*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 14:23:08 +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/t12902630713xb6mlhmbqb40oc.htm/, Retrieved Sat, 20 Nov 2010 15:24:43 +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/t12902630713xb6mlhmbqb40oc.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 «

16 24 14 11 12 24 26 19 25 11 7 8 25 23 15 17 6 17 8 30 25 14 18 12 10 8 19 23 13 18 8 12 9 22 19 19 16 10 12 7 22 29 15 20 10 11 4 25 25 14 16 11 11 11 23 21 15 18 16 12 7 17 22 16 17 11 13 7 21 25 16 23 13 14 12 19 24 16 30 12 16 10 19 18 16 23 8 11 10 15 22 17 18 12 10 8 16 15 15 15 11 11 8 23 22 15 12 4 15 4 27 28 20 21 9 9 9 22 20 18 15 8 11 8 14 12 16 20 8 17 7 22 24 16 31 14 17 11 23 20 16 27 15 11 9 23 21 19 34 16 18 11 21 20 16 21 9 14 13 19 21 17 31 14 10 8 18 23 17 19 11 11 8 20 28 16 16 8 15 9 23 24 15 20 9 15 6 25 24 16 21 9 13 9 19 24 14 22 9 16 9 24 23 15 17 9 13 6 22 23 12 24 10 9 6 25 29 14 25 16 18 16 26 24 16 26 11 18 5 29 18 14 25 8 12 7 32 25 7 17 9 17 9 25 21 10 32 16 9 6 29 26 14 33 11 9 6 28 22 16 13 16 12 5 17 22 16 32 12 18 12 28 22 16 25 12 12 7 29 23 14 29 14 18 10 26 30 20 22 9 14 9 25 23 14 18 10 15 8 14 17 14 17 9 16 5 25 23 11 20 10 10 8 26 23 14 15 12 11 8 20 25 15 20 14 14 10 18 24 16 33 14 9 6 32 24 14 29 10 12 8 25 23 16 23 1 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 13.2522145863475 + 0.0923250546673155Concern[t] -0.0427279901581466Doubts[t] -0.0293172689010877Expectations[t] -0.0197865743236952Critisism[t] -0.106730229334144Standards[t] + 0.139579173878108Organization[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) 13.2522145863475 1.504009 8.8113 0 0 Concern 0.0923250546673155 0.039774 2.3212 0.021603 0.010801 Doubts -0.0427279901581466 0.071763 -0.5954 0.552456 0.276228 Expectations -0.0293172689010877 0.066075 -0.4437 0.657893 0.328946 Critisism -0.0197865743236952 0.083118 -0.2381 0.812161 0.40608 Standards -0.106730229334144 0.052239 -2.0431 0.042768 0.021384 Organization 0.139579173878108 0.050894 2.7425 0.006829 0.003415 Multiple Linear Regression - Regression Statistics Multiple R 0.28527509482277 R-squared 0.0813818797261403 Adjusted R-squared 0.0451206381363827 F-TEST (value) 2.24432137892177 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 0.0419327428945955 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.20293550134255 Sum Squared Residuals 737.644573107455 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 16 15.377428203164 0.622571796835987 2 19 15.2688848502365 3.73111514976348 3 15 14.1962588757634 0.80374112423664 4 14 15.1323110467088 -1.13231104670877 5 13 14.3462945117006 -1.34629451170062 6 19 15.5115533094782 3.48844669052183 7 15 15.0910231365047 -0.0910231365047432 8 14 14.1956326705673 -0.195632670567322 9 15 14.9964324073879 0.00356759261211682 10 16 15.0802466389080 0.919753361092036 11 16 15.4943721308662 0.505627869133822 12 16 15.3268390712721 0.673160928727901 13 16 15.9832996065879 0.0167003934120774 14 17 14.3358683436863 2.66413165631366 15 15 14.3022465127492 0.697753487250799 16 15 14.6967986274768 0.303201372523214 17 20 14.8080726661258 5.1919273338742 18 18 13.9952108084499 4.00478919155015 19 16 15.1218272945677 0.878172705432253 20 16 15.1368417328180 0.86315826718202 21 16 15.0798694599226 0.920130540077404 22 19 15.5125041062708 3.48749589372917 23 16 15.0421098862061 0.957890113793886 24 17 16.3538110064017 0.646188993598278 25 17 15.8292124626895 1.17078753731046 26 16 14.6648582357191 1.33514176428087 27 15 14.8373297285330 0.162670271466959 28 16 15.5693109740363 0.430689025963693 29 14 14.9004539014515 -0.900453901451533 30 15 14.7996006164576 0.200399383542408 31 12 16.0377014398412 -4.03770143984122 32 14 14.6073112914882 -0.607311291488232 33 16 13.9732628832358 2.02673711676415 34 14 14.8023157929464 -0.802315792946436 35 7 14.0236227821235 -7.02362278212351 36 10 15.6742754972600 -5.67427549725997 37 14 15.5286540365397 -1.52865403653973 38 16 14.5743802826987 1.42561971730130 39 16 15.0110261256623 0.988973874337695 40 16 14.6724361725601 1.32756382743994 41 14 16.0182619796846 -2.01826197968461 42 20 14.8523582099196 5.14764179008043 43 14 14.7673567859217 -0.767356785921694 44 14 14.4112446960756 -0.411244696075594 45 11 14.6553055310207 -3.65530553102069 46 14 14.9984467322278 -0.99844673222781 47 15 15.3209723546876 -0.320972354687619 48 16 15.2527074964849 0.74729250351507 49 14 15.5343267145585 -1.53432671455850 50 16 14.4035063079841 1.59649369201594 51 14 15.6383904217565 -1.63839042175646 52 12 15.1279791945909 -3.12797919459086 53 16 15.9349482386139 0.0650517613860827 54 9 14.3886856780754 -5.38868567807539 55 14 13.9858228532050 0.0141771467949624 56 16 16.0733728526849 -0.0733728526849043 57 16 15.3396377980656 0.660362201934421 58 15 14.4599717051683 0.540028294831744 59 16 15.3368039548818 0.663196045118234 60 12 14.1034719803858 -2.10347198038577 61 16 14.8352560514755 1.16474394852448 62 16 15.0522915601785 0.947708439821472 63 14 15.2913983228153 -1.29139832281525 64 16 14.7343590472365 1.26564095276351 65 17 14.5092090437565 2.49079095624346 66 18 15.9755830952166 2.02441690478340 67 18 16.2935199349910 1.70648006500895 68 12 14.1318680827179 -2.1318680827179 69 16 14.5773890609484 1.42261093905161 70 10 14.9691488490518 -4.96914884905182 71 14 15.9413161873238 -1.94131618732378 72 18 15.1884634564070 2.81153654359298 73 18 15.7669184413230 2.23308155867696 74 16 15.2988838860584 0.70111611394156 75 17 15.5308592304150 1.46914076958496 76 16 15.2348691854691 0.765130814530894 77 16 14.6025490240880 1.39745097591204 78 13 15.0916190466583 -2.09161904665835 79 16 15.6351902273082 0.364809772691838 80 16 15.2699503756012 0.73004962439877 81 20 15.2988907038860 4.70110929611403 82 16 15.9915596990592 0.00844030094082513 83 15 15.1817552301293 -0.181755230129346 84 15 14.7715941524953 0.228405847504681 85 16 16.1847912960147 -0.184791296014749 86 14 15.32874610633 -1.32874610633000 87 16 14.9172522136361 1.08274778636389 88 16 15.2097512972237 0.790248702776306 89 15 14.7675175254820 0.232482474518029 90 12 15.2055462291260 -3.20554622912597 91 17 16.0212260606730 0.978773939326954 92 16 14.9305934008049 1.06940659919505 93 15 15.2925263780727 -0.292526378072747 94 13 14.7411258401995 -1.74112584019952 95 16 15.6287858911462 0.371214108853806 96 16 15.0476010227839 0.952398977216122 97 16 16.0902670359112 -0.090267035911169 98 16 15.2988554029631 0.701144597036892 99 14 15.1415439899500 -1.14154398994997 100 16 15.0475289728128 0.952471027187227 101 16 14.7871535421160 1.21284645788398 102 20 14.7707560965866 5.22924390341344 103 15 14.0579321112798 0.94206788872024 104 16 14.7640238816421 1.23597611835787 105 13 16.1703347361151 -3.17033473611508 106 17 14.8199999707771 2.18000002922290 107 16 14.8692399317325 1.13076006826751 108 16 14.5702869988116 1.42971300118842 109 12 14.8878353458285 -2.88783534582852 110 16 15.0832311921507 0.916768807849265 111 16 14.7780842216846 1.22191577831542 112 17 16.2177330465255 0.782266953474543 113 13 14.5977670489683 -1.59776704896826 114 12 13.1531697933760 -1.15316979337598 115 18 13.4897260171415 4.51027398285853 116 14 15.0160995294844 -1.01609952948437 117 14 13.3791892191095 0.620810780890483 118 13 14.4865574749015 -1.48655747490150 119 16 15.3461460161102 0.65385398388977 120 13 14.7420596185223 -1.74205961852228 121 16 15.4710219629883 0.528978037011681 122 13 14.0032970962407 -1.00329709624071 123 16 14.040828414969 