*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 23:21:00 +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/28/t1293492266exmojc41t6wjk4u.htm/, Retrieved Tue, 28 Dec 2010 00:24:37 +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/28/t1293492266exmojc41t6wjk4u.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 14 11 12 24 26 9 11 7 8 25 23 9 6 17 8 30 25 9 12 10 8 19 23 9 8 12 9 22 19 9 10 12 7 22 29 10 10 11 4 25 25 10 11 11 11 23 21 10 16 12 7 17 22 10 11 13 7 21 25 10 13 14 12 19 24 10 12 16 10 19 18 10 8 11 10 15 22 10 12 10 8 16 15 10 11 11 8 23 22 10 4 15 4 27 28 10 9 9 9 22 20 10 8 11 8 14 12 10 8 17 7 22 24 10 14 17 11 23 20 10 15 11 9 23 21 10 16 18 11 21 20 10 9 14 13 19 21 10 14 10 8 18 23 10 11 11 8 20 28 10 8 15 9 23 24 10 9 15 6 25 24 10 9 13 9 19 24 10 9 16 9 24 23 10 9 13 6 22 23 10 10 9 6 25 29 10 16 18 16 26 24 10 11 18 5 29 18 10 8 12 7 32 25 10 9 17 9 25 21 10 16 9 6 29 26 10 11 9 6 28 22 10 16 12 5 17 22 10 12 18 12 28 22 10 12 12 7 29 23 10 14 18 10 26 30 10 9 14 9 25 23 10 10 15 8 14 17 10 9 16 5 25 23 10 10 10 8 26 23 10 12 11 8 20 25 10 14 14 10 18 24 10 14 9 6 32 24 10 10 12 8 25 23 10 14 17 7 25 21 10 16 5 4 23 24 10 9 12 8 21 24 10 10 12 8 20 28 10 6 6 4 15 16 10 8 24 20 30 20 10 13 12 8 24 29 10 10 12 8 26 27 10 8 14 6 24 22 10 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 15 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 ParentalCriticism[t] = + 16.601138887406 -1.41670508965093Month[t] + 0.150238793812559DoubtsActions[t] + 0.440939298378178ParentalExpectations[t] + 0.0298388827345439Standards[t] -0.103111653402745`Organization `[t] + 0.000949138149842271t + 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) 16.601138887406 9.443287 1.758 0.080763 0.040382 Month -1.41670508965093 0.948296 -1.4939 0.137262 0.068631 DoubtsActions 0.150238793812559 0.061372 2.448 0.015504 0.007752 ParentalExpectations 0.440939298378178 0.053182 8.2911 0 0 Standards 0.0298388827345439 0.045855 0.6507 0.51621 0.258105 `Organization ` -0.103111653402745 0.049627 -2.0777 0.039415 0.019708 t 0.000949138149842271 0.004025 0.2358 0.813893 0.406947 Multiple Linear Regression - Regression Statistics Multiple R 0.630420955153921 R-squared 0.397430580697182 Adjusted R-squared 0.373644945724703 F-TEST (value) 16.7088488979595 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 9.43689570931383e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.14243533599839 Sum Squared Residuals 697.684433678052 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 8.8406478113907 3.15935218860930 2 8 6.96629721753314 1.03370278246686 3 8 10.5684164772692 -2.5684164772692 4 8 8.26221888637267 -0.262218886372668 5 9 9.04605470784323 -0.046054707843233 6 7 8.31636489959075 -1.31636489959075 7 4 6.96163291152608 -2.96163291152608 8 11 7.46558969163038 3.53441030836962 9 7 8.3765271474112 -1.37652714741119 10 7 7.87724218560636 -0.877242185606358 11 12 8.66304209769315 3.33695790230685 12 10 10.0143009592033 -0.0143009592032610 13 10 6.67779628566282 3.32220371433718 14 8 7.59038175723848 0.40961824276152 15 8 7.36912200527653 0.630877994723465 16 4 7.58284239077288 -3.58284239077288 17 9 6.3650485212657 2.63495147873431 18 8 7.68381962770494 0.316180372295060 19 7 9.33177577716726 -2.33177577716726 20 11 10.6764431745380 0.32355682546202 21 9 8.07888366282857 0.921116337171431 22 11 11.3600805713719 -0.360080571371874 23 13 8.38281154044926 4.61718845955074 24 8 7.13513526460915 