Verbetering Workshop 7 (seasonal dummies)

*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: Fri, 27 Nov 2009 06:26:49 -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/27/t1259328573z75fflusrlq2cj1.htm/, Retrieved Fri, 27 Nov 2009 14:29:46 +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/27/t1259328573z75fflusrlq2cj1.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

384 257.9 367.6 275.8 457.1 319.4 429.4 299.8 442.2 331.1 507.5 339.3 348.5 209.6 393.2 280.9 426.8 285.5 403 247.6 454.8 275.1 413 262.3 388.9 267.8 406.5 448.2 447.4 563.4 474.4 346.6 428.5 455.1 472.8 424.4 411 381.2 463.9 382.9 497.3 466.6 474 400.2 518.1 493.6 566 367.5 509.4 307.1 445.1 316.7 466.6 314.2 600.5 403.7 538.7 370.6 548 343.7 591.9 383 547.3 365.4 610.2 417.2 621.6 411 582.4 420.8 635.8 493 663.9 471.8 624.2 452.4 654.1 464.8 723.5 541.5 641.2 484 565.5 449.4 698.6 436.8 651 490 721.6 475.4 643.5 393.6 604 486.8 618.2 536.7 783.5 467 672.9 475.5 726.7 532.8 738.6 554.1 692.2 507.3 669.5 455.2 546.2 465.3 715 563.2 789.8 680.1 684 518.2 639 426.6 768.5 612.4 643.8 518.1 623 540 692.8 541.7 936.5 627.6 795.9 637 695.7 564.2 648.3 665 675.2 703.2 826.5 824.4 742.4 700.3 793.9 1219.6 685.3 764.7 756.1 479.9 704 543.4 860.6 593.3 795.9 584.3 816.7 645.9 777.9 548.9 746.4 421.8 694.7 460.3 909.2 553.4 783.6 424.4 730 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation yt[t] = + 169.803669378881 + 0.982878385352796xt[t] + 53.0505660825984M1[t] -0.269148200396778M2[t] + 11.6519447450388M3[t] + 65.945969813359M4[t] -11.0060367652886M5[t] + 7.85788440982509M6[t] + 30.8704282258714M7[t] -12.3135781387198M8[t] + 44.8369121538511M9[t] + 68.197242675119M10[t] -10.0188622503012M11[t] + 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) 169.803669378881 52.293214 3.2471 0.001557 0.000779 xt 0.982878385352796 0.057437 17.1122 0 0 M1 53.0505660825984 54.201379 0.9788 0.329903 0.164951 M2 -0.269148200396778 54.063772 -0.005 0.996037 0.498019 M3 11.6519447450388 53.698271 0.217 0.82863 0.414315 M4 65.945969813359 53.631333 1.2296 0.221538 0.110769 M5 -11.0060367652886 53.445423 -0.2059 0.837237 0.418618 M6 7.85788440982509 53.938598 0.1457 0.884446 0.442223 M7 30.8704282258714 53.811682 0.5737 0.567391 0.283696 M8 -12.3135781387198 53.529792 -0.23 0.818506 0.409253 M9 44.8369121538511 53.309205 0.8411 0.402183 0.201091 M10 68.197242675119 53.65466 1.271 0.206471 0.103235 M11 -10.0188622503012 53.32958 -0.1879 0.851337 0.425668 Multiple Linear Regression - Regression Statistics Multiple R 0.863673532333926 R-squared 0.745931970454162 Adjusted R-squared 0.717438359663974 F-TEST (value) 26.1789204585837 F-TEST (DF numerator) 12 F-TEST (DF denominator) 107 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 119.105356593924 Sum Squared Residuals 1517911.19872213 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 384 476.338571043963 -92.3385710439632 2 367.6 440.612379858785 -73.0123798587849 3 457.1 495.386970405603 -38.2869704056027 4 429.4 530.416579121008 -101.016579121008 5 442.2 484.228666003903 -42.0286660039031 6 507.5 511.15218993891 -3.6521899389097 7 348.5 406.685407174698 -58.1854071746983 8 393.2 433.580629685761 -40.3806296857615 9 426.8 495.252360550955 -68.4523605509554 10 403 481.361600267352 -78.3616002673522 11 454.8 430.174650939134 24.6253490608661 12 413 427.612669856919 -14.6126698569194 13 388.9 486.069067058958 -97.1690670589582 14 406.5 