*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: Thu, 03 Feb 2011 09:54:14 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Feb/03/t12967269814o51cmdanmpfcl6.htm/, Retrieved Thu, 03 Feb 2011 10:56:21 +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/2011/Feb/03/t12967269814o51cmdanmpfcl6.htm/}, year = {2011}, } @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 = {2011}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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Dataseries X:

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5393 552486 3.90 3.0 628232 5147 516610 3.90 2.2 612117 4846 487587 3.88 2.3 595404 3995 403620 3.89 2.8 597141 4491 459427 3.89 2.8 593408 4676 473058 3.93 2.8 590072 5461 583054 3.94 2.2 579799 4758 509448 3.97 2.6 574205 5302 551582 4.00 2.8 572775 5066 524752 4.04 2.5 572942 3491 370725 4.18 2.4 619567 4944 531443 4.32 2.3 625809 5148 537833 4.37 1.9 619916 5351 551410 4.40 1.7 587625 5178 520983 4.38 2.0 565742 4025 395542 4.36 2.1 557274 4449 442878 4.36 1.7 560576 4594 454919 4.40 1.8 548854 4603 488905 4.41 1.8 531673 4911 496085 4.43 1.8 525919 5236 540146 4.42 1.3 511038 4652 496529 4.46 1.3 498662 3479 372656 4.61 1.3 555362 4556 486704 4.78 1.2 564591 4815 495334 4.88 1.4 541657 4949 504697 4.95 2.2 527070 4499 464856 4.95 2.9 509846 3865 388472 4.93 3.1 514258 3657 377508 4.93 3.5 516922 4814 468895 4.91 3.6 507561 4614 471295 4.88 4.4 492622 4539 482956 4.83 4.1 490243 4492 483404 4.83 5.1 469357 4779 495548 4.85 5.8 477580 3193 333806 4.99 5.9 528379 3894 4116 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Nieuwe_woningen[t] = -53.6847847883118 + 0.0098347095728283Bewoonbare_opp[t] -31.5645873061969Rentevoet[t] + 10.4884037764686Inflatie[t] + 8.20050280286885e-05Werkloosheid[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) -53.6847847883118 688.410608 -0.078 0.938124 0.469062 Bewoonbare_opp 0.0098347095728283 0.000293 33.5967 0 0 Rentevoet -31.5645873061969 71.334489 -0.4425 0.659872 0.329936 Inflatie 10.4884037764686 13.000087 0.8068 0.42326 0.21163 Werkloosheid 8.20050280286885e-05 0.000714 0.1149 0.908974 0.454487 Multiple Linear Regression - Regression Statistics Multiple R 0.98063307085055 R-squared 0.961641219645778 Adjusted R-squared 0.958851490165471 F-TEST (value) 344.707695292357 F-TEST (DF numerator) 4 F-TEST (DF denominator) 55 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 144.642445947059 Sum Squared Residuals 1150679.04432514 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5393 5339.73607186906 53.263928130939 2 5147 4977.19379718641 169.806202813585 3 4846 4692.07060334455 153.929396655454 4 3995 3871.35054339173 123.649456608269 5 4491 4419.89005575293 71.1099442470712 6 4676 4552.4108296744 123.589170325600 7 5461 5626.73841805534 -165.738418055339 8 4758 4905.63447300235 -147.634473002349 9 5302 5321.04360208992 -19.0436020899229 10 5066 5052.78293446543 13.2170655345680 11 3491 3536.32772492273 -45.327724922731 12 4944 5111.98657083299 -167.98657083299 13 5148 5168.57351849729 -20.5735184972924 14 5351 5296.40672763303 54.5932723669718 15 5178 4999.14931631129 178.850683688706 16 4025 3766.45922633256 258.540773667436 17 4449 4228.07045776393 220.929542236073 18 4594 4345.3151896772 248.684810322800 19 4603 4677.83305495972 -74.8330549597193 20 4911 4747.34312101523 163.656878984775 21 5236 5174.52138666635 61.4786133336542 22 4652 4743.28338150916 -91.283381509163 23 3479 3524.9433995875 -45.9433995875004 24 4556 4640.9143611334 -84.9143611333986 25 4815 4722.84842345877 92.1515765412291 26 4949 4819.91580375505 129.084196244951 27 4499 4434.02056770476 64.9794322952415 28 3865 3685.89689037892 179.103109621078 29 3657 3582.48295752769 74.5170424723116 30 4814 4482.16004431614 331.839955683858 31 4614 4513.87593481757 100.124065182429 32 4539 4626.79510141701 -87.7951014170103 33 4492 4639.9766980667 -147.976698066699 34 4779 4766.79432936201 12.2056706379903 35 