Workshop 7

*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, 19 Nov 2009 12:58:04 -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/19/t12586607242vaig3bhwkhga0u.htm/, Retrieved Thu, 19 Nov 2009 20:58:56 +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/19/t12586607242vaig3bhwkhga0u.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:

Workshop 7 link 4

Dataseries X:

» Textbox « » Textfile « » CSV «

461 0 455 462 452 449 461 0 461 455 462 452 463 0 461 461 455 462 462 0 463 461 461 455 456 0 462 463 461 461 455 0 456 462 463 461 456 0 455 456 462 463 472 0 456 455 456 462 472 0 472 456 455 456 471 0 472 472 456 455 465 0 471 472 472 456 459 0 465 471 472 472 465 0 459 465 471 472 468 0 465 459 465 471 467 0 468 465 459 465 463 0 467 468 465 459 460 0 463 467 468 465 462 0 460 463 467 468 461 0 462 460 463 467 476 0 461 462 460 463 476 0 476 461 462 460 471 0 476 476 461 462 453 0 471 476 476 461 443 0 453 471 476 476 442 0 443 453 471 476 444 0 442 443 453 471 438 0 444 442 443 453 427 0 438 444 442 443 424 0 427 438 444 442 416 0 424 427 438 444 406 0 416 424 427 438 431 0 406 416 424 427 434 0 431 406 416 424 418 0 434 431 406 416 412 0 418 434 431 406 404 0 412 418 434 431 409 0 404 412 418 434 412 1 409 404 412 418 406 1 412 409 404 412 398 1 406 412 409 404 397 1 398 406 412 409 385 1 397 398 406 412 390 1 385 397 398 406 413 1 390 385 397 398 413 1 413 39 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -5.32826335158439 + 2.34295047914645X[t] + 1.09404972823779Y1[t] -0.103435969619101Y2[t] + 0.290853961965319Y3[t] -0.283179283774372Y4[t] + 13.4961062988867M1[t] + 9.49932734168887M2[t] + 5.38342892233694M3[t] -0.316430489186691M4[t] + 2.27378015665203M5[t] + 0.634821026614046M6[t] + 7.50051641234214M7[t] + 26.0146635332518M8[t] + 5.80947840878837M9[t] -2.57233748576951M10[t] -7.79427250169785M11[t] + 0.000594829630836294t + 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) -5.32826335158439 24.839465 -0.2145 0.831269 0.415634 X 2.34295047914645 3.093838 0.7573 0.453424 0.226712 Y1 1.09404972823779 0.152273 7.1848 0 0 Y2 -0.103435969619101 0.213236 -0.4851 0.630335 0.315167 Y3 0.290853961965319 0.21023 1.3835 0.174379 0.087189 Y4 -0.283179283774372 0.143258 -1.9767 0.055176 0.027588 M1 13.4961062988867 3.476256 3.8824 0.000389 0.000194 M2 9.49932734168887 4.024368 2.3605 0.023348 0.011674 M3 5.38342892233694 4.349921 1.2376 0.223267 0.111633 M4 -0.316430489186691 3.768009 -0.084 0.933503 0.466752 M5 2.27378015665203 3.42345 0.6642 0.510484 0.255242 M6 0.634821026614046 3.428797 0.1851 0.854076 0.427038 M7 7.50051641234214 3.475034 2.1584 0.037112 0.018556 M8 26.0146635332518 3.594372 7.2376 0 0 M9 5.80947840878837 5.640431 1.03 0.309369 0.154685 M10 -2.57233748576951 5.415976 -0.475 0.637469 0.318735 M11 -7.79427250169785 4.401038 -1.771 0.084375 0.042187 t 0.000594829630836294 0.083163 0.0072 0.99433 0.497165 Multiple Linear Regression - Regression Statistics Multiple R 0.988776823652894 R-squared 0.977679606993106 Adjusted R-squared 0.967950204913177 F-TEST (value) 100.487121301117 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.80066799932126 Sum Squared Residuals 898.81011634858 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 461 462.492138554731 -1.49213855473124 2 461 467.843306352255 -6.84330635225514 3 463 458.239616373319 4.76038362668138 4 462 458.455830006114 3.54416999388604 5 456 