610.060613493607 -203.560613493607 15 447.4 735.209296431685 -287.809296431685 16 474.4 576.415287555519 -102.015287555519 17 428.5 606.10558578765 -177.605585787650 18 472.8 594.795140532433 -121.995140532433 19 411 575.347338101238 -164.347338101238 20 463.9 533.834224991747 -69.9342249917467 21 497.3 673.251636138347 -175.951636138347 22 474 631.348841872189 -157.348841872189 23 518.1 644.93357813872 -126.83357813872 24 566 531.011475996033 34.9885240039665 25 509.4 524.696187603323 -15.2961876033231 26 445.1 480.812105819715 -35.7121058197146 27 466.6 490.276002801768 -23.6760028017682 28 600.5 632.537643359164 -32.0376433591637 29 538.7 523.052362225339 15.6476377746615 30 548 515.476854834462 32.5231451655380 31 591.9 577.116519194873 14.7834808051268 32 547.3 516.633853248073 30.6661467519272 33 610.2 624.697443901919 -14.4974439019185 34 621.6 641.963928433999 -20.3639284339991 35 582.4 573.380031685036 9.01996831496368 36 635.8 654.36271335781 -18.5627133578095 37 663.9 686.576257670929 -22.6762576709286 38 624.2 614.188702712089 10.0112972879109 39 654.1 638.2974876359 15.8025123641007 40 723.5 767.978284860779 -44.4782848607790 41 641.2 634.510771124346 6.68922887565443 42 565.5 619.367100166253 -53.8671001662526 43 698.6 629.995376326854 68.6046236731464 44 651 639.100500063031 11.8994999369688 45 721.6 681.900965929451 39.6990340705487 46 643.5 624.86184452886 18.6381554711394 47 604 638.250005118321 -34.2500051183209 48 618.2 697.314498797727 -79.1144987977266 49 783.5 681.858441421235 101.641558578765 50 672.9 636.893193413739 36.0068065862613 51 726.7 705.13321783989 21.5667821601106 52 738.6 780.362552516224 -41.7625525162243 53 692.2 657.411837503066 34.7881624969343 54 669.5 625.067794801299 44.4322051987012 55 546.2 658.007410309408 -111.807410309408 56 715 711.047197870856 3.95280212914403 57 789.8 883.096171411169 -93.2961714111688 58 684 747.328491343819 -63.328491343819 59 639 579.080726320082 59.9192736799175 60 768.5 771.718392568933 -3.21839256893334 61 643.8 732.083526912763 -88.2835269127631 62 623 700.288849268994 -77.288849268994 63 692.8 713.88083546953 -21.0808354695295 64 936.5 852.604113839655 83.8958861603452 65 795.9 784.891164083323 11.0088359166765 66 695.7 732.201538804754 -36.5015388047536 67 648.3 854.288223864362 -205.988223864362 68 675.2 848.650171820247 -173.450171820247 69 826.5 1024.92552241758 -198.425522417577 70 742.4 926.310645316563 -183.910645316563 71 793.9 1358.50328590485 -564.60328590485 72 685.3 921.410770658164 -236.110770658164 73 756.1 694.537572592286 61.5624274077138 74 704 703.630635779194 0.36936422080643 75 860.6 764.597360153734 96.0026398462664 76 795.9 810.045479753879 -14.1454797538787 77 816.7 793.638781712963 23.0612182870367 78 777.9 717.163499508856 60.7365004911442 79 746.4 615.252200546562 131.147799453438 80 694.7 609.909012018053 84.7909879819469 81 909.2 758.565479986969 150.634520013031 82 783.6 655.134498797727 128.465501202273 83 730.4 621.934223921464 108.465776078536 84 847.7 707.634721843931 140.065278156069 85 758.7 660.038541266403 98.661458733597 86 839.2 687.216566743802 151.983433256198 87 784.8 769.511752080498 15.2882479195023 88 906.1 769.944041631485 136.155958368515 89 838.2 789.019253301805 49.1807466981948 90 729 693.672706098924 35.327293901076 91 768.1 713.245175566236 54.8548244337645 92 710.5 699.842384277834 10.657615722166 93 863 749.031559649047 113.968440350953 