*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: Mon, 22 Nov 2010 21:30:25 +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/22/t1290461310r8hwzrufdx2kjdx.htm/, Retrieved Mon, 22 Nov 2010 22:28:33 +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/22/t1290461310r8hwzrufdx2kjdx.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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13768040.14 14731798.37 17487530.67 16471559.62 16198106.13 15213975.95 17535166.38 17637387.4 16571771.60 17972385.83 16198892.67 16896235.55 16554237.93 16697955.94 19554176.37 19691579.52 15903762.33 15930700.75 18003781.65 17444615.98 18329610.38 17699369.88 16260733.42 15189796.81 14851949.20 15672722.75 18174068.44 17180794.3 18406552.23 17664893.45 18466459.42 17862884.98 16016524.60 16162288.88 17428458.32 17463628.82 17167191.42 16772112.17 19629987.60 19106861.48 17183629.01 16721314.25 18344657.85 18161267.85 19301440.71 18509941.2 18147463.68 17802737.97 16192909.22 16409869.75 18374420.60 17967742.04 20515191.95 20286602.27 18957217.20 19537280.81 16471529.53 18021889.62 18746813.27 20194317.23 19009453.59 19049596.62 19211178.55 20244720.94 20547653.75 21473302.24 19325754.03 19673603.19 20605542.58 21053177.29 20056915.06 20159479.84 16141449.72 18203628.31 20359793.22 21289464.94 19711553.27 20432335.71 15638580.70 17180395.07 14384486.00 15816786.32 13 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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Invoer[t] = + 1840687.45143575 + 0.905502755008777Uitvoer[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) 1840687.45143575 822921.763846 2.2368 0.029161 0.01458 Uitvoer 0.905502755008777 0.047639 19.0076 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.92826203881921 R-squared 0.861670412712797 Adjusted R-squared 0.859285419828535 F-TEST (value) 361.28846270306 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 727953.374739134 Sum Squared Residuals 30735134716057.5 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14731798.37 14307685.7292772 424112.640722807 2 16471559.62 17675694.6514212 -1204135.03142125 3 15213975.95 16508117.1780753 -1294141.22807532 4 17637387.4 17718828.918063 -81441.5180630424 5 17972385.83 16846472.290612 1125913.53938803 6 16896235.55 16508829.3922122 387406.157787759 7 16697955.94 16830595.5041216 -132639.564121552 8 19691579.52 19547048.0263983 144531.493601713 9 15930700.75 16241588.0562556 -310887.306255565 10 17444615.98 18143161.3360872 -698545.356087222 11 17699369.88 18438200.1487632 -738830.268763235 12 15189796.81 16564826.3617091 -1375029.55170905 13 15672722.75 15289168.3692862 383554.380713841 14 17180794.3 18297356.4935738 -1116562.19357383 15 17664893.45 18507871.2059137 -842977.755913708 16 17862884.98 18562117.3315035 -699232.351503543 17 16162288.88 16343694.6024016 -181405.722401607 18 17463628.82 17622204.4757514 -158575.6557514 19 16772112.17 17385626.5780088 -613514.408008799 20 19106861.48 19615695.3040239 -508833.824023891 21 16721314.25 17400510.8610395 -679196.611039503 22 18161267.85 18451825.6743042 -290557.824304147 23 18509941.2 19318195.1899793 -808253.989979326 24 17802737.97 18273265.8100975 -470527.840097479 25 16409869.75 16503411.3617528 -93541.6117527853 26 17967742.04 18478775.9264258 -511033.886425786 27 20286602.27 20417250.2816946 -130648.011694643 28 19537280.81 19006499.8533355 530780.956664467 29 18021889.62 16755702.8200592 1266186.79994082 30 20194317.23 18815978.5150559 1378338.71494414 31 19049596.62 19053800.0483922 -4203.42839224455 32 20244720.94 19236462.5554263 1008258.38457372 33 21473302.24 20446644.5310272 1026657.70897281 34 19673603.19 19340210.9682227 333392.221777266 35 21053177.29 20499063.0260764 554114.263923578 36 20159479.84 20002279.2952428 157200.544757212 37 18203628.31 16456814.6427314 1746813.66726859 38 21289464.94 20276536.3035548 1012928.63644522 39 20432335.71 19689553.242923 742782.467076975 40 17180395.07 16001465.3597128 1178929.71028715 41 15816786.32 14865879.1538209 950907.16617906 42 15071819.75 14386986.0204398 