]
[ 0.5 0. ]
[ 1.23 1. ]
[ 0.84 1. ]
[ 0.14 0. ]
[ 0.69 1. ]
[-0.46 0. ]
[-0.18 0. ]
[ 0.1 0. ]
[ 1.01 1. ]
[ 0.61 1. ]
[ 0.13 0. ]
[ 0.94 1. ]
[ 0.56 0. ]
[ 0.13 0. ]
[ 0.71 1. ]
[ 1.31 1. ]
[ 0.6 1. ]
[ 1.11 1. ]
[ 1.21 1. ]
[ 0.27 0. ]
[-0.58 0. ]
[ 0.14 0. ]
[ 1.03 1. ]
[ 0.49 0. ]
[ 0.92 1. ]
[ 1.05 1. ]
[ 1.41 1. ]
[ 0.31 0. ]
[-0.48 0. ]
[ 1.23 1. ]
[ 0.63 0. ]
[ 0.53 1. ]
[ 0.02 0. ]
[ 1.01 1. ]
[ 0.99 1. ]
[ 0.32 0. ]
[ 0.86 1. ]
[ 0.95 1. ]
[ 0.82 1. ]
[ 1.21 1. ]
[ 0.9 1. ]
[ 0.66 1. ]
[ 0.37 1. ]
[ 0.27 0. ]
[ 0.69 1. ]
[-0.18 0. ]
[ 0.5 1. ]
[ 0.66 0. ]
[ 0.13 0. ]
[ 0.66 1. ]
[-0.04 0. ]
[ 0.14 0. ]
[ 0.52 1. ]]#Evaluating the model performance
from sklearn.metrics import r2_score
r2_score(y_test, y_pred)
Output:
0.6259734883274091Polynomial Regression
# Import the libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd#Import the dataset
dataset = pd.read_csv('Breast_cancer_data.csv')
X = dataset.iloc[:, :-1].values
y = dataset.iloc[:, -1].values#Split the dataset into Training and Test set
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)# Train the Polynomial Regression Model on the Training set
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
poly_reg = PolynomialFeatures(degree = 2)
X_poly = poly_reg.fit_transform(X_train)
regressor = LinearRegression()
regressor.fit(X_poly, y_train)
output:
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)
# Predict the test results
y_pred = regressor.predict(poly_reg.transform(X_test))
np.set_printoptions(precision=2)
print(np.concatenate((y_pred.reshape(len(y_pred),1), y_test.reshape(len(y_test),1)),1))
output:
[[ 0.38 0. ]
[ 0.68 1. ]
[ 0.95 1. ]
[ 0.9 1. ]
[ 0.89 1. ]
[ 0.91 1. ]
[ 1.19 1. ]
[ 0.99 1. ]
[ 1.09 1. ]
[ 0.99 1. ]
[ 0.54 1. ]
[ 0.48 1. ]
[ 1.07 1. ]
[ 0.44 1. ]
[ 0.57 1. ]
[ 0.44 0. ]
[ 0.84 1. ]
[-0.09 0. ]
[-0.07 0. ]
[-0.11 0. ]
[ 0.61 0. ]
[ 0.11 0. ]
[ 0.9 1. ]
[ 0.97 1. ]
[ 0.11 0. ]
[ 1.21 1. ]
[ 1.17 1. ]
[ 0.11 0. ]
[ 0.97 1. ]
[ 0.06 0. ]
[ 1.14 1. ]
[-0.03 0. ]
[ 0.77 1. ]
[ 0.19 0. ]
[ 1.16 1. ]
[ 0.46 0. ]
[ 0.92 1. ]
[ 0.06 0. ]
[ 0.79 1. ]
[ 0.21 0. ]
[ 0.36 0. ]
[ 0.88 1. ]
[ 0.37 0. ]
[ 1.07 1. ]
[ 0.84 1. ]
[ 0.02 0. ]
[ 0.96 1. ]
[ 0.66 1. ]
[ 0.96 1. ]
[ 0.03 0. ]
[ 0.07 0. ]
[ 0.2 0. ]
[ 0.03 0. ]
[ 1.01 1. ]
[ 0.94 1. ]
[ 1.06 1. ]
[ 1.17 1. ]
[ 0.93 1. ]
[ 0.95 1. ]
[-0.26 0. ]
[ 0.19 0. ]
[ 0.35 0. ]
[ 1.12 1. ]
[ 0.92 1. ]
[ 0.1 0. ]
[ 0.85 1. ]
[-0.42 0. ]
[-0.11 0. ]
[-0.02 0. ]
[ 1.02 1. ]
[ 0.65 1. ]
[-0.12 0. ]
[ 1.03 1. ]
[ 0.52 0. ]
[ 0.02 0. ]
[ 0.76 1. ]
[ 0.96 1. ]
[ 0.64 1. ]
[ 1.07 1. ]
[ 0.98 1. ]
[ 0.25 0. ]
[-0.88 0. ]
[-0.12 0. ]
[ 1.05 1. ]
[ 0.48 0. ]
[ 1.16 1. ]
[ 1.15 1. ]
[ 0.84 1. ]
[ 0.14 0. ]
[-0.38 0. ]
[ 1.11 1. ]
[ 0.6 0. ]
[ 0.55 1. ]
[ 0.2 0. ]
[ 1.01 1. ]
[ 0.92 1. ]
[ 0.01 0. ]
[ 0.93 1. ]
[ 0.99 1. ]
[ 0.89 1. ]
[ 0.72 1. ]
[ 0.97 1. ]
[ 0.64 1. ]
[ 0.39 1. ]
[ 0.08 0. ]
[ 0.98 1. ]
[-0.65 0. ]
[ 0.5 1. ]