94 778.3 702.017797779055 76.2822022209449 95 827.7 639.429459180744 188.270540819256 96 853.1 801.597895483658 51.5021045163417 97 859.3 814.252159928257 45.0478400717431 98 779.2 713.950858825398 65.2491411746021 99 724.6 695.009570470756 29.5904295292443 100 829.2 794.41771342677 34.7822865732308 101 862.9 822.63369408087 40.2663059191292 102 601.6 668.216155918287 -66.6161559182866 103 964.9 740.667482517578 224.232517482422 104 766.3 679.595089539567 86.7049104604335 105 847.8 787.953543709018 59.846456290982 106 992.7 755.486381942247 237.213618057753 107 865.3 664.197994491635 201.102005508365 108 1054.1 886.420300139605 167.679699860395 109 972.5 963.649674501882 8.8503254981181 110 857.4 731.446094084678 125.953905915322 111 1043.3 850.697506710639 192.602493289361 112 1061 980.378303935518 80.6216960644816 113 989.4 950.407884176734 38.9921158232656 114 963.2 853.587019395824 109.612980604176 115 1181.9 1135.19486639819 46.7051336018092 116 1256.4 1201.30693648483 55.0930635151694 117 1492.7 1306.22531630555 186.474683694453 118 1360.8 1318.08596971819 42.7140302818122 119 1342.8 1208.51604430001 134.283955699987 120 1464 1506.61656129722 -42.616561297219 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0098860822815344 0.0197721645630688 0.990113917718466 17 0.00211227907396922 0.00422455814793844 0.99788772092603 18 0.000737482989050658 0.00147496597810132 0.99926251701095 19 0.00049123652548627 0.00098247305097254 0.999508763474514 20 0.000343221421122599 0.000686442842245198 0.999656778578877 21 0.000154019584361669 0.000308039168723339 0.999845980415638 22 6.83904242630176e-05 0.000136780848526035 0.999931609575737 23 1.89754909607471e-05 3.79509819214942e-05 0.99998102450904 24 0.000167366770440008 0.000334733540880016 0.99983263322956 25 0.000475434028639092 0.000950868057278185 0.999524565971361 26 0.000376972553655711 0.000753945107311421 0.999623027446344 27 0.000205714982051149 0.000411429964102297 0.999794285017949 28 0.000564666484900926 0.00112933296980185 0.999435333515099 29 0.000777601424771632 0.00155520284954326 0.999222398575228 30 0.000523865105022342 0.00104773021004468 0.999476134894978 31 0.00281462249363718 0.00562924498727436 0.997185377506363 32 0.00277099959469696 0.00554199918939392 0.997229000405303 33 0.00378755538086966 0.00757511076173932 0.99621244461913 34 0.00573274088172983 0.0114654817634597 0.99426725911827 35 0.0042891077820156 0.0085782155640312 0.995710892217984 36 0.00291400848530788 0.00582801697061577 0.997085991514692 37 0.00376055267165271 0.00752110534330543 0.996239447328347 38 0.00575745143559892 0.0115149028711978 0.9942425485644 39 0.00819124510378489 0.0163824902075698 0.991808754896215 40 0.00694063560977714 0.0138812712195543 0.993059364390223 41 0.00597598545748317 0.0119519709149663 0.994024014542517 42 0.00386454708514244 0.00772909417028488 0.996135452914858 43 0.00545925502974195 0.0109185100594839 0.994540744970258 44 0.00380911480998602 0.00761822961997204 0.996190885190014 45 0.00422817451301952 0.00845634902603905 0.99577182548698 46 0.00380219302826786 0.00760438605653571 0.996197806971732 47 0.0024985931843985 0.004997186368797 0.997501406815602 48 0.00197664023615277 0.00395328047230554 0.998023359763847 49 0.0031508630015224 0.0063017260030448 0.996849136998478 50 0.00293385572762185 0.00586771145524369 0.997066144272378 51 0.00259277913863388 0.00518555827726775 0.997407220861366 