ws 8 -1

*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: Wed, 01 Dec 2010 11:07:19 +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/01/t1291201526o9m0rbfgqexff5t.htm/, Retrieved Wed, 01 Dec 2010 12:05:49 +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/01/t1291201526o9m0rbfgqexff5t.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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 622302.290621278 + 0.951593363958837X[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) 622302.290621278 875432.84121 0.7109 0.480026 0.240013 X 0.951593363958837 0.050064 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 746250.058393388 Sum Squared Residuals 32299570679823.8 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13768040.14 14640983.8586929 -872943.718692889 2 17487530.67 16296529.1190656 1191001.55093439 3 16198106.13 15099820.8440706 1098285.28592938 4 17535166.38 17405923.0980325 129243.281967519 5 16571771.6 17724705.3809571 -1152933.78095711 6 16198892.67 16700647.9158867 -501755.245886667 7 16554237.93 16511966.3548023 42271.5751976807 8 19554176.37 19360678.6877210 193497.682278985 9 15903762.33 15781851.4075353 121910.922464657 10 18003781.65 17222483.0939996 781298.556000439 11 18329610.38 17464905.2146822 864705.165317807 12 16260733.42 15076812.1349004 1183921.28509961 13 14851949.2 15536361.2546880 -684412.05468797 14 18174068.44 16971432.1340431 1202636.30595691 15 18406552.23 17432097.6726812 974454.5573188 16 18466459.42 17620505.0987493 845954.321250743 17 16016524.6 16002229.1352150 14295.4647850197 18 17428458.32 17240575.5863736 187882.733626429 19 17167191.42 16582532.9311665 584658.488833477 20 19629987.6 18804264.88107 825722.718930002 21 17183629.01 16534193.9675916 649435.042408389 22 18344657.85 17904444.2577603 440213.592239749 23 19301440.71 18236239.5038095 1065201.20619045 24 18147463.68 17563269.6031713 584194.076828708 25 16192909.22 16237825.4481501 -44916.2281501340 26 18374420.6 17720286.3812095 654134.21879051 27 20515191.95 19926898.3880256 588293.561974445 28 18957217.2 19213849.0592176 -256631.859217607 29 16471529.53 17771812.8590119 -1300283.32901192 30 18746813.27 19839080.5563689 -1092267.28636888 31 19009453.59 18749772.0203060 259681.569694032 32 19211178.55 19887044.3923238 -675865.842323786 33 20547653.75 21056154.2044877 -508500.454487705 34 19325754.03 19343572.5313847 -17818.5013846826 35 20605542.58 20656366.0900342 -50823.5100341689 36 20056915.06 19805929.5272272 250985.532772766 37 16141449.72 17944754.1903905 -1803304.47039049 38 20359793.22 20881215.8497596 -521422.629759599 39 19711553.27 20065577.3624365 -354024.09243645 40 15638580.7 16971052.2294244 -1332471.52942440 41 14384486 15673451.1918882 -1288965.19188819 42 13855616.12 14964545.947505 -1108929.82750501 43 14308336.46 14440504.3003432 -132167.840343172 44 15290621.44 15532618.2954139 -241996.85541391 45 14423755.53 14274702.0031838 149053.52681624 46 13779681.49 13831377.5121879 -51696.0221879407 47 15686348.94 15339591.6733863 346757.266613676 48 14733828.17 14171310.2517935 562517.918206471 49 12522497.94 13523732.2117143 -1001234.27171434 50 16189383.57 15969210.1872323 220173.382767750 51 16059123.25 16603260.5663681 -544137.316368076 52 16007123.26 15861125.4913968 145997.768603215 53 15806842.33 16673652.7347005 -866810.404700534 54 15159951.13 15861673.3998239 -701722.269823885 55 15692144.17 15732267.7788722 -40123.6088722397 56 18908869.11 18383696.4512063 525172.658793719 57 16969881.42 17715326.6956284 -745445.275628403 58 16997477.78 17115977.1676824 -118499.387682369 59 19858875.65 19218402.9473246 640472.70267543 60 17681170.13 16993091.2459249 688078.884075113 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.954437822118796 0.0911243557624073 0.0455621778812036 6 0.920212295682767 0.159575408634467 0.0797877043172333 7 0.858402391152146 0.283195217695708 0.141597608847854 8 0.807106331174334 0.385787337651333 0.192893668825666 9 0.716815997318223 0.566368005363554 0.283184002681777 10 0.704398213476034 0.591203573047931 0.295601786523966 11 0.698346114475468 0.603307771049064 0.301653885524532 12 0.742845612670912 0.514308774658177 0.257154387329088 13 0.763382396725437 0.473235206549127 0.236617603274563 14 0.818608352080664 0.362783295838673 0.181391647919337 15 0.823956937096124 0.352086125807752 0.176043062903876 16 0.810363629461834 0.379272741076332 0.189636370538166 17 0.754362696778803 0.491274606442393 0.245637303221197 18 0.689434531596438 0.621130936807123 0.310565468403562 19 0.644766349519168 0.710467300961664 0.355233650480832 20 0.626037777556035 0.74792444488793 0.373962222443965 21 0.594787388945015 0.81042522210997 0.405212611054985 22 0.538325935527661 0.923348128944678 0.461674064472339 23 0.591560693012293 0.816878613975414 0.408439306987707 24 0.56183103179368 0.87633793641264 0.43816896820632 25 0.502169005067732 0.995661989864536 0.497830994932268 26 0.490356481934352 0.980712963868705 0.509643518065648 27 0.476606194183095 0.95321238836619 0.523393805816905 28 0.464396080623263 0.928792161246526 0.535603919376737 29 0.6939767176612 0.612046564677601 0.306023282338800 30 0.785176742558876 0.429646514882247 0.214823257441124 31 0.746156521348277 0.507686957303445 0.253843478651723 32 0.728229558405805 0.543540883188391 0.271770441594195 33 0.678353224615811 0.643293550768377 0.321646775384189 34 0.610238388575136 0.779523222849728 0.389761611424864 35 0.537161479583728 0.925677040832544 0.462838520416272 36 0.491918632589797 0.983837265179594 0.508081367410203 37 0.817399304243678 0.365201391512643 0.182600695756322 38 0.778185373822069 0.443629252355863 0.221814626177932 39 0.726547062371612 0.546905875256776 0.273452937628388 40 0.866838206761335 0.266323586477329 0.133161793238664 41 0.941853091732224 0.116293816535553 0.0581469082677764 42 0.967722740309507 0.0645545193809863 0.0322772596904932 43 0.947849674503664 0.104300650992672 0.052150325496336 44 0.92025365749556 0.159492685008879 0.0797463425044396 45 0.889288047372794 0.221423905254411 0.110711952627206 46 0.84322918738987 0.313541625220259 0.156770812610130 47 0.815299461014158 0.369401077971683 0.184700538985842 48 0.899492139521855 0.201015720956290 0.100507860478145 49 0.862847348716423 0.274305302567153 0.137152651283577 50 0.832405788525435 0.335188422949129 0.167594211474565 51 0.774525606184692 0.450948787630616 0.225474393815308 52 0.72842205135809 0.543155897283820 0.271577948641910 53 0.734424903387573 0.531150193224853 0.265575096612427 54 0.667001972600282 0.665996054799435 0.332998027399718 55 0.499443774486659 0.998887548973318 0.500556225513341 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 2 0.0392156862745098 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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