[ 0.58 0. ]
[-0.01 0. ]
[ 0.77 1. ]
[-0.05 0. ]
[-0.02 0. ]
[ 0.56 1. ]]
# Evaluating the model performance
from sklearn.metrics import r2_score
r2_score(y_test, y_pred)
output:
0.714466598440052Random Forest Regression (RFR)
Repeat steps 1-3 above
# Train the random forest regression model on the whole dataset
from sklearn.ensemble import RandomForestRegressor
regressor = RandomForestRegressor(n_estimators = 10, random_state = 0)
regressor.fit(X_train, y_train)
output:
RandomForestRegressor(bootstrap=True, ccp_alpha=0.0, criterion='mse',
max_depth=None, max_features='auto', max_leaf_nodes=None,
max_samples=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
n_estimators=10, n_jobs=None, oob_score=False,
random_state=0, verbose=0, warm_start=False)# Predict the test results
y_pred = regressor.predict(X_test)
np.set_printoptions(precision=2)
print(np.concatenate((y_pred.reshape(len(y_pred),1), y_test.reshape(len(y_test),1)),1))
output:
[[0.2 0. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[0.9 1. ]
[1. 1. ]
[1. 1. ]
[0.1 1. ]
[1. 1. ]
[0.3 0. ]
[0.5 1. ]
[0. 0. ]
[0. 0. ]
[0. 0. ]
[0.9 0. ]
[0. 0. ]
[0.9 1. ]
[1. 1. ]
[0.2 0. ]
[1. 1. ]
[1. 1. ]
[0. 0. ]
[1. 1. ]
[0. 0. ]
[1. 1. ]
[0.1 0. ]
[0.9 1. ]
[0.4 0. ]
[1. 1. ]
[0.7 0. ]
[1. 1. ]
[0.1 0. ]
[1. 1. ]
[0. 0. ]
[0.5 0. ]
[1. 1. ]
[0.3 0. ]
[1. 1. ]
[1. 1. ]
[0. 0. ]
[1. 1. ]
[0.9 1. ]
[1. 1. ]
[0. 0. ]
[0. 0. ]
[0. 0. ]
[0. 0. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[0. 0. ]
[0. 0. ]
[0.1 0. ]
[1. 1. ]
[1. 1. ]
[0. 0. ]
[1. 1. ]
[0. 0. ]
[0. 0. ]
[0. 0. ]
[1. 1. ]
[0.5 1. ]
[0. 0. ]
[1. 1. ]
[1. 0. ]
[0. 0. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[1. 1. ]
[0. 0. ]
[0. 0. ]
[0.3 0. ]
[1. 1. ]
[1. 0. ]
[1. 1. ]
[0.9 1. ]
[1. 1. ]
[0. 0. ]
[0. 0. ]
[1. 1. ]
[0.5 0. ]
[0.7 1. ]
[0. 0. ]
[0.9 1. ]
[1. 1. ]
[0. 0. ]
[1. 1. ]
[1. 1. ]
[0.7 1. ]
[1. 1. ]
[1. 1. ]
[0.9 1. ]
[0. 1. ]
[0. 0. ]
[0.7 1. ]
[0. 0. ]
[0.2 1. ]
[0.5 0. ]
[0. 0. ]
[0.7 1. ]
[0. 0. ]
[0. 0. ]
[0.6 1. ]]# Model performance evaluation
from sklearn.metrics import r2_score
r2_score(y_test, y_pred)
output:
0.7056779930136551Decision Tree Regression (DTR)
Repeat steps 1-3 above
# Train the decision tree regression model on the training set
from sklearn.tree import DecisionTreeRegressor
regressor = DecisionTreeRegressor(random_state = 0)
regressor.fit(X_train, y_train)
output:
DecisionTreeRegressor(ccp_alpha=0.0, criterion='mse', max_depth=None,
max_features=None, max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=2,
min_weight_fraction_leaf=0.0, presort='deprecated',
random_state=0, splitter='best')# Predict the test results
y_pred = regressor.predict(X_test)
np.set_printoptions(precision=2)
print(np.concatenate((y_pred.reshape(len(y_pred),1), y_test.reshape(len(y_test),1)),1))
output:
[[0. 0.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[0. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[0. 1.]
