*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: Mon, 27 Dec 2010 18:35:09 +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/Dec/27/t1293474860syz3c9twzt091xk.htm/, Retrieved Mon, 27 Dec 2010 19:34:32 +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/Dec/27/t1293474860syz3c9twzt091xk.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 «

14 11 12 24 26 11 7 8 25 23 6 17 8 30 25 12 10 8 19 23 8 12 9 22 19 10 12 7 22 29 10 11 4 25 25 11 11 11 23 21 16 12 7 17 22 11 13 7 21 25 13 14 12 19 24 12 16 10 19 18 8 11 10 15 22 12 10 8 16 15 11 11 8 23 22 4 15 4 27 28 9 9 9 22 20 8 11 8 14 12 8 17 7 22 24 14 17 11 23 20 15 11 9 23 21 16 18 11 21 20 9 14 13 19 21 14 10 8 18 23 11 11 8 20 28 8 15 9 23 24 9 15 6 25 24 9 13 9 19 24 9 16 9 24 23 9 13 6 22 23 10 9 6 25 29 16 18 16 26 24 11 18 5 29 18 8 12 7 32 25 9 17 9 25 21 16 9 6 29 26 11 9 6 28 22 16 12 5 17 22 12 18 12 28 22 12 12 7 29 23 14 18 10 26 30 9 14 9 25 23 10 15 8 14 17 9 16 5 25 23 10 10 8 26 23 12 11 8 20 25 14 14 10 18 24 14 9 6 32 24 10 12 8 25 23 14 17 7 25 21 16 5 4 23 24 9 12 8 21 24 10 12 8 20 28 6 6 4 15 16 8 24 20 30 20 13 12 8 24 29 10 12 8 26 27 8 14 6 24 22 7 7 4 22 28 15 13 8 14 16 9 12 9 24 25 10 13 6 24 24 12 14 7 24 28 13 8 9 24 24 10 11 5 19 23 11 9 5 31 30 8 11 8 22 24 9 13 8 27 21 13 10 6 19 25 11 11 8 25 2 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Standards[t] = + 8.36783562150566 -0.118995175185963DoubtsActions[t] + 0.330380406024557ParentalExpectations[t] + 0.104695476872945ParentalCriticism[t] + 0.446177005333338`Organization `[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) 8.36783562150566 2.477477 3.3776 0.000926 0.000463 DoubtsActions -0.118995175185963 0.109196 -1.0897 0.27753 0.138765 ParentalExpectations 0.330380406024557 0.108435 3.0468 0.002722 0.001361 ParentalCriticism 0.104695476872945 0.14126 0.7412 0.459727 0.229864 `Organization ` 0.446177005333338 0.078835 5.6596 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.471880297692617 R-squared 0.222671015350473 Adjusted R-squared 0.202480652112823 F-TEST (value) 11.0285789675763 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 6.84458814070865e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.76591016754695 Sum Squared Residuals 2184.04022606516 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.1930354963144 0.806964503685572 2 25 20.4711864742823 4.52881352571771 3 30 25.2623204211244 4.73767957887564 4 19 21.34333251717 -2.34333251717 5 22 20.8000614855026 1.19993851449745 6 22 24.8144502347181 -2.81445023471812 7 25 22.3852753767414 2.61472462325863 8 23 21.2144405183327 1.78555948166732 9 17 20.9772401462690 -3.97724014626897 10 21 23.2411274442234 -2.24112744422336 11 19 23.4108178789074 -4.41081787890738 12 19 21.3041208803965 -2.30412088039654 13 15 21.9129075723510 -6.91290757235096 14 16 17.7739164745033 -1.77391647450329 15 23 21.3465310930472 1.65346890695282 16 27 25.7592990679554 1.24070093204461 17 22 20.1361020975763 1.86389790242374 18 14 17.2417465652717 -3.24174656527169 19 22 24.4734575885461 -2.47345758854614 20 23 22.3935604235888 0.606439576411209 21 23 20.5290688638429 2.47093113615707 22 21 22.4859504792414 -1.48595047924142 23 19 22.6529630405242 -3.65296304052416 24 18 21.1053421667981 -3.10534216679807 25 20 24.0235931250472 -4.02359312504721 26 23 24.0220877302429 -1.02208773024292 27 25 23.5890061244381 1.41099387556188 28 19 23.2423317430078 -4.24233174300784 29 24 23.7872959557482 0.212704044251827 30 22 22.4820683070557 -0.482068307055666 31 25 23.7186135397715 1.28138646022850 32 26 24.7941358849395 1.2058641150605 33 29 21.5603994832669 7.43960051673311 34 32 23.2677325637567 8.7322674362433 35 25 23.2253223511061 1.77467764889395 36 29 