About the Diabete dataset

This a REGRESSION problem. Ten numeric predictive variables: age, sex, body mass index, average blood pressure, and six blood serum measurements. They were obtained for each of n = 442 diabetes patients, as well as the response of interest, a quantitative measure (integer between 25 and 346) of disease progression one year after baseline.

The goal is to predict as well as possible the future disease progression one year after (target value) as a function of the 10 predictive variables.

Note: Each of the 10 feature variables have been mean centered and scaled by the standard deviation times n_samples (i.e. the sum of squares of each column totals 1).

Loading and pre-processing Diabete dataset

In [9]:
import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets

# Load the diabetes dataset
diabetes = datasets.load_diabetes()

# Print dataset description
print(diabetes.DESCR)

# Input vectors
diabetes_X = diabetes.data

# Split the data into training/testing sets
diabetes_X_train = diabetes_X[:-20]
diabetes_X_test = diabetes_X[-20:]

# Split the targets into training/testing sets
diabetes_y_train = diabetes.target[:-20]
diabetes_y_test = diabetes.target[-20:]

Diabetes dataset
================

Notes
-----

Ten baseline variables, age, sex, body mass index, average blood
pressure, and six blood serum measurements were obtained for each of n =
442 diabetes patients, as well as the response of interest, a
quantitative measure of disease progression one year after baseline.

Data Set Characteristics:

  :Number of Instances: 442

  :Number of Attributes: First 10 columns are numeric predictive values

  :Target: Column 11 is a quantitative measure of disease progression one year after baseline

  :Attributes:
    :Age:
    :Sex:
    :Body mass index:
    :Average blood pressure:
    :S1:
    :S2:
    :S3:
    :S4:
    :S5:
    :S6:

Note: Each of these 10 feature variables have been mean centered and scaled by the standard deviation times `n_samples` (i.e. the sum of squares of each column totals 1).

Source URL:
http://www4.stat.ncsu.edu/~boos/var.select/diabetes.html

For more information see:
Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani (2004) "Least Angle Regression," Annals of Statistics (with discussion), 407-499.
(http://web.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf)

Baseline method: linear regression

In [10]:
from sklearn import linear_model
from sklearn.metrics import mean_squared_error, r2_score

# Create linear regression object
regr = linear_model.LinearRegression()

# Train the model using the training sets
regr.fit(diabetes_X_train, diabetes_y_train)

# The coefficients
print('Coefficients: \n', regr.coef_)

# Make predictions using the testing set
diabetes_y_pred = regr.predict(diabetes_X_test)

# The mean squared error on test set
print("Mean squared error (on test set): %.2f"
      % mean_squared_error(diabetes_y_test, diabetes_y_pred))

# Explained variance score: 1 is perfect prediction
print('Variance score (max_value=1 for perfect prediction): %.2f' % r2_score(diabetes_y_test, diabetes_y_pred))

('Coefficients: \n', array([ 3.03499549e-01, -2.37639315e+02,  5.10530605e+02,  3.27736980e+02,
       -8.14131709e+02,  4.92814588e+02,  1.02848452e+02,  1.84606489e+02,
        7.43519617e+02,  7.60951722e+01]))
Mean squared error (on test set): 2004.57
Variance score (max_value=1 for perfect prediction): 0.59
In [ ]: