*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 16:57:04 +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/t1291222540nfcdqw5tky9xt59.htm/, Retrieved Wed, 01 Dec 2010 17:55:40 +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/t1291222540nfcdqw5tky9xt59.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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162556 1081 807 213118 6282154 29790 309 444 81767 4321023 87550 458 412 153198 4111912 84738 588 428 -26007 223193 54660 302 315 126942 1491348 42634 156 168 157214 1629616 40949 481 263 129352 1398893 45187 353 267 234817 1926517 37704 452 228 60448 983660 16275 109 129 47818 1443586 25830 115 104 245546 1073089 12679 110 122 48020 984885 18014 239 393 -1710 1405225 43556 247 190 32648 227132 24811 505 280 95350 929118 6575 159 63 151352 1071292 7123 109 102 288170 638830 21950 519 265 114337 856956 37597 248 234 37884 992426 17821 373 277 122844 444477 12988 119 73 82340 857217 22330 84 67 79801 711969 13326 102 103 165548 702380 16189 295 290 116384 358589 7146 105 83 134028 297978 15824 64 56 63838 585715 27664 282 236 74996 657954 11920 182 73 31080 209458 8568 37 34 32168 786690 14416 361 139 49857 439798 3369 28 26 87161 688779 11819 85 70 106113 574339 6984 45 40 80570 741409 4519 49 42 102129 597793 2220 22 12 301670 644190 18562 155 211 102313 377934 10327 91 74 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 rijkdom[t] = -128263.368737775 + 15.5975953485900Kosten[t] -1747.05931782307transacties[t] + 4992.99917296018orders[t] + 3.72194258279855dividenden[t] -3998.48313872465t + 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) -128263.368737775 370139.085568 -0.3465 0.730598 0.365299 Kosten 15.5975953485900 6.720786 2.3208 0.024995 0.012497 transacties -1747.05931782307 775.971398 -2.2514 0.029401 0.014701 orders 4992.99917296018 1567.368995 3.1856 0.002656 0.001328 dividenden 3.72194258279855 1.372511 2.7118 0.009511 0.004755 t -3998.48313872465 8852.84823 -0.4517 0.653732 0.326866 Multiple Linear Regression - Regression Statistics Multiple R 0.839819542959623 R-squared 0.70529686473691 Adjusted R-squared 0.671807872093378 F-TEST (value) 21.0605577851895 F-TEST (DF numerator) 5 F-TEST (DF denominator) 44 p-value 1.08826281319807e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 637021.159167832 Sum Squared Residuals 17855022118011.3 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6282154 5337213.02698188 944940.973018117 2 4321023 2309774.41317395 2011248.58682605 3 4111912 3052467.30611131 1059444.69388869 4 223193 2190387.93975230 -1967194.93975230 5 1491348 2221962.43816803 -730614.438168033 6 1629616 1664157.70121067 -34541.701210665 7 1398893 1436717.14880635 -37824.1488063535 8 1926517 2134951.53862300 -208434.538622995 9 983660 997559.003060841 -13899.0030608410 10 1443586 717245.94226669 726340.05773331 11 1073089 1462907.41046439 -389818.410464391 12 984885 617213.801988892 367671.198011108 13 1405225 1639068.40926536 -233843.409265356 14 227132 1133786.90312661 -906654.903126609 15 929118 1069413.36057326 -140295.360573264 16 1071292 510415.060613959 560876.939386041 17 638830 1306272.73365619 -667442.733656194 18 856956 984107.896640445 -127151.896640445 19 992426 1258281.41240670 -265855.412406695 20 444477 1258357.67519822 -813880.675198224 21 857217 453403.686809275 403813.313190725 22 711969 616857.008285398 95111.991714602 23 702380 939864.089780948 -237484.089780948 24 358589 1394044.33398823 -1035455.33398823 25 297978 613057.19262673 -315079.192626729 26 585715 419989.946397259 165725.053602741 27 657954 1160077.34737211 -502123.34737211 28 209458 107904.559188801 101553.440811199 29 786690 114269.043310585 672420.956689415 30 439798 225540.434303684 214257.565696316 31 688779 205640.507748383 483138.492251617 32 574339 524089.543628775 50249.4563712248 33 741409 269699.505111312 471709.494888688 34 597793 310492.070655495 287300.929344505 35 644190 910695.487116985 -266505.487116985 36 377934 1180845.54583455 -802911.545834555 37 640273 425047.171328003 215225.828671997 38 697458 479584.105749342 217873.894250658 39 550608 742872.051742991 -192264.051742991 40 207393 473049.117637745 -265656.117637745 41 301607 -160154.326905311 461761.326905311 42 345783 449779.405952064 -103996.405952064 43 501749 169081.651449792 332667.348550208 44 379983 496288.646787364 -116305.646787364 45 387475 107805.678417071 279669.321582929 46 377305 205358.411888497 171946.588111503 47 370837 409362.855874288 -38525.8558742878 48 430866 487914.854674141 -57048.8546741411 49 469107 348874.981297508 120232.018702492 50 194493 138864.969858935 55628.0301410646 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.999999941849828 1.16300343650822e-07 5.8150171825411e-08 10 0.999999999759312 4.81376774772458e-10 2.40688387386229e-10 11 0.999999999783318 4.33363051684857e-10 2.16681525842429e-10 12 0.999999999109225 1.78155057318659e-09 8.90775286593295e-10 13 0.999999999967466 6.50680475653816e-11 3.25340237826908e-11 14 0.999999999997863 4.27309858434314e-12 2.13654929217157e-12 15 0.999999999993956 1.20879341755901e-11 6.04396708779504e-12 16 0.999999999998022 3.95617749773152e-12 1.97808874886576e-12 17 0.999999999997558 4.88382585441313e-12 2.44191292720657e-12 18 0.99999999999541 9.17854322261338e-12 4.58927161130669e-12 19 0.9999999999958 8.39856344119724e-12 4.19928172059862e-12 20 0.999999999985104 2.97921754652953e-11 1.48960877326477e-11 21 0.999999999990061 1.98772073725135e-11 9.93860368625675e-12 22 0.999999999963856 7.22884199347525e-11 3.61442099673762e-11 23 0.999999999809154 3.81692339878664e-10 1.90846169939332e-10 24 0.999999999484753 1.0304947804461e-09 5.1524739022305e-10 25 0.999999999765154 4.69692417676995e-10 2.34846208838498e-10 26 0.999999999173783 1.65243385297642e-09 8.26216926488208e-10 27 0.999999997432407 5.13518537579299e-09 2.56759268789649e-09 28 0.999999999836996 3.26007828943011e-10 1.63003914471506e-10 29 0.99999999955272 8.9456158136654e-10 4.4728079068327e-10 30 0.99999999840971 3.18057881035703e-09 1.59028940517851e-09 31 0.999999990653862 1.8692276725044e-08 9.346138362522e-09 32 0.99999994572622 1.08547560325012e-07 5.4273780162506e-08 33 0.999999775169548 4.49660904262627e-07 2.24830452131313e-07 34 0.99999864165643 2.71668713925775e-06 1.35834356962887e-06 35 0.999994180992653 1.16380146948068e-05 5.81900734740341e-06 36 0.999974587799996 5.08244000087935e-05 2.54122000043967e-05 37 0.999902831092587 0.000194337814825764 9.7168907412882e-05 38 0.99987830066188 0.000243398676239999 0.000121699338119999 39 0.999444484874247 0.00111103025150701 0.000555515125753507 40 0.998986145004081 0.00202770999183769 0.00101385499591884 41 0.99492759473684 0.0101448105263195 0.00507240526315976 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 32 0.96969696969697 NOK 5% type I error level 33 1 NOK 10% type I error level 33 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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