684833.729560222 43 14521120.61 14796925.5355583 -275804.925558291 44 15668789.39 15686387.291152 -17597.9011520302 45 14346884.11 14901437.8214238 -554553.71142384 46 13881008.13 14318227.0037742 -437218.873774206 47 15465943.69 16044719.6326348 -578775.942634767 48 14238232.92 15182209.4511967 -943976.531196685 49 13557713.21 13179843.8356975 377869.374302509 50 16127590.29 16500218.8759646 -372628.585964589 51 16793894.2 16382267.7973363 411626.402663736 52 16014007.43 16335181.6631308 -321174.233130834 53 16867867.15 16153826.7292401 714040.420759884 54 16014583.21 15568064.9654492 446518.24455082 55 15878594.85 16049967.2293657 -171372.379365677 56 18664899.14 18962720.5246411 -297821.38464112 57 17962530.06 17206961.829418 755568.230581982 58 17332692.2 17231950.4094262 100741.790573769 59 19542066.35 19822954.0638875 -280887.713887474 60 17203555.19 17851035.7159297 -647480.525929652 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.93971569595487 0.120568608090258 0.0602843040451292 6 0.902251991028378 0.195496017943245 0.0977480089716223 7 0.830512542960936 0.338974914078128 0.169487457039064 8 0.794485105839819 0.411029788320362 0.205514894160181 9 0.71323559385083 0.57352881229834 0.28676440614917 10 0.655505488861211 0.688989022277578 0.344494511138789 11 0.593082450867115 0.81383509826577 0.406917549132885 12 0.742534791503925 0.514930416992151 0.257465208496075 13 0.686417599110339 0.627164801779321 0.313582400889661 14 0.699361378094633 0.601277243810733 0.300638621905367 15 0.661405397376593 0.677189205246814 0.338594602623407 16 0.609691101352668 0.780617797294665 0.390308898647332 17 0.527698547279295 0.94460290544141 0.472301452720705 18 0.456533772604557 0.913067545209113 0.543466227395443 19 0.408532873168604 0.817065746337208 0.591467126831396 20 0.36635153116141 0.732703062322819 0.63364846883859 21 0.338867150399735 0.67773430079947 0.661132849600265 22 0.29030626526698 0.58061253053396 0.70969373473302 23 0.288964700686769 0.577929401373539 0.71103529931323 24 0.256190208553535 0.51238041710707 0.743809791446465 25 0.203495661627801 0.406991323255602 0.796504338372199 26 0.185895464187863 0.371790928375727 0.814104535812137 27 0.195868916903934 0.391737833807868 0.804131083096066 28 0.237917997047008 0.475835994094017 0.762082002952992 29 0.446297542697187 0.892595085394374 0.553702457302813 30 0.699956892973357 0.600086214053285 0.300043107026643 31 0.650885422705684 0.698229154588631 0.349114577294316 32 0.716610702769205 0.566778594461589 0.283389297230795 33 0.75959976759998 0.48080046480004 0.24040023240002 34 0.70570809403793 0.588583811924139 0.294291905962069 35 0.658452148377833 0.683095703244334 0.341547851622167 36 0.587462037912924 0.825075924174152 0.412537962087076 37 0.871729026598814 0.256541946802371 0.128270973401186 38 0.897445902514426 0.205108194971148 0.102554097485574 39 0.90823861072483 0.18352277855034 0.0917613892751701 40 0.961269059016169 0.0774618819676629 0.0387309409838314 41 0.976880786722956 0.0462384265540875 0.0231192132770437 42 0.97972118507264 0.0405576298547209 0.0202788149273605 43 0.967359566703971 0.065280866592057 0.0326404332960285 44 0.946271373726712 0.107457252546575 0.0537286262732876 45 0.935238640888295 0.12952271822341 0.064761359111705 46 0.918653237304903 0.162693525390195 0.0813467626950973 47 0.910103657623737 0.179792684752526 0.0898963423762628 48 0.973775540772444 0.0524489184551127 0.0262244592275564 49 0.95419957601197 0.091600847976061 0.0458004239880305 50 0.946979780752776 0.106040438494449 0.0530202192472243 51 0.910024761136154 0.179950477727691 0.0899752388638455 52 0.899295412437805 0.20140917512439 0.100704587562195 53 0.870212627805282 0.259574744389436 0.129787372194718 54 0.775465777901892 0.449068444196217 0.224534222098108 55 0.690745837840894 0.618508324318212 0.309254162159106 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 2 0.0392156862745098 OK 10% type I error level 6 0.117647058823529 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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