0.86486473539085 25 8 6.67042681815486 1.32957318184514 26 9 8.48638003019435 0.513619969805654 27 6 8.69724572762584 -2.69724572762584 28 9 7.63728297261206 1.36271702738794 29 9 9.2133560729719 -0.213356072971898 30 6 7.83180955051812 -1.83180955051812 31 6 5.69008701675497 0.309912983245029 32 16 11.1063197529320 4.89368024706796 33 5 11.0642614906392 -6.06426149063919 34 7 7.3365935314667 -0.3365935314667 35 9 9.89605238978916 -0.896052389789164 36 6 7.02495596152595 -1.02495596152594 37 6 6.65731886148943 -0.657318861489429 38 5 8.40405215375662 -3.40405215375662 39 12 10.7779096170053 1.22209038299473 40 7 8.05995019421785 -1.05995019421785 41 10 10.1957144882390 -0.195714488239030 42 9 8.37365515489804 0.626344845101964 43 8 9.2562245955751 -1.25622459557510 44 5 9.25743202795408 -4.25743202795408 45 8 6.79282305238195 1.20717694761805 46 8 7.14993247332234 0.850067526677662 47 10 8.81761098216549 1.18238901783451 48 6 7.03160798670806 -1.03160798670806 49 8 7.64865931900313 0.351340680996865 50 7 10.6614834310996 -3.66148343109959 51 4 5.3026258506591 -1.30262585065909 52 8 7.27880075529918 0.721199244700818 53 8 6.98770319091606 1.01229680908394 54 4 4.83020679070682 -0.830206790706819 55 20 13.1036775146962 6.89632248530384 56 8 7.4575108643387 0.542489135661306 57 8 7.27364469332544 0.726355306674562 58 6 8.31187534215115 -2.31187534215115 59 4 4.39766291195563 -0.397662911955634 60 8 9.2447869698316 -1.24478696983160 61 9 7.27374799344865 1.72625200655135 62 6 7.96898687719197 -1.96898687719197 63 7 8.29890628773413 -1.29890628773413 64 9 6.21690504303844 2.78309495696156 65 5 7.04387293461517 -2.04387293461517 66 5 5.94946728881653 -0.949467288816528 67 8 6.73169861809062 1.26830138190938 68 8 8.22329452069033 -0.223294520690335 69 6 6.85122326346855 -0.851223263468548 70 8 7.17166740877871 0.828332591221287 71 7 7.32298001040457 -0.322980010404573 72 7 6.07807727656424 0.92192272343576 73 9 8.59436054118218 0.405639458817822 74 11 11.0095397666120 -0.00953976661196645 75 6 8.63969270541552 -2.63969270541552 76 8 7.73131494218165 0.268685057818353 77 6 8.39155082308347 -2.39155082308347 78 9 8.66591220812366 0.334087791876342 79 8 6.41738476848161 1.58261523151839 80 6 8.37237234724173 -2.37237234724173 81 10 8.30847959981552 1.69152040018448 82 8 6.09004038223493 1.90995961776507 83 8 8.34642525909655 -0.346425259096550 84 10 9.04204710673246 0.957952893267536 85 5 5.92854636411674 -0.928546364116737 86 7 9.3454673507971 -2.34546735079711 87 5 7.17051449965076 -2.17051449965076 88 8 6.28546530107713 1.71453469892287 89 14 9.91364904500649 4.08635095499351 90 7 7.65508622807581 -0.655086228075807 91 8 8.829534178024 -0.829534178024006 92 6 4.89237614706084 1.10762385293916 93 5 6.27913123439787 -1.27913123439787 94 6 9.23400674288517 -3.23400674288517 95 10 6.56933943715599 3.43066056284401 96 12 11.5612597163829 0.438740283617103 97 9 9.15195047208361 -0.151950472083608 98 12 10.8783870359195 1.12161296408053 99 7 7.54322856034637 -0.543228560346373 100 8 8.34157909749244 -0.341579097492441 101 10 9.16737793926587 0.83262206073413 102 6 7.27543726990533 -1.27543726990533 103 10 11.2088362340758 -1.2088362340758 104 10 8.70695834721845 1.29304165278155 105 10 7.09396259817717 2.90603740182283 106 5 8.44895823576181 -3.44895823576181 107 7 6.93115088858718 0.0688491114128244 108 10 8.64121890522414 1.35878109477586 109 11 9.7460873369803 1.2539126630197 110 6 8.2153464008538 -2.2153464008538 111 7 