Workshop 7 multiple regression

*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: Fri, 03 Dec 2010 12:20:20 +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/03/t1291378745yqb5ixqdvvv6pxw.htm/, Retrieved Fri, 03 Dec 2010 13:19:17 +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/03/t1291378745yqb5ixqdvvv6pxw.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:

Mini-tutorial Gender

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 5 2 2 1 1 1 1 4 1 3 1 4 1 1 7 3 3 1 5 1 1 7 2 2 1 2 2 2 5 2 1 1 1 2 2 5 1 1 1 1 2 1 4 1 3 1 2 2 2 4 3 3 2 1 1 1 6 1 1 1 1 1 2 5 1 1 1 1 2 1 1 1 1 1 3 2 2 5 1 1 1 1 1 1 4 2 1 2 1 1 2 6 3 1 1 1 1 2 7 2 2 1 2 1 2 7 3 3 1 4 2 1 2 2 1 1 1 2 1 6 1 1 1 1 1 1 3 1 1 1 2 1 2 6 1 1 1 3 2 2 6 1 3 1 1 1 1 5 1 1 1 1 2 2 6 3 2 1 1 1 2 4 1 3 2 1 2 2 3 3 1 2 2 1 2 4 1 1 1 1 1 2 5 1 1 2 1 1 2 6 1 1 2 1 2 1 6 3 3 2 1 2 1 4 1 1 1 1 2 2 6 1 3 1 1 1 1 6 1 1 1 1 2 2 5 1 3 1 1 1 2 6 3 1 1 1 1 2 4 1 1 1 1 2 1 6 1 1 1 1 1 2 7 1 3 1 1 2 1 5 2 3 1 1 1 1 6 1 3 1 1 2 2 6 1 1 2 1 1 1 5 2 2 2 4 2 2 7 2 3 1 1 1 2 6 2 2 1 1 1 1 3 1 1 1 4 2 1 4 1 1 1 2 1 2 5 2 3 1 2 1 2 4 2 3 2 1 1 1 3 1 1 1 1 2 2 5 3 1 1 2 1 2 5 1 1 1 1 2 1 4 1 2 1 1 2 1 5 1 1 1 1 1 2 1 2 2 1 1 1 2 2 1 1 2 1 1 2 3 3 3 1 1 2 1 4 2 2 1 2 1 1 3 3 3 1 1 2 1 7 1 1 1 1 2 1 2 1 1 1 1 1 1 4 3 1 1 2 1 1 2 1 1 1 1 2 2 5 1 1 1 2 1 2 6 1 2 1 4 2 2 6 1 2 1 1 2 2 6 1 1 1 1 1 1 6 2 2 1 1 1 2 6 3 3 1 2 1 2 6 1 1 1 3 1 1 6 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Member[t] = + 1.30267905579266 + 0.0638572513593550Provison[t] + 0.0593542522425081Mother[t] + 0.00438665208409937Father[t] + 0.0498968809279368Illness[t] -0.0440151152769835Tobacco[t] -0.130198915314923Gender[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) 1.30267905579266 0.275443 4.7294 5e-06 3e-06 Provison 0.0638572513593550 0.028267 2.2591 0.025319 0.01266 Mother 0.0593542522425081 0.053809 1.1031 0.271768 0.135884 Father 0.00438665208409937 0.049651 0.0883 0.929717 0.464858 Illness 0.0498968809279368 0.117561 0.4244 0.671858 0.335929 Tobacco -0.0440151152769835 0.042108 -1.0453 0.297569 0.148784 Gender -0.130198915314923 0.082834 -1.5718 0.118105 0.059052 Multiple Linear Regression - Regression Statistics Multiple R 0.284268140970020 R-squared 0.0808083759705509 Adjusted R-squared 0.0440407110093729 F-TEST (value) 2.19781093131354 F-TEST (DF numerator) 6 F-TEST (DF denominator) 150 p-value 0.0462273521497196 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.487546698306195 Sum Squared Residuals 35.6552674543908 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 1.62512997157864 0.374870028421361 2 1 1.37425977422996 -0.374259774229960 3 1 1.64052491751606 -0.64052491751606 4 1 1.57863044370548 -0.578630443705482 5 2 1.49054440417966 0.509455595820344 6 2 1.43119015193715 0.568809848062853 7 1 1.33209108946901 -0.332091089469008 8 2 1.67491050547387 0.325089494526134 9 1 1.62524631861143 -0.625246318611425 10 2 1.43119015193715 0.568809848062852 11 1 1.08773091594576 -0.0877309159457599 12 2 1.56138906725207 0.43861093274793 13 1 1.60678294906316 -0.60678294906316 14 2 1.74395482309644 0.256045176903559 15 2 1.70882935902040 0.291170640979595 16 2 1.55434111747812 0.445658882521878 17 1 1.29897265010159 -0.29897265010159 18 1 1.62524631861143 -0.625246318611425 19 1 1.38965944925638 -0.389659449256376 20 2 1.40701717274254 0.592982827257464 21 2 1.63401962277962 0.365980377220376 22 1 1.43119015193715 -0.431190151937147 23 2 1.74834147518054 0.251658524819459 24 2 1.42600308567393 0.573996914326072 25 2 1.55826483466933 0.441735165330671 26 2 1.49753181589271 0.502468184107285 27 2 1.61128594818001 0.388714051819993 28 2 1.54494428422444 0.455055715775560 29 1 1.67242609287765 -0.672426092877654 30 1 1.36733290057779 -0.367332900577792 31 2 1.63401962277962 0.365980377220376 32 1 1.49504740329650 -0.495047403296503 33 2 1.57016237142027 0.429837628579731 34 2 