1.95917158503099 124 15 15.3555181860132 -0.355518186013225 125 16 15.240391639993 0.759608360007 126 15 14.9410078052256 0.0589921947743524 127 17 14.9247826265099 2.07521737349013 128 15 15.2154582522641 -0.215458252264068 129 12 15.2859884400631 -3.28598844006306 130 16 15.9344603599183 0.0655396400816665 131 10 14.1654807098006 -4.16548070980057 132 16 15.0582427102926 0.941757289707381 133 12 15.1900290208836 -3.19002902088364 134 14 15.3337666935367 -1.33376669353674 135 15 15.7562983412273 -0.756298341227266 136 13 14.6087468770138 -1.60874687701377 137 15 14.6517841457615 0.348215854238486 138 11 13.4153204682324 -2.41532046823244 139 12 15.058595555758 -3.05859555575799 140 8 13.8644917867719 -5.86449178677194 141 16 14.4811529347381 1.51884706526189 142 15 14.8471707423442 0.152829257655816 143 17 12.9249350188131 4.07506498118689 144 16 15.3545324851204 0.645467514879553 145 10 14.5354775240592 -4.53547752405919 146 18 15.2729679063679 2.72703209363208 147 13 15.0370151997097 -2.03701519970971 148 16 14.8034164516378 1.19658354836216 149 13 14.5622041209489 -1.56220412094892 150 10 14.9902132507904 -4.99021325079041 151 15 14.5948064843922 0.405193515607761 152 16 15.3146740465502 0.685325953449797 153 16 16.4890094965522 -0.489009496552171 154 14 14.0167283962363 -0.0167283962363217 155 10 14.0151949172672 -4.01519491726715 156 17 14.8406329567038 2.15936704329619 157 13 15.5467163713719 -2.54671637137193 158 15 14.8129539201865 0.187046079813482 159 16 15.5341997190859 0.465800280914103 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.488556417715588 0.977112835431177 0.511443582284411 11 0.329962424612357 0.659924849224715 0.670037575387643 12 0.244954713264310 0.489909426528621 0.75504528673569 13 0.165446229031046 0.330892458062092 0.834553770968954 14 0.360704514634253 0.721409029268507 0.639295485365747 15 0.259413250458449 0.518826500916899 0.74058674954155 16 0.179103287177424 0.358206574354847 0.820896712822576 17 0.353465551156741 0.706931102313482 0.646534448843259 18 0.398076127500165 0.79615225500033 0.601923872499835 19 0.324586950054611 0.649173900109222 0.675413049945389 20 0.255910847337315 0.51182169467463 0.744089152662685 21 0.195843907068208 0.391687814136417 0.804156092931792 22 0.253299640490657 0.506599280981315 0.746700359509343 23 0.195371181602738 0.390742363205477 0.804628818397262 24 0.167258003581173 0.334516007162347 0.832741996418827 25 0.129545607431574 0.259091214863147 0.870454392568426 26 0.0989222742446379 0.197844548489276 0.901077725755362 27 0.0745832589969523 0.149166517993905 0.925416741003048 28 0.0537858834468016 0.107571766893603 0.946214116553198 29 0.049183422282424 0.098366844564848 0.950816577717576 30 0.0353403704879967 0.0706807409759934 0.964659629512003 31 0.132168766605320 0.264337533210641 0.86783123339468 32 0.106527560937318 0.213055121874635 0.893472439062682 33 0.083233913555106 0.166467827110212 0.916766086444894 34 0.0681092200381022 0.136218440076204 0.931890779961898 35 0.593698083212179 0.812603833575643 0.406301916787821 36 0.825667292678199 0.348665414643603 0.174332707321801 37 0.800845691395442 0.398308617209117 0.199154308604558 38 0.765703551293074 0.468592897413851 0.234296448706926 39 0.73575214838048 0.528495703239039 0.264247851619519 40 0.718421885548184 0.563156228903632 0.281578114451816 41 0.687203723215676 0.625592553568648 0.312796276784324 42 0.844639582866687 0.310720834266625 0.155360417133313 43 0.850618382483236 0.298763235033527 0.149381617516764 44 0.81929638592471 0.36140722815058 0.18070361407529 45 0.87673279203472 0.246534415930559 0.123267207965279 46 0.854717195345696 0.290565609308608 0.145282804654304 47 0.824891852301315 0.35021629539737 0.175108147698685 48 