*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, 09 Dec 2009 12:54:54 -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/Dec/09/t1260388660e5dj61so9p3v9nx.htm/, Retrieved Wed, 09 Dec 2009 20:57:53 +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/Dec/09/t1260388660e5dj61so9p3v9nx.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:

hypotheseLT

Dataseries X:

» Textbox « » Textfile « » CSV «

627 0 696 0 825 0 677 0 656 0 785 0 412 0 352 0 839 0 729 0 696 0 641 0 695 0 638 0 762 0 635 0 721 0 854 0 418 0 367 0 824 0 687 0 601 0 676 0 740 0 691 0 683 0 594 0 729 0 731 0 386 0 331 0 707 0 715 0 657 0 653 0 642 0 643 0 718 0 654 0 632 0 731 0 392 1 344 1 792 1 852 1 649 1 629 1 685 1 617 1 715 1 715 1 629 1 916 1 531 1 357 1 917 1 828 1 708 1 858 1 775 1 785 1 1006 1 789 1 734 1 906 1 532 1 387 1 991 1 841 1

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 653.402013422819 + 62.2332214765102X[t] + 8.56897837434788M1[t] -7.4617076808352M2[t] + 98.6742729306487M3[t] -9.1897464578672M4[t] -3.38709917971661M5[t] + 133.248881431767M6[t] -252.820674869500M7[t] -342.018027591349M8[t] + 146.284619686801M9[t] + 76.2539336316181M10[t] -28.835980611484M11[t] + 0.364019388516028t + 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) 653.402013422819 33.056482 19.7662 0 0 X 62.2332214765102 29.648835 2.099 0.040337 0.020168 M1 8.56897837434788 38.502366 0.2226 0.82469 0.412345 M2 -7.4617076808352 38.473572 -0.1939 0.846922 0.423461 M3 98.6742729306487 38.458109 2.5658 0.012999 0.006499 M4 -9.1897464578672 38.455993 -0.239 0.812003 0.406001 M5 -3.38709917971661 38.467225 -0.0881 0.93015 0.465075 M6 133.248881431767 38.491794 3.4617 0.001035 0.000517 M7 -252.820674869500 38.515048 -6.5642 0 0 M8 -342.018027591349 38.488216 -8.8863 0 0 M9 146.284619686801 38.474711 3.8021 0.000356 0.000178 M10 76.2539336316181 38.474549 1.9819 0.052403 0.026201 M11 -28.835980611484 40.15672 -0.7181 0.475689 0.237845 t 0.364019388516028 0.716524 0.508 0.613424 0.306712 Multiple Linear Regression - Regression Statistics Multiple R 0.930548288163138 R-squared 0.865920116603346 Adjusted R-squared 0.834794429386265 F-TEST (value) 27.8201123902628 F-TEST (DF numerator) 13 F-TEST (DF denominator) 56 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 63.483240536844 Sum Squared Residuals 225686.822427293 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 627 662.33501118568 -35.3350111856805 2 696 646.668344519016 49.3316554809842 3 825 753.168344519016 71.8316554809844 4 677 645.668344519016 31.3316554809842 5 656 651.835011185682 4.16498881431766 6 785 788.835011185683 -3.8350111856826 7 412 403.129474272931 8.87052572706928 8 352 314.296140939597 37.7038590604026 9 839 802.962807606264 36.0371923937363 10 729 733.296140939598 -4.29614093959782 11 696 628.570246085011 67.4297539149887 12 641 657.770246085011 -16.7702460850112 13 695 666.703243847875 28.2967561521248 14 638 651.036577181208 -13.0365771812081 15 762 757.536577181208 4.4634228187919 16 635 650.036577181208 -15.0365771812081 17 721 656.203243847875 64.7967561521252 18 854 793.203243847875 60.7967561521252 19 418 407.497706935123 10.5022930648769 20 367 318.66437360179 48.3356263982103 21 824 807.331040268456 16.6689597315435 22 687 737.66437360179 -50.6643736017897 23 601 632.938478747204 -31.9384787472036 24 676 662.138478747204 13.8615212527964 25 740 671.071476510067 68.9285234899325 26 691 655.4048098434 35.5951901565996 27 683 761.9048098434 -78.9048098434004 28 594 654.4048098434 -60.4048098434004 29 729 660.571476510067 68.4285234899329 30 731 797.571476510067 -66.5714765100671 31 386 411.865939597315 -25.8659395973154 32 331 323.032606263982 7.96739373601793 33 707 811.699272930649 -104.699272930649 34 715 742.032606263982 -27.0326062639820 35 657 637.306711409396 19.6932885906041 36 653 666.506711409396 -13.5067114093959 37 