*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: Tue, 23 Nov 2010 15:18:29 +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/23/t129052569867ukczwwrc4v27l.htm/, Retrieved Tue, 23 Nov 2010 16:22:04 +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/23/t129052569867ukczwwrc4v27l.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:

» Textbox « » Textfile « » CSV «

9 26 24 14 11 12 24 9 23 25 11 7 8 25 9 25 17 6 17 8 30 9 23 18 12 10 8 19 9 19 18 8 12 9 22 9 29 16 10 12 7 22 10 25 20 10 11 4 25 10 21 16 11 11 11 23 10 22 18 16 12 7 17 10 25 17 11 13 7 21 10 24 23 13 14 12 19 10 18 30 12 16 10 19 10 22 23 8 11 10 15 10 15 18 12 10 8 16 10 22 15 11 11 8 23 10 28 12 4 15 4 27 10 20 21 9 9 9 22 10 12 15 8 11 8 14 10 24 20 8 17 7 22 10 20 31 14 17 11 23 10 21 27 15 11 9 23 10 20 34 16 18 11 21 10 21 21 9 14 13 19 10 23 31 14 10 8 18 10 28 19 11 11 8 20 10 24 16 8 15 9 23 10 24 20 9 15 6 25 10 24 21 9 13 9 19 10 23 22 9 16 9 24 10 23 17 9 13 6 22 10 29 24 10 9 6 25 10 24 25 16 18 16 26 10 18 26 11 18 5 29 10 25 25 8 12 7 32 10 21 17 9 17 9 25 10 26 32 16 9 6 29 10 22 33 11 9 6 28 10 22 13 16 12 5 17 10 22 32 12 18 12 28 10 23 25 12 12 7 29 10 30 29 14 18 10 26 10 23 22 9 14 9 25 10 17 18 10 15 8 14 10 23 17 9 16 5 25 10 23 20 10 10 8 26 10 25 15 12 11 8 20 10 24 20 14 14 10 18 10 24 33 14 9 6 32 10 23 29 10 12 8 25 10 21 23 14 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 12 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation YT[t] = + 28.2103187556997 -1.21064258019503T1[t] -0.0662911074151968X1[t] + 0.220046465031066X2[t] -0.137980253016112X3[t] -0.267847267331188X4[t] + 0.415218299040598X5[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) 28.2103187556997 14.945205 1.8876 0.060988 0.030494 T1 -1.21064258019503 1.484765 -0.8154 0.416133 0.208066 X1 -0.0662911074151968 0.06322 -1.0486 0.296039 0.148019 X2 0.220046465031066 0.112769 1.9513 0.052859 0.02643 X3 -0.137980253016112 0.105245 -1.311 0.191823 0.095912 X4 -0.267847267331188 0.131479 -2.0372 0.043366 0.021683 X5 0.415218299040598 0.076262 5.4447 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.475140658091823 R-squared 0.225758644971930 Adjusted R-squared 0.195196486220822 F-TEST (value) 7.3868684084283 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 5.99882120422279e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.50319920019948 Sum Squared Residuals 1865.40550471430 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 24.0374886522374 1.96251134776263 2 23 25.3495865301589 -2.34958653015892 3 25 25.4759720293670 -0.47597202936704 4 23 23.1284201938044 -0.128420193804447 5 19 22.9500814574386 -3.95008145743856 6 29 24.0584511369935 4.94154886300653 7 25 24.7698210792691 0.23017892073088 8 21 22.5496645045615 -1.54966450456147 9 22 21.9594136369515 0.0405863630485405 10 25 22.4483653623576 2.55163463764240 11 24 20.1830584601753 3.81694153982470 12 18 19.758708271868 -1.75870827186801 13 22 18.3715882325683 3.6284117674317 14 15 20.6721227164876 -5.67212271648763 15 22 23.4194974139702 -1.41949741397023 16 28 24.2583867344211 3.74161326557895 17 20 22.1745527790774 -2.17455277907735 18 12 19.0223933275116 -7.02239332751165 19 24 21.4526499319950 2.54735006800504 20 20 21.3875557703300 -1.38755577033004 21 21 23.2363427177809 -2.23634271778094 22 20 20.6603585270493 -0.660358527049277 23 21 19.1676075475502 1.83239245244975 24 23 21.0808678482334 1.91913215176660 25 28 21.9086780871876 6.09132191281235 26 24 21.8732986320662 2.12670136793380 27 24 23.4621590675112 0.537840932488764 28 24 20.3769768698911 3.62302313010889 29 23 21.9728364986306 1.02716350136943 30 23 22.6913379986673 0.308662001332743 31 29 24.2449226209782 4.75507737902181 32 24 21.9938336523331 2.00616634766691 