1.74395482309644 0.256045176903559 35 2 1.36733290057779 0.632667099422208 36 1 1.62524631861143 -0.625246318611425 37 2 1.56767795882406 0.432322041175943 38 1 1.62951662366278 -0.629516623662777 39 1 1.50382070746470 -0.503820707464702 40 2 1.67514319953936 0.324856800460638 41 1 1.41278259136074 -0.412782591360741 42 2 1.75723112638149 0.242768873618513 43 2 1.68898722293803 0.311012777061967 44 1 1.17143030338749 -0.171430303387487 45 1 1.45351670061573 -0.453516700615731 46 2 1.58550150838579 0.414498491614207 47 2 1.61555625323136 0.384443746768642 48 1 1.30347564921844 -0.303475649218437 49 2 1.63608245646010 0.363917543539897 50 2 1.43119015193715 0.568809848062852 51 1 1.37171955266189 -0.371719552661892 52 1 1.56138906725207 -0.56138906725207 53 2 1.36970096614126 0.630299033858743 54 2 1.41971419410194 0.580285805898058 55 2 1.43095745787165 0.569042542128348 56 1 1.51725760494234 -0.517257604942339 57 1 1.43095745787165 -0.430957457871652 58 1 1.55890465465586 -0.558904654655858 59 1 1.36981731317400 -0.369817313174005 60 1 1.57222520510075 -0.572225205100748 61 1 1.23961839785908 -0.239618397859082 62 2 1.51737395197509 0.482626048024913 63 2 1.36738870954965 0.632611290450348 64 2 1.49943405538060 0.500565944619398 65 2 1.62524631861143 0.374753681388575 66 1 1.68898722293803 -0.688987222938033 67 2 1.70871301198766 0.291286988012343 68 2 1.53721608805746 0.462783911942542 69 1 1.50382070746470 -0.503820707464702 70 1 1.56127272021932 -0.561272720219322 71 1 1.4310738049044 -0.4310738049044 72 2 1.68887087590528 0.311129124094715 73 1 1.69337387502213 -0.693373875022132 74 1 1.62524631861143 -0.625246318611425 75 1 1.68199981122497 -0.681999811224973 76 1 1.69337387502213 -0.693373875022132 77 2 1.68391650370756 0.316083496292439 78 1 1.58561785541854 -0.585617855418541 79 2 1.49302881677587 0.506971183224132 80 2 1.62951662366278 0.370483376337223 81 2 1.69337387502213 0.306626124977868 82 2 1.4354604569885 0.564539543011501 83 1 1.68887087590528 -0.688870875905285 84 2 1.74834147518054 0.251658524819459 85 2 1.68898722293803 0.311012777061967 86 1 1.31224895338664 -0.312248953386636 87 2 1.64935875974515 0.350641240254851 88 2 1.56138906725207 0.43861093274793 89 1 1.49504740329650 -0.495047403296503 90 1 1.36733290057779 -0.367332900577792 91 2 1.61825890689837 0.381741093101634 92 2 1.62512997157868 0.374870028421322 93 2 1.64497210766105 0.355027892338951 94 1 1.55878830762311 -0.55878830762311 95 2 1.51731341391420 0.482686586085802 96 1 1.73900045089872 -0.739000450898717 97 2 1.69337387502213 0.306626124977868 98 1 1.55878830762311 -0.55878830762311 99 1 1.70871301198766 -0.708713011987657 100 2 1.62524631861143 0.374753681388575 101 2 1.28178708262004 0.718212917379962 102 1 1.36733290057779 -0.367332900577792 103 2 1.49481470923101 0.505185290768993 104 2 1.69337387502213 0.306626124977868 105 1 1.60084064535132 -0.600840645351318 106 1 1.74395482309644 -0.743954823096441 107 1 1.62963297069552 -0.629632970695525 108 1 1.28951527878702 -0.289515278787019 109 2 1.75284447429739 0.247155525702612 110 1 1.18014779858383 -0.180147798583826 111 1 1.49753181589271 -0.497531815892715 112 1 1.19987358763345 -0.19987358763345 113 1 1.64497210766105 -0.644972107661049 114 2 1.55694187710708 0.443058122892918 115 1 1.56132852919118 -0.561328529191182 116 2 1.75284447429739 0.247155525702612 117 1 1.63401962277962 -0.634019622779624 118 2 1.49753181589271 0.502468184107285 119 2 1.62501362454593 0.374986375454070 120 1 1.49320097278047 -0.493200972780475 121 1 1.72999445266502 -0.729994452665023 122 2 1.68910356997078 0.310896430029219 123 2 1.36733290057779 0.632667099422208 124 1 1.56127272021932 -0.561272720219322 125 2 1.47075807706914 0.529241922930857 126 2 1.67761315914087 0.322386840859126 127 2 1.43119015193715 0.568809848062852 128 2 1.61814255986562 0.381857440134382 129 1 1.47663984272010 -0.476639842720097 130 2 1.62068278143369 0.379317218566310 131 2 1.62951662366278 0.370483376337223 132 2 1.64508845469380 0.354911545306203 133 2 1.49481470923101 0.505185290768993 134 1 1.64058545557695 -0.64058545557695 135 1 1.75272812726464 -0.75272812726464 136 2 1.66481424374342 0.335185756256579 137 2 1.57851409667273 0.421485903327266 138 2 1.70871301198766 0.291286988012343 139 2 1.56577571933617 0.434224280663831 140 1 1.49054440417966 -0.490544404179655 141 2 1.38717503666016 0.612824963339836 142 2 1.69337387502213 0.306626124977868 143 2 1.74983658874739 0.250163411252605 144 1 1.70375863978993 -0.703758639789933 145 1 1.37171955266189 -0.371719552661892 146 2 1.55878830762311 0.44121169237689 147 2 1.51477319234613 0.485226807653873 148 2 1.68910356997078 0.310896430029219 149 1 1.58123120333444 -0.581231203334442 150 2 1.69349022205488 0.30650977794512 151 2 1.55181534890475 0.448184651095249 152 2 1.62963297069552 0.370367029304475 153 1 1.49481470923101 -0.494814709231007 154 1 1.36733290057779 -0.367332900577792 155 2 1.80781207445580 0.192187925544203 156 1 1.50191846797681 -0.501918467976814 157 2 1.85770895538373 0.142291044616267 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.351630915580457 0.703261831160915 0.648369084419543 11 0.667088203752405 0.665823592495191 0.332911796247595 12 0.588323414294063 0.823353171411874 0.411676585705937 13 0.573124331670336 0.853751336659328 0.426875668329664 14 0.490169402994510 0.980338805989021 0.509830597005489 15 0.475960665836679 0.951921331673357 0.524039334163321 16 0.539373722708847 0.921252554582305 0.460626277291153 17 0.649874798262385 0.70025040347523 0.350125201737615 18 0.66662688034639 0.66674623930722 0.33337311965361 19 0.59102810373895 0.8179437925221 0.40897189626105 20 0.66406633449884 0.67186733100232 0.33593366550116 21 0.624671051490684 0.750657897018633 0.375328948509316 22 0.653401586276698 0.693196827446604 0.346598413723302 23 0.583419337818924 0.833161324362152 0.416580662181076 24 0.560462030486562 0.879075939026876 0.439537969513438 25 0.569627452211614 0.86074509557677 0.430372547788385 26 0.596224663834491 0.807550672331017 0.403775336165509 27 0.553956290668399 0.892087418663203 0.446043709331601 28 0.500252078369269 0.999495843261462 0.499747921630731 29 0.671092649632264 0.657814700735473 0.328907350367736 30 0.66078941668471 0.678421166630581 0.339210583315290 31 0.62439427854767 0.751211442904661 0.375605721452330 32 0.642317758341667 0.715364483316666 0.357682241658333 33 0.610983120417559 0.778033759164883 0.389016879582441 34 0.561436549816651 0.877126900366698 0.438563450183349 35 0.581207957782957 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0.389681924342969 0.779363848685938 0.610318075657031 54 0.405932510737418 0.811865021474837 0.594067489262582 55 0.399486554624722 0.798973109249445 0.600513445375278 56 0.409840967365237 0.819681934730475 0.590159032634763 57 0.423164606736036 0.846329213472071 0.576835393263964 58 0.439024637296977 0.878049274593954 0.560975362703023 59 0.420866574884276 0.841733149768552 0.579133425115724 60 0.437164512593189 0.874329025186379 0.56283548740681 61 0.400938157026348 0.801876314052695 0.599061842973652 62 0.406292295805872 0.812584591611743 0.593707704194128 63 0.454179684248324 0.908359368496648 0.545820315751676 64 0.452301907667636 0.904603815335271 0.547698092332364 65 0.429561965242208 0.859123930484416 0.570438034757792 66 0.480352003255016 0.960704006510032 0.519647996744984 67 0.44833774947198 0.89667549894396 0.55166225052802 68 0.442410653429994 0.884821306859988 0.557589346570006 69 0.446573769445521 0.893147538891042 0.553426230554479 70 0.459852618056318 0.919705236112636 0.540147381943682 71 0.445874725611738 0.891749451223476 0.554125274388262 72 0.418252343058283 0.836504686116567 0.581747656941717 73 0.463601609539741 0.927203219079481 0.536398390460259 