0.802258517598653 0.395482964802695 0.197741482401347 49 0.787331425987653 0.425337148024693 0.212668574012347 50 0.765285466972374 0.469429066055252 0.234714533027626 51 0.742066944329438 0.515866111341125 0.257933055670562 52 0.786506572057239 0.426986855885522 0.213493427942761 53 0.749461777749827 0.501076444500346 0.250538222250173 54 0.916439467509771 0.167121064980458 0.0835605324902288 55 0.903323239996905 0.193353520006190 0.0966767600030949 56 0.88111796838937 0.23776406322126 0.11888203161063 57 0.859894471403494 0.280211057193011 0.140105528596506 58 0.832268944747529 0.335462110504943 0.167731055252471 59 0.810413699480358 0.379172601039284 0.189586300519642 60 0.816199342473288 0.367601315053423 0.183800657526712 61 0.792514150119388 0.414971699761224 0.207485849880612 62 0.762617471262455 0.474765057475089 0.237382528737545 63 0.735344188744165 0.52931162251167 0.264655811255835 64 0.710828824210725 0.578342351578549 0.289171175789275 65 0.720267041441244 0.559465917117513 0.279732958558756 66 0.71920007211688 0.561599855766239 0.280799927883119 67 0.698423735765447 0.603152528469105 0.301576264234553 68 0.6965008386479 0.606998322704199 0.303499161352099 69 0.672630832663763 0.654738334672474 0.327369167336237 70 0.818090192269689 0.363819615460623 0.181909807730311 71 0.813943728940954 0.372112542118092 0.186056271059046 72 0.83009113317227 0.339817733655461 0.169908866827730 73 0.828369005659964 0.343261988680073 0.171630994340036 74 0.799897939868001 0.400204120263998 0.200102060131999 75 0.778953263882348 0.442093472235303 0.221046736117652 76 0.746945748019325 0.50610850396135 0.253054251980675 77 0.722177463471115 0.555645073057769 0.277822536528885 78 0.718531738247402 0.562936523505196 0.281468261752598 79 0.678823865490028 0.642352269019943 0.321176134509972 80 0.63943247217795 0.7211350556441 0.36056752782205 81 0.779851419433708 0.440297161132583 0.220148580566292 82 0.744915802882577 0.510168394234846 0.255084197117423 83 0.706740700817222 0.586518598365555 0.293259299182778 84 0.666202437129621 0.667595125740758 0.333797562870379 85 0.622480758725619 0.755038482548762 0.377519241274381 86 0.593744772361577 0.812510455276845 0.406255227638423 87 0.558375877923186 0.883248244153629 0.441624122076814 88 0.519988425951628 0.960023148096744 0.480011574048372 89 0.476174100857689 0.952348201715377 0.523825899142311 90 0.525079203213106 0.949841593573788 0.474920796786894 91 0.489884941219415 0.97976988243883 0.510115058780585 92 0.455502283521237 0.911004567042474 0.544497716478763 93 0.408922996870666 0.817845993741331 0.591077003129334 94 0.392009119818521 0.784018239637042 0.607990880181479 95 0.353464518536353 0.706929037072706 0.646535481463647 96 0.323191459968426 0.646382919936851 0.676808540031574 97 0.282981879956985 0.565963759913971 0.717018120043015 98 0.252851152789222 0.505702305578444 0.747148847210778 99 0.223707032988589 0.447414065977177 0.776292967011411 100 0.196127253372990 0.392254506745980 0.80387274662701 101 0.176693429131554 0.353386858263107 0.823306570868446 102 0.359777043480455 0.719554086960911 0.640222956519545 103 0.326323622230001 0.652647244460002 0.673676377769999 104 0.310793192153489 0.621586384306979 0.68920680784651 105 0.331057275310586 0.662114550621172 0.668942724689414 106 0.322081385626516 0.644162771253031 0.677918614373484 107 0.295156255332109 0.590312510664219 0.70484374466789 108 0.282632411438968 0.565264822877937 0.717367588561032 109 0.303616352164521 0.607232704329043 0.696383647835479 110 0.270166011365103 0.540332022730207 0.729833988634897 111 0.259405898793114 0.518811797586228 0.740594101206886 112 0.262656386507563 0.525312773015125 0.737343613492437 113 0.233885366643656 0.467770733287312 