*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, 18 Nov 2009 10:10:17 -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/Nov/18/t125856426243hc4j4h5zvhyuh.htm/, Retrieved Wed, 18 Nov 2009 18:11:15 +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/Nov/18/t125856426243hc4j4h5zvhyuh.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:

ws7lineairtrend

Dataseries X:

» Textbox « » Textfile « » CSV «

7291 4071 6820 4351 8031 4871 7862 4649 7357 4922 7213 4879 7079 4853 7012 4545 7319 4733 8148 5191 7599 4983 6908 4593 7878 4656 7407 4513 7911 4857 7323 4681 7179 4897 6758 4547 6934 4692 6696 4390 7688 5341 8296 5415 7697 4890 7907 5120 7592 4422 7710 4797 9011 5689 8225 5171 7733 4265 8062 5215 7859 4874 8221 4590 8330 4994 8868 4988 9053 5110 8811 5141 8120 4395 7953 4523 8878 5306 8601 5365 8361 5496 9116 5647 9310 5443 9891 5546 10147 5912 10317 5665 10682 5963 10276 5861 10614 5366 9413 5619 11068 6721 9772 6054 10350 6619 10541 6856 10049 6193 10714 6317 10759 6618 11684 6585 11462 6852 10485 6586 11056 6154 10184 6193 11082 7606 10554 6588 11315 7143 10847 7629 11104 7041 11026 7146 11073 7200 12073 7739 12328 7953 11172 7082

