*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: Thu, 02 Dec 2010 19:12:54 +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/02/t1291317117hj56tl15d6t1fp5.htm/, Retrieved Thu, 02 Dec 2010 20:12:08 +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/02/t1291317117hj56tl15d6t1fp5.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 24 14 11 12 24 26 9 25 11 7 8 25 23 9 17 6 17 8 30 25 9 18 12 10 8 19 23 9 18 8 12 9 22 19 9 16 10 12 7 22 29 10 20 10 11 4 25 25 10 16 11 11 11 23 21 10 18 16 12 7 17 22 10 17 11 13 7 21 25 10 23 13 14 12 19 24 10 30 12 16 10 19 18 10 23 8 11 10 15 22 10 18 12 10 8 16 15 10 15 11 11 8 23 22 10 12 4 15 4 27 28 10 21 9 9 9 22 20 10 15 8 11 8 14 12 10 20 8 17 7 22 24 10 31 14 17 11 23 20 10 27 15 11 9 23 21 10 34 16 18 11 21 20 10 21 9 14 13 19 21 10 31 14 10 8 18 23 10 19 11 11 8 20 28 10 16 8 15 9 23 24 10 20 9 15 6 25 24 10 21 9 13 9 19 24 10 22 9 16 9 24 23 10 17 9 13 6 22 23 10 24 10 9 6 25 29 10 25 16 18 16 26 24 10 26 11 18 5 29 18 10 25 8 12 7 32 25 10 17 9 17 9 25 21 10 32 16 9 6 29 26 10 33 11 9 6 28 22 10 13 16 12 5 17 22 10 32 12 18 12 28 22 10 25 12 12 7 29 23 10 29 14 18 10 26 30 10 22 9 14 9 25 23 10 18 10 15 8 14 17 10 17 9 16 5 25 23 10 20 10 10 8 26 23 10 15 12 11 8 20 25 10 20 14 14 10 18 24 10 33 14 9 6 32 24 10 29 10 12 8 25 23 10 23 14 17 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 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 PersonalStandards[t] = + 22.4503451046685 -1.49932963098338month[t] + 0.330887218059848ConcernoverMistakes[t] -0.356681047835005Doubtsaboutactions[t] + 0.198030325271138ParentalExpectations[t] + 0.00613248856872935ParentalCriticism[t] + 0.393045515742641`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) 22.4503451046685 14.596982 1.538 0.126125 0.063062 month -1.49932963098338 1.442617 -1.0393 0.30031 0.150155 ConcernoverMistakes 0.330887218059848 0.055592 5.9521 0 0 Doubtsaboutactions -0.356681047835005 0.107249 -3.3257 0.001106 0.000553 ParentalExpectations 0.198030325271138 0.101714 1.9469 0.053385 0.026693 ParentalCriticism 0.00613248856872935 0.129654 0.0473 0.962337 0.481169 `Organization ` 0.393045515742641 0.072189 5.4447 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.60953344822544 R-squared 0.371531024505596 Adjusted R-squared 0.346723038630816 F-TEST (value) 14.9762671738422 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.02393657389166e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.40838004054157 Sum Squared Residuals 1765.79228411584 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 24.37524383968 -0.375243839679987 2 25 23.7803863986577 1.21961360134230 3 30 25.6830881775506 4.31691182244938 4 19 21.7015858002172 -2.70158580021719 5 22 21.9583210676976 0.0416789323023574 6 22 24.5013747161969 -2.50137471619689 7 25 22.536984103505 2.46301589649499 8 23 19.3274995404412 3.67250045955884 9 17 18.7724146241247 -1.77241462412469 10 21 21.6020995177389 -0.602099517738928 11 19 22.7097079828002 -3.70970798280015 12 19 23.4081221360031 -4.40812213600306 13 15 23.100666237539 -8.10066623753901 14 16 17.0578920432927 -1.05789204329267 15 23 19.3712603724178 3.62873962758224 16 27 24.0012304943487 2.99876950565127 17 22 20.8939265829880 1.10607341701197 18 14 16.5108483584964 -2.51084835849636 19 22 24.0638801007654 -2.06388010076539 20 23 24.0159011037181 -1.01590110371805 21 23 21.528269770622 1.47173022937799 22 21 24.4932309874987 -3.49323098749872 23 19 22.3016536793613 -3.30165367936128 