21.6661114726557 7.33388852734429 37 28 20.4763793272522 7.52362067274783 38 17 20.7678491925231 -3.76784919252308 39 28 23.9589806675249 4.0410193324751 40 29 21.8993978523462 7.10060214765384 41 26 27.0810154060738 -1.08101540607378 42 25 23.1265351436991 1.87346485630094 43 14 20.5561628656647 -6.55616286566468 44 25 23.3685140482564 1.63148595174361 45 26 21.5813228675419 4.41867713245808 46 20 22.5660669338612 -2.56606693386123 47 18 23.0824317499755 -5.08243174997553 48 32 21.0117478123610 10.9882521876390 49 25 22.2420836795910 2.75791632040896 50 25 22.4209555214303 2.57904447856965 51 23 19.2428448841449 3.75715511585508 52 21 22.8072558601103 -1.80725586011034 53 20 24.4729687062577 -4.47296870625773 54 15 17.1937609993624 -2.1937609993624 55 30 26.3624536087330 3.63754639126702 56 24 24.5621601860332 -0.562160186033174 57 26 24.0267917009244 1.97320829907561 58 24 22.4852668829328 1.51473311706715 59 22 22.7592702942010 -0.759270294201049 60 14 18.8542491723524 -4.85424917235241 61 24 23.3581283423166 0.641871657683379 62 24 22.8092501372030 1.19074986279696 63 24 24.7910436910620 -0.791043691061968 64 24 21.1144490121412 2.88555098785880 65 19 21.5976168429476 -2.59761684294764 66 31 23.9410998930459 7.05890010695407 67 22 22.5958706292717 -0.595870629271744 68 27 21.7991052501349 5.20089474986512 69 19 21.9073003989048 -2.90730039890482 70 25 22.6850621090472 2.31493789095281 71 20 21.9292015477567 -1.92920154775668 72 21 21.2652421598304 -0.265242159830383 73 27 24.7954465657236 2.20455343427637 74 23 23.9434766704274 -0.943476670427398 75 25 24.0351831297715 0.964816870228544 76 20 21.3497296689244 -1.34972966892436 77 21 22.7794464417925 -1.77944644179253 78 22 23.2157266234745 -1.21572662347451 79 23 24.02039454917 -1.02039454917002 80 25 21.7979009513504 3.2020990486496 81 25 24.090582359951 0.909417640049017 82 17 23.7262149903103 -6.72621499031035 83 19 21.8882967299103 -2.88829672991033 84 25 24.4571636131404 0.54283638685958 85 19 21.9152029454635 -2.91520294546347 86 20 23.7860916569637 -3.78609165696369 87 26 22.043793848281 3.95620615171902 88 23 23.4520237927735 -0.45202379277354 89 27 23.5076108092217 3.49238919077833 90 17 21.2450341920514 -4.24503419205142 91 17 22.8730407962296 -5.87304079622963 92 19 21.7523239830101 -2.75232398301007 93 17 20.8178608557126 -3.81786085571257 94 22 21.6853029279188 0.314697072081198 95 21 24.0247974238317 -3.02479742383169 96 32 26.9728202573038 5.02717974269615 97 21 23.185922928064 -2.18592292806399 98 21 23.3938084870056 -2.39380848700559 99 18 21.3640293672374 -3.36402936723738 100 18 20.7877560642822 -2.78775606428224 101 23 22.5502618407439 0.449738159256078 102 19 21.4973242407364 -2.49732424073636 103 20 21.7598936133614 -1.75989361336142 104 21 23.2344291964492 -2.23442919644919 105 20 24.3221755585685 -4.32217555856854 106 17 17.5522200995371 -0.552220099537088 107 18 19.0375557090409 -1.03755570904088 108 19 19.3314341718807 -0.331434171880745 109 22 22.178976616873 -0.178976616873015 110 15 20.6643580144346 -5.66435801443462 111 14 20.5906705317567 -6.59067053175667 112 18 24.6665545668863 -6.66655456688631 113 24 20.4644882265081 3.53551177349188 114 35 22.2183760399151 12.7816239600849 115 29 21.7106291868555 7.2893708131445 116 21 22.9425450107020 -1.94254501070202 117 25 20.3543733624576 4.64562663754237 118 20 19.1378483112522 0.86215168874784 119 22 23.3081166791271 -1.30811667912714 120 13 15.9210149194817 -2.92101491948168 121 26 19.6062275614572 6.39377243854283 122 17 18.8951539901988 -1.89515399019876 123 25 20.9562422001818 4.04375779981822 124 20 21.1807546507364 -1.18075465073641 125 19 20.5182688374269 -1.51826883742691 126 21 23.7749905345279 -2.77499053452786 127 22 