WS7 verbetering van 0900218

*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: Mon, 23 Nov 2009 12:20:12 -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/Nov/23/t12590043598o0hcn3p98v4j9n.htm/, Retrieved Mon, 23 Nov 2009 20:26:11 +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/Nov/23/t12590043598o0hcn3p98v4j9n.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:

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No (this computation is public)

User-defined keywords:

WS7 verbetering van 0900218

Dataseries X:

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562325 0 543599 555332 560854 562325 560854 0 562325 543599 555332 560854 555332 0 560854 562325 543599 555332 543599 0 555332 560854 562325 543599 536662 0 543599 555332 560854 562325 542722 0 536662 543599 555332 560854 593530 0 542722 536662 543599 555332 610763 0 593530 542722 536662 543599 612613 0 610763 593530 542722 536662 611324 0 612613 610763 593530 542722 594167 0 611324 612613 610763 593530 595454 0 594167 611324 612613 610763 590865 0 595454 594167 611324 612613 589379 0 590865 595454 594167 611324 584428 0 589379 590865 595454 594167 573100 0 584428 589379 590865 595454 567456 0 573100 584428 589379 590865 569028 0 567456 573100 584428 589379 620735 0 569028 567456 573100 584428 628884 0 620735 569028 567456 573100 628232 0 628884 620735 569028 567456 612117 0 628232 628884 620735 569028 595404 0 612117 628232 628884 620735 597141 0 595404 612117 628232 628884 593408 0 597141 595404 612117 628232 590072 0 593408 597141 595404 612117 579799 0 590072 593408 597141 595404 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 Y[t] = + 75744.9251019103 -4888.87495858883X[t] + 1.04546691668887Y1[t] + 0.12070711220331Y2[t] -0.0303882134946645Y3[t] -0.24593865845572Y4[t] -155.130121957233M1[t] -12526.561651817M2[t] -20641.7467802384M3[t] -17459.8643153813M4[t] -19460.0609453609M5[t] -5421.11108199365M6[t] + 42011.6219070151M7[t] -4236.452480527M8[t] -32524.6109074917M9[t] -37120.7696857113M10[t] -22687.316687933M11[t] -40.1271933262733t + 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) 75744.9251019103 32170.068106 2.3545 0.022435 0.011217 X -4888.87495858883 5381.503348 -0.9085 0.367909 0.183954 Y1 1.04546691668887 0.12715 8.2223 0 0 Y2 0.12070711220331 0.183766 0.6569 0.514229 0.257114 Y3 -0.0303882134946645 0.184018 -0.1651 0.869489 0.434744 Y4 -0.24593865845572 0.126537 -1.9436 0.05747 0.028735 M1 -155.130121957233 4807.165608 -0.0323 0.974382 0.487191 M2 -12526.561651817 5469.028515 -2.2905 0.026163 0.013081 M3 -20641.7467802384 5346.495751 -3.8608 0.00032 0.00016 M4 -17459.8643153813 5055.559218 -3.4536 0.001122 0.000561 M5 -19460.0609453609 4816.093767 -4.0406 0.00018 9e-05 M6 -5421.11108199365 4650.529596 -1.1657 0.24916 0.12458 M7 42011.6219070151 5090.467455 8.253 0 0 M8 -4236.452480527 9584.580338 -0.442 0.660353 0.330176 M9 -32524.6109074917 9534.474333 -3.4113 0.001273 0.000636 M10 -37120.7696857113 8804.514669 -4.2161 0.000102 5.1e-05 M11 -22687.316687933 4972.788325 -4.5623 3.2e-05 1.6e-05 t -40.1271933262733 86.419521 -0.4643 0.644387 0.322194 Multiple Linear Regression - Regression Statistics Multiple R 0.988572746420317 R-squared 0.97727607496501 Adjusted R-squared 0.96970143328668 F-TEST (value) 129.019446261178 F-TEST (DF numerator) 17 F-TEST (DF denominator) 51 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7036.8908123995 Sum Squared Residuals 2525409447.58725 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 562325 555556.153058417 6768.84694158285 2 560854 561835.330751172 -981.330751171633 3 555332 556117.116159019 -785.116159019176 4 543599 555624.791548303 -12025.7915483029 5 536662 536090.713461709 571.286538291323 6 542722 541950.455064703 771.544935296557 7 593530 596555.863319091 -3025.86331909153 8 610763 607213.631257977 3549.3687420234 9 612613 604556.68786974 8056.31213025965 10 611324 600900.30873719 10423.6912628101 11 594167 601150.004401634 -6983.00440163432 12 595454 601410.047442848 -5956.04744284753 13 590865 600073.518014322 -9208.51801432193 14 589379 583858.047173534 5520.95282646628 15 584428 577775.706008043 6652.29399195739 