In [1]:

    

%matplotlib inline

import pandas
import statistics
import numpy as np
import matplotlib.pylab as plt
from sklearn.cross_validation import train_test_split
from sklearn.linear_model import LassoLarsCV
from sklearn import preprocessing


    

In [2]:

    

# bug fix for display formats to avoid run time errors
pandas.set_option('display.float_format', lambda x:'%.2f'%x)

#load the data
data = pandas.read_csv('..\separatedData.csv')

# convert to numeric format
data["breastCancer100th"] = pandas.to_numeric(data["breastCancer100th"], errors='coerce')
data["meanSugarPerson"]   = pandas.to_numeric(data["meanSugarPerson"], errors='coerce')
data["meanFoodPerson"]   = pandas.to_numeric(data["meanFoodPerson"], errors='coerce')
data["meanCholesterol"]   = pandas.to_numeric(data["meanCholesterol"], errors='coerce')

# listwise deletion of missing values
sub1 = data[['breastCancer100th', 'meanFoodPerson', 'meanCholesterol', 'meanSugarPerson']].dropna()

#Split into training and testing sets
predvar = sub1[[ 'meanSugarPerson', 'meanFoodPerson', 'meanCholesterol']]
targets = sub1['breastCancer100th']


    

In [3]:

    

# standardize predictors to have mean=0 and sd=1
predictors = predvar.copy()
predictors['meanSugarPerson']=preprocessing.scale(predictors['meanSugarPerson'].astype('float64'))
predictors['meanFoodPerson']=preprocessing.scale(predictors['meanFoodPerson'].astype('float64'))
predictors['meanCholesterol']=preprocessing.scale(predictors['meanCholesterol'].astype('float64'))

# split data into train and test sets - Train = 70%, Test = 30%
pred_train, pred_test, tar_train, tar_test = train_test_split(predictors, targets,
                                                              test_size=.3, random_state=123)


    

In [4]:

    

# specify the lasso regression model
model=LassoLarsCV(cv=10, precompute=False).fit(pred_train,tar_train)

# print variable names and regression coefficients
dict(zip(predictors.columns, model.coef_))


    

    
Out[4]:





{'meanCholesterol': 16.739257253156911,
 'meanFoodPerson': 2.6688475418098832,
 'meanSugarPerson': 2.5710138593832852}

In [5]:

    

# plot coefficient progression
m_log_alphas = -np.log10(model.alphas_)
ax = plt.gca()
plt.plot(m_log_alphas, model.coef_path_.T)
plt.axvline(-np.log10(model.alpha_), linestyle='--', color='k',
            label='alpha CV')
plt.ylabel('Regression Coefficients')
plt.xlabel('-log(alpha)')
plt.title('Regression Coefficients Progression for Lasso Paths')


    

    
Out[5]:





<matplotlib.text.Text at 0xc8f1d56f98>






    

In [6]:

    

# plot mean square error for each fold
m_log_alphascv = -np.log10(model.cv_alphas_)
plt.figure()
plt.plot(m_log_alphascv, model.cv_mse_path_, ':')
plt.plot(m_log_alphascv, model.cv_mse_path_.mean(axis=-1), 'k',
         label='Average across the folds', linewidth=2)
plt.axvline(-np.log10(model.alpha_), linestyle='--', color='k',
            label='alpha CV')
plt.legend()
plt.xlabel('-log(alpha)')
plt.ylabel('Mean squared error')
plt.title('Mean squared error on each fold')


    

    
Out[6]:





<matplotlib.text.Text at 0xc8f2350a20>






    

In [7]:

    

# MSE from training and test data
from sklearn.metrics import mean_squared_error
train_error = mean_squared_error(tar_train, model.predict(pred_train))
test_error = mean_squared_error(tar_test, model.predict(pred_test))
print ('training data MSE')
print(train_error)
print ('test data MSE')
print(test_error)


    

    




training data MSE
167.849476371
test data MSE
209.885898511

In [8]:

    

# R-square from training and test data
rsquared_train=model.score(pred_train,tar_train)
rsquared_test=model.score(pred_test,tar_test)
print ('training data R-square')
print(rsquared_train)
print ('test data R-square')
print(rsquared_test)


    

    




training data R-square
0.71692405706
test data R-square
0.633973360069