Commons Math example source code file (multipleOLSRegressionTestCases)
The Commons Math multipleOLSRegressionTestCases source code
# Licensed to the Apache Software Foundation (ASF) under one or more
# contributor license agreements. See the NOTICE file distributed with
# this work for additional information regarding copyright ownership.
# The ASF licenses this file to You under the Apache License, Version 2.0
# (the "License"); you may not use this file except in compliance with
# the License. You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
#------------------------------------------------------------------------------
# R source file to validate OLS multiple regression tests in
# org.apache.commons.math.stat.regression.OLSMultipleLinearRegressionTest
#
# To run the test, install R, put this file and testFunctions
# into the same directory, launch R from this directory and then enter
# source("<name-of-this-file>")
#
#------------------------------------------------------------------------------
tol <- 1E-8 # error tolerance for tests
#------------------------------------------------------------------------------
# Function definitions
source("testFunctions") # utility test functions
options(digits=16) # override number of digits displayed
# function to verify OLS computations
verifyRegression <- function(model, expectedBeta, expectedResiduals,
expectedErrors, modelName) {
betaHat <- as.vector(coefficients(model))
residuals <- as.vector(residuals(model))
errors <- as.vector(as.matrix(coefficients(summary(model)))[,2])
output <- c("Parameter test dataset = ", modelName)
if (assertEquals(expectedBeta,betaHat,tol,"Parameters")) {
displayPadded(output, SUCCEEDED, WIDTH)
} else {
displayPadded(output, FAILED, WIDTH)
}
output <- c("Residuals test dataset = ", modelName)
if (assertEquals(expectedResiduals,residuals,tol,"Residuals")) {
displayPadded(output, SUCCEEDED, WIDTH)
} else {
displayPadded(output, FAILED, WIDTH)
}
output <- c("Errors test dataset = ", modelName)
if (assertEquals(expectedErrors,errors,tol,"Errors")) {
displayPadded(output, SUCCEEDED, WIDTH)
} else {
displayPadded(output, FAILED, WIDTH)
}
}
#--------------------------------------------------------------------------
cat("Multiple regression OLS test cases\n")
# Perfect fit
x1 <- c(0,2,0,0,0,0)
x2 <- c(0,0,3,0,0,0)
x3 <- c(0,0,0,4,0,0)
x4 <- c(0,0,0,0,5,0)
x5 <- c(0,0,0,0,0,6)
y <- c(11, 12, 13, 14, 15, 16)
model <- lm(y ~ x1 + x2 + x3 + x4 + x5)
expectedBeta <- c(11.0,0.5,0.666666666666667,0.75,0.8,0.8333333333333333)
expectedResiduals <- c(0,0,0,0,0,0)
expectedErrors <- c(NaN,NaN,NaN,NaN,NaN,NaN)
verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
"perfect fit")
# Longly
#
# Data Source: J. Longley (1967) "An Appraisal of Least Squares Programs for the
# Electronic Computer from the Point of View of the User",
# Journal of the American Statistical Association,
# vol. 62. September, pp. 819-841.
#
# Certified values (and data) are from NIST:
# http://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA/Longley.dat
#
design <- matrix(c(60323,83.0,234289,2356,1590,107608,1947,
61122,88.5,259426,2325,1456,108632,1948,
60171,88.2,258054,3682,1616,109773,1949,
61187,89.5,284599,3351,1650,110929,1950,
63221,96.2,328975,2099,3099,112075,1951,
63639,98.1,346999,1932,3594,113270,1952,
64989,99.0,365385,1870,3547,115094,1953,
63761,100.0,363112,3578,3350,116219,1954,
66019,101.2,397469,2904,3048,117388,1955,
67857,104.6,419180,2822,2857,118734,1956,
68169,108.4,442769,2936,2798,120445,1957,
66513,110.8,444546,4681,2637,121950,1958,
68655,112.6,482704,3813,2552,123366,1959,
69564,114.2,502601,3931,2514,125368,1960,
69331,115.7,518173,4806,2572,127852,1961,
