Multiple Linear Regression Minitutorial

*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: Sat, 20 Nov 2010 08:26:22 +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/Nov/20/t1290241524mymbobqpolr4klp.htm/, Retrieved Sat, 20 Nov 2010 09:25:35 +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/Nov/20/t1290241524mymbobqpolr4klp.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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44164 -9 -7,7 544686 2,2 40399 -13 -4,9 537034 2,2 36763 -8 -2,4 551531 2,2 37903 -13 -3,6 563250 1,6 35532 -15 -7 574761 1,6 35533 -15 -7 580112 1,6 32110 -15 -7,9 575093 -0,1 33374 -10 -8,8 557560 -0,1 35462 -12 -14,2 564478 -0,1 33508 -11 -17,8 580523 -2,7 36080 -11 -18,2 596594 -2,7 34560 -17 -22,8 586570 -2,7 38737 -18 -23,6 536214 -4,1 38144 -19 -27,6 523597 -4,1 37594 -22 -29,4 536535 -4,1 36424 -24 -31,8 536322 -3,7 36843 -24 -31,4 532638 -3,7 37246 -20 -27,6 528222 -3,7 38661 -25 -28,8 516141 -1,3 40454 -22 -21,9 501866 -1,3 44928 -17 -13,9 506174 -1,3 48441 -9 -8 517945 1,1 48140 -11 -2,8 533590 1,1 45998 -13 -3,3 528379 1,1 47369 -11 -1,3 477580 1,9 49554 -9 0,5 469357 1,9 47510 -7 -1,9 490243 1,9 44873 -3 2 492622 1,6 45344 -3 1,7 507561 1,6 42413 -6 1,9 516922 1,6 36912 -4 0,1 514258 1,8 43452 -8 2,4 509846 1,8 42142 -1 2,3 527070 1,8 44382 -2 4,7 541657 2,7 43636 -2 5 564591 2,7 44167 -1 7,2 555362 2,7 44423 1 8,5 498662 3,3 42868 2 6,8 511038 3,3 43908 2 5, 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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Vacatures[t] = + 69102.1319508772 -926.024591786786Consumentenvertrouwen[t] + 1529.41439826299producentenvertrouwen[t] -0.0510966580069667nietwerkendewerkzoekende[t] -4442.616338432economischegroei[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) 69102.1319508772 8293.311645 8.3323 0 0 Consumentenvertrouwen -926.024591786786 153.875303 -6.018 0 0 producentenvertrouwen 1529.41439826299 152.294807 10.0425 0 0 nietwerkendewerkzoekende -0.0510966580069667 0.015278 -3.3444 0.001173 0.000587 economischegroei -4442.616338432 711.826041 -6.2412 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.72263598843952 R-squared 0.522202771787963 Adjusted R-squared 0.502499793304993 F-TEST (value) 26.5037477576959 F-TEST (DF numerator) 4 F-TEST (DF denominator) 97 p-value 7.32747196252603e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5990.2985007334 Sum Squared Residuals 3480716584.40522 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 44164 28054.4722026001 16109.5277973999 2 40399 36431.9225119531 3967.07748804693 3 36763 34884.5872975496 1878.41270245041 4 37903 39746.1810464435 -1843.18104644348 5 35532 35810.0476456047 -278.047645604689 6 35533 35536.6294286094 -3.62942860941348 7 32110 41969.0583720441 -9859.05837204408 8 33374 36858.3401595096 -3484.3401595096 9 35462 30098.0649123708 5363.93508762917 10 33508 34397.1050890387 -889.105089038684 11 36080 32964.1649389035 3115.83506109648 12 34560 31997.1991574763 2562.80084252368 13 38737 40492.3784150563 -1755.37841505632 14 38144 35945.4319478650 2198.56805213496 15 37594 35309.4712450579 2284.52875494212 16 36424 31724.7629255830 4699.23707441704 17 36843 32524.7687729858 4318.23122701417 18 37246 34858.0879609968 2387.91203900319 19 38661 27607.9331551605 11053.0668448395 20 40454 36112.2235208643 4341.77647913574 21 44928 43497.2913453402 1430.70865465976 22 48441 33848.9015871608 14592.0984128392 23 48140 42854.4984271829 5285.50157281706 24 45998 44208.1050964993 1789.89490350068 25 47369 44456.450768802 2912.54923119797 26 49554 45777.5153208931 3776.48467910687 27 47510 39187.6667823549 8322.33321764513 28 44873 42659.5105205644 2213.48947943559 29 45344 41437.3532271194 3906.64677288056 30 42413 44042.9940665292 -1629.99406652918 31 36912 38685.5971953264 -1773.59719532638 32 43452 46132.7871336051 -2680.78713360515 33 42142 38617.5847137593 3524.41528624066 34 44382 38470.5022064409 5911.49779355911 35 43636 37757.475771188 5878.52422881199 36 44167 40667.7339123261 3499.2660876739 37 44423 41035.5341524302 3387.46584756976 38 42868 36877.1328441021 5990.86715589786 39 43908 34587.3490780375 9320.65092196252 40 42013 33415.3808130303 8597.61918696973 41 38846 32367.7957863283 6478.20421367171 42 35087 35609.1286624861 -522.128662486090 43 33026 45260.6000237158 -12234.6000237158 44 34646 34658.3949197161 -12.3949197161296 45 37135 34449.5194386785 2685.48056132152 46 37985 36139.5219999273 1845.47800007272 47 43121 37367.8237925552 5753.17620744479 48 43722 39522.0664097503 4199.93359024971 49 43630 40651.7911994433 2978.20880055668 50 42234 