7.49124720019924 -0.491247200199236 112 12 8.85975079578624 3.14024920421376 113 11 6.36560475530708 4.63439524469292 114 11 10.8223314553362 0.177668544663818 115 11 5.46594559906795 5.53405440093205 116 5 7.63024610145471 -2.63024610145471 117 8 10.2449469104578 -2.24494691045777 118 6 6.80482294995854 -0.804822949958538 119 9 9.4462437582705 -0.446243758270487 120 4 6.7755796691547 -2.77557966915471 121 4 5.79549010385074 -1.79549010385074 122 7 8.35125570969704 -1.35125570969704 123 11 9.61417592770903 1.38582407229097 124 6 4.41831358186891 1.58168641813109 125 7 7.07416795979127 -0.0741679597912713 126 8 9.95732271130627 -1.95732271130626 127 4 6.34770760870298 -2.34770760870298 128 8 7.09376688533228 0.906233114667723 129 9 8.17777847660046 0.822221523399537 130 8 7.70917096194147 0.290829038058529 131 11 8.80338612376012 2.19661387623988 132 8 7.51487235382208 0.48512764617792 133 5 6.76819610572183 -1.76819610572183 134 4 5.89716839983827 -1.89716839983827 135 8 7.46173525527868 0.538264744721324 136 10 11.8424156426398 -1.84241564263980 137 6 8.3132015214279 -2.31320152142790 138 9 9.38631050343167 -0.386310503431667 139 9 7.2111369805229 1.7888630194771 140 13 8.92112385109479 4.07887614890521 141 9 7.88244442405994 1.11755557594006 142 10 9.58269183403904 0.417308165960961 143 20 14.8512010241742 5.14879897582581 144 5 6.06285773606914 -1.06285773606914 145 11 10.4386233426502 0.561376657349783 146 6 8.15778529610135 -2.15778529610135 147 9 10.2085791693770 -1.20857916937699 148 7 7.34142533291684 -0.341425332916843 149 9 8.1768676331841 0.823132366815906 150 10 8.48606382780396 1.51393617219604 151 9 6.98676626660848 2.01323373339152 152 8 10.2786599686877 -2.27865996868767 153 7 11.3667477763246 -4.3667477763246 154 6 9.4351535187033 -3.4351535187033 155 13 11.7065172211981 1.29348277880191 156 6 8.0681076160001 -2.06810761600011 157 8 7.77823157992087 0.221768420079131 158 10 9.53924465910727 0.460755340892733 159 16 11.8116962653403 4.18830373465973 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.831910067261135 0.336179865477729 0.168089932738864 11 0.831306090968018 0.337387818063965 0.168693909031982 12 0.832139793477843 0.335720413044314 0.167860206522157 13 0.905982798322304 0.188034403355391 0.0940172016776957 14 0.87479225985205 0.2504154802959 0.12520774014795 15 0.821336011636488 0.357327976727024 0.178663988363512 16 0.786155505261463 0.427688989477073 0.213844494738537 17 0.772307160993796 0.455385678012409 0.227692839006204 18 0.721728047292155 0.55654390541569 0.278271952707845 19 0.657443930540386 0.685112138919228 0.342556069459614 20 0.586748204770537 0.826503590458927 0.413251795229463 21 0.512653025819394 0.974693948361211 0.487346974180606 22 0.433083757057529 0.866167514115058 0.566916242942471 23 0.66912286861259 0.661754262774819 0.330877131387409 24 0.6364729622779 0.727054075444201 0.363527037722101 25 0.572192169635247 0.855615660729507 0.427807830364753 26 0.507336096561327 0.985327806877345 0.492663903438673 27 0.522175379424799 0.955649241150402 0.477824620575201 28 0.464840073321386 0.929680146642771 0.535159926678614 29 0.399620797286401 0.799241594572802 0.600379202713599 30 0.399359729921399 0.798719459842799 0.6006402700786 31 0.338261434240252 0.676522868480504 0.661738565759748 32 0.58897448658219 0.82205102683562 0.41102551341781 33 0.823616269255729 0.352767461488542 0.176383730744271 34 0.797314738229094 0.405370523541812 0.202685261770906 35 0.755249835789373 