70551,116.9,554894,4007,2827,130081,1962),
nrow = 16, ncol = 7, byrow = TRUE)
y <- design[,1]
x1 <- design[,2]
x2 <- design[,3]
x3 <- design[,4]
x4 <- design[,5]
x5 <- design[,6]
x6 <- design[,7]
model <- lm(y ~ x1 + x2 + x3 + x4 + x5 + x6)
estimates <- matrix(c(-3482258.63459582,890420.383607373,
15.0618722713733,84.9149257747669,
-0.358191792925910E-01,0.334910077722432E-01,
-2.02022980381683,0.488399681651699,
-1.03322686717359,0.214274163161675,
-0.511041056535807E-01,0.226073200069370,
1829.15146461355,455.478499142212),
nrow = 7, ncol = 2, byrow = TRUE)
expectedBeta <- estimates[,1]
expectedErrors <- estimates[,2]
expectedResiduals <- c( 267.340029759711,-94.0139423988359,46.28716775752924,
-410.114621930906,309.7145907602313,-249.3112153297231,-164.0489563956039,
-13.18035686637081,14.30477260005235,455.394094551857,-17.26892711483297,
-39.0550425226967,-155.5499735953195,-85.6713080421283,341.9315139607727,
-206.7578251937366)
verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
"Longly")
# Swiss Fertility (R dataset named "swiss")
design <- matrix(c(80.2,17.0,15,12,9.96,
83.1,45.1,6,9,84.84,
92.5,39.7,5,5,93.40,
85.8,36.5,12,7,33.77,
76.9,43.5,17,15,5.16,
76.1,35.3,9,7,90.57,
83.8,70.2,16,7,92.85,
92.4,67.8,14,8,97.16,
82.4,53.3,12,7,97.67,
82.9,45.2,16,13,91.38,
87.1,64.5,14,6,98.61,
64.1,62.0,21,12,8.52,
66.9,67.5,14,7,2.27,
68.9,60.7,19,12,4.43,
61.7,69.3,22,5,2.82,
68.3,72.6,18,2,24.20,
71.7,34.0,17,8,3.30,
55.7,19.4,26,28,12.11,
54.3,15.2,31,20,2.15,
65.1,73.0,19,9,2.84,
65.5,59.8,22,10,5.23,
65.0,55.1,14,3,4.52,
56.6,50.9,22,12,15.14,
57.4,54.1,20,6,4.20,
72.5,71.2,12,1,2.40,
74.2,58.1,14,8,5.23,
72.0,63.5,6,3,2.56,
60.5,60.8,16,10,7.72,
58.3,26.8,25,19,18.46,
65.4,49.5,15,8,6.10,
75.5,85.9,3,2,99.71,
69.3,84.9,7,6,99.68,
77.3,89.7,5,2,100.00,
70.5,78.2,12,6,98.96,
79.4,64.9,7,3,98.22,
65.0,75.9,9,9,99.06,
92.2,84.6,3,3,99.46,
79.3,63.1,13,13,96.83,
70.4,38.4,26,12,5.62,
65.7,7.7,29,11,13.79,
72.7,16.7,22,13,11.22,
64.4,17.6,35,32,16.92,
77.6,37.6,15,7,4.97,
67.6,18.7,25,7,8.65,
35.0,1.2,37,53,42.34,
44.7,46.6,16,29,50.43,
42.8,27.7,22,29,58.33),
nrow = 47, ncol = 5, byrow = TRUE)
y <- design[,1]
x1 <- design[,2]
x2 <- design[,3]
x3 <- design[,4]
x4 <- design[,5]
model <- lm(y ~ x1 + x2 + x3 + x4)
estimates <- matrix(c(91.05542390271397,6.94881329475087,
-0.22064551045715,0.07360008972340,
-0.26058239824328,0.27410957467466,
-0.96161238456030,0.19454551679325,
0.12441843147162,0.03726654773803),
nrow = 5, ncol = 2, byrow = TRUE)
expectedBeta <- estimates[,1]
expectedErrors <- estimates[,2]
expectedResiduals <- c(7.1044267859730512,1.6580347433531366,
4.6944952770029644,8.4548022690166160,13.6547432343186212,
-9.3586864458500774,7.5822446330520386,15.5568995563859289,
0.8113090736598980,7.1186762732484308,7.4251378771228724,
2.6761316873234109,0.8351584810309354,7.1769991119615177,
-3.8746753206299553,-3.1337779476387251,-0.1412575244091504,
1.1186809170469780,-6.3588097346816594,3.4039270429434074,
2.3374058329820175,-7.9272368576900503,-7.8361010968497959,
-11.2597369269357070,0.9445333697827101,6.6544245101380328,
-0.9146136301118665,-4.3152449403848570,-4.3536932047009183,
-3.8907885169304661,-6.3027643926302188,-7.8308982189289091,
-3.1792280015332750,-6.7167298771158226,-4.8469946718041754,
-10.6335664353633685,11.1031134362036958,6.0084032641811733,
5.4326230830188482,-7.2375578629692230,2.1671550814448222,
15.0147574652763112,4.8625103516321015,-7.1597256413907706,
-0.4515205619767598,-10.2916870903837587,-15.7812984571900063)
verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
"Swiss Fertility")
displayDashes(WIDTH)
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