21.8467083157554 0.153291684244595 128 24 23.1312391143805 0.86876088561947 129 21 24.3460709845131 -3.34607098451311 130 26 22.3280765834893 3.67192341651070 131 24 20.5366703143818 3.46332968561822 132 16 21.4687248441103 -5.46872484411032 133 23 23.0551430341336 -0.05514303413362 134 18 21.0701509043975 -3.07015090439751 135 16 22.2420836795910 -6.24208367959104 136 26 24.2913553506422 1.70864464935784 137 19 20.3371761842872 -1.33717618428724 138 21 17.9773991587832 3.02260084121677 139 21 23.0309465121692 -2.03094651216925 140 22 18.8391594957312 3.16084050426883 141 23 16.8640641896464 6.13593581035358 142 29 22.7584484957053 6.24155150429467 143 21 21.1867125042838 -0.186712504283820 144 21 20.1272963482529 0.872703651747063 145 23 23.4049096094414 -0.40490960944143 146 27 21.4345182740381 5.56548172596185 147 25 22.3329683404394 2.66703165956062 148 21 20.5874719558795 0.412528044120516 149 10 18.0040042783166 -8.00400427831657 150 20 22.0116947797580 -2.01169477975795 151 26 21.927207270664 4.07279272933602 152 24 23.2958112579068 0.704188742093177 153 29 27.6688787137532 1.33112128624683 154 19 17.9045016544135 1.09549834558649 155 24 23.9510781209662 0.048921879033757 156 19 21.589714296389 -2.58971429638899 157 24 21.8818995781560 2.11810042184404 158 22 22.6394533205194 -0.639453320519371 159 17 23.3398082696307 -6.3398082696307 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.577458368607618 0.845083262784764 0.422541631392382 9 0.411398285318162 0.822796570636324 0.588601714681838 10 0.304158410703853 0.608316821407707 0.695841589296147 11 0.248994180393547 0.497988360787093 0.751005819606454 12 0.159183313546883 0.318366627093766 0.840816686453117 13 0.658164310241884 0.683671379516232 0.341835689758116 14 0.566209156446478 0.867581687107043 0.433790843553522 15 0.496410684448257 0.992821368896515 0.503589315551743 16 0.414790414632067 0.829580829264133 0.585209585367934 17 0.334979128164712 0.669958256329424 0.665020871835288 18 0.311515459630605 0.623030919261209 0.688484540369395 19 0.251932471990605 0.50386494398121 0.748067528009395 20 0.261779023765504 0.523558047531008 0.738220976234496 21 0.262792543471793 0.525585086943585 0.737207456528207 22 0.207578789941351 0.415157579882702 0.792421210058649 23 0.180241713845024 0.360483427690049 0.819758286154976 24 0.163111295620553 0.326222591241106 0.836888704379447 25 0.170574735051306 0.341149470102612 0.829425264948694 26 0.129529170741851 0.259058341483703 0.870470829258149 27 0.10245035049894 0.20490070099788 0.89754964950106 28 0.103379199019793 0.206758398039585 0.896620800980207 29 0.078727915265083 0.157455830530166 0.921272084734917 30 0.0571691786619078 0.114338357323816 0.942830821338092 31 0.0422401962100992 0.0844803924201984 0.9577598037899 32 0.0426721890256378 0.0853443780512756 0.957327810974362 33 0.101530711618916 0.203061423237832 0.898469288381084 34 0.298144815894904 0.596289631789809 0.701855184105096 35 0.256980189062473 0.513960378124945 0.743019810937527 36 0.368695041998832 0.737390083997663 0.631304958001168 37 0.48852648208069 0.97705296416138 0.51147351791931 38 0.553474081771517 0.893051836456966 0.446525918228483 39 0.581854473403704 0.836291053192591 0.418145526596296 40 0.67908378559323 0.64183242881354 0.32091621440677 41 0.635589608068724 0.728820783862552 0.364410391931276 42 0.595277806231784 0.809444387536431 0.404722193768216 43 0.696464862199142 0.607070275601715 0.303535137800858 44 0.654582298392632 0.690835403214737 0.345417701607368 45 0.661850202437888 0.676299595124224 0.338149797562112 46 0.64413700604461 0.71172598791078 0.35586299395539 47 0.675983125497229 0.648033749005541 0.324016874502771 48 0.884675712615963 0.230648574768073 