0.489500328421254 0.244750164210627 36 0.740494643777261 0.519010712445478 0.259505356222739 37 0.693065438607915 0.61386912278417 0.306934561392085 38 0.837278304334994 0.325443391330012 0.162721695665006 39 0.845269432007387 0.309461135985225 0.154730567992613 40 0.812714472832781 0.374571054334437 0.187285527167219 41 0.774490361927260 0.451019276145481 0.225509638072740 42 0.746840266011872 0.506319467976255 0.253159733988128 43 0.716611213415592 0.566777573168817 0.283388786584408 44 0.78022080689613 0.439558386207739 0.219779193103869 45 0.765623968522375 0.46875206295525 0.234376031477625 46 0.729209070293384 0.541581859413231 0.270790929706616 47 0.696921831421757 0.606156337156486 0.303078168578243 48 0.656366316572664 0.687267366854673 0.343633683427336 49 0.616003633866088 0.767992732267824 0.383996366133912 50 0.663891805849651 0.672216388300697 0.336108194150349 51 0.652287333314966 0.695425333370068 0.347712666685034 52 0.61801835313445 0.7639632937311 0.38198164686555 53 0.58018869677934 0.83962260644132 0.41981130322066 54 0.536987532023803 0.926024935952394 0.463012467976197 55 0.944951332609293 0.110097334781414 0.0550486673907069 56 0.931062678447182 0.137874643105635 0.0689373215528176 57 0.916304645783391 0.167390708433218 0.0836953542166089 58 0.914971451307935 0.170057097384129 0.0850285486920645 59 0.89486433294034 0.210271334119321 0.105135667059660 60 0.879358064515612 0.241283870968776 0.120641935484388 61 0.873185940177256 0.253628119645489 0.126814059822744 62 0.864709694424078 0.270580611151844 0.135290305575922 63 0.845459377306958 0.309081245386085 0.154540622693042 64 0.867372440841957 0.265255118316087 0.132627559158044 65 0.860855840530292 0.278288318939415 0.139144159469708 66 0.838493279580811 0.323013440838378 0.161506720419189 67 0.821400673531826 0.357198652936348 0.178599326468174 68 0.790480848550278 0.419038302899444 0.209519151449722 69 0.759480333823619 0.481039332352762 0.240519666176381 70 0.7288049028804 0.5423901942392 0.2711950971196 71 0.688603590817711 0.622792818364578 0.311396409182289 72 0.655110311412555 0.68977937717489 0.344889688587445 73 0.613855619406048 0.772288761187904 0.386144380593952 74 0.567946047024503 0.864107905950994 0.432053952975497 75 0.586429776345993 0.827140447308015 0.413570223654007 76 0.541426760640596 0.917146478718808 0.458573239359404 77 0.547706391760991 0.904587216478018 0.452293608239009 78 0.503135728359786 0.993728543280427 0.496864271640214 79 0.480728201116366 0.961456402232733 0.519271798883634 80 0.48832122472992 0.97664244945984 0.51167877527008 81 0.469641431476857 0.939282862953715 0.530358568523142 82 0.45884466121306 0.91768932242612 0.54115533878694 83 0.413113229828574 0.826226459657147 0.586886770171426 84 0.378329738353452 0.756659476706904 0.621670261646548 85 0.342796945969138 0.685593891938276 0.657203054030862 86 0.347797507577829 0.695595015155658 0.652202492422171 87 0.352750511087353 0.705501022174706 0.647249488912647 88 0.332637344238746 0.665274688477492 0.667362655761254 89 0.446613281462112 0.893226562924225 0.553386718537888 90 0.403276758574349 0.806553517148698 0.596723241425651 91 0.363461349891206 0.726922699782413 0.636538650108794 92 0.330894023603386 0.661788047206772 0.669105976396614 93 0.301330686938495 0.602661373876991 0.698669313061505 94 0.35247420459394 0.70494840918788 0.64752579540606 95 0.417395204629504 0.834790409259008 0.582604795370496 96 0.375162050724342 0.750324101448684 