642 675.43970917226 -33.4397091722599 38 643 659.773042505593 -16.7730425055927 39 718 766.273042505593 -48.2730425055928 40 654 658.773042505593 -4.77304250559275 41 632 664.93970917226 -32.9397091722595 42 731 801.93970917226 -70.9397091722594 43 392 478.467393736018 -86.467393736018 44 344 389.634060402685 -45.6340604026846 45 792 878.300727069351 -86.3007270693513 46 852 808.634060402685 43.3659395973154 47 649 703.908165548099 -54.9081655480985 48 629 733.108165548098 -104.108165548098 49 685 742.041163310962 -57.0411633109624 50 617 726.374496644295 -109.374496644295 51 715 832.874496644295 -117.874496644295 52 715 725.374496644295 -10.3744966442953 53 629 731.541163310962 -102.541163310962 54 916 868.541163310962 47.458836689038 55 531 482.83562639821 48.1643736017897 56 357 394.002293064877 -37.0022930648770 57 917 882.668959731544 34.3310402684563 58 828 813.002293064877 14.9977069351232 59 708 708.27639821029 -0.276398210290772 60 858 737.476398210291 120.523601789709 61 775 746.409395973155 28.5906040268453 62 785 730.742729306488 54.2572706935124 63 1006 837.242729306488 168.757270693512 64 789 729.742729306488 59.2572706935124 65 734 735.909395973154 -1.90939597315432 66 906 872.909395973154 33.0906040268457 67 532 487.203859060403 44.7961409395974 68 387 398.370525727069 -11.3705257270693 69 991 887.037192393736 103.962807606264 70 841 817.37052572707 23.6294742729308 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.408441754453173 0.816883508906346 0.591558245546827 18 0.363053788636595 0.72610757727319 0.636946211363405 19 0.231306039955762 0.462612079911525 0.768693960044238 20 0.155798614843686 0.311597229687372 0.844201385156314 21 0.100414442665162 0.200828885330324 0.899585557334838 22 0.0675941802724733 0.135188360544947 0.932405819727527 23 0.084441195625729 0.168882391251458 0.915558804374271 24 0.0593682220997772 0.118736444199554 0.940631777900223 25 0.0952281054219894 0.190456210843979 0.90477189457801 26 0.0795133255364059 0.159026651072812 0.920486674463594 27 0.150210816771051 0.300421633542101 0.84978918322895 28 0.122079874906202 0.244159749812405 0.877920125093798 29 0.211878623816001 0.423757247632001 0.788121376183999 30 0.212712585237741 0.425425170475481 0.78728741476226 31 0.155632147061364 0.311264294122728 0.844367852938636 32 0.144785211521003 0.289570423042005 0.855214788478997 33 0.202236548170474 0.404473096340948 0.797763451829526 34 0.152118915249178 0.304237830498355 0.847881084750822 35 0.132041395924903 0.264082791849806 0.867958604075097 36 0.0916316863861793 0.183263372772359 0.90836831361382 37 0.0620615421197921 0.124123084239584 0.937938457880208 38 0.0441701858975508 0.0883403717951017 0.95582981410245 39 0.0281955231063068 0.0563910462126135 0.971804476893693 40 0.0200634490419236 0.0401268980838472 0.979936550958076 41 0.0209450871610194 0.0418901743220387 0.97905491283898 42 0.0127362398834531 0.0254724797669062 0.987263760116547 43 0.00733921547486367 0.0146784309497273 0.992660784525136 44 0.00601040256017692 0.0120208051203538 0.993989597439823 45 0.00360574145717533 0.00721148291435067 0.996394258542825 46 0.0283325358082796 0.0566650716165592 0.97166746419172 47 0.0177421628262654 0.0354843256525308 0.982257837173735 48 0.0342755063991048 0.0685510127982096 0.965724493600895 49 0.0183395061397966 0.0366790122795933 0.981660493860203 50 0.0193820344118218 0.0387640688236437 0.980617965588178 51 0.686882898763557 0.626234202472886 0.313117101236443 52 0.622328940644581 0.755342118710838 0.377671059355419 53 0.77298857517378 0.454022849652439 0.227011424826220 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0270270270270270 NOK 5% type I error level 9 0.243243243243243 NOK 10% type I error level 13 0.351351351351351 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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