24 18 23.7904279083418 -5.79042790834182 25 20 23.053082339113 -3.053082339113 26 23 22.3565355551212 0.643464444878814 27 25 23.3050059138194 1.69499408618061 28 19 23.2582299470431 -4.25822994704315 29 24 23.7901626251738 0.209837374826234 30 22 21.5232380933549 0.476761906645076 31 25 25.0489193653102 -0.0489193653101547 32 26 23.1180905307743 2.8819094692257 33 29 22.8066525192973 6.1933474807027 34 32 25.1212100804516 6.87878991954841 35 25 21.5476658286604 3.45233417133962 36 29 24.376794275551 4.62320572444901 37 28 24.9189046698153 3.08109533018471 38 17 17.105713556688 -0.105713556687991 39 28 26.0504042627731 1.94959573722694 40 29 22.9083948576263 6.09160514237371 41 26 27.4764796617272 -1.47647966172718 42 25 23.3941019746315 1.60589802536851 43 14 19.5474967968037 -5.54749679680365 44 25 22.1111965805996 2.88880341940039 45 26 21.5773927010235 4.42260729897649 46 20 20.1937158718107 -0.193715871810681 47 18 21.3481003036481 -3.34810030364814 48 32 24.6349525577956 7.36504744220444 49 25 24.9514383141044 0.0485616858955814 50 25 21.737318920707 3.26268107929301 51 23 20.8009936574846 2.19900634251539 52 21 22.0614054790237 -1.06140547902374 53 20 23.938680930279 -3.93868093027899 54 15 16.4581620642669 -1.45816206426694 55 30 26.6047304105651 3.39526958943494 56 24 25.2470066108757 -1.24700661087571 57 26 24.2074098506560 1.79259014934395 58 24 21.6849039507184 2.31509604928158 59 22 21.3469447486746 0.653055251325386 60 14 15.6514365191043 -1.65143651910432 61 24 22.1296962652753 1.87030373472474 62 24 22.8831514335020 1.11684856649805 63 24 23.2843597785227 0.715640221477318 64 24 19.8486924751679 4.15130752483210 65 19 18.4481533799900 0.551846620010022 66 31 26.7335874349483 4.2664125650517 67 22 26.5215900363656 -4.52159003636563 68 27 21.4111864751268 5.5888135248732 69 19 17.641416213208 1.35858378679201 70 25 22.2048330099449 2.79516699005507 71 20 24.9347351874032 -4.93473518740321 72 21 21.3990237169588 -0.3990237169588 73 27 27.4183665916093 -0.418366591609338 74 23 24.3746124922624 -1.37461249226241 75 25 25.6833747379211 -0.683374737921115 76 20 22.1800239742600 -2.18002397426005 77 21 19.2023750134258 1.79762498657421 78 22 22.3862171288093 -0.386217128809271 79 23 22.8914164817495 0.108583518250498 80 25 24.0565898806006 0.943410119399396 81 25 23.3218681797845 1.67813182021553 82 17 23.7195093287429 -6.71950932874289 83 19 21.3959632834841 -2.39596328348412 84 25 23.8842472412004 1.11575275879955 85 19 22.3010541105851 -3.30105411058514 86 20 23.1266938500491 -3.12669385004909 87 26 22.4809582943909 3.51904170560905 88 23 20.6564751885690 2.34352481143104 89 27 24.3430597171288 2.65694028287115 90 17 20.8503426134519 -3.85034261345193 91 17 23.3211586348698 -6.32115863486977 92 19 20.0366456476630 -1.03664564766296 93 17 19.6807349899718 -2.68073498997179 94 22 22.0379172391335 -0.0379172391335114 95 21 23.3856638961778 -2.38566389617783 96 32 28.5991521791672 3.40084782083280 97 21 24.6614106338104 -3.66141063381038 98 21 24.3080160450159 -3.30801604501587 99 18 21.2070236612869 -3.20702366128693 100 18 21.2610760499861 -3.26107604998605 101 23 22.7863799272109 0.213620072789081 102 19 20.5907043961488 -1.59070439614882 103 20 20.9772930432377 -0.977293043237723 104 21 22.2383514483243 -1.23835144832433 105 20 23.7118985607275 -3.71189856072748 106 17 18.8403733336065 -1.84037333360655 107 18 20.2572364317288 -2.25723643172879 108 19 20.7196144481076 -1.71961444810765 109 22 22.0275626605593 -0.0275626605593270 110 15 18.7557114974235 -3.75571149742348 111 14 18.7922903692776 -4.79229036927756 112 18 26.5436099628167 -8.54360996281669 113 24 21.2628726079605 2.73712739203951 114 35 23.5462389082472 11.4537610917528 115 29 18.9866943088691 10.0133056911309 116 21 21.935944950304 -0.935944950303993 117 25 20.5220323095179 4.47796769048213 118 20 18.4455726336298 1.5544273663702 119 22 23.1944342306498 -1.19443423064979 120 13 16.8696658909449 -3.8696658909449 121 26 23.1870301698962 2.81296983010383 122 17 16.8739978966045 0.126002103395526 123 25 20.0507796496234 4.94922035037664 124 20 20.6180234596576 -0.618023459657552 125 19 18.0635928969879 0.936407103012104 126 21 22.6069239300865 -1.60692393008647 127 22 21.004834267862 0.995165732137998 128 24 22.5978785256876 1.40212147431243 129 21 22.893008601785 -1.89300860178502 130 26 25.4363237012179 0.563676298782062 131 24 20.5297469521146 3.4702530478854 132 16 20.2204944956761 -4.22049449567611 133 23 22.3001815014718 0.699818498528157 134 18 20.7446456449081 -2.74464564490807 135 16 22.3043405696256 -6.30434056962563 136 26 24.0921955799838 1.90780442001622 137 19 19.0502342475757 -0.0502342475756936 138 21 16.8720244761895 4.12797552381047 139 21 22.0933317973676 -1.09333179736762 140 22 18.451482961083 3.54851703891702 141 23 19.7302332118958 3.26976678810421 142 29 24.7822738737025 4.21772612629751 143 21 19.2106400938892 1.78935990611077 144 21 19.9054317541314 1.09456824586862 145 23 21.8498010024399 1.15019899756014 146 27 22.9941022404284 4.00589775957157 147 25 25.3939958500130 -0.393995850012971 148 21 20.946835038333 0.0531649616670011 149 10 17.0822628583037 -7.08226285830371 150 20 22.5777789638073 -2.5777789638073 151 26 22.4585531426257 3.54144685737425 152 24 23.6656316258617 0.334368374138264 153 29 31.7071557621354 -2.70715576213540 154 19 19.0522038357562 -0.0522038357562483 155 24 22.0525408015156 1.94745919848439 156 19 20.7371470618696 -1.73714706186964 157 24 23.3888420951761 0.611157904823943 158 22 21.7784950813887 0.221504918611301 159 17 23.7292621014340 -6.72926210143396 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.167714889966933 0.335429779933865 0.832285110033067 11 0.476210991442604 0.952421982885208 0.523789008557396 12 0.405776124415941 0.811552248831883 0.594223875584059 13 0.830643149947592 0.338713700104815 0.169356850052408 14 0.753480229424357 0.493039541151287 0.246519770575643 15 0.7354879303151 0.529024139369801 0.264512069684901 16 0.653774398960162 0.692451202079675 0.346225601039838 17 0.593366635761728 0.813266728476544 0.406633364238272 18 0.576949200610541 0.846101598778918 0.423050799389459 19 0.500266958164621 0.999466083670757 0.499733041835379 20 0.496535965699451 0.993071931398902 0.503464034300549 21 0.492737994079345 0.98547598815869 0.507262005920655 22 0.422900668072017 0.845801336144034 0.577099331927983 23 0.362242801923997 0.724485603847995 0.637757198076003 24 0.380403008269029 0.760806016538059 0.61959699173097 25 0.349260129619774 0.698520259239547 0.650739870380226 26 0.288300058994306 0.576600117988611 0.711699941005694 27 0.247644327088461 0.495288654176923 0.752355672911539 28 0.239279245221542 0.478558490443084 0.760720754778458 29 0.197924209740586 0.395848419481172 0.802075790259414 30 0.154172407490281 0.308344814980563 0.845827592509719 31 0.126005235524187 0.252010471048374 0.873994764475813 32 0.161026065024854 0.322052130049708 0.838973934975146 33 0.269830637476094 0.539661274952187 