16 573100 575384.912264607 -2284.91226460719 17 567456 562077.687685438 5378.31231456238 18 569028 569324.441802125 -296.441802124826 19 620735 619241.130630049 1493.86936995139 20 628884 630158.142690745 -1274.14269074531 21 628232 617931.077141959 10300.9228580410 22 612117 611638.890071816 478.10992818433 23 595404 596141.431712132 -737.431712132128 24 597141 597386.196502404 -245.196502404337 25 593408 597639.595320935 -4231.59532093511 26 590072 586006.156544797 4065.84345520306 27 579799 577970.155411051 1828.84458894949 28 574205 569655.393872364 4549.6061276357 29 572775 561546.16804567 11228.8319543303 30 572942 574507.36692102 -1565.36692101927 31 619567 624598.474025943 -5031.47402594289 32 625809 628494.56152413 -2685.56152412951 33 619916 612666.666954228 7249.33304577212 34 587625 601164.976026857 -13539.9760268567 35 565742 569431.229433163 -3689.22943316277 36 557274 563946.641665753 -6672.64166575337 37 560576 554687.519079839 5888.48092016072 38 548854 553312.53478552 -4458.53478551965 39 531673 538940.0372057 -7267.0372056998 40 525919 524686.963291196 1232.03670880439 41 511038 514101.275122861 -3063.27512286059 42 498662 510364.073773918 -11702.0737739176 43 555362 547422.064343337 7939.93565666267 44 564591 560785.303763868 3805.69623613218 45 541657 552985.623286316 -11328.6232863157 46 527070 526807.330117852 262.66988214788 47 509846 508956.958340511 889.041659488638 48 514258 510263.426425758 3994.57357424185 49 516922 518685.339909586 -1763.33990958627 50 507561 513702.378631626 -6141.37863162606 51 492622 500183.988904966 -7561.98890496644 52 490243 485411.539068891 4831.46093110939 53 469357 478710.089381974 -9353.08938197417 54 477580 473342.329113321 4237.67088667938 55 528379 530557.091798031 -2178.09179803117 56 533590 539589.914997204 -5999.91499720404 57 517945 527728.150613534 -9783.1506135343 58 506174 503798.495046286 2375.50495371436 59 501866 491345.376112559 10520.6238874406 60 516141 507261.687963237 8879.31203676338 61 528222 525675.8746169 2546.12538309974 62 532638 530643.552113352 1994.44788664802 63 536322 529188.996311222 7133.00368877853 64 536535 532837.399954639 3697.6000453606 65 523597 528359.066302349 -4762.06630234924 66 536214 527659.333324914 8554.66667508582 67 586570 585768.375883549 801.624116451526 68 596594 593989.445766077 2604.55423392328 69 580523 585017.794134223 -4494.7941342228 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.349722509041018 0.699445018082035 0.650277490958982 22 0.583419317171238 0.833161365657524 0.416580682828762 23 0.441536221550944 0.883072443101889 0.558463778449056 24 0.317040621389934 0.634081242779867 0.682959378610066 25 0.221528718578436 0.443057437156872 0.778471281421564 26 0.148213657459771 0.296427314919541 0.85178634254023 27 0.0923237216165477 0.184647443233095 0.907676278383452 28 0.0853479910836218 0.170695982167244 0.914652008916378 29 0.176640136666255 0.353280273332510 0.823359863333745 30 0.120900767493031 0.241801534986063 0.879099232506969 31 0.0838014508724947 0.167602901744989 0.916198549127505 32 0.0616295674799535 0.123259134959907 0.938370432520046 33 0.247119955385411 0.494239910770821 0.752880044614589 34 0.640801678127126 0.718396643745748 0.359198321872874 35 0.576893809822887 0.846212380354226 0.423106190177113 36 0.670610004135195 0.65877999172961 0.329389995864805 37 0.662678704316761 0.674642591366477 0.337321295683238 38 0.581706459950553 0.836587080098895 0.418293540049447 39 0.511780408621534 0.976439182756933 0.488219591378466 40 0.542642631843244 0.914714736313512 0.457357368156756 41 0.443171783664633 0.886343567329266 0.556828216335367 42 0.553063937473795 0.893872125052411 0.446936062526205 43 0.877991401303975 0.24401719739205 0.122008598696025 44 0.92466330199727 0.150673396005458 0.0753366980027292 45 0.934284650909401 0.131430698181197 0.0657153490905987 46 0.908511136966727 0.182977726066546 0.0914888630332728 47 0.822121158546576 0.355757682906849 0.177878841453424 48 0.757017914083885 0.48596417183223 0.242982085916115 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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