Paper. Multi Regression without Dummies or Lin. Trend.

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 12 Dec 2009 11:05:52 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/12/t1260641320oir3ikr7ts9o9wv.htm/, Retrieved Sat, 12 Dec 2009 19:08:53 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/12/t1260641320oir3ikr7ts9o9wv.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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593530 3922 18004 707169 610763 3759 17537 703434 612613 4138 20366 701017 611324 4634 22782 696968 594167 3996 19169 688558 595454 4308 13807 679237 590865 4143 29743 677362 589379 4429 25591 676693 584428 5219 29096 670009 573100 4929 26482 667209 567456 5761 22405 662976 569028 5592 27044 660194 620735 4163 17970 652270 628884 4962 18730 648024 628232 5208 19684 629295 612117 4755 19785 624961 595404 4491 18479 617306 597141 5732 10698 607691 593408 5731 31956 596219 590072 5040 29506 591130 579799 6102 34506 584528 574205 4904 27165 576798 572775 5369 26736 575683 572942 5578 23691 574369 619567 4619 18157 566815 625809 4731 17328 573074 619916 5011 18205 567739 587625 5299 20995 571942 565742 4146 17382 570274 557274 4625 9367 568800 560576 4736 31124 558115 548854 4219 26551 550591 531673 5116 30651 548872 525919 4205 25859 547009 511038 4121 25100 545946 498662 5103 25778 539702 555362 4300 20418 542427 564591 4578 18688 542968 541657 3809 20424 536640 527070 5526 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkzoekend[t] = + 226473.427381757 + 21.4576880953638Bouw[t] -1.90264946961537Auto[t] + 0.469588601620351Krediet[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 226473.427381757 45628.410339 4.9634 7e-06 3e-06 Bouw 21.4576880953638 5.89434 3.6404 0.000588 0.000294 Auto -1.90264946961537 0.64903 -2.9315 0.004847 0.002424 Krediet 0.469588601620351 0.061879 7.5888 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.77380861565493 R-squared 0.598779773661799 Adjusted R-squared 0.577662919643999 F-TEST (value) 28.3555388107086 F-TEST (DF numerator) 3 F-TEST (DF denominator) 57 p-value 2.37367903110908e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 27599.8633201017 Sum Squared Residuals 43419889951.4327 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 593530 608453.680860078 -14923.6808600785 2 610763 604090.701575795 6672.29842420542 3 612613 605705.574364279 6907.42563572088 4 611324 609850.422293028 1473.57770697200 5 594167 599085.449682279 -4918.44968227912 6 595454 611605.219468407 -16151.2194684070 7 590865 576863.600356843 14001.3996431568 8 589379 590586.144975476 -1207.14497547625 9 584428 597730.201966581 -13302.2019665813 10 573100 595166.150047963 -22066.1500479635 11 567456 618788.279880269 -51332.2798802691 12 569028 605029.144212899 -36001.1442128991 13 620735 587909.729132674 32825.2708673256 14 628884 601614.535121482 27269.4648785176 15 628232 596283.073879181 31948.9261208187 16 612117 584335.376576128 27781.6234238722 17 595404 577560.706380866 17843.2936191344 18 597141 614479.11842571 -17338.1184257097 19 593408 568624.017874742 24783.982125258 20 590072 556068.510207757 34003.4897922427 21 579799 566243.103669059 13555.8963309408 22 574205 550874.223196735 23330.7768032654 23 572775 561144.693492737 11630.3065072630 24 572942 570805.878517118 2136.12148288225 25 619567 557209.945501875 62357.0544981248 26 625809 564129.658036409 61679.3419635911 27 619916 565963.931928613 53952.0680713865 28 587625 568809.034972462 18815.9650275383 29 565742 550159.319344725 15582.6806552752 30 557274 574995.113842583 -17721.1138425829 31 560576 530963.418502433 29612.5814975668 32 548854 525037.42514309 23816.5748569103 33 531673 535676.885733023 -4003.88573302257 34 525919 524371.584571724 1547.41542827570 35 511038 523514.077035629 -12476.0770356294 36 498662 540363.41917636 -41701.4191763600 37 555362 534610.725732337 20751.2742676633 38 564591 544121.594038759 20469.4059612410 39 541657 521346.075743118 20310.9242568816 40 527070 548505.934558052 -21435.9345580520 41 