0.730169362523906 34 0.548348511466785 0.903302977066431 0.451651488533216 35 0.527129136516387 0.945741726967226 0.472870863483613 36 0.6042615937632 0.7914768124736 0.3957384062368 37 0.599699991500923 0.800600016998154 0.400300008499077 38 0.552943250244732 0.894113499510536 0.447056749755268 39 0.520711430201337 0.958577139597325 0.479288569798663 40 0.61443759464056 0.771124810718879 0.385562405359439 41 0.579743712412594 0.840512575174812 0.420256287587406 42 0.53628142495944 0.92743715008112 0.46371857504056 43 0.624380021332456 0.751239957335087 0.375619978667544 44 0.595123184173712 0.809753631652576 0.404876815826288 45 0.630094268326734 0.739811463346532 0.369905731673266 46 0.578866952807933 0.842266094384134 0.421133047192067 47 0.565302863105698 0.869394273788605 0.434697136894302 48 0.680914670410683 0.638170659178634 0.319085329589317 49 0.63746549008639 0.72506901982722 0.36253450991361 50 0.623632942998632 0.752734114002735 0.376367057001367 51 0.583966517586341 0.832066964827318 0.416033482413659 52 0.539257650179664 0.921484699640673 0.460742349820336 53 0.564890851254894 0.870218297490213 0.435109148745106 54 0.52700227886588 0.945995442268241 0.472997721134121 55 0.59021603073109 0.81956793853782 0.40978396926891 56 0.552954559757482 0.894090880485037 0.447045440242518 57 0.514684615603537 0.970630768792927 0.485315384396463 58 0.483846996379702 0.967693992759404 0.516153003620298 59 0.436800024657378 0.873600049314755 0.563199975342622 60 0.395523010634588 0.791046021269176 0.604476989365412 61 0.366785627756045 0.73357125551209 0.633214372243955 62 0.327325950492418 0.654651900984836 0.672674049507582 63 0.287269697402832 0.574539394805664 0.712730302597168 64 0.327904537198601 0.655809074397202 0.672095462801399 65 0.287124497834104 0.574248995668209 0.712875502165896 66 0.301395022534726 0.602790045069451 0.698604977465274 67 0.358424453674014 0.716848907348028 0.641575546325986 68 0.437598741919298 0.875197483838595 0.562401258080702 69 0.400053505849953 0.800107011699906 0.599946494150047 70 0.385556170704761 0.771112341409521 0.614443829295239 71 0.44979259131525 0.8995851826305 0.55020740868475 72 0.403910549032159 0.807821098064318 0.596089450967841 73 0.362437469142519 0.724874938285038 0.63756253085748 74 0.327384315881735 0.65476863176347 0.672615684118265 75 0.295795624677827 0.591591249355654 0.704204375322173 76 0.271636437346599 0.543272874693199 0.7283635626534 77 0.249547904307031 0.499095808614063 0.750452095692969 78 0.214465001125081 0.428930002250162 0.785534998874919 79 0.182827529312924 0.365655058625848 0.817172470687076 80 0.157191698452156 0.314383396904312 0.842808301547844 81 0.137699547974615 0.275399095949230 0.862300452025385 82 0.221313054921496 0.442626109842992 0.778686945078504 83 0.203279956975708 0.406559913951417 0.796720043024292 84 0.176281758004978 0.352563516009956 0.823718241995022 85 0.176867198607590 0.353734397215181 0.82313280139241 86 0.172691264466091 0.345382528932181 0.82730873553391 87 0.179798783239274 0.359597566478548 0.820201216760726 88 0.168630293967603 0.337260587935206 0.831369706032397 89 0.158619798245149 0.317239596490298 0.841380201754851 90 0.162288626205746 0.324577252411491 0.837711373794254 91 0.234836173026185 0.46967234605237 0.765163826973815 92 0.20139934095589 0.40279868191178 0.79860065904411 93 0.184757199150369 0.369514398300738 0.815242800849631 94 0.155997893454410 0.311995786908821 0.84400210654559 95 0.140973320796948 