Illustrates how to use the LinearRegressionModel class to perform a multiple linear regression in IronPython.
import numerics
from System import Array, Char
from Extreme.Mathematics import *
from Extreme.Statistics import *
# Illustrates building multiple linear regression models using
# the LinearRegressionModel class in the
# Extreme.Statistics namespace of the Extreme
# Optimization Numerical Libraries for .NET.
# Multiple linear regression can be performed using
# the LinearRegressionModel class.
#
# This QuickStart sample uses old economic data about 50 countries
# from Belsley, Kuh and Welsch. The fields are as follows:
# DispInc: Per capita disposable income.
# Growth: Percent rate of change of DispInc.
# Pop15: Percentage of population under 15.
# Pop75: Percentage of population over 75.
# Savings: Aggregate savings divided by disposable income.
#
# We want to investigate the effect of the first four variables
# on the savings ratio.
# First, read the data from a file into an ADO.NET DataTable.
# For the sake of clarity, we put this code in its own method.
#/ Reads the data from a text file into a <see cref="DataTable"/>.
import clr
clr.AddReference("System.Data")
from System.Data import *
from System.IO import *
def ReadData():
data = DataTable("savings")
data.Columns.Add("Key", str)
whitespace = Array[Char]([ ' ', '\t' ])
sr = StreamReader(r"..\Data\savings.dat")
# Read the header and extract the field names.
line = sr.ReadLine()
pos = 0
while True:
while Char.IsWhiteSpace(line[pos]):
pos = pos + 1
pos2 = line.IndexOfAny(whitespace, pos)
if pos2 < 0:
data.Columns.Add(line.Substring(pos), float)
break
else:
data.Columns.Add(line.Substring(pos, pos2 - pos), float)
pos = pos2
if pos < 0:
break
# Now read the data and add them to the table.
# Assumes all columns except the first are numerical.
rowData = Array.CreateInstance(object, data.Columns.Count)
line = sr.ReadLine()
while line != None and line.Length > 0:
column = 0
pos = 0
while True:
while Char.IsWhiteSpace(line[pos]):
pos = pos + 1
pos2 = line.IndexOfAny(whitespace, pos)
if pos2 < 0:
field = line.Substring(pos)
else:
field = line.Substring(pos, pos2 - pos)
if column == 0:
rowData[column] = field
else:
rowData[column] = float.Parse(field)
column = column + 1
pos = pos2
if pos < 0 or column >= data.Columns.Count:
break
data.Rows.Add(rowData)
line = sr.ReadLine()
return data
dataTable = ReadData()
# Next, create a VariableCollection from the data table:
data = VariableCollection(dataTable)
# Now create the regression model. Parameters are the name
# of the dependent variable, a string array containing
# the names of the independent variables, and the VariableCollection
# containing all variables.
model = LinearRegressionModel(data, "Savings", \
Array[str]([ "Pop15", "Pop75", "DispInc", "Growth"]))
# We can set model options now, such as whether to include a constant:
model.NoIntercept = False
# The Compute method performs the actual regression analysis.
model.Compute()
# The Parameters collection contains information about the regression
# parameters.
print "Variable Value Std.Error t-stat p-Value"
for parameter in model.Parameters:
# Parameter objects have the following properties:
print "{0:20}{1:10.5f}{2:10.5f}{3:8.2f} {4:7.4f}".format( # Name, usually the name of the variable:
parameter.Name, # Estimated value of the parameter:
parameter.Value, # Standard error:
parameter.StandardError, # The value of the t statistic for the hypothesis that the parameter
# is zero.
parameter.Statistic, # Probability corresponding to the t statistic.
parameter.PValue)
print
# In addition to these properties, Parameter objects have a GetConfidenceInterval
# method that returns a confidence interval at a specified confidence level.
# Notice that individual parameters can be accessed using their numeric index.
# Parameter 0 is the intercept, if it was included.
confidenceInterval = model.Parameters[0].GetConfidenceInterval(0.95)
print "95% confidence interval for constant:{0:.4f} - {1:.4f}".format(confidenceInterval.LowerBound, confidenceInterval.UpperBound)
# Parameters can also be accessed by name:
confidenceInterval = model.Parameters["DispInc"].GetConfidenceInterval(0.95)
print "95% confidence interval for Growth: {0:.4f} - {1:.4f}".format(confidenceInterval.LowerBound, confidenceInterval.UpperBound)
print
# There is also a wealth of information about the analysis available
# through various properties of the LinearRegressionModel object:
print "Residual standard error: {0:.3f}".format(model.StandardError)
print "R-Squared: {0:.4f}".format(model.RSquared)
print "Adjusted R-Squared: {0:.4f}".format(model.AdjustedRSquared)
print "F-statistic: {0:.4f}".format(model.FStatistic)
print "Corresponding p-value: {0:F5}".format(model.PValue)
print
# Much of this data can be summarized in the form of an ANOVA table:
print model.AnovaTable.ToString()