33 18 25.0192850575274 -7.01928505752743 34 25 25.9632786504055 -0.963278650405518 35 21 22.5815300817310 -1.58153008173104 36 26 26.6957457480054 -0.695745748005403 37 22 25.1140040163943 -3.11400401639428 38 22 22.8265637086898 -0.82656370868982 39 22 22.5514357077084 -0.551435707708401 40 23 25.597809613408 -2.59780961340799 41 30 22.8956598965973 7.1043401034027 42 23 22.6640153037034 0.335984696296611 43 17 18.7116919232637 -1.71169192326374 44 23 23.7908994040719 -0.790899404071903 45 23 24.2516305620011 -1.25163056200108 46 25 22.3938889818795 2.6061110181205 47 24 20.7224544830737 3.27754551692626 48 24 27.4350166076499 -3.43501660764987 49 23 22.9638317901915 0.0361682098085093 50 21 23.8197102970576 -2.81971029705757 51 24 25.6897981449798 -1.68979814497982 52 24 21.8121143105652 2.18788568943480 53 28 21.4843602617253 6.51563973827473 54 16 21.0239734605562 -5.02397346055621 55 20 19.7961912185799 0.203808781420062 56 29 23.4076262084897 5.59237379151032 57 27 23.8430878411385 3.15691215886153 58 22 23.1637478787013 -1.16374787870127 59 28 23.9462766584402 4.05372334155984 60 16 20.3530491841121 -4.35304918411208 61 25 22.856213047771 2.143786952229 62 24 23.4766566321187 0.523343367881268 63 28 23.6435042566640 4.35649574333604 64 24 24.2220288125445 -0.222028812544515 65 23 22.6735750918463 0.326424908153681 66 30 26.8926706105080 3.10732938949196 67 24 21.2834820011933 2.71651799880672 68 21 24.0991527443775 -3.09915274437747 69 25 23.2701385800396 1.72986141996036 70 25 23.9184784749754 1.08152152502456 71 22 20.7817857396728 1.21821426032725 72 23 22.4276112295295 0.572388770470475 73 26 22.8261427894469 3.1738572105531 74 23 21.6022041971754 1.39779580282461 75 25 23.0644124230201 1.93558757697994 76 21 21.2854869394797 -0.285486939479683 77 25 23.6415164544428 1.35848354555722 78 24 22.14479090909 1.85520909091001 79 29 23.5123597023566 5.48764029764338 80 22 23.647883644284 -1.64788364428402 81 27 23.5680895071284 3.43191049287155 82 26 19.6290819723257 6.37091802767428 83 22 21.3049635323155 0.695036467684501 84 24 22.0327432801393 1.96725671986070 85 27 23.1059173146214 3.89408268537864 86 24 21.3540418746079 2.64595812539212 87 24 24.8509010035633 -0.85090100356334 88 29 24.3555973150957 4.64440268490435 89 22 22.1416478096984 -0.141647809698437 90 21 20.5728437393499 0.427156260650136 91 24 20.4451840742043 3.55481592579566 92 24 21.7194362584081 2.28056374159187 93 23 21.9413988203372 1.05860117966277 94 20 22.3039684205901 -2.30396842059012 95 27 21.3481089215037 5.65189107849627 96 26 23.4245663221755 2.57543367782448 97 25 21.9468473960217 3.05315260397831 98 21 20.0638274017009 0.936172598299126 99 21 20.7680155733594 0.231984426640604 100 19 20.3833611957976 -1.38336119579757 101 21 21.5815065428908 -0.581506542890763 102 21 21.2761526393298 -0.276152639329836 103 16 19.7627574909190 -3.76275749091905 104 22 20.6424325518234 1.35756744817658 105 29 21.7679585179577 7.23204148204232 106 15 21.7289577426614 -6.72895774266144 107 17 20.6913473995302 -3.69134739953016 108 15 19.9102562803143 -4.91025628031433 109 21 21.6460446218128 -0.646044621812849 110 21 21.0230224835545 -0.0230224835545169 111 19 19.2848425566571 -0.284842556657119 112 24 18.0601917928712 5.93980820712883 113 20 22.2492483774651 -2.24924837746510 114 17 25.0896164950748 -8.08961649507482 115 23 24.8187204846044 -1.81872048460443 116 24 22.390211609342 1.60978839065802 117 14 22.0566557391386 -8.05665573913863 118 19 22.8529153427126 -3.85291534271264 119 24 22.1817391564752 1.81826084352477 120 13 20.4211887148614 -7.42118871486136 121 22 25.3603868886685 -3.36038688866847 122 16 21.1243457414569 -5.12434574145691 123 19 23.2285530941963 -4.22855309419634 124 25 22.7392989214982 