509846 533972.144942107 -24126.1449421067 42 514258 537207.4815129 -22949.4815129005 43 516922 511553.527408822 5368.47259117761 44 507561 523383.077673436 -15822.077673436 45 492622 512178.90420725 -19556.9042072498 46 490243 512862.331064657 -22619.3310646572 47 469357 513605.583749702 -44248.5837497025 48 477580 522136.546567519 -44556.5465675194 49 528379 516043.413929716 12335.5860702842 50 533590 517738.939192846 15851.0608071537 51 517945 525046.688702559 -7101.68870255919 52 506174 515923.505829981 -9749.50582998092 53 501866 536070.913437983 -34204.9134379826 54 516141 565157.678824496 -49016.6788244956 55 528222 509090.851922228 19131.1480777723 56 532638 528822.383962422 3815.61603757782 57 536322 535027.36666387 1294.63333612943 58 536535 546386.92267365 -9851.92267364996 59 523597 566021.81575367 -42424.8157536696 60 536214 580161.102562642 -43947.1025626422 61 586570 584671.139398263 1898.86060173689 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.049963962664105 0.09992792532821 0.950036037335895 8 0.0157654347024423 0.0315308694048846 0.984234565297558 9 0.00636541134066913 0.0127308226813383 0.99363458865933 10 0.00358568081220047 0.00717136162440095 0.9964143191878 11 0.00198343504531564 0.00396687009063128 0.998016564954684 12 0.000778930459825818 0.00155786091965164 0.999221069540174 13 0.00705414441657754 0.0141082888331551 0.992945855583423 14 0.0229533430816159 0.0459066861632319 0.977046656918384 15 0.0201257554391902 0.0402515108783805 0.97987424456081 16 0.0123788161126373 0.0247576322252745 0.987621183887363 17 0.0176833511503884 0.0353667023007769 0.982316648849612 18 0.0128242890373003 0.0256485780746006 0.9871757109627 19 0.00714609418836677 0.0142921883767335 0.992853905811633 20 0.00490942383262973 0.00981884766525946 0.99509057616737 21 0.00245196443134936 0.00490392886269872 0.99754803556865 22 0.00356387015780611 0.00712774031561221 0.996436129842194 23 0.00280914531595592 0.00561829063191184 0.997190854684044 24 0.00202190434530157 0.00404380869060314 0.997978095654698 25 0.00338968037517873 0.00677936075035745 0.996610319624821 26 0.00869673531913785 0.0173934706382757 0.991303264680862 27 0.0255640650809996 0.0511281301619993 0.974435934919 28 0.0376553090415726 0.0753106180831453 0.962344690958427 29 0.141594228733979 0.283188457467957 0.858405771266021 30 0.299075406292177 0.598150812584354 0.700924593707823 31 0.396340129782531 0.792680259565063 0.603659870217469 32 0.487731794278049 0.975463588556099 0.512268205721951 33 0.568524137206347 0.862951725587305 0.431475862793653 34 0.615787341588737 0.768425316822526 0.384212658411263 35 0.673723071370062 0.652553857259876 0.326276928629938 36 0.781080233251251 0.437839533497497 0.218919766748749 37 0.8101435876376 0.379712824724801 0.189856412362400 38 0.900181224110683 0.199637551778634 0.0998187758893171 39 0.905088858294506 0.189822283410988 0.094911141705494 40 0.936584705554151 0.126830588891698 0.063415294445849 41 0.931751719703566 0.136496560592867 0.0682482802964337 42 0.925196767413678 0.149606465172645 0.0748032325863225 43 0.917528834188887 0.164942331622226 0.0824711658111132 44 0.915699831691903 0.168600336616194 0.0843001683080968 45 0.883953915918702 0.232092168162596 0.116046084081298 46 0.846339183781376 0.307321632437249 0.153660816218624 47 0.92487798140786 0.150244037184280 0.0751220185921399 48 0.925183704262344 0.149632591475312 0.074816295737656 49 0.894110358651663 0.211779282696673 0.105889641348337 50 0.890249349507463 0.219501300985074 0.109750650492537 51 0.844970762830194 0.310058474339613 0.155029237169806 52 0.743680541354453 0.512638917291094 0.256319458645547 53 0.64504953945264 0.709900921094721 0.354950460547361 54 0.52835048218553 0.94329903562894 0.47164951781447 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 9 0.1875 NOK 5% type I error level 19 0.395833333333333 NOK 10% type I error level 22 0.458333333333333 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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