Mini-tutorial Mate van angst

*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, 22 Nov 2010 10:33:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k.htm/, Retrieved Mon, 22 Nov 2010 11:34:11 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k.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 «

69 24 14 11 12 24 26 53 25 11 7 8 25 23 43 17 6 17 8 30 25 60 18 12 10 8 19 23 49 18 8 12 9 22 19 62 16 10 12 7 22 29 45 20 10 11 4 25 25 50 16 11 11 11 23 21 75 17 11 13 7 21 25 82 18 16 12 7 17 22 60 23 13 14 12 19 24 59 30 12 16 10 19 18 21 23 8 11 10 15 22 40 18 12 10 8 16 15 62 22 11 13 11 24 18 54 15 11 11 8 23 22 47 20 9 15 6 25 24 59 31 14 17 11 23 20 37 20 10 10 8 26 23 43 15 12 11 8 20 25 48 30 9 15 9 27 26 79 32 16 9 6 29 26 62 19 20 8 7 19 25 16 25 7 18 11 35 17 38 22 9 16 9 24 23 58 25 8 12 7 32 25 60 19 9 13 8 27 21 72 14 15 13 8 14 16 67 19 11 11 8 20 28 55 19 10 12 7 17 21 47 23 10 12 8 20 21 59 31 14 10 8 18 23 49 17 9 17 9 25 21 47 12 4 15 4 27 28 57 26 13 12 8 24 29 39 21 10 13 6 24 24 49 28 11 13 6 25 22 26 23 10 15 10 23 21 53 33 14 9 6 32 24 75 26 16 5 4 23 24 65 27 15 11 9 23 21 49 21 9 9 9 22 20 48 18 9 12 8 21 24 45 13 14 13 6 21 25 31 17 9 11 5 23 26 67 18 12 13 9 21 13 61 26 11 18 5 29 18 49 24 9 13 10 19 15 69 21 12 14 9 22 24 54 21 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 Anxiety[t] = + 20.3838257780381 + 0.113181873884428Concern[t] + 2.57520207109418Doubts[t] + 0.356521545363305Pexpectations[t] -0.0846338978898613Pcriticism[t] -0.0783139174114985Standards[t] -0.028565001972493Organization[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) 20.3838257780381 7.937237 2.5681 0.011222 0.005611 Concern 0.113181873884428 0.207946 0.5443 0.58707 0.293535 Doubts 2.57520207109418 0.374663 6.8734 0 0 Pexpectations 0.356521545363305 0.351851 1.0133 0.312595 0.156297 Pcriticism -0.0846338978898613 0.443961 -0.1906 0.849076 0.424538 Standards -0.0783139174114985 0.276392 -0.2833 0.777312 0.388656 Organization -0.028565001972493 0.267905 -0.1066 0.915233 0.457616 Multiple Linear Regression - Regression Statistics Multiple R 0.559188538520539 R-squared 0.312691821612736 Adjusted R-squared 0.284638426576521 F-TEST (value) 11.1463094291822 F-TEST (DF numerator) 6 F-TEST (DF denominator) 147 p-value 3.13000736440472e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.4087517401793 Sum Squared Residuals 19133.4635915494 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 69 59.4369259017397 9.5630740982603 2 53 50.7443320609542 2.25566793904584 3 43 40.0793825770384 2.92061742296162 4 60 54.0667091554162 5.93329084458376 5 49 44.2736283195318 4.72637168046824 6 62 49.081286490006 12.9187135099940 7 45 49.3107123895055 -4.31071238950551 8 50 51.1116375225459 -1.11163752254592 9 75 52.3187659056494 22.6812340943506 10 82 65.3503872652049 16.6496127347951 11 60 58.2668061838538 1.73319381614617 12 59 57.537578128292 1.46242187170806 13 21 44.8608846616637 -23.8608846616637 14 40 54.5301709234307 -14.5301709234307 15 62 52.5111529450851 9.48884705491493 16 54 51.2237923403586 2.77620765964142 17 47 48.0208937060573 -1.02089370605732 18 59 62.7026661182472 -3.70266611824718 19 37 48.5944713391162 -11.5944713391162 20 43 53.9482411577698 -10.9482411577698 21 48 48.685052912464 -0.685052912464035 22 79 64.8959757445589 14.1040242554411 23 62 74.0959684012723 -12.0959684012723 24 16 43.4996099196242 -27.4996099196242 25 38 48.4567562249039 -10.4567562249039 26 58 44.2806400465525 13.7193599534475 27 60 46.9544681167610 13.0455318832390 28 72 63.0006771101159 8.9993228898841 29 67 51.7400715762958 15.2599284237042 30 55 50.0409217144968 4.95907828550324 31 47 50.1740735599101 -3.17407355991012 32 59 60.7667915755137 -1.76679157551365 33 49 48.2261844873785 0.773815512621455 34 47 34.1378083125778 12.8621916874222 35 57 57.69744970942 -0.697449709419993 36 39 50.0745484777208 -11.0745484777208 37 49 53.4208397525395 -4.42083975253948 38 26 50.8394286479858 -24.8394286479858 39 53 