0.624837949275658 97 0.330370778522082 0.660741557044164 0.669629221477918 98 0.299019522442374 0.598039044884747 0.700980477557626 99 0.259897677495876 0.519795354991751 0.740102322504125 100 0.222645725104875 0.445291450209749 0.777354274895125 101 0.192950624295937 0.385901248591874 0.807049375704063 102 0.170923262407725 0.341846524815449 0.829076737592275 103 0.152791359743201 0.305582719486403 0.847208640256799 104 0.133322357299393 0.266644714598786 0.866677642700607 105 0.161763853658237 0.323527707316474 0.838236146341763 106 0.207774927670788 0.415549855341576 0.792225072329212 107 0.175545563228339 0.351091126456678 0.82445443677166 108 0.156077429518101 0.312154859036203 0.843922570481899 109 0.136387527481929 0.272775054963859 0.86361247251807 110 0.133862532654805 0.26772506530961 0.866137467345195 111 0.109776908604995 0.219553817209990 0.890223091395005 112 0.144199514342541 0.288399028685083 0.855800485657459 113 0.271050959066605 0.542101918133211 0.728949040933395 114 0.231577524464518 0.463155048929036 0.768422475535482 115 0.585287614101031 0.829424771797938 0.414712385898969 116 0.57409785288531 0.85180429422938 0.42590214711469 117 0.570648370020571 0.858703259958859 0.429351629979429 118 0.51980993355304 0.96038013289392 0.48019006644696 119 0.464720289969902 0.929440579939805 0.535279710030098 120 0.551503822493342 0.896992355013316 0.448496177506658 121 0.522527800232345 0.954944399535311 0.477472199767655 122 0.537047087661633 0.925905824676733 0.462952912338367 123 0.488801319895305 0.97760263979061 0.511198680104695 124 0.497346814413719 0.994693628827438 0.502653185586281 125 0.438777000174339 0.877554000348677 0.561222999825661 126 0.443977397344226 0.887954794688452 0.556022602655774 127 0.434071417352019 0.868142834704038 0.565928582647981 128 0.397735441273798 0.795470882547595 0.602264558726202 129 0.35664630810253 0.71329261620506 0.64335369189747 130 0.308346182184952 0.616692364369904 0.691653817815048 131 0.299021869892456 0.598043739784912 0.700978130107544 132 0.247113544556771 0.494227089113542 0.752886455443229 133 0.203676810053944 0.407353620107888 0.796323189946056 134 0.171957287465722 0.343914574931444 0.828042712534278 135 0.134942577184651 0.269885154369302 0.865057422815349 136 0.127662529011725 0.255325058023449 0.872337470988276 137 0.168974002130001 0.337948004260003 0.831025997869999 138 0.175454423186929 0.350908846373858 0.82454557681307 139 0.156449812570418 0.312899625140837 0.843550187429582 140 0.188128559189593 0.376257118379185 0.811871440810407 141 0.138596567420454 0.277193134840908 0.861403432579546 142 0.10448783273871 0.20897566547742 0.89551216726129 143 0.168616912170835 0.33723382434167 0.831383087829165 144 0.118995963353294 0.237991926706588 0.881004036646706 145 0.0914086132633148 0.182817226526630 0.908591386736685 146 0.0578852639306328 0.115770527861266 0.942114736069367 147 0.033795603200056 0.067591206400112 0.966204396799944 148 0.0167448987067478 0.0334897974134957 0.983255101293252 149 0.0073729823901137 0.0147459647802274 0.992627017609886 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 2 0.0142857142857143 OK 10% type I error level 3 0.0214285714285714 OK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = 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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Software written by Ed van Stee & Patrick Wessa

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