43140.8911898672 -906.891189867241 51 39351 40909.8909056911 -1558.89090569111 52 39327 36714.2054606881 2612.79453931186 53 35704 31728.8598795329 3975.14012046708 54 30466 28185.3137994141 2280.68620058590 55 28155 33308.210752132 -5153.21075213205 56 29257 35724.5910558006 -6467.5910558006 57 29998 32415.1736204804 -2417.17362048039 58 32529 36310.3779001089 -3781.37790010886 59 34787 26608.2483587155 8178.7516412845 60 33855 27033.0109776433 6821.98902235673 61 34556 29857.1326843072 4698.86731569281 62 31348 29172.7494315626 2175.25056843736 63 30805 25010.5681811399 5794.43181886011 64 28353 26227.3519730299 2125.64802697011 65 24514 27818.045649982 -3304.04564998198 66 21106 33273.1357084174 -12167.1357084174 67 21346 25566.3333811368 -4220.33338113682 68 23335 29464.0067284783 -6129.00672847826 69 24379 30567.2041319656 -6188.20413196562 70 26290 25493.5826423893 796.417357610708 71 30084 24364.5799410918 5719.42005890821 72 29429 31073.6552675832 -1644.65526758320 73 30632 27431.2367494190 3200.76325058096 74 27349 33908.7958069672 -6559.79580696718 75 27264 29714.0503890574 -2450.05038905739 76 27474 27656.8709612175 -182.870961217473 77 24482 24146.1930736927 335.806926307265 78 21453 24546.6061149014 -3093.60611490137 79 18788 34832.5442287871 -16044.5442287871 80 19282 33989.3762323806 -14707.3762323806 81 19713 37268.3072400654 -17555.3072400654 82 21917 27600.9918421603 -5683.99184216033 83 23812 28175.0248733515 -4363.02487335148 84 23785 25816.8347956602 -2031.83479566018 85 24696 23333.4151692862 1362.58483071378 86 24562 27155.0972995167 -2593.09729951670 87 23580 25831.6312044993 -2251.63120449928 88 24939 32483.8116230223 -7544.81162302226 89 23899 33456.8448652567 -9557.84486525669 90 21454 28877.9260009730 -7423.92600097303 91 19761 26324.806246967 -6563.80624696699 92 19815 23997.4782757931 -4182.47827579312 93 20780 21217.4313598365 -437.431359836535 94 23462 24314.1406504574 -852.140650457438 95 25005 24200.859359656 804.140640344007 96 24725 25222.2748243713 -497.274824371342 97 26198 33716.9150344123 -7518.91503441235 98 27543 33142.8625078004 -5599.86250780044 99 26471 31594.1990552076 -5123.19905520757 100 26558 29381.9271607852 -2823.92716078519 101 25317 24742.1326813945 574.867318605512 102 22896 26367.4568509797 -3471.4568509797 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0570565678721079 0.114113135744216 0.942943432127892 9 0.0188438379024477 0.0376876758048954 0.981156162097552 10 0.0180831755546810 0.0361663511093620 0.98191682444532 11 0.0207151950449877 0.0414303900899755 0.979284804955012 12 0.00786569748308558 0.0157313949661712 0.992134302516914 13 0.00455164814413508 0.00910329628827016 0.995448351855865 14 0.00230067668721353 0.00460135337442706 0.997699323312786 15 0.000877139308932088 0.00175427861786418 0.999122860691068 16 0.000537501443384009 0.00107500288676802 0.999462498556616 17 0.000231273443964451 0.000462546887928902 0.999768726556036 18 9.00228748117058e-05 0.000180045749623412 0.999909977125188 19 7.20431568003076e-05 0.000144086313600615 0.9999279568432 20 3.40349197805348e-05 6.80698395610695e-05 0.99996596508022 21 0.000106069072966311 0.000212138145932623 0.999893930927034 22 0.000522674768407104 0.00104534953681421 0.999477325231593 23 0.00273605856504501 0.00547211713009002 0.997263941434955 24 0.00249485661195985 0.00498971322391969 0.99750514338804 25 0.00237878282276263 0.00475756564552527 0.997621217177237 26 0.00177943600584732 0.00355887201169464 0.998220563994153 27 0.00175520417723348 0.00351040835446696 0.998244795822766 28 0.00205292386103170 0.00410584772206340 0.997947076138968 29 0.00146852454861534 0.00293704909723068 0.998531475451385 30 0.00103429600386131 0.00206859200772262 0.998965703996139 31 0.00456502926595685 0.0091300585319137 0.995434970734043 32 0.00301642573312122 0.00603285146624245 0.996983574266879 33 0.00208959087698784 0.00417918175397568 0.997910409123012 34 0.00196949398680734 0.00393898797361467 0.998030506013193 35 0.0023591342493253 0.0047182684986506 0.997640865750675 36 0.00203468335452791 0.00406936670905582 0.997965316645472 37 0.00181184634298936 0.00362369268597872 0.99818815365701 38 0.00169755954360755 0.0033951190872151 0.998302440456392 39 0.00176169873363375 0.00352339746726750 0.998238301266366 40 0.00216095931013706 0.00432191862027411 0.997839040689863 41 0.00212197984380341 0.00424395968760682 0.997878020156197 42 0.00262466243252787 0.00524932486505575 0.997375337567472 43 0.0065613537251783 0.0131227074503566 0.993438646274822 44 0.00608482397349653 0.0121696479469931 0.993915176026503 45 0.00405046558133179 0.00810093116266357 0.995949534418668 46 0.00461224928237222 0.00922449856474443 0.995387750717628 47 0.0193144457036964 0.0386288914073929 0.980685554296304 48 0.0405770408065051 0.0811540816130102 0.959422959193495 49 0.0578487670368021 0.115697534073604 0.942151232963198 50 0.0744282673897202 0.148856534779440 0.92557173261028 51 0.0890384521931302 0.178076904386260 0.91096154780687 52 0.144014297070578 0.288028594141157 0.855985702929422 53 0.178672558403227 0.357345116806453 0.821327441596773 54 0.201704227670532 0.403408455341064 0.798295772329468 55 0.260250022995794 0.520500045991589 0.739749977004206 56 0.291603912222103 0.583207824444206 0.708396087777897 57 0.273418958230598 0.546837916461197 0.726581041769402 58 0.281470535991955 0.56294107198391 0.718529464008045 59 0.419832293824083 0.839664587648167 0.580167706175917 60 0.589854755780364 0.820290488439272 0.410145244219636 61 0.813672844711018 0.372654310577963 0.186327155288982 62 0.913535825466542 0.172928349066916 0.086464174533458 63 0.958632082053807 0.082735835892385 0.0413679179461925 64 0.972239662820692 0.0555206743586167 0.0277603371793084 65 0.979584424253125 0.0408311514937507 0.0204155757468754 66 0.993936040397862 0.0121279192042762 0.00606395960213812 67 0.9966326692204 0.00673466155919936 0.00336733077959968 68 0.997061157254128 0.00587768549174385 0.00293884274587192 69 0.99640126290764 0.00719747418472039 0.00359873709236019 70 0.994192985606413 0.0116140287871744 0.00580701439358718 71 0.995059205525296 0.00988158894940709 0.00494079447470354 72 0.995742107004366 0.0085157859912683 0.00425789299563415 73 0.998354994013078 0.00329001197384455 0.00164500598692227 74 0.999035574095375 0.00192885180925008 0.00096442590462504 75 0.999574182090695 0.000851635818609253 0.000425817909304626 76 0.999947816619123 0.00010436676175478 5.218338087739e-05 77 0.999978018547754 4.39629044917057e-05 2.19814522458528e-05 78 0.999974596559061 5.08068818775768e-05 2.54034409387884e-05 79 0.999992318492407 1.53630151864082e-05 7.68150759320408e-06 80 0.99999802075253 3.95849494130434e-06 1.97924747065217e-06 81 0.999999371886501 1.25622699789141e-06 6.28113498945704e-07 82 0.999999362528653 1.27494269381119e-06 6.37471346905596e-07 83 0.999998157327852 3.68534429537323e-06 1.84267214768661e-06 84 0.999994090187792 1.18196244160114e-05 5.9098122080057e-06 85 0.999989082393869 2.18352122624038e-05 1.09176061312019e-05 86 0.999967431489525 6.51370209499556e-05 3.25685104749778e-05 87 0.999905921072994 0.000188157854012126 9.4078927006063e-05 88 0.999996458830103 7.08233979372583e-06 3.54116989686291e-06 89 0.999996144497174 7.71100565107532e-06 3.85550282553766e-06 90 0.999981994005635 3.60119887302146e-05 1.80059943651073e-05 91 0.999901863991593 0.00019627201681487 9.8136008407435e-05 92 0.999626352318477 0.00074729536304594 0.00037364768152297 93 0.998937139191606 0.00212572161678796 0.00106286080839398 94 0.993304883615423 0.0133902327691534 0.0066951163845767 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 58 0.666666666666667 NOK 5% type I error level 69 0.793103448275862 NOK 10% type I error level 72 0.827586206896552 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/10ekdz1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/10ekdz1290241573.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/1iaxq1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/1iaxq1290241573.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/2iaxq1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/2iaxq1290241573.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/3iaxq1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/3iaxq1290241573.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/4bkxt1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/4bkxt1290241573.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/5bkxt1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/5bkxt1290241573.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/6bkxt1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/6bkxt1290241573.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/73bww1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/73bww1290241573.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/8ekdz1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/8ekdz1290241573.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/9ekdz1290241573.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t1290241524mymbobqpolr4klp/9ekdz1290241573.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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