2.26070107850183 125 25 24.1556659998062 0.844334000193828 126 23 21.4297237607164 1.57027623928362 127 24 23.5535090421773 0.446490957822704 128 26 23.5032601759348 2.49673982406516 129 26 21.4883530022328 4.51164699776715 130 25 24.1320517727117 0.86794822728832 131 18 22.2911756530787 -4.29117565307866 132 21 19.8686050301926 1.13139496980740 133 26 23.6503640710713 2.34963592892873 134 23 21.9643249916158 1.03567500838418 135 23 19.7571959581477 3.24280404185232 136 22 22.5985262477796 -0.598526247779605 137 20 22.3975581072706 -2.39755810727064 138 13 22.0664261853111 -9.0664261853111 139 24 21.3905116856181 2.60948831438186 140 15 21.5031177034133 -6.50311770341333 141 14 23.0933834365365 -9.09338343653651 142 22 24.0488715152901 -2.04887151529010 143 10 17.6446697470617 -7.64466974706174 144 24 24.4269628455801 -0.42696284558013 145 22 21.8304203794509 0.169579620549057 146 24 25.7882219661376 -1.78822196613757 147 19 21.6534545779183 -2.65345457791828 148 20 22.0853596160821 -2.08535961608210 149 13 17.1094479686178 -4.10944796861783 150 20 20.1000300761381 -0.100030076138146 151 22 23.1856636465606 -1.18566364656058 152 24 23.3832623766880 0.616737623311959 153 29 23.2741564748344 5.72584352516564 154 12 20.9762473114534 -8.97624731145337 155 20 20.9222015621339 -0.922201562133892 156 21 21.4456831015455 -0.445683101545463 157 24 23.6330707117065 0.366929288293533 158 22 21.8927187463586 0.107281253641439 159 20 17.7211420634604 2.27885793653958 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.527028364314465 0.94594327137107 0.472971635685535 11 0.562072176923444 0.875855646153113 0.437927823076556 12 0.488820121855344 0.977640243710688 0.511179878144656 13 0.54034099712171 0.91931800575658 0.45965900287829 14 0.741634141692736 0.516731716614527 0.258365858307264 15 0.654767779922359 0.690464440155282 0.345232220077641 16 0.623840203621298 0.752319592757404 0.376159796378702 17 0.538160411878577 0.923679176242846 0.461839588121423 18 0.67610282272044 0.647794354559119 0.323897177279559 19 0.601320656317024 0.797358687365952 0.398679343682976 20 0.588507053429423 0.822985893141155 0.411492946570577 21 0.524600811963486 0.950798376073029 0.475399188036514 22 0.455193000843373 0.910386001686746 0.544806999156627 23 0.404513233049431 0.809026466098862 0.595486766950569 24 0.408928632535248 0.817857265070495 0.591071367464752 25 0.571312477989045 0.85737504402191 0.428687522010955 26 0.51003663759639 0.97992672480722 0.48996336240361 27 0.443017030640340 0.886034061280681 0.55698296935966 28 0.437463608820323 0.874927217640646 0.562536391179677 29 0.373317525584628 0.746635051169255 0.626682474415373 30 0.312925469300045 0.625850938600089 0.687074530699955 31 0.346705302599348 0.693410605198696 0.653294697400652 32 0.295684869186510 0.591369738373021 0.70431513081349 33 0.521856236679298 0.956287526641405 0.478143763320702 34 0.470720695493072 0.941441390986144 0.529279304506928 35 0.432758547622968 0.865517095245937 0.567241452377032 36 0.375438918825547 0.750877837651095 0.624561081174453 37 0.348812634024332 0.697625268048664 0.651187365975668 38 0.297200139553495 0.594400279106991 0.702799860446505 39 0.249829277049070 0.499658554098139 0.75017072295093 40 0.222496241741993 0.444992483483986 0.777503758258007 41 0.375109750067578 0.750219500135156 0.624890249932422 42 0.323329351373810 0.646658702747619 0.67667064862619 43 0.291309744409828 0.582619488819655 0.708690255590172 44 0.247741142935441 0.495482285870882 0.752258857064559 45 0.211344650754324 0.422689301508648 0.788655349245676 46 0.191943416447860 0.383886832895720 0.80805658355214 47 0.179511293187929 0.359022586375858 0.820488706812071 48 0.164434998681521 0.328869997363043 0.835565001318479 49 0.134347119861454 