0.115324287384037 49 0.869680387429959 0.260639225140082 0.130319612570041 50 0.852223745607089 0.295552508785821 0.147776254392911 51 0.838443053506026 0.323113892987949 0.161556946493974 52 0.816679564227403 0.366640871545194 0.183320435772597 53 0.836453653973235 0.32709269205353 0.163546346026765 54 0.826268410392088 0.347463179215824 0.173731589607912 55 0.86738091418794 0.265238171624121 0.132619085812060 56 0.842103228456081 0.315793543087837 0.157896771543919 57 0.818125607065535 0.363748785868929 0.181874392934464 58 0.789347470969026 0.421305058061949 0.210652529030974 59 0.757980530833597 0.484038938332805 0.242019469166403 60 0.782772406141315 0.43445518771737 0.217227593858685 61 0.746898880089543 0.506202239820914 0.253101119910457 62 0.711598835498374 0.576802329003251 0.288401164501626 63 0.676154731550486 0.647690536899028 0.323845268449514 64 0.656173180992021 0.687653638015957 0.343826819007979 65 0.637960748803958 0.724078502392083 0.362039251196042 66 0.731479879871037 0.537040240257925 0.268520120128963 67 0.692942919314452 0.614114161371096 0.307057080685548 68 0.730340048195513 0.539319903608974 0.269659951804487 69 0.719384941464706 0.561230117070589 0.280615058535294 70 0.694887502168604 0.610224995662791 0.305112497831396 71 0.664481958592122 0.671036082815757 0.335518041407878 72 0.621972907526948 0.756054184946105 0.378027092473052 73 0.594594258012002 0.810811483975995 0.405405741987998 74 0.551519819791228 0.896960360417544 0.448480180208772 75 0.512843029801774 0.97431394039645 0.487156970198226 76 0.471789198736818 0.943578397473636 0.528210801263182 77 0.439465250747376 0.878930501494753 0.560534749252624 78 0.398688758176164 0.797377516352327 0.601311241823836 79 0.360697625774934 0.721395251549868 0.639302374225066 80 0.352380626267448 0.704761252534896 0.647619373732552 81 0.314128046508630 0.628256093017259 0.68587195349137 82 0.402244118665782 0.804488237331564 0.597755881334218 83 0.382037982013947 0.764075964027894 0.617962017986053 84 0.340228217874080 0.680456435748161 0.65977178212592 85 0.324520677193769 0.649041354387537 0.675479322806231 86 0.32171220004027 0.64342440008054 0.67828779995973 87 0.332659648797704 0.665319297595408 0.667340351202296 88 0.292827233137478 0.585654466274956 0.707172766862522 89 0.288855780757766 0.577711561515531 0.711144219242234 90 0.294597671222206 0.589195342444413 0.705402328777794 91 0.345042847709159 0.690085695418319 0.654957152290841 92 0.321412399648721 0.642824799297441 0.67858760035128 93 0.316926436399077 0.633852872798154 0.683073563600923 94 0.277198410490016 0.554396820980031 0.722801589509984 95 0.261015038793945 0.522030077587891 0.738984961206055 96 0.298346490476031 0.596692980952062 0.701653509523969 97 0.269237355549853 0.538474711099706 0.730762644450147 98 0.243850671509886 0.487701343019772 0.756149328490114 99 0.231989287037004 0.463978574074009 0.768010712962996 100 0.213266891312724 0.426533782625448 0.786733108687276 101 0.180705406137698 0.361410812275397 0.819294593862302 102 0.160762541460046 0.321525082920092 0.839237458539954 103 0.137375074443936 0.274750148887872 0.862624925556064 104 0.119655497759547 0.239310995519095 0.880344502240453 105 0.126435116261269 0.252870232522538 0.873564883738731 106 0.103065410900694 0.206130821801388 0.896934589099306 107 0.0846761716238637 0.169352343247727 0.915323828376136 108 0.0683615775819038 0.136723155163808 0.931638422418096 109 0.0536717996657176 0.107343599331435 0.946328200334282 110 0.0698106126006068 0.139621225201214 0.930189387399393 111 0.109320021731762 0.218640043463524 0.890679978268238 112 0.172875143244749 0.345750286489498 0.827124856755251 113 0.160863663700123 0.321727327400245 0.839136336299877 114 