74 0.49430832809617 0.98861665619234 0.50569167190383 75 0.53450211036311 0.93099577927378 0.46549788963689 76 0.577248001425121 0.845503997149758 0.422751998574879 77 0.564725090505617 0.870549818988766 0.435274909494383 78 0.584443485420642 0.831113029158717 0.415556514579358 79 0.58998616340297 0.82002767319406 0.41001383659703 80 0.57331594909913 0.85336810180174 0.42668405090087 81 0.546529248727802 0.906941502544396 0.453470751272198 82 0.564933702748998 0.870132594502004 0.435066297251002 83 0.603980836510656 0.792038326978687 0.396019163489344 84 0.570531137478424 0.858937725043152 0.429468862521576 85 0.542543862703831 0.914912274592339 0.457456137296169 86 0.511360082875296 0.977279834249408 0.488639917124704 87 0.488476204930675 0.97695240986135 0.511523795069325 88 0.478670764306747 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0.591889394545756 0.816221210908487 0.408110605454244 124 0.582806045495914 0.834387909008172 0.417193954504086 125 0.564027457552535 0.87194508489493 0.435972542447465 126 0.508785835610543 0.982428328778914 0.491214164389457 127 0.516053620152634 0.967892759694733 0.483946379847366 128 0.466354381297476 0.932708762594952 0.533645618702524 129 0.474338875747611 0.948677751495222 0.525661124252389 130 0.425293766667273 0.850587533334546 0.574706233332727 131 0.40364003044998 0.80728006089996 0.59635996955002 132 0.354728841514421 0.709457683028843 0.645271158485579 133 0.372532743193274 0.745065486386548 0.627467256806726 134 0.43601892592237 0.87203785184474 0.56398107407763 135 0.560192129589606 0.879615740820787 0.439807870410394 136 0.485706402485618 0.971412804971235 0.514293597514382 137 0.434456130519983 0.868912261039966 0.565543869480017 138 0.374705365801195 0.74941073160239 0.625294634198805 139 0.366304833189277 0.732609666378553 0.633695166810723 140 0.413124393395239 0.826248786790479 0.586875606604761 141 0.510637152257131 0.978725695485738 0.489362847742869 142 0.454502555567542 0.909005111135085 0.545497444432458 143 0.418284463878569 0.836568927757138 0.581715536121431 144 0.80604160814567 0.38791678370866 0.19395839185433 145 0.747359635401971 0.505280729196057 0.252640364598029 146 0.612691150831759 0.774617698336483 0.387308849168241 147 0.753980376230438 0.492039247539123 0.246019623769562 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 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/10qujv1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/10qujv1291378809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/11tmj1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/11tmj1291378809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/21tmj1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/21tmj1291378809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/31tmj1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/31tmj1291378809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/4u2lm1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/4u2lm1291378809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/5u2lm1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/5u2lm1291378809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/64b2p1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/64b2p1291378809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/7fkjs1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/7fkjs1291378809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/8fkjs1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/8fkjs1291378809.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/9fkjs1291378809.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291378745yqb5ixqdvvv6pxw/9fkjs1291378809.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') }

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Software written by Ed van Stee & Patrick Wessa

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