*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, 02 Dec 2010 15:18:47 +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/02/t1291303081js7hjweul8h2wqv.htm/, Retrieved Thu, 02 Dec 2010 16:18:01 +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/02/t1291303081js7hjweul8h2wqv.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:

Micha

Dataseries X:

» Textbox « » Textfile « » CSV «

162556 807 213118 6282154 29790 444 81767 4321023 87550 412 153198 4111912 84738 428 -26007 223193 54660 315 126942 1491348 42634 168 157214 1629616 40949 263 129352 1398893 45187 267 234817 1926517 37704 228 60448 983660 16275 129 47818 1443586 25830 104 245546 1073089 12679 122 48020 984885 18014 393 -1710 1405225 43556 190 32648 227132 24811 280 95350 929118 6575 63 151352 1071292 7123 102 288170 638830 21950 265 114337 856956 37597 234 37884 992426 17821 277 122844 444477 12988 73 82340 857217 22330 67 79801 711969 13326 103 165548 702380 16189 290 116384 358589 7146 83 134028 297978 15824 56 63838 585715 27664 236 74996 657954 11920 73 31080 209458 8568 34 32168 786690 14416 139 49857 439798 3369 26 87161 688779 11819 70 106113 574339 6984 40 80570 741409 4519 42 102129 597793 2220 12 301670 644190 18562 211 102313 377934 10327 74 88577 640273 5336 80 112477 697458 2365 83 191778 550608 4069 131 79804 207393 8636 203 128294 301607 13718 56 96448 345783 4525 89 93 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Wealth[t] = -42000.8185908956 + 15.9214989697913Costs[t] + 2669.75885268391Orders[t] + 2.98822899621563Dividends[t] -4099.56734915861t + 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) -42000.8185908956 314242.402391 -0.1337 0.894161 0.447081 Costs 15.9214989697913 6.324037 2.5176 0.014757 0.007379 Orders 2669.75885268391 1168.612151 2.2846 0.026221 0.01311 Dividends 2.98822899621563 1.271689 2.3498 0.0224 0.0112 t -4099.56734915861 6197.911928 -0.6614 0.51109 0.255545 Multiple Linear Regression - Regression Statistics Multiple R 0.8155944379683 R-squared 0.665194287244827 Adjusted R-squared 0.640844780862632 F-TEST (value) 27.3185943404278 F-TEST (DF numerator) 4 F-TEST (DF denominator) 55 p-value 1.64890323617328e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 618138.706379022 Sum Squared Residuals 21015250317816.2 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6282154 5333375.58192474 948778.418075258 2 4321023 1853812.95194609 2467210.04805391 3 4111912 2897359.06723487 1214552.93276513 4 223193 2355698.80915878 -2132505.80915878 5 1491348 2028076.28218514 -536728.282185141 6 1629616 1530509.88505418 99106.1149458233 7 1398893 1669951.64665333 -271058.646653331 8 1926517 2059159.99843476 -132642.998434765 9 983660 1310744.75719886 -327084.757198863 10 1443586 663415.929788135 780170.070211865 11 1073089 1335558.85674196 -262469.856741959 12 984885 579878.395082897 405006.604917103 13 1405225 1235620.04583311 169604.954166890 14 227132 1198895.92992751 -971763.929927506 15 929118 1323994.09565187 -394876.095651872 16 1071292 617559.202303258 453732.797696742 17 638830 1135148.72644845 -496318.726448447 18 856956 1282835.10621271 -425879.106212711 19 992426 1216637.63736300 -224211.637363003 20 444477 1266354.07257114 -821877.072571138 21 857217 519639.867490744 337577.132509256 22 711969 640673.276979881 71295.7230201192 23 702380 845559.523341843 -143179.523341843 24 358589 1239374.82262514 -880785.822625143 25 297978 591381.36999582 -293403.369995821 26 585715 443621.288439671 142093.711560329 27 657954 1141931.52151572 -483977.521515719 28 209458 320762.116800883 -111304.116800883 29 786690 162424.282798194 624265.717201806 30 439798 584617.103670244 -144819.103670244 31 688779 214422.881323347 474356.118676653 32 574339 518962.285723295 55376.7142767048 33 741409 281461.172024343 459947.827975657 34 597793 307877.856349429 289915.143650571 35 644190 783356.199422065 -139166.199422065 36 377934 975003.411922775 -597069.411922775 37 640273 432987.024247672 207285.975752328 38 697458 436860.481665942 