0.618145584873364 0.763708830253272 0.381854415126636 115 0.751847501745419 0.496304996509163 0.248152498254581 116 0.716422943864542 0.567154112270917 0.283577056135458 117 0.764754045726061 0.470491908547879 0.235245954273939 118 0.72173398737155 0.5565320252569 0.27826601262845 119 0.684694502203198 0.630610995593604 0.315305497796802 120 0.687433569412676 0.625132861174649 0.312566430587324 121 0.758798794349162 0.482402411301676 0.241201205650838 122 0.731242462174978 0.537515075650045 0.268757537825022 123 0.727836433738481 0.544327132523037 0.272163566261519 124 0.678170334544695 0.643659330910611 0.321829665455305 125 0.705089673640587 0.589820652718826 0.294910326359413 126 0.677509951598562 0.644980096802875 0.322490048401438 127 0.622942851026256 0.754114297947488 0.377057148973744 128 0.567888266542879 0.864223466914242 0.432111733457121 129 0.535792404259696 0.928415191480608 0.464207595740304 130 0.50480134731199 0.99039730537602 0.49519865268801 131 0.504134783897922 0.991730432204157 0.495865216102078 132 0.544445723577495 0.911108552845011 0.455554276422505 133 0.47787416543642 0.95574833087284 0.52212583456358 134 0.453171001247837 0.906342002495674 0.546828998752163 135 0.585330452002216 0.829339095995569 0.414669547997784 136 0.525243312919468 0.949513374161064 0.474756687080532 137 0.499897765902443 0.999795531804885 0.500102234097557 138 0.449398459419815 0.89879691883963 0.550601540580185 139 0.40130218129451 0.80260436258902 0.59869781870549 140 0.367840349597461 0.735680699194921 0.632159650402540 141 0.490007143901871 0.980014287803742 0.509992856098129 142 0.619821294324429 0.760357411351142 0.380178705675571 143 0.748212811962031 0.503574376075938 0.251787188037969 144 0.694647917821116 0.610704164357768 0.305352082178884 145 0.603040622605337 0.793918754789325 0.396959377394663 146 0.616254207609986 0.767491584780029 0.383745792390014 147 0.608178734994246 0.783642530011507 0.391821265005754 148 0.488239162192335 0.97647832438467 0.511760837807665 149 0.700816403043473 0.598367193913054 0.299183596956527 150 0.633487922474754 0.733024155050491 0.366512077525246 151 0.579208340585275 0.84158331882945 0.420791659414725 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 2 0.0138888888888889 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/10jt7i1293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/10jt7i1293474897.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/1uss61293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/1uss61293474897.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/2uss61293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/2uss61293474897.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/341rr1293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/341rr1293474897.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/441rr1293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/441rr1293474897.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/541rr1293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/541rr1293474897.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/6fbqc1293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/6fbqc1293474897.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/7qkqx1293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/7qkqx1293474897.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/8qkqx1293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/8qkqx1293474897.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/9qkqx1293474897.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474860syz3c9twzt091xk/9qkqx1293474897.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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