0.281946641593895 0.859026679203052 96 0.144329651570415 0.288659303140831 0.855670348429585 97 0.145774159414261 0.291548318828523 0.854225840585739 98 0.141811927130382 0.283623854260764 0.858188072869618 99 0.134598310814225 0.269196621628450 0.865401689185775 100 0.129416485832775 0.258832971665550 0.870583514167225 101 0.105746053067436 0.211492106134872 0.894253946932564 102 0.0875952675229617 0.175190535045923 0.912404732477038 103 0.0701683379098852 0.140336675819770 0.929831662090115 104 0.056440974889137 0.112881949778274 0.943559025110863 105 0.0596509851692635 0.119301970338527 0.940349014830737 106 0.0487286338811894 0.0974572677623789 0.95127136611881 107 0.0425851102931952 0.0851702205863904 0.957414889706805 108 0.0369451247293547 0.0738902494587094 0.963054875270645 109 0.028094480523947 0.056188961047894 0.971905519476053 110 0.0276120326923326 0.0552240653846652 0.972387967307667 111 0.0347623099698411 0.0695246199396821 0.96523769003016 112 0.148031913163637 0.296063826327273 0.851968086836363 113 0.136114951998963 0.272229903997926 0.863885048001037 114 0.549103563368251 0.901792873263499 0.450896436631749 115 0.850962456133838 0.298075087732324 0.149037543866162 116 0.817546776560484 0.364906446879033 0.182453223439516 117 0.872513350277217 0.254973299445567 0.127486649722783 118 0.847454888396848 0.305090223206305 0.152545111603152 119 0.818754231632925 0.362491536734151 0.181245768367075 120 0.852182839569344 0.295634320861312 0.147817160430656 121 0.828843023539678 0.342313952920645 0.171156976460322 122 0.788417255940558 0.423165488118883 0.211582744059441 123 0.819781614122325 0.360436771755349 0.180218385877675 124 0.777004047153697 0.445991905692606 0.222995952846303 125 0.737437204360765 0.52512559127847 0.262562795639235 126 0.6885490789282 0.6229018421436 0.3114509210718 127 0.651568356838167 0.696863286323666 0.348431643161833 128 0.609273687051868 0.781452625896265 0.390726312948132 129 0.550292312697758 0.899415374604485 0.449707687302242 130 0.487014672794253 0.974029345588506 0.512985327205747 131 0.484712723736008 0.969425447472016 0.515287276263992 132 0.482597109188469 0.965194218376939 0.517402890811531 133 0.432056864620903 0.864113729241807 0.567943135379097 134 0.383808125714437 0.767616251428874 0.616191874285563 135 0.531448566370668 0.937102867258665 0.468551433629332 136 0.492168817469643 0.984337634939285 0.507831182530357 137 0.418692563784427 0.837385127568853 0.581307436215573 138 0.428167527188235 0.85633505437647 0.571832472811765 139 0.356583342636536 0.713166685273072 0.643416657363464 140 0.320359437679118 0.640718875358235 0.679640562320883 141 0.285913182586271 0.571826365172541 0.71408681741373 142 0.336504411054373 0.673008822108745 0.663495588945627 143 0.478094113575687 0.956188227151374 0.521905886424313 144 0.400992750579691 0.801985501159381 0.599007249420309 145 0.319884142938733 0.639768285877466 0.680115857061267 146 0.3079444732906 0.6158889465812 0.6920555267094 147 0.254742419681059 0.509484839362119 0.74525758031894 148 0.159091561128108 0.318183122256215 0.840908438871892 149 0.304106957247093 0.608213914494187 0.695893042752907 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 6 0.0428571428571429 OK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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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Software written by Ed van Stee & Patrick Wessa

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