*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, 31 Dec 2009 01:31:33 -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/31/t12622484275j193919bmh866n.htm/, Retrieved Thu, 31 Dec 2009 09:34:05 +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/31/t12622484275j193919bmh866n.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:

» Textbox « » Textfile « » CSV «

28029 0 29383 0 36438 0 32034 0 22679 0 24319 0 18004 0 17537 0 20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 0 26482 0 22405 0 27044 0 17970 0 18730 0 19684 0 19785 0 18479 0 10698 0 31956 0 29506 0 34506 0 27165 0 26736 0 23691 0 18157 0 17328 0 18205 0 20995 0 17382 0 9367 0 31124 0 26551 0 30651 0 25859 0 25100 0 25778 0 20418 0 18688 0 20424 0 24776 0 19814 1 12738 1 31566 1 30111 1 30019 1 31934 1 25826 1 26835 1 20205 1 17789 1 20520 1 22518 1 15572 1 11509 1 25447 1 24090 1 27786 1 26195 1 20516 1 22759 1 19028 1 16971 1 20036 1 22485 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation inschrijvingen[t] = + 12488.0487394958 + 693.383403361335dummyvariabele[t] + 17908.0363795518M1[t] + 15834.2475490196M2[t] + 19743.2920518207M3[t] + 16637.1698879552M4[t] + 12267.7143907563M5[t] + 13493.4255602241M6[t] + 7417.80339635855M7[t] + 6326.34789915966M8[t] + 8390.05906862745M9[t] + 10772.7702380952M10[t] + 6427.68883053221M11[t] -31.711169467787t + 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) 12488.0487394958 1072.021088 11.6491 0 0 dummyvariabele 693.383403361335 941.525527 0.7364 0.464533 0.232266 M1 17908.0363795518 1261.585219 14.1949 0 0 M2 15834.2475490196 1260.734128 12.5595 0 0 M3 19743.2920518207 1260.276638 15.6658 0 0 M4 16637.1698879552 1260.213177 13.2019 0 0 M5 12267.7143907563 1260.543805 9.7321 0 0 M6 13493.4255602241 1261.268213 10.6983 0 0 M7 7417.80339635855 1262.385721 5.876 0 0 M8 6326.34789915966 1263.895288 5.0054 6e-06 3e-06 M9 8390.05906862745 1265.795511 6.6283 0 0 M10 10772.7702380952 1268.084633 8.4953 0 0 M11 6427.68883053221 1315.908095 4.8846 9e-06 5e-06 t -31.711169467787 22.286605 -1.4229 0.160318 0.080159 Multiple Linear Regression - Regression Statistics Multiple R 0.947075845926344 R-squared 0.8969526579371 Adjusted R-squared 0.87303095352964 F-TEST (value) 37.4953491046992 F-TEST (DF numerator) 13 F-TEST (DF denominator) 56 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2080.33496163293 Sum Squared Residuals 242356438.945168 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 28029 30364.3739495798 -2335.37394957985 2 29383 28258.8739495798 1124.12605042019 3 36438 32136.2072829132 4301.79271708683 4 32034 28998.3739495798 3035.62605042019 5 22679 24597.2072829132 -1918.20728291320 6 24319 25791.2072829132 -1472.20728291316 7 18004 19683.8739495798 -1679.87394957982 8 17537 18560.7072829132 -1023.70728291319 9 20366 20592.7072829132 -226.707282913172 10 22782 22943.7072829132 -161.70728291316 11 19169 18566.9147058824 602.08529411764 12 13807 12107.5147058823 1699.48529411765 13 29743 29983.8399159664 -240.839915966381 14 25591 27878.3399159664 -2287.33991596639 15 29096 31755.6732492997 -2659.67324929972 16 26482 28617.8399159664 -2135.83991596639 17 22405 24216.6732492997 -1811.67324929971 18 27044 25410.6732492997 1633.32675070028 19 17970 19303.3399159664 -1333.33991596639 20 18730 18180.1732492997 549.826750700287 21 19684 20212.1732492997 -528.173249299717 22 19785 22563.1732492997 -2778.17324929972 23 18479 18186.3806722689 292.619327731095 24 10698 11726.9806722689 -1028.98067226891 25 31956 29603.3058823529 2352.69411764706 26 29506 27497.8058823529 2008.19411764706 27 34506 31375.1392156863 3130.86078431373 28 27165 28237.3058823529 -1072.30588235294 29 26736 23836.1392156863 2899.86078431373 30 23691 25030.1392156863 -1339.13921568627 31 18157 18922.8058823529 -765.805882352943 32 17328 17799.6392156863 -471.639215686269 33 18205 19831.6392156863 -1626.63921568627 34 20995 22182.6392156863 -1187.63921568628 35 17382 17805.8466386555 -423.846638655461 36 9367 11346.4466386555 -1979.44663865547 37 31124 29222.7718487395 1901.22815126050 38 26551 27117.2718487395 -566.271848739501 39 30651 30994.6051820728 -343.605182072827 40 25859 27856.7718487395 -1997.7718487395 41 25100 23455.6051820728 1644.39481792718 42 25778 24649.6051820728 1128.39481792717 43 20418 18542.2718487395 1875.7281512605 44 18688 17419.1051820728 1268.89481792717 45 20424 19451.1051820728 972.89481792717 46 24776 21802.1051820728 2973.89481792717 47 19814 18118.6960084034 1695.30399159664 48 12738 11659.2960084034 1078.70399159664 49 31566 29535.6212184874 2030.37878151261 50 30111 27430.1212184874 2680.8787815126 51 30019 31307.4545518207 -1288.45455182073 52 31934 28169.6212184874 3764.3787815126 53 25826 23768.4545518207 2057.54544817928 54 26835 24962.4545518207 1872.54544817927 55 20205 18855.1212184874 1349.87878151260 56 17789 17731.9545518207 57.0454481792766 57 20520 19763.9545518207 756.045448179274 58 22518 22114.9545518207 403.045448179271 59 15572 17738.1619747899 -2166.16197478991 60 11509 11278.7619747899 230.238025210080 61 25447 29155.0871848739 -3708.08718487395 62 24090 27049.5871848740 -2959.58718487396 63 27786 30926.9205182073 -3140.92051820728 64 26195 27789.0871848740 -1594.08718487395 65 20516 23387.9205182073 -2871.92051820728 66 22759 24581.9205182073 -1822.92051820728 67 19028 18474.5871848740 553.412815126046 68 16971 17351.4205182073 -380.420518207279 69 20036 19383.4205182073 652.579481792718 70 22485 21734.4205182073 750.579481792714 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.901060478565992 0.197879042868015 0.0989395214340077 18 0.938675786030006 0.122648427939987 0.0613242139699936 19 0.911388221692058 0.177223556615883 0.0886117783079416 20 0.883024590435255 0.233950819129489 0.116975409564745 21 0.825177278506483 0.349645442987035 0.174822721493517 22 0.838560347564551 0.322879304870898 0.161439652435449 23 0.768200184164679 0.463599631670642 0.231799815835321 24 0.71489371442669 0.570212571146619 0.285106285573309 25 0.811823936324147 0.376352127351706 0.188176063675853 26 0.79986620372942 0.400267592541159 0.200133796270579 27 0.814762428664917 0.370475142670166 0.185237571335083 28 0.779375090765789 0.441249818468422 0.220624909234211 29 0.826748170548535 0.346503658902929 0.173251829451465 30 0.81113204212167 0.377735915756658 0.188867957878329 31 0.799807592765341 0.400384814469318 0.200192407234659 32 0.764783452547636 0.470433094904728 0.235216547452364 33 0.823172637363127 0.353654725273746 0.176827362636873 34 0.920450722184413 0.159098555631174 0.079549277815587 35 0.888062764103948 0.223874471792104 0.111937235896052 36 0.91971353446405 0.160572931071900 0.0802864655359501 37 0.911121691297239 0.177756617405522 0.0888783087027609 38 0.881430254316702 0.237139491366596 0.118569745683298 39 0.85211590280273 0.295768194394541 0.147884097197270 40 0.92980287607044 0.140394247859121 0.0701971239295604 41 0.906240329030324 0.187519341939352 0.0937596709696758 42 0.865817553598973 0.268364892802054 0.134182446401027 43 0.83599172875489 0.32801654249022 0.16400827124511 44 0.772009420741217 0.455981158517565 0.227990579258783 45 0.725895543977045 0.54820891204591 0.274104456022955 46 0.688726582075107 0.622546835849786 0.311273417924893 47 0.601473543687609 0.797052912624782 0.398526456312391 48 0.531342304329501 0.937315391340999 0.468657695670499 49 0.535133427952028 0.929733144095944 0.464866572047972 50 0.577821784966144 0.844356430067712 0.422178215033856 51 0.489459711892398 0.978919423784797 0.510540288107602 52 0.577312668242269 0.845374663515463 0.422687331757731 53 0.729771962575126 0.540456074849748 0.270228037424874 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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