WS7

*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: Tue, 23 Nov 2010 15:38:30 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290526962n7vzzsvmhntcedd.htm/, Retrieved Tue, 23 Nov 2010 16:42:44 +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/2010/Nov/23/t1290526962n7vzzsvmhntcedd.htm/}, year = {2010}, } @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 = {2010}, 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:

» Textbox « » Textfile « » CSV «

475 2 60 0 0 0 530 1 67 1 0 0 550 2 91 1 1 0 550 1 150 0 2 0 625 3 110 1 2 0 650 2 86 1 2 1 650 2 86 0 0 1 720 3 145 1 2 1 795 3 150 1 0 0 515 2 85 1 2 0 535 2 100 1 2 0 550 2 84 0 0 0 600 2 94 1 0 0 600 2 149 0 1 0 660 3 105 1 2 0 695 2 106 1 0 0 720 3 132 1 0 0 750 2 130 1 2 0 750 3 165 1 2 0 850 2 127 1 2 1 850 2 119 1 0 1 875 3 126 1 2 1 900 2 133 1 2 1 595 2 89 1 1 1 765 3 147 1 2 1 495 1 59 1 0 1 525 1 58 0 0 1 525 1 56 0 0 1 595 2 90 1 2 0 650 1 80 1 0 1 695 3 135 0 0 1 615 2 125 0 2 0 460 2 80 1 0 0 650 2 100 1 1 1 650 2 76 1 0 1 475 1 65 1 1 0 530 2 75 1 1 0 575 2 95 1 2 1 650 2 85 1 1 1 650 1 106 1 0 1 875 2 135 1 0 1 500 2 95 0 1 1 625 2 60 1 2 0 730 2 112 1 2 1 750 2 150 1 1 1 700 2 100 0 2 0 830 2 125 1 0 1 995 2 100 1 2 1 850 3 150 1 2 1

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 10 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Bewoonbareopp[t] = -5.67046259550761 + 0.137285102691268Huurprijs[t] + 14.8450455533362Slaapkamers[t] -12.2215844419713Terras[t] + 3.47547927851639Garage[t] -8.17900748560341Nieuwbouw[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) -5.67046259550761 16.156965 -0.351 0.727331 0.363666 Huurprijs 0.137285102691268 0.03138 4.3749 7.6e-05 3.8e-05 Slaapkamers 14.8450455533362 5.942266 2.4982 0.016385 0.008192 Terras -12.2215844419713 7.584623 -1.6114 0.114418 0.057209 Garage 3.47547927851639 3.542126 0.9812 0.33199 0.165995 Nieuwbouw -8.17900748560341 6.93058 -1.1801 0.244435 0.122217 Multiple Linear Regression - Regression Statistics Multiple R 0.754739307243435 R-squared 0.5696314218983 Adjusted R-squared 0.519588563979497 F-TEST (value) 11.3828715143040 F-TEST (DF numerator) 5 F-TEST (DF denominator) 43 p-value 4.94771190018284e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20.6986735197444 Sum Squared Residuals 18422.7086755096 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 60 89.230052289517 -29.2300522895171 2 67 69.7141029422292 -2.71410294222919 3 91 90.7803298279072 0.219670172092798 4 150 91.6323479950587 58.3676520049413 5 110 119.397237361605 -9.39723736160492 6 86 99.805311889947 -13.8053118899470 7 86 105.075937774886 -19.0759377748855 8 145 124.260314631672 20.7396853683281 9 150 135.784746262088 14.2152537379124 10 85 89.4508305122292 -4.45083051222923 11 100 92.1965325660546 7.80346743394542 12 84 99.5264349913622 -15.5264349913622 13 94 94.1691056839542 -0.169105683954195 14 149 109.866169404442 39.1338305955581 15 105 124.202215955799 -19.2022159557993 16 106 107.211190439625 -1.21119043962463 17 132 125.488363560243 6.51163643975744 18 130 121.712829644677 8.28717035532286 19 165 136.557875198013 28.4421248019866 20 127 127.262332428201 -0.262332428200508 21 119 120.311373871168 -1.31137387116772 22 126 145.539505548818 -19.5395055488184 23 133 134.126587562764 -1.12658756276389 24 89 88.7791519634108 0.220848036589164 25 147 130.438144252779 16.5618557472210 26 59 56.7301168624314 2.26988313756857 27 58 73.0702543851408 -15.0702543851408 28 56 73.0702543851408 -17.0702543851408 29 90 100.433638727531 -10.4336387275306 30 80 78.009307779578 1.99069222042207 31 135 126.098812949329 8.9011870506712 32 125 115.400925223327 9.59907477667266 33 80 74.9491913071767 5.05080869282329 34 100 96.3298326114306 3.67016738856944 35 76 92.8543533329142 -16.8543533329142 36 65 65.6389015727259 -0.638901572725882 37 75 88.0346277740819 -13.0346277740818 38 95 89.5089291881019 5.49107081189812 39 85 96.3298326114306 -11.3298326114306 40 106 78.009307779578 27.9906922204221 41 135 123.743501438449 11.2564985615506 42 95 87.9586516497118 7.04134835028825 43 60 104.552191808269 -44.5521918082687 44 112 110.788120105248 1.21187989475162 45 150 110.058342880557 39.9416571194427 46 100 127.070158952085 -27.0701589520851 47 125 117.565671817342 7.43432818265764 48 100 147.168672318434 -47.1686723184343 49 150 142.107377981537 7.89262201846325 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.639535037189642 0.720929925620715 0.360464962810358 10 0.474228592317122 0.948457184634245 0.525771407682878 11 0.331811638300985 0.66362327660197 0.668188361699015 12 0.233113406242643 0.466226812485286 0.766886593757357 13 0.171811973172700 0.343623946345399 0.8281880268273 14 0.224010923430696 0.448021846861392 0.775989076569304 15 0.402728859975848 0.805457719951696 0.597271140024152 16 0.359892870990939 0.719785741981879 0.64010712900906 17 0.318309037612756 0.636618075225511 0.681690962387244 18 0.537139972264797 0.925720055470406 0.462860027735203 19 0.561220914260816 0.877558171478368 0.438779085739184 20 0.574893436376837 0.850213127246327 0.425106563623163 21 0.478909801339613 0.957819602679225 0.521090198660387 22 0.519563805267091 0.960872389465817 0.480436194732909 23 0.469372237362704 0.938744474725407 0.530627762637296 24 0.446340514906215 0.89268102981243 0.553659485093785 25 0.43492805224124 0.86985610448248 0.56507194775876 26 0.38468841895092 0.76937683790184 0.61531158104908 27 0.340132760039722 0.680265520079444 0.659867239960278 28 0.365629758179990 0.731259516359981 0.63437024182001 29 0.326731306170856 0.653462612341713 0.673268693829144 30 0.264478655734893 0.528957311469786 0.735521344265107 31 0.223720927750334 0.447441855500668 0.776279072249666 32 0.255562683872338 0.511125367744676 0.744437316127662 33 0.196534413706365 0.393068827412729 0.803465586293635 34 0.136840424489702 0.273680848979404 0.863159575510298 35 0.248296841172924 0.496593682345847 0.751703158827076 36 0.193029806407509 0.386059612815017 0.806970193592491 37 0.127909954367605 0.255819908735211 0.872090045632395 38 0.0762628874026975 0.152525774805395 0.923737112597303 39 0.093774190466938 0.187548380933876 0.906225809533062 40 0.075430086530888 0.150860173061776 0.924569913469112 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 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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