[1. 1.]
[1. 0.]
[0. 1.]
[0. 0.]
[0. 0.]
[0. 0.]
[1. 0.]
[0. 0.]
[1. 1.]
[1. 1.]
[0. 0.]
[1. 1.]
[1. 1.]
[0. 0.]
[1. 1.]
[0. 0.]
[1. 1.]
[0. 0.]
[0. 1.]
[0. 0.]
[1. 1.]
[0. 0.]
[1. 1.]
[0. 0.]
[1. 1.]
[0. 0.]
[1. 0.]
[1. 1.]
[0. 0.]
[1. 1.]
[0. 1.]
[0. 0.]
[1. 1.]
[1. 1.]
[1. 1.]
[0. 0.]
[0. 0.]
[0. 0.]
[0. 0.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[0. 0.]
[0. 0.]
[0. 0.]
[1. 1.]
[1. 1.]
[0. 0.]
[1. 1.]
[0. 0.]
[0. 0.]
[0. 0.]
[1. 1.]
[0. 1.]
[0. 0.]
[1. 1.]
[1. 0.]
[0. 0.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[0. 0.]
[0. 0.]
[0. 0.]
[1. 1.]
[1. 0.]
[1. 1.]
[1. 1.]
[1. 1.]
[0. 0.]
[0. 0.]
[1. 1.]
[0. 0.]
[1. 1.]
[0. 0.]
[1. 1.]
[1. 1.]
[0. 0.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[1. 1.]
[0. 1.]
[0. 0.]
[1. 1.]
[0. 0.]
[0. 1.]
[0. 0.]
[0. 0.]
[1. 1.]
[0. 0.]
[0. 0.]
[0. 1.]]
#Model performance evaluation
from sklearn.metrics import r2_score
r2_score(y_test, y_pred)
output:
0.49317243569387104Support Vector Regression (SVR)
Repeat step 1 above
#Import the dataset
dataset = pd.read_csv('Breast_cancer_data.csv')
X = dataset.iloc[:, :-1].values
y = dataset.iloc[:, -1].values
y = y.reshape(len(y),1)# Split data into train and test sets
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)
#Feature scaling
from sklearn.preprocessing import StandardScaler
sc_X = StandardScaler()
sc_y = StandardScaler()
X_train = sc_X.fit_transform(X_train)
y_train = sc_y.fit_transform(y_train)#Train the SVR model on the training set
from sklearn.svm import SVR
regressor = SVR(kernel = 'rbf')
regressor.fit(X_train, y_train)
output:
SVR(C=1.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1, gamma='scale',
kernel='rbf', max_iter=-1, shrinking=True, tol=0.001, verbose=False)#Predicting the test results
y_pred = sc_y.inverse_transform(regressor.predict(sc_X.transform(X_test)))
np.set_printoptions(precision=2)
print(np.concatenate((y_pred.reshape(len(y_pred),1), y_test.reshape(len(y_test),1)),1))
output:
[[ 4.09e-01 0.00e+00]
[ 8.40e-01 1.00e+00]
[ 1.04e+00 1.00e+00]
[ 9.56e-01 1.00e+00]
[ 9.91e-01 1.00e+00]
[ 1.02e+00 1.00e+00]
[ 1.05e+00 1.00e+00]
[ 1.05e+00 1.00e+00]
[ 9.41e-01 1.00e+00]
[ 1.00e+00 1.00e+00]
[ 8.40e-01 1.00e+00]
[ 4.55e-01 1.00e+00]
[ 9.77e-01 1.00e+00]
[ 3.91e-01 1.00e+00]
[ 6.21e-01 1.00e+00]
[ 5.37e-01 0.00e+00]
