*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 10:58:28 +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/t129673066513h8wi0olysyv2j.htm/, Retrieved Thu, 03 Feb 2011 11:58:06 +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/t129673066513h8wi0olysyv2j.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 'Herman Ole Andreas Wold' @ www.yougetit.org Multiple Linear Regression - Estimated Regression Equation Nieuwe_woningen[t] = -368.704882813088 + 0.0108542066944278Bewoonbare_opp[t] -18.9409113862806Rentevoet[t] -5.39488006602951Inflatie[t] -0.000424993211229427Werkloosheid[t] + 23.8207869773999M1[t] + 116.809162250339M2[t] + 150.989897599058M3[t] + 338.352307679011M4[t] + 290.816527018872M5[t] + 278.038545345547M6[t] + 36.5263718942795M7[t] + 22.5934611318237M8[t] + 0.326019864122348M9[t] + 27.0627574642159M10[t] + 197.459552174564M11[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) -368.704882813088 1369.314759 -0.2693 0.788987 0.394493 Bewoonbare_opp 0.0108542066944278 0.000345 31.4722 0 0 Rentevoet -18.9409113862806 120.135793 -0.1577 0.875444 0.437722 Inflatie -5.39488006602951 11.38254 -0.474 0.637871 0.318936 Werkloosheid -0.000424993211229427 0.001374 -0.3093 0.758553 0.379277 M1 23.8207869773999 73.001923 0.3263 0.745742 0.372871 M2 116.809162250339 77.92593 1.499 0.141021 0.07051 M3 150.989897599058 88.449233 1.7071 0.094856 0.047428 M4 338.352307679011 95.570663 3.5403 0.000958 0.000479 M5 290.816527018872 92.187163 3.1546 0.002896 0.001448 M6 278.038545345547 95.702543 2.9052 0.005723 0.002862 M7 36.5263718942795 106.172854 0.344 0.732464 0.366232 M8 22.5934611318237 112.997918 0.1999 0.842444 0.421222 M9 0.326019864122348 128.147376 0.0025 0.997982 0.498991 M10 27.0627574642159 125.259222 0.2161 0.829944 0.414972 M11 197.459552174564 87.717951 2.2511 0.029427 0.014713 Multiple Linear Regression - Regression Statistics Multiple R 0.99053889917122 R-squared 0.981167310771334 Adjusted R-squared 0.974747075807015 F-TEST (value) 152.824206002489 F-TEST (DF numerator) 15 F-TEST (DF denominator) 44 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 113.311643492556 Sum Squared Residuals 564939.256243305 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5393 5294.86461426031 98.1353857396855 2 5147 5009.61213981573 137.38786018427 3 4846 4735.71347603247 110.286523967529 4 3995 4008.05565024662 -13.0556502466196 5 4491 4567.84708223993 -76.8470822399338 6 4676 4703.68293291556 -27.6829329155645 7 5461 5663.5035532093 -202.503553209296 8 4758 4850.2871371524 -92.2871371524021 9 5302 5284.31137768499 17.6886223150133 10 5066 5020.61960337166 45.3803966283359 11 3491 3497.24795549833 -6.24795549832794 12 4944 5039.48974762685 -95.4897476268459 13 5148 5136.38430683251 11.6156931674878 14 5351 5390.97445085112 -39.9744508511252 15 5178 5102.95471975774 75.0452802422617 16 4025 3932.19276061578 92.8072393842163 17 4449 4399.20633248601 49.793667513987 18 4594 4520.80849958027 73.1915004197298 19 4603 4655.2997940941 -52.2997940940972 20 4911 4721.36668010732 189.633319892678 21 5236 5186.55761312599 49.4423868740125 22 4652 4744.36849686195 -92.3684968619465 23 3479 3543.28389392879 -64.2838939287853 24 4556 4577.12217756483 -21.1221775648256 25 4815 4701.38849546964 113.611504530361 26 4949 4896.56241614485 52.4375838551532 27 4499 4501.84436960486 -2.84436960486112 28 3865 3857.54382770421 7.45617229578556 29 3657 3687.71239090524 -30.7123909052422 30 4814 4670.68548808703 143.314511912966 31 4614 4457.82470757371 156.175292426285 32 4539 4574.03926951362 -35.0392695136196 33 4492 4560.11604098873 -68.1160409887302 34 4779 4711.01631123607 67.9836887639305 35 3193 3101.05156103835 91.9484389616544 36 3894 3745.7452244251 148.254775574905 37 4531 4691.71193599459 -160.711935994595 38 4008 4111.88776244622 -103.887762446222 39 3764 3899.98387681197 -135.983876811966 40 3290 3323.71638505147 -33.7163850514663 41 3644 3559.10633344231 84.8936665576945 42 3438 3794.83435728623 -356.834357286234 43 3833 3781.4108332139 51.5891667861003 44 3922 3977.97200629759 -55.9720062975854 45 3524 3426.09321982192 97.9067801780836 46 3493 3434.41210381761 58.5878961823902 47 2814 2764.91739011275 49.082609887248 48 3899 3902.45286326828 -3.45286326827837 49 3653 3715.65064744294 -62.650647442939 50 3969 4014.96323074208 -45.963230742076 51 3427 3473.50355779296 -46.5035577929637 52 3067 3120.49137638192 -53.4913763819161 53 3301 3328.12786092651 -27.1278609265056 54 3211 3042.9887221309 168.011277869102 55 3382 3334.96111190899 47.0388880910076 56 3613 3619.33490692907 -6.33490692907135 57 3783 3879.92174837838 -96.921748378379 58 3971 4050.58348471271 -79.5834847127102 59 2842 2912.49919942179 -70.4991994217892 60 4161 4189.18998711496 -28.1899871149551 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.0637492144509842 0.127498428901968 0.936250785549016 20 0.0530023238579718 0.106004647715944 0.946997676142028 21 0.251834914464362 0.503669828928724 0.748165085535638 22 0.46277660265279 0.92555320530558 0.53722339734721 23 0.358580062381823 0.717160124763645 0.641419937618177 24 0.258534519418015 0.51706903883603 0.741465480581985 25 0.224436863079561 0.448873726159122 0.775563136920439 26 0.170822726383042 0.341645452766085 0.829177273616958 27 0.14299118654147 0.285982373082939 0.85700881345853 28 0.0932020545655183 0.186404109131037 0.906797945434482 29 0.0591355582162045 0.118271116432409 0.940864441783795 30 0.216109986878585 0.43221997375717 0.783890013121415 31 0.350970412899469 0.701940825798937 0.649029587100531 32 0.323230451398235 0.64646090279647 0.676769548601765 33 0.299637905491147 0.599275810982293 0.700362094508853 34 0.4556542609978 0.9113085219956 0.5443457390022 35 0.406095904964768 0.812191809929535 0.593904095035232 36 0.307639103129178 0.615278206258355 0.692360896870822 37 0.49430527057762 0.988610541155241 0.50569472942238 38 0.461341071856925 0.92268214371385 0.538658928143075 39 0.402935952887179 0.805871905774358 0.597064047112821 40 0.302492492112653 0.604984984225307 0.697507507887347 41 0.861935813243656 0.276128373512688 0.138064186756344 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 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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