458.046638111461 -2.04663811146130 6 455 450.529119335177 4.47088066482284 7 456 456.064763110499 -0.0647631104988569 8 472 474.315046270879 -2.31504627087866 9 472 472.920037398912 -0.920037398912489 10 471 463.457874065820 7.54212593418048 11 465 461.512968258955 3.48703174104504 12 459 458.316104650086 0.683895349913938 13 465 465.578269264926 -0.578269264926175 14 468 467.305054836483 0.694945163517022 15 467 465.805236544615 1.19476345538506 16 463 462.145813800065 0.854186199934795 17 460 459.637342515452 0.362657484547555 18 462 453.99018109552 8.0098189044801 19 461 462.474642112125 -1.47464211212481 20 476 479.948617644391 -3.94861764439084 21 476 477.689455017998 -1.6894550179979 22 471 466.89948187927 4.10051812072972 23 453 460.853881765038 -7.853881765038 24 443 445.225344579566 -2.22534457956645 25 442 448.189126069023 -6.18912606902336 26 444 440.313777012906 3.68622298709427 27 438 440.678696337565 -2.67869633756482 28 427 430.749200322785 -3.74920032278551 29 424 422.790961813059 1.20903818694096 30 416 416.696761654408 -0.69676165440799 31 406 413.62064407375 -7.62064407374966 32 431 424.264786734487 6.73521326551277 33 434 430.968505497391 3.03149450260911 34 418 422.640429027241 -4.64042902724146 35 412 409.707127167159 2.29287283284123 36 404 406.385751434503 -2.38575143450301 37 409 406.247469312065 2.75253068793536 38 412 413.677716830384 -1.67771683038393 39 406 411.699626584204 -5.69962658420436 40 398 402.845459804049 -4.84545980404912 41 397 396.761148738355 0.238851261644903 42 385 392.261560843548 -7.26156084354795 43 390 385.474934296596 4.52506570340376 44 413 412.675736831985 0.324263168015478 45 413 413.910042178716 -0.910042178716053 46 401 408.002215027669 -7.00221502766874 47 397 394.926022808848 2.07397719115172 48 397 393.072799335844 3.92720066415553 49 409 403.492996799255 5.50700320074541 50 419 414.860144967972 4.13985503202778 51 424 421.576824160297 2.42317583970274 52 428 423.803696066986 4.1963039330138 53 430 429.763908821672 0.236091178327881 54 424 428.522377071347 -4.522377071347 55 433 428.365016407030 4.63498359296957 56 456 456.795812518259 -0.79581251825874 57 459 458.511959906983 0.488040093017333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.0142782756275300 0.0285565512550599 0.98572172437247 22 0.0901791780515696 0.180358356103139 0.90982082194843 23 0.580698873925569 0.838602252148863 0.419301126074431 24 0.518239515504973 0.963520968990054 0.481760484495027 25 0.409050342554841 0.818100685109682 0.590949657445159 26 0.391728703520848 0.783457407041696 0.608271296479152 27 0.292258057939326 0.584516115878653 0.707741942060674 28 0.200753515846438 0.401507031692876 0.799246484153562 29 0.345057640479393 0.690115280958787 0.654942359520607 30 0.444892270685478 0.889784541370956 0.555107729314522 31 0.563021853111973 0.873956293776055 0.436978146888027 32 0.93568559738746 0.128628805225079 0.0643144026125396 33 0.935807539101316 0.128384921797368 0.0641924608986838 34 0.938080041638737 0.123839916722526 0.061919958361263 35 0.940711750208794 0.118576499582411 0.0592882497912057 36 0.869662859285067 0.260674281429865 0.130337140714932 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 1 0.0625 NOK 10% type I error level 1 0.0625 OK

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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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