0.268694239722909 0.865652880138546 50 0.124730083768584 0.249460167537169 0.875269916231415 51 0.102953973858230 0.205907947716460 0.89704602614177 52 0.0878355009662445 0.175671001932489 0.912164499033756 53 0.147397588452460 0.294795176904920 0.85260241154754 54 0.17678910553817 0.35357821107634 0.82321089446183 55 0.165267186538772 0.330534373077544 0.834732813461228 56 0.222686975466120 0.445373950932241 0.77731302453388 57 0.215131908819760 0.430263817639519 0.78486809118024 58 0.184153643078553 0.368307286157106 0.815846356921447 59 0.197351138089914 0.394702276179828 0.802648861910086 60 0.225091998997229 0.450183997994458 0.774908001002771 61 0.198880236978436 0.397760473956871 0.801119763021564 62 0.167118258423565 0.334236516847130 0.832881741576435 63 0.182344870750504 0.364689741501009 0.817655129249496 64 0.153254812636126 0.306509625272252 0.846745187363874 65 0.126438968516460 0.252877937032921 0.87356103148354 66 0.122883295308345 0.24576659061669 0.877116704691655 67 0.112248217370943 0.224496434741885 0.887751782629058 68 0.111344923410117 0.222689846820234 0.888655076589883 69 0.0947565847496519 0.189513169499304 0.905243415250348 70 0.0773605143249671 0.154721028649934 0.922639485675033 71 0.062868133666416 0.125736267332832 0.937131866333584 72 0.0496562158630926 0.0993124317261851 0.950343784136907 73 0.0466154231049725 0.093230846209945 0.953384576895028 74 0.037341364225939 0.074682728451878 0.96265863577406 75 0.0310314374719754 0.0620628749439508 0.968968562528025 76 0.0238009755904018 0.0476019511808035 0.976199024409598 77 0.0186859014162132 0.0373718028324264 0.981314098583787 78 0.0149571406805746 0.0299142813611493 0.985042859319425 79 0.0224781081564358 0.0449562163128717 0.977521891843564 80 0.0179212062081237 0.0358424124162474 0.982078793791876 81 0.0175253641063660 0.0350507282127321 0.982474635893634 82 0.0313505859668954 0.0627011719337908 0.968649414033105 83 0.0241773878607795 0.0483547757215591 0.97582261213922 84 0.0201726522414727 0.0403453044829455 0.979827347758527 85 0.0220913036379968 0.0441826072759936 0.977908696362003 86 0.0195779068105891 0.0391558136211783 0.98042209318941 87 0.0148833956440960 0.0297667912881921 0.985116604355904 88 0.0194348449283248 0.0388696898566496 0.980565155071675 89 0.0152819340229259 0.0305638680458517 0.984718065977074 90 0.0114350397674320 0.0228700795348639 0.988564960232568 91 0.0114936015000235 0.022987203000047 0.988506398499976 92 0.0100487965261464 0.0200975930522928 0.989951203473854 93 0.00770634889142421 0.0154126977828484 0.992293651108576 94 0.00637095445167176 0.0127419089033435 0.993629045548328 95 0.0116764304090461 0.0233528608180922 0.988323569590954 96 0.0105750728633661 0.0211501457267323 0.989424927136634 97 0.0100579317377319 0.0201158634754638 0.989942068262268 98 0.0076964588109711 0.0153929176219422 0.992303541189029 99 0.00567885222764847 0.0113577044552969 0.994321147772351 100 0.00434752048485551 0.00869504096971102 0.995652479515144 101 0.00321226565962361 0.00642453131924722 0.996787734340376 102 0.00228563328783020 0.00457126657566040 0.99771436671217 103 0.00244396470857392 0.00488792941714784 0.997556035291426 104 0.00191465160345204 0.00382930320690408 0.998085348396548 105 0.00811412982528491 0.0162282596505698 0.991885870174715 106 0.0181671846008460 0.0363343692016919 0.981832815399154 107 0.0180295512597242 0.0360591025194485 0.981970448740276 108 0.0227211535015447 0.0454423070030894 0.977278846498455 109 0.0175296500642828 0.0350593001285656 0.982470349935717 110 0.0128035457053405 0.0256070914106810 0.98719645429466 111 0.00926976201671084 0.0185395240334217 0.99073023798329 112 0.0227330945126734 0.0454661890253467 0.977266905487327 113 0.0205964481526728 