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation UitvEU[t] = + 3229.18086786427 + 0.775005380369865`Uitvniet-EU`[t] + 602.002399837294M1[t] -66.8932962291957M2[t] + 324.782311390216M3[t] + 7.9480638912125M4[t] -144.622544295902M5[t] -326.972854496486M6[t] -181.870377665479M7[t] + 57.0435993134617M8[t] + 19.4300421381953M9[t] + 558.521977890767M10[t] + 404.810300258041M11[t] + 37.8448603157037t + 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) 3229.18086786427 539.659339 5.9837 0 0 `Uitvniet-EU` 0.775005380369865 0.124985 6.2008 0 0 M1 602.002399837294 247.08625 2.4364 0.017925 0.008963 M2 -66.8932962291957 244.062486 -0.2741 0.784995 0.392497 M3 324.782311390216 247.752033 1.3109 0.195053 0.097526 M4 7.9480638912125 240.258442 0.0331 0.973723 0.486862 M5 -144.622544295902 240.479129 -0.6014 0.549921 0.274961 M6 -326.972854496486 243.014952 -1.3455 0.183706 0.091853 M7 -181.870377665479 239.794385 -0.7584 0.451257 0.225628 M8 57.0435993134617 240.370829 0.2373 0.813249 0.406624 M9 19.4300421381953 240.790641 0.0807 0.935964 0.467982 M10 558.521977890767 242.109867 2.3069 0.024651 0.012326 M11 404.810300258041 241.848851 1.6738 0.099552 0.049776 t 37.8448603157037 5.61985 6.7341 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.971523217935695 R-squared 0.943857362988128 Adjusted R-squared 0.931273668485467 F-TEST (value) 75.0063793100301 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 414.815225630724 Sum Squared Residuals 9980156.94207399 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7291 7024.07503150298 266.924968497024 2 6820 6610.02570225576 209.974297744245 3 8031 7442.54896798321 588.451032016793 4 7862 6991.5083863578 870.491613642203 5 7357 7088.35910732736 268.640892672641 6 7213 6910.52842608657 302.471573913425 7 7079 7073.32562334367 5.67437665633055 8 7012 7111.3828034844 -99.3828034843946 9 7319 7257.31511813437 61.6848818656335 10 8148 8189.20437841204 -41.2043784120417 11 7599 7912.13644197809 -313.136441978086 12 6908 7242.9189036915 -334.918903691501 13 7878 7931.5915028078 -53.5915028078012 14 7407 7189.71489766412 217.285102335875 15 7911 7885.83721644647 25.1627835535269 16 7323 7470.44688231808 -147.446882318077 17 7179 7523.12229660656 -344.122296606556 18 6758 7107.36496359222 -349.364963592224 19 6934 7402.68808089257 -468.688080892565 20 6696 7445.39529331551 -749.395293315509 21 7688 8182.65671318769 -494.656713187689 22 8296 8816.94390740333 -520.943907403335 23 7697 8294.19926539213 -597.199265392133 24 7907 8105.48506293486 -198.485062934864 25 7592 8204.3785675897 -612.378567589696 26 7710 7863.9547494776 -153.954749477609 27 9011 8984.78001670265 26.2199832973547 28 8225 8304.33784248776 -79.3378424877546 29 7733 7487.45722000125 245.542779998755 30 8062 8079.20688146774 -17.2068814677377 31 7859 7997.87738390832 -138.877383908324 32 8221 8054.53469317793 166.465306822073 33 8330 8367.86816998779 -37.8681699877897 34 8868 8940.15493377385 -72.154933773846 35 9053 8918.83877286195 134.161227138053 36 8811 8575.89849971107 235.101500288925 37 8120 8637.59174610815 -517.591746108154 38 7953 8105.74159904471 -152.74159904471 39 8878 9142.09127980943 -264.091279809431 40 8601 8908.82721006795 -307.827210067953 41 8361 8895.627167025 -534.627167024994 42 9116 8868.14752957596 247.852470424036 43 9310 8892.99376912722 417.006230872778 44 9891 9249.57816059996 641.421839400038 45 10147 9533.46143295577 613.53856704423 46 10317 9918.9719000727 398.028099927311 47 10682 10034.0566861059 647.943313894114 48 10276 9588.04069736582 687.959302634178 49 10614 9844.26029423574 769.739705764263 50 9413 9409.28581971853 3.71418028147302 51 11068 10692.8622168212 375.137783178766 52 9772 9896.94424093123 -124.944240931234 53 10350 10220.0965329688 129.903467031203 54 10541 10259.2673582316 281.732641768425 55 10049 9928.38612819306 120.613871806935 56 10714 10301.2456326536 412.754367346428 57 10759 10534.7535552853 224.246444714661 58 11684 11086.1151738014 597.88482619859 59 11462 11177.1747930431 284.825206956859 60 10485 10604.0579219224 -119.057921922419 61 11056 10909.1028577556 146.897142244365 62 10184 10308.2772318393 -124.277231839274 63 11082 11832.880302237 -750.880302237009 64 10554 10764.9354378372 -210.935437837186 65 11315 11080.3376760711 234.66232392895 66 10847 11312.4848410459 -465.484841045925 67 11104 11039.7290145352 64.2709854648451 68 11026 11397.8634167686 -371.863416768635 69 11073 11439.9450104490 -366.945010449045 70 12073 12434.6097065367 -361.609706536678 71 12328 12484.5940406188 -156.594040618807 72 11172 11442.5989143743 -270.598914374317 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.293393460512848 0.586786921025695 0.706606539487152 18 0.161653887338108 0.323307774676216 0.838346112661892 19 0.0865860441037416 0.173172088207483 0.913413955896258 20 0.0482536657087932 0.0965073314175864 0.951746334291207 21 0.0282264914129479 0.0564529828258957 0.971773508587052 22 0.0128888115021452 0.0257776230042904 0.987111188497855 23 0.0121385785493342 0.0242771570986685 0.987861421450666 24 0.0176302740796030 0.0352605481592060 0.982369725920397 25 0.0123080210475604 0.0246160420951208 0.98769197895244 26 0.00781508322250022 0.0156301664450004 0.9921849167775 27 0.00361184329503227 0.00722368659006454 0.996388156704968 28 0.00157937160943415 0.0031587432188683 0.998420628390566 29 0.0547111072563548 0.109422214512710 0.945288892743645 30 0.0560410392883727 0.112082078576745 0.943958960711627 31 0.072388884997132 0.144777769994264 0.927611115002868 32 0.176566699319651 0.353133398639301 0.82343330068035 33 0.175204612319234 0.350409224638468 0.824795387680766 34 0.178246393982698 0.356492787965396 0.821753606017302 35 0.251609767505102 0.503219535010204 0.748390232494898 36 0.275706168302752 0.551412336605505 0.724293831697248 37 0.500676134565613 0.998647730868775 0.499323865434387 38 0.463254299606981 0.926508599213962 0.536745700393019 39 0.448740083885972 0.897480167771944 0.551259916114028 40 0.466321414882969 0.932642829765938 0.533678585117031 41 0.887606814037652 0.224786371924696 0.112393185962348 42 0.910519468349573 0.178961063300855 0.0894805316504275 43 0.937104687520307 0.125790624959386 0.0628953124796932 44 0.94445553718272 0.111088925634559 0.0555444628172796 45 0.935265838963123 0.129468322073754 0.064734161036877 46 0.967463958640863 0.0650720827182733 0.0325360413591367 47 0.974938468930376 0.0501230621392478 0.0250615310696239 48 0.97236581053784 0.0552683789243195 0.0276341894621597 49 0.958381840006128 0.0832363199877436 0.0416181599938718 50 0.929909325818657 0.140181348362687 0.0700906741813434 51 0.94912333841408 0.101753323171839 0.0508766615859196 52 0.91099619533751 0.178007609324978 0.0890038046624892 53 0.894441695234006 0.211116609531988 0.105558304765994 54 0.834028396323078 0.331943207353844 0.165971603676922 55 0.86220548895877 0.275589022082460 0.137794511041230 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0512820512820513 NOK 5% type I error level 7 0.179487179487179 NOK 10% type I error level 13 0.333333333333333 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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