multipleOLSRegressionTestCases

# 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                       # default 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, expectedStdError, expectedRSquare, expecteAdjRSquare, modelName) {
    betaHat <- as.vector(coefficients(model))
    residuals <- as.vector(residuals(model))
    errors <-  as.vector(as.matrix(coefficients(summary(model)))[,2])
    stdError <- summary(model)$sigma
    rSquare <- summary(model)$r.squared
    adjRSquare <- summary(model)$adj.r.squared
    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)
    }
    output <- c("Standard Error test dataset = ", modelName)
    if (assertEquals(expectedStdError,stdError,tol,"Regression Standard Error")) {
        displayPadded(output, SUCCEEDED, WIDTH)
    } else {
        displayPadded(output, FAILED, WIDTH)
    }
    output <- c("RSquared test dataset = ", modelName)
    if (assertEquals(expectedRSquare,rSquare,tol,"RSquared")) {
        displayPadded(output, SUCCEEDED, WIDTH)
    } else {
        displayPadded(output, FAILED, WIDTH)
    }
    output <- c("Adjusted RSquared test dataset = ", modelName)
    if (assertEquals(expecteAdjRSquare,adjRSquare,tol,"Adjusted RSquared")) {
        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)
expectedStdError <- NaN
expectedRSquare <- 1
expectedAdjRSquare <- NaN
verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
 expectedStdError, expectedRSquare, expectedAdjRSquare, "perfect fit") 

# Longley
#
# 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)
expectedStdError <- 304.8540735619638
expectedRSquare <- 0.995479004577296
expectedAdjRSquare <- 0.992465007628826

verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
expectedStdError, expectedRSquare, expectedAdjRSquare, "Longley") 

# Model with no intercept
model <- lm(y ~ 0 + x1 + x2 + x3 + x4 + x5 + x6)

estimates <- matrix(c(-52.99357013868291, 129.54486693117232, 
         0.07107319907358, 0.03016640003786,
        -0.42346585566399, 0.41773654056612, 
        -0.57256866841929, 0.27899087467676,
        -0.41420358884978, 0.32128496193363, 
         48.41786562001326, 17.68948737819961),
         nrow = 6, ncol = 2, byrow = TRUE)

expectedBeta <- estimates[,1]
expectedErrors <- estimates[,2]
expectedResiduals <- c(279.90274927293092, -130.32465380836874, 90.73228661967445,
  -401.31252201634948, -440.46768772620027, -543.54512853774793, 201.32111639536299,
   215.90889365977932, 73.09368242049943, 913.21694494481869, 424.82484953610174, 
   -8.56475876776709, -361.32974610842876, 27.34560497213464, 151.28955976355002,
   -492.49937355336846)
expectedStdError <- 475.1655079819517
expectedRSquare <- 0.9999670130706
expectedAdjRSquare <- 0.999947220913

verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
expectedStdError, expectedRSquare, expectedAdjRSquare, "Longley No Intercept") 

# 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)

expectedStdError <- 7.73642194433223
expectedRSquare <- 0.649789742860228
expectedAdjRSquare <- 0.6164363850373927

verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
expectedStdError, expectedRSquare, expectedAdjRSquare, "Swiss Fertility") 

# model with no intercept
model <- lm(y ~ 0 + x1 + x2 + x3 + x4)

estimates <- matrix(c(0.52191832900513, 0.10470063765677,
      2.36588087917963, 0.41684100584290,
     -0.94770353802795, 0.43370143099691, 
      0.30851985863609, 0.07694953606522),
     nrow = 4, ncol = 2, byrow = TRUE)

expectedBeta <- estimates[,1]
expectedErrors <- estimates[,2]

expectedResiduals <- c(44.138759883538249, 27.720705122356215, 35.873200836126799, 
  34.574619581211977, 26.600168342080213, 15.074636243026923, -12.704904871199814,
  1.497443824078134, 2.691972687079431, 5.582798774291231, -4.422986561283165, 
  -9.198581600334345, 4.481765170730647, 2.273520207553216, -22.649827853221336,
  -17.747900013943308, 20.298314638496436, 6.861405135329779, -8.684712790954924,
  -10.298639278062371, -9.896618896845819, 4.568568616351242, -15.313570491727944,
  -13.762961360873966, 7.156100301980509, 16.722282219843990, 26.716200609071898,
  -1.991466398777079, -2.523342564719335, 9.776486693095093, -5.297535127628603,
  -16.639070567471094, -10.302057295211819, -23.549487860816846, 1.506624392156384,
  -17.939174438345930, 13.105792202765040, -1.943329906928462, -1.516005841666695,
  -0.759066561832886, 20.793137744128977, -2.485236153005426, 27.588238710486976,
  2.658333257106881, -15.998337823623046, -5.550742066720694, -14.219077806826615)

expectedStdError <- 17.24710630547
expectedRSquare <- 0.946350722085
expectedAdjRSquare <- 0.9413600915813

verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
expectedStdError, expectedRSquare, expectedAdjRSquare, "Swiss Fertility No Intercept") 

displayDashes(WIDTH)