52 0.00183992436574145 0.0036798487314829 0.998160075634259 53 0.00138575413822938 0.00277150827645876 0.99861424586177 54 0.00100427916375323 0.00200855832750645 0.998995720836247 55 0.00103643902055473 0.00207287804110945 0.998963560979445 56 0.000627925728889727 0.00125585145777945 0.99937207427111 57 0.000510048837177101 0.00102009767435420 0.999489951162823 58 0.000382477423432174 0.000764954846864347 0.999617522576568 59 0.000291955252886069 0.000583910505772139 0.999708044747114 60 0.000176832261105487 0.000353664522210975 0.999823167738894 61 0.00014927029289483 0.00029854058578966 0.999850729707105 62 0.000117781509677019 0.000235563019354038 0.999882218490323 63 8.34090482877503e-05 0.000166818096575501 0.999916590951712 64 9.98152092942444e-05 0.000199630418588489 0.999900184790706 65 5.88863083112e-05 0.0001177726166224 0.999941113691689 66 3.45783451538429e-05 6.91566903076857e-05 0.999965421654846 67 0.000159621445188868 0.000319242890377736 0.999840378554811 68 0.000346469106507081 0.000692938213014162 0.999653530893493 69 0.000981588723303047 0.00196317744660609 0.999018411276697 70 0.00257745992033896 0.00515491984067792 0.99742254007966 71 0.812135472941199 0.375729054117602 0.187864527058801 72 0.98615078845511 0.0276984230897796 0.0138492115448898 73 0.983455819095542 0.0330883618089158 0.0165441809044579 74 0.98711502377197 0.0257699524560583 0.0128849762280291 75 0.987871308089168 0.0242573838216642 0.0121286919108321 76 0.988572475092564 0.0228550498148723 0.0114275249074362 77 0.9849126608295 0.0301746783410004 0.0150873391705002 78 0.98123012469851 0.0375397506029803 0.0187698753014901 79 0.981413144893563 0.0371737102128746 0.0185868551064373 80 0.975821855428242 0.0483562891435153 0.0241781445717577 81 0.978254485387048 0.0434910292259039 0.0217455146129520 82 0.976190706655359 0.047618586689283 0.0238092933446415 83 0.978464460240908 0.043071079518184 0.021535539759092 84 0.977601085786282 0.0447978284274351 0.0223989142137175 85 0.972291015144632 0.0554179697107368 0.0277089848553684 86 0.971595534459586 0.0568089310808274 0.0284044655404137 87 0.968755298087912 0.0624894038241762 0.0312447019120881 88 0.96606651304195 0.0678669739161024 0.0339334869580512 89 0.950713277257794 0.0985734454844128 0.0492867227422064 90 0.927671718600997 0.144656562798007 0.0723282813990033 91 0.922286251586765 0.155427496826469 0.0777137484132347 92 0.904496314235518 0.191007371528965 0.0955036857644824 93 0.877914899949807 0.244170200100386 0.122085100050193 94 0.868315138225212 0.263369723549576 0.131684861774788 95 0.84110037427498 0.317799251450041 0.158899625725021 96 0.796535896614686 0.406928206770629 0.203464103385314 97 0.725329036522073 0.549341926955854 0.274670963477927 98 0.657000770636565 0.68599845872687 0.342999229363435 99 0.70675659864255 0.5864868027149 0.29324340135745 100 0.628375761336833 0.743248477326334 0.371624238663167 101 0.513175464543044 0.973649070913913 0.486824535456956 102 0.622417625967872 0.755164748064256 0.377582374032128 103 0.59195735239169 0.816085295216621 0.408042647608310 104 0.442395365607659 0.884790731215318 0.557604634392341 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 48 0.539325842696629 NOK 5% type I error level 68 0.764044943820225 NOK 10% type I error level 73 0.820224719101124 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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