[ 1.01e+00 1.00e+00]
[ 8.56e-03 0.00e+00]
[ 2.87e-02 0.00e+00]
[ 3.42e-02 0.00e+00]
[ 8.67e-01 0.00e+00]
[ 6.42e-02 0.00e+00]
[ 9.75e-01 1.00e+00]
[ 1.05e+00 1.00e+00]
[ 4.10e-03 0.00e+00]
[ 9.70e-01 1.00e+00]
[ 9.34e-01 1.00e+00]
[ 1.22e-01 0.00e+00]
[ 1.04e+00 1.00e+00]
[-6.41e-02 0.00e+00]
[ 1.03e+00 1.00e+00]
[ 8.64e-04 0.00e+00]
[ 9.20e-01 1.00e+00]
[-3.60e-02 0.00e+00]
[ 9.54e-01 1.00e+00]
[ 3.89e-01 0.00e+00]
[ 1.04e+00 1.00e+00]
[-2.01e-03 0.00e+00]
[ 8.25e-01 1.00e+00]
[ 4.86e-02 0.00e+00]
[ 6.78e-01 0.00e+00]
[ 9.44e-01 1.00e+00]
[ 3.30e-01 0.00e+00]
[ 1.00e+00 1.00e+00]
[ 9.74e-01 1.00e+00]
[-4.28e-03 0.00e+00]
[ 9.41e-01 1.00e+00]
[ 6.77e-01 1.00e+00]
[ 1.03e+00 1.00e+00]
[ 4.82e-02 0.00e+00]
[ 1.81e-02 0.00e+00]
[ 2.24e-02 0.00e+00]
[-6.66e-02 0.00e+00]
[ 1.04e+00 1.00e+00]
[ 1.03e+00 1.00e+00]
[ 1.03e+00 1.00e+00]
[ 1.03e+00 1.00e+00]
[ 1.08e+00 1.00e+00]
[ 1.05e+00 1.00e+00]
[ 1.58e-02 0.00e+00]
[ 7.41e-02 0.00e+00]
[ 2.42e-01 0.00e+00]
[ 9.40e-01 1.00e+00]
[ 1.03e+00 1.00e+00]
[-7.70e-02 0.00e+00]
[ 1.01e+00 1.00e+00]
[-1.71e-02 0.00e+00]
[ 2.28e-01 0.00e+00]
[ 1.65e-03 0.00e+00]
[ 1.04e+00 1.00e+00]
[ 7.87e-01 1.00e+00]
[-4.95e-02 0.00e+00]
[ 1.05e+00 1.00e+00]
[ 5.54e-01 0.00e+00]
[-1.71e-02 0.00e+00]
[ 9.57e-01 1.00e+00]
[ 9.56e-01 1.00e+00]
[ 7.25e-01 1.00e+00]
[ 1.00e+00 1.00e+00]
[ 9.87e-01 1.00e+00]
[ 2.62e-01 0.00e+00]
[ 6.49e-02 0.00e+00]
[-8.02e-02 0.00e+00]
[ 1.03e+00 1.00e+00]
[ 5.86e-01 0.00e+00]
[ 1.05e+00 1.00e+00]
[ 9.93e-01 1.00e+00]
[ 9.28e-01 1.00e+00]
[-8.39e-02 0.00e+00]
[ 3.60e-02 0.00e+00]
[ 9.70e-01 1.00e+00]
[ 7.68e-01 0.00e+00]
[ 5.21e-01 1.00e+00]
[ 1.66e-01 0.00e+00]
[ 1.04e+00 1.00e+00]
[ 1.05e+00 1.00e+00]
[-4.20e-02 0.00e+00]
[ 1.05e+00 1.00e+00]
[ 1.05e+00 1.00e+00]
[ 1.01e+00 1.00e+00]
[ 9.54e-01 1.00e+00]
[ 1.05e+00 1.00e+00]
[ 6.85e-01 1.00e+00]
[ 3.63e-01 1.00e+00]
[-1.97e-02 0.00e+00]
[ 5.18e-01 1.00e+00]
[ 7.57e-02 0.00e+00]
[ 5.03e-01 1.00e+00]
[ 6.45e-01 0.00e+00]
[-5.32e-02 0.00e+00]
[ 8.48e-01 1.00e+00]
[ 1.84e-02 0.00e+00]
[-1.92e-02 0.00e+00]
[ 6.24e-01 1.00e+00]]
#Model performance evaluation
from sklearn.metrics import r2_score
r2_score(y_test, y_pred)
output:
0.7661368518523295From the model performance evaluations of all the models, the best model is the SVR model with an R2 of 0.766