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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 04 Dec 2010 10:41:06 +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/Dec/04/t1291459161f8g4rbdyj6zufor.htm/, Retrieved Sat, 04 Dec 2010 11:39:31 +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/Dec/04/t1291459161f8g4rbdyj6zufor.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:

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14731798.37 0 16471559.62 0 15213975.95 0 17637387.4 0 17972385.83 0 16896235.55 0 16697955.94 0 19691579.52 0 15930700.75 0 17444615.98 0 17699369.88 0 15189796.81 0 15672722.75 0 17180794.3 0 17664893.45 0 17862884.98 0 16162288.88 0 17463628.82 0 16772112.17 0 19106861.48 0 16721314.25 0 18161267.85 0 18509941.2 0 17802737.97 0 16409869.75 0 17967742.04 0 20286602.27 0 19537280.81 0 18021889.62 0 20194317.23 0 19049596.62 0 20244720.94 0 21473302.24 0 19673603.19 0 21053177.29 0 20159479.84 0 18203628.31 0 21289464.94 0 20432335.71 1 17180395.07 1 15816786.32 1 15071819.75 1 14521120.61 1 15668789.39 1 14346884.11 1 13881008.13 1 15465943.69 1 14238232.92 1 13557713.21 1 16127590.29 1 16793894.2 1 16014007.43 1 16867867.15 1 16014583.21 1 15878594.85 1 18664899.14 1 17962530.06 1 17332692.2 1 19542066.35 1 17203555.19 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 14777846.6460840 -5435351.76592437X[t] -972195.513708682M1[t] + 1000225.61833893M2[t] + 2238343.42157142M3[t] + 1686531.61561905M4[t] + 888521.409666667M5[t] + 928532.133714285M6[t] + 264428.631761904M7[t] + 2236060.05980952M8[t] + 727773.619857142M9[t] + 619602.179904761M10[t] + 1655201.76395238M11[t] + 119862.627952381t + 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) 14777846.6460840 686873.998931 21.5146 0 0 X -5435351.76592437 603979.003702 -8.9992 0 0 M1 -972195.513708682 768267.289565 -1.2654 0.212086 0.106043 M2 1000225.61833893 766583.781812 1.3048 0.198457 0.099228 M3 2238343.42157142 775923.029046 2.8847 0.005943 0.002971 M4 1686531.61561905 772771.494939 2.1824 0.03422 0.01711 M5 888521.409666667 769980.017442 1.154 0.254479 0.12724 M6 928532.133714285 767552.524987 1.2097 0.232563 0.116281 M7 264428.631761904 765492.480336 0.3454 0.731341 0.365671 M8 2236060.05980952 763802.856615 2.9275 0.005296 0.002648 M9 727773.619857142 762486.116319 0.9545 0.344833 0.172416 M10 619602.179904761 761544.193642 0.8136 0.420058 0.210029 M11 1655201.76395238 760978.480407 2.1751 0.0348 0.0174 t 119862.627952381 16944.135918 7.074 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.8369133092218 R-squared 0.700423887152586 Adjusted R-squared 0.61576107265223 F-TEST (value) 8.27309948631155 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 3.12367016697124e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1202914.31937307 Sum Squared Residuals 66562131548627.2 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14731798.37 13925513.7603277 806284.60967227 2 16471559.62 16017797.5203277 453762.099672268 3 15213975.95 17375777.9515126 -2161802.00151261 4 17637387.4 16943828.7735126 693558.626487397 5 17972385.83 16265681.1955126 1706704.63448739 6 16896235.55 16425554.5475126 470681.002487396 7 16697955.94 15881313.6735126 816642.266487394 8 19691579.52 17972807.7295126 1718771.79048740 9 15930700.75 16584383.9175126 -653683.167512603 10 17444615.98 16596075.1055126 848540.874487393 11 17699369.88 17751537.3175126 -52167.4375126055 12 15189796.81 16216198.1815126 -1026401.37151260 13 15672722.75 15363865.2957563 308857.454243697 14 17180794.3 17456149.0557563 -275354.755756299 15 17664893.45 18814129.4869412 -1149236.03694118 16 17862884.98 18382180.3089412 -519295.328941176 17 16162288.88 17704032.7309412 -1541743.85094118 18 17463628.82 17863906.0829412 -400277.262941176 19 16772112.17 17319665.2089412 -547553.038941176 20 19106861.48 