260597.518334058 39 550608 630436.96506448 -79828.9650644799 40 207393 447012.103266425 -239619.103266425 41 301607 852747.88313204 -551140.88313204 42 345783 441943.681589344 -96160.6815893441 43 501749 371699.856486442 130049.143513558 44 379983 473098.445141067 -93115.4451410666 45 387475 157986.872333110 229488.127666890 46 377305 199075.270347247 178229.729652753 47 370837 603235.154516543 -232398.154516543 48 430866 687625.543049717 -256759.543049717 49 469107 354322.540425556 114784.459574444 50 194493 127155.29055608 67337.7094439199 51 530670 362521.105205040 168148.894794960 52 518365 576673.855243524 -58308.8552435236 53 491303 680072.615811201 -188769.615811201 54 527021 359799.223016033 167221.776983967 55 233773 579018.395251971 -345245.395251971 56 405972 155273.567516702 250698.432483298 57 652925 -49526.4962785979 702451.496278598 58 446211 193344.759748833 252866.240251167 59 341340 170037.450076304 171302.549923696 60 387699 348682.454449138 39016.5455508623 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.997140474029396 0.00571905194120871 0.00285952597060436 9 0.999999984434015 3.11319693294107e-08 1.55659846647053e-08 10 0.99999999999919 1.62172001154219e-12 8.10860005771095e-13 11 0.999999999998945 2.10930653405723e-12 1.05465326702861e-12 12 0.999999999999229 1.54202677297281e-12 7.71013386486407e-13 13 0.999999999999967 6.53604704721324e-14 3.26802352360662e-14 14 0.999999999999998 3.739284204768e-15 1.869642102384e-15 15 0.999999999999997 5.28156872774791e-15 2.64078436387396e-15 16 1 5.95424975150389e-16 2.97712487575194e-16 17 1 9.26210498796022e-16 4.63105249398011e-16 18 1 1.12274508467804e-15 5.6137254233902e-16 19 1 2.62294992432246e-16 1.31147496216123e-16 20 1 8.99887764060649e-16 4.49943882030324e-16 21 1 1.45323304045917e-16 7.26616520229583e-17 22 1 2.54072460716500e-16 1.27036230358250e-16 23 1 1.11747018211046e-15 5.58735091055229e-16 24 0.999999999999998 4.38758006829298e-15 2.19379003414649e-15 25 0.999999999999997 5.19255975599411e-15 2.59627987799705e-15 26 0.999999999999994 1.23728249854256e-14 6.1864124927128e-15 27 0.99999999999999 2.01890606152338e-14 1.00945303076169e-14 28 0.999999999999998 3.3724395883887e-15 1.68621979419435e-15 29 0.999999999999998 3.66220198245120e-15 1.83110099122560e-15 30 0.999999999999989 2.21162893006839e-14 1.10581446503420e-14 31 0.99999999999996 8.02707903678107e-14 4.01353951839053e-14 32 0.99999999999976 4.78923395762952e-13 2.39461697881476e-13 33 0.999999999999547 9.05473827053027e-13 4.52736913526513e-13 34 0.999999999997764 4.47144634491074e-12 2.23572317245537e-12 35 0.999999999986884 2.62322988523811e-11 1.31161494261905e-11 36 0.999999999929854 1.40292909737269e-10 7.01464548686344e-11 37 0.999999999857464 2.85071623031067e-10 1.42535811515533e-10 38 0.99999999992703 1.45939533307164e-10 7.29697666535818e-11 39 0.999999999771287 4.5742621349062e-10 2.2871310674531e-10 40 0.999999999238672 1.52265571977943e-09 7.61327859889713e-10 41 0.999999996109395 7.78121015541112e-09 3.89060507770556e-09 42 0.999999978077764 4.38444728817214e-08 2.19222364408607e-08 43 0.999999904474492 1.9105101540558e-07 9.552550770279e-08 44 0.99999944749783 1.105004341214e-06 5.52502170607e-07 45 0.999997116385475 5.76722905035026e-06 2.88361452517513e-06 46 0.999986069462716 2.786107456729e-05 1.3930537283645e-05 47 0.9999397916416 0.000120416716801121 6.02083584005603e-05 48 0.999715372687427 0.000569254625145964 0.000284627312572982 49 0.998746864383265 0.00250627123347017 0.00125313561673509 50 0.999918380688764 0.000163238622471801 8.16193112359004e-05 51 0.999560260843643 0.00087947831271471 0.000439739156357355 52 0.998781325870283 0.002437348259434 0.001218674129717 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 45 1 NOK 5% type I error level 45 1 NOK 10% type I error level 45 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal 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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