0.766114633356344 114 0.209512640443392 0.419025280886785 0.790487359556608 115 0.428182198514553 0.856364397029105 0.571817801485447 116 0.379995527617288 0.759991055234577 0.620004472382712 117 0.354168503447041 0.708337006894081 0.645831496552959 118 0.318714306341284 0.637428612682568 0.681285693658716 119 0.276915474633958 0.553830949267916 0.723084525366042 120 0.278356125379673 0.556712250759345 0.721643874620327 121 0.235338616521556 0.470677233043111 0.764661383478444 122 0.201671913328553 0.403343826657105 0.798328086671448 123 0.211920158132045 0.42384031626409 0.788079841867955 124 0.189725853117546 0.379451706235093 0.810274146882454 125 0.153789732316692 0.307579464633384 0.846210267683308 126 0.123240741148366 0.246481482296732 0.876759258851634 127 0.163889277854082 0.327778555708163 0.836110722145919 128 0.148976475124514 0.297952950249028 0.851023524875486 129 0.136757978892567 0.273515957785134 0.863242021107433 130 0.105713553848620 0.211427107697240 0.89428644615138 131 0.127803980303434 0.255607960606868 0.872196019696566 132 0.129280138753374 0.258560277506748 0.870719861246626 133 0.114209432839598 0.228418865679197 0.885790567160402 134 0.0865045497282974 0.173009099456595 0.913495450271703 135 0.0645729241076109 0.129145848215222 0.935427075892389 136 0.0516684413210905 0.103336882642181 0.94833155867891 137 0.0356159301691033 0.0712318603382067 0.964384069830897 138 0.0385242260661448 0.0770484521322896 0.961475773933855 139 0.0285621330350841 0.0571242660701683 0.971437866964916 140 0.161779187544235 0.32355837508847 0.838220812455765 141 0.127376440574270 0.254752881148539 0.87262355942573 142 0.087777971316509 0.175555942633018 0.912222028683491 143 0.254037718371909 0.508075436743818 0.745962281628091 144 0.209567748517625 0.419135497035251 0.790432251482375 145 0.293337620908569 0.586675241817138 0.706662379091431 146 0.226617775671976 0.453235551343951 0.773382224328024 147 0.149224202627937 0.298448405255874 0.850775797372063 148 0.108685827584711 0.217371655169421 0.89131417241529 149 0.0677526445897472 0.135505289179494 0.932247355410253 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 5 0.0357142857142857 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/10grv41290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/10grv41290262977.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/1khfv1290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/1khfv1290262977.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/2khfv1290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/2khfv1290262977.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/3khfv1290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/3khfv1290262977.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/4d8wy1290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/4d8wy1290262977.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/5d8wy1290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/5d8wy1290262977.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/6d8wy1290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/6d8wy1290262977.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/750d11290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/750d11290262977.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/8grv41290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/8grv41290262977.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/9grv41290262977.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/20/t12902630713xb6mlhmbqb40oc/9grv41290262977.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') }

Copyright

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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