19411159.2649412 -304297.784941177 21 16721314.25 18022735.4529412 -1301421.20294118 22 18161267.85 18034426.6409412 126841.209058825 23 18509941.2 19189888.8529412 -679947.652941176 24 17802737.97 17654549.7169412 148188.253058822 25 16409869.75 16802216.8311849 -392347.081184874 26 17967742.04 18894500.5911849 -926758.551184874 27 20286602.27 20252481.0223697 34121.2476302537 28 19537280.81 19820531.8443697 -283251.034369749 29 18021889.62 19142384.2663697 -1120494.64636975 30 20194317.23 19302257.6183697 892059.611630253 31 19049596.62 18758016.7443697 291579.875630253 32 20244720.94 20849510.8003697 -604789.860369747 33 21473302.24 19461086.9883697 2012215.25163025 34 19673603.19 19472778.1763697 200825.013630254 35 21053177.29 20628240.3883697 424936.901630252 36 20159479.84 19092901.2523698 1066578.58763025 37 18203628.31 18240568.3666134 -36940.0566134465 38 21289464.94 20332852.1266134 956612.813386555 39 20432335.71 16255480.7918739 4176854.91812605 40 17180395.07 15823531.6138739 1356863.45612605 41 15816786.32 15145384.0358739 671402.28412605 42 15071819.75 15305257.3878739 -233437.63787395 43 14521120.61 14761016.5138739 -239895.903873950 44 15668789.39 16852510.5698740 -1183721.17987395 45 14346884.11 15464086.7578739 -1117202.64787395 46 13881008.13 15475777.9458739 -1594769.81587395 47 15465943.69 16631240.1578739 -1165296.46787395 48 14238232.92 15095901.0218740 -857668.10187395 49 13557713.21 14243568.1361176 -685854.926117647 50 16127590.29 16335851.8961176 -208261.606117648 51 16793894.2 17693832.3273025 -899938.12730252 52 16014007.43 17261883.1493025 -1247875.71930252 53 16867867.15 16583735.5713025 284131.578697477 54 16014583.21 16743608.9233025 -729025.71330252 55 15878594.85 16199368.0493025 -320773.199302521 56 18664899.14 18290862.1053025 374037.034697479 57 17962530.06 16902438.2933025 1060091.76669748 58 17332692.2 16914129.4813025 418562.718697479 59 19542066.35 18069591.6933025 1472474.65669748 60 17203555.19 16534252.5573025 669302.63269748 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.65220236420314 0.695595271593721 0.347797635796861 18 0.481944810151692 0.963889620303385 0.518055189848308 19 0.33682497705829 0.67364995411658 0.66317502294171 20 0.254009142005840 0.508018284011681 0.74599085799416 21 0.183032217732100 0.366064435464199 0.8169677822679 22 0.113492966488392 0.226985932976784 0.886507033511608 23 0.0682674166928898 0.136534833385780 0.93173258330711 24 0.100521318214508 0.201042636429016 0.899478681785492 25 0.0591944450164192 0.118388890032838 0.94080555498358 26 0.0363337431507734 0.0726674863015468 0.963666256849227 27 0.132092021275128 0.264184042550256 0.867907978724872 28 0.0897422304895836 0.179484460979167 0.910257769510416 29 0.0861860871679871 0.172372174335974 0.913813912832013 30 0.0820814614541912 0.164162922908382 0.917918538545809 31 0.0545257995742466 0.109051599148493 0.945474200425753 32 0.0397074573125641 0.0794149146251281 0.960292542687436 33 0.132037962369093 0.264075924738186 0.867962037630907 34 0.0843707570107479 0.168741514021496 0.915629242989252 35 0.0597325545320037 0.119465109064007 0.940267445467996 36 0.0477148169393997 0.0954296338787994 0.9522851830606 37 0.026711112697436 0.053422225394872 0.973288887302564 38 0.0174309329032817 0.0348618658065635 0.982569067096718 39 0.193895141182171 0.387790282364342 0.806104858817829 40 0.627831560547712 0.744336878904577 0.372168439452288 41 0.670213891044644 0.659572217910712 0.329786108955356 42 0.81990537881838 0.360189242363239 0.180094621181619 43 0.961885724963097 0.0762285500738056 0.0381142750369028 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 0.0370370370370370 OK 10% type I error level 6 0.222222222222222 NOK

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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