3193 3176.90430520722 16.0956947927764 36 3894 3932.54232173802 -38.5423217380231 37 4531 4760.57621167498 -229.576211674983 38 4008 4133.68877367723 -125.688773677227 39 3764 3884.82346414323 -120.823464143234 40 3290 3196.07468869544 93.925311304557 41 3644 3452.29972071624 191.700279283764 42 3438 3678.18007980946 -240.180079809460 43 3833 3868.16066454686 -35.1606645468609 44 3922 4060.80898480764 -138.808984807636 45 3524 3561.34822014776 -37.3482201477646 46 3493 3538.10816343838 -45.1081634383786 47 2814 2788.70915994278 25.290840057217 48 3899 4017.36322158735 -118.363221587350 49 3653 3814.69193125164 -161.691931251642 50 3969 3996.68838492534 -27.688384925343 51 3427 3486.87570129358 -59.8757012935767 52 3067 3010.63497152472 56.365028475278 53 3301 3251.58431284509 49.4156871549139 54 3211 3002.88183615055 208.118163849447 55 3382 3499.09199150516 -117.091991505156 56 3613 3768.13362543468 -155.133625434676 57 3783 4024.95199133376 -241.951991333763 58 3971 4163.88038989557 -192.880389895568 59 2842 3000.27432794457 -158.274327944569 60 4161 4337.97703928362 -176.977039283616 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.177430069119407 0.354860138238815 0.822569930880593 9 0.237621442023453 0.475242884046907 0.762378557976547 10 0.129585550570043 0.259171101140085 0.870414449429957 11 0.175326869287120 0.350653738574241 0.82467313071288 12 0.108883918866323 0.217767837732647 0.891116081133677 13 0.127224411753646 0.254448823507292 0.872775588246354 14 0.184048565794579 0.368097131589158 0.815951434205421 15 0.314619574685519 0.629239149371039 0.68538042531448 16 0.345740068286803 0.691480136573606 0.654259931713197 17 0.334542264723814 0.669084529447628 0.665457735276186 18 0.37123042448814 0.74246084897628 0.62876957551186 19 0.471403474094899 0.942806948189798 0.528596525905101 20 0.469971751899505 0.93994350379901 0.530028248100495 21 0.438221115036548 0.876442230073096 0.561778884963452 22 0.517682143307874 0.964635713384252 0.482317856692126 23 0.559784997595208 0.880430004809585 0.440215002404792 24 0.497608001834029 0.995216003668057 0.502391998165971 25 0.476036062095338 0.952072124190676 0.523963937904662 26 0.488401752653438 0.976803505306875 0.511598247346562 27 0.443594622394104 0.887189244788208 0.556405377605896 28 0.414998378006617 0.829996756013234 0.585001621993383 29 0.362836729588284 0.725673459176567 0.637163270411716 30 0.821178646108474 0.357642707783052 0.178821353891526 31 0.88656714316935 0.226865713661299 0.113432856830649 32 0.902262413323891 0.195475173352218 0.097737586676109 33 0.905939412149938 0.188121175700125 0.0940605878500624 34 0.953711139375774 0.092577721248452 0.046288860624226 35 0.933010125835672 0.133979748328655 0.0669898741643276 36 0.909548571769012 0.180902856461975 0.0904514282309876 37 0.891160634613459 0.217678730773083 0.108839365386541 38 0.855702470757511 0.288595058484978 0.144297529242489 39 0.870030805361531 0.259938389276938 0.129969194638469 40 0.818787961573389 0.362424076853222 0.181212038426611 41 0.920793265926068 0.158413468147863 0.0792067340739316 42 0.975786363747348 0.0484272725053043 0.0242136362526522 43 0.964929417409769 0.0701411651804628 0.0350705825902314 44 0.951767533023887 0.0964649339522263 0.0482324669761131 45 0.923108113186721 0.153783773626558 0.0768918868132791 46 0.879012615363293 0.241974769273414 0.120987384636707 47 0.831553141294426 0.336893717411147 0.168446858705574 48 0.761141710574286 0.477716578851427 0.238858289425713 49 0.859443582011358 0.281112835977285 0.140556417988642 50 0.77252220044571 0.45495559910858 0.22747779955429 51 0.802192834634338 0.395614330731324 0.197807165365662 52 0.92563867953331 0.148722640933381 0.0743613204666905 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 1 0.0222222222222222 OK 10% type I error level 4 0.0888888888888889 OK

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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