0.0411928963053457 0.979403551847327 114 0.0571932627148997 0.114386525429799 0.9428067372851 115 0.0484501837172544 0.0969003674345088 0.951549816282746 116 0.03926472906088 0.07852945812176 0.96073527093912 117 0.115712576239433 0.231425152478866 0.884287423760567 118 0.110870623556605 0.221741247113209 0.889129376443395 119 0.0982975543600397 0.196595108720079 0.90170244563996 120 0.171823904570047 0.343647809140094 0.828176095429953 121 0.163706791636379 0.327413583272758 0.83629320836362 122 0.195062023880454 0.390124047760909 0.804937976119546 123 0.188042980511619 0.376085961023238 0.811957019488381 124 0.187225642039559 0.374451284079119 0.81277435796044 125 0.169993306586364 0.339986613172728 0.830006693413636 126 0.138332383081952 0.276664766163903 0.861667616918048 127 0.108170210302971 0.216340420605943 0.891829789697029 128 0.111622507273308 0.223245014546615 0.888377492726692 129 0.160124830965551 0.320249661931103 0.839875169034449 130 0.137944002820249 0.275888005640498 0.862055997179751 131 0.120411351115570 0.240822702231139 0.87958864888443 132 0.104288622865573 0.208577245731146 0.895711377134427 133 0.0956630435677012 0.191326087135402 0.904336956432299 134 0.0780905262947188 0.156181052589438 0.921909473705281 135 0.106568501534917 0.213137003069834 0.893431498465083 136 0.0790195243729827 0.158039048745965 0.920980475627017 137 0.0576295417966279 0.115259083593256 0.942370458203372 138 0.146858066608715 0.29371613321743 0.853141933391285 139 0.208120044670052 0.416240089340104 0.791879955329948 140 0.188513100213958 0.377026200427915 0.811486899786042 141 0.406025649917164 0.812051299834327 0.593974350082836 142 0.356376040738363 0.712752081476726 0.643623959261637 143 0.666004373267961 0.667991253464077 0.333995626732039 144 0.60479794654466 0.79040410691068 0.39520205345534 145 0.49417312937125 0.9883462587425 0.50582687062875 146 0.423286503602423 0.846573007204845 0.576713496397577 147 0.433583274988949 0.867166549977897 0.566416725011051 148 0.303283812156224 0.606567624312449 0.696716187843776 149 0.211402600164403 0.422805200328805 0.788597399835597 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0357142857142857 NOK 5% type I error level 37 0.264285714285714 NOK 10% type I error level 44 0.314285714285714 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/104bsr1290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/104bsr1290525496.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/1xsdx1290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/1xsdx1290525496.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/281ui1290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/281ui1290525496.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/381ui1290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/381ui1290525496.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/481ui1290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/481ui1290525496.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/5istl1290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/5istl1290525496.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/6istl1290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/6istl1290525496.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/7t2s61290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/7t2s61290525496.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/84bsr1290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/84bsr1290525496.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/94bsr1290525496.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t129052569867ukczwwrc4v27l/94bsr1290525496.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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