59.6809417279654 -6.68094172796545 40 75 63.4870796239928 11.5129203760072 41 65 62.826714215431 2.17328578456895 42 49 46.0902463742168 2.90975362578319 43 48 46.8689531960648 1.13104680393517 44 45 59.6762785212841 -14.6762785212841 45 31 46.4393936317187 -15.4393936317187 46 67 55.1806620785182 11.8193379214818 47 61 54.862721967721 6.13727803227902 48 49 48.1490110415304 0.850988958469589 49 69 55.4842003064259 13.5157996935741 50 54 47.6370143000145 6.36298569998545 51 80 51.4941658226116 28.5058341773884 52 57 39.4028117500114 17.5971882499886 53 34 48.6212732611854 -14.6212732611854 54 69 59.2096212620797 9.79037873792027 55 44 51.5473788690402 -7.54737886904024 56 70 44.4886614035045 25.5113385964955 57 51 52.3257211882739 -1.32572118827390 58 66 49.081286490006 16.9187135099940 59 18 39.04295110312 -21.04295110312 60 74 47.7406952597359 26.2593047402641 61 59 66.7581293129185 -7.7581293129185 62 48 46.3090425800344 1.69095741996561 63 55 57.4886319064142 -2.48863190641422 64 44 48.7668689906469 -4.76686899064692 65 56 53.6952453478197 2.30475465218029 66 65 51.3191513196825 13.6808486803175 67 77 60.3566279838175 16.6433720161825 68 46 51.4858462326123 -5.4858462326123 69 70 64.9537456915625 5.04625430843751 70 39 44.8956902805788 -5.89569028057885 71 55 47.3874057259911 7.61259427400891 72 44 48.0976563846827 -4.09765638468274 73 45 52.0988968571177 -7.09889685711767 74 45 37.2488837052199 7.75111629478015 75 25 61.6767173029837 -36.6767173029837 76 49 55.424099648864 -6.42409964886396 77 65 56.8069862729469 8.19301372705311 78 45 46.4076306700835 -1.40763067008355 79 71 60.2853189927822 10.7146810072178 80 48 50.0154344560508 -2.01543445605076 81 41 51.5971277844792 -10.5971277844792 82 40 45.3302800226934 -5.33028002269341 83 64 60.3010507797081 3.6989492202919 84 56 62.3968660417721 -6.39686604177207 85 52 58.0364004491070 -6.03640044910705 86 41 49.4196181697217 -8.41961816972174 87 45 50.2038354778423 -5.20383547784227 88 42 49.3107123895055 -7.31071238950551 89 54 66.9665762450859 -12.9665762450859 90 40 51.1716612850448 -11.1716612850448 91 40 48.1510685296297 -8.1510685296297 92 51 55.5043844151319 -4.50438441513193 93 48 48.6714199473914 -0.671419947391398 94 80 68.7057652622751 11.2942347377249 95 38 46.3706507228887 -8.37065072288875 96 57 41.7905940687434 15.2094059312566 97 51 49.6345729244494 1.36542707555062 98 46 42.0340929423563 3.96590705764373 99 58 60.077969689071 -2.07796968907100 100 67 60.099175994978 6.90082400502204 101 72 65.4832310524002 6.51676894759981 102 26 34.5624993697622 -8.5624993697622 103 54 45.463677588767 8.536322411233 104 53 53.947936956661 -0.94793695666104 105 69 51.2618723389369 17.7381276610631 106 64 67.2183308617871 -3.21833086178706 107 47 47.6653992167658 -0.665399216765783 108 43 61.0049575044314 -18.0049575044314 109 66 64.0866165921385 1.9133834078615 110 54 56.2319074417817 -2.23190744178168 111 62 54.5540422151346 7.44595778486536 112 52 47.1198540412709 4.88014595872906 113 64 49.8678607257055 14.1321392742945 114 55 46.9376893042502 8.06231069574979 115 74 52.8670948488954 21.1329051511046 116 32 44.5034980851813 -12.5034980851813 117 38 35.8467759053801 2.15322409461985 118 66 60.4864017843469 5.51359821565308 119 37 46.4393936317187 -9.4393936317187 120 26 43.5013840867387 -17.5013840867387 121 64 50.631171070157 13.3688289298430 122 28 41.0115309335622 -13.0115309335622 123 65 52.1930394260313 12.8069605739687 124 48 45.2511779692258 2.74882203077417 125 44 45.6456476830613 -1.64564768306127 126 64 54.8735200871087 9.12647991289129 127 39 58.9385153043637 -19.9385153043637 128 50 57.6099171189342 -7.60991711893422 129 52 60.750044346486 -8.75004434648594 130 48 54.0667091554162 -6.06670915541624 131 70 54.056893814811 15.9431061851890 132 66 60.4236814555312 5.57631854446884 133 61 65.3223309810183 -4.32233098101833 134 31 44.6778106162347 -13.6778106162347 135 61 61.1310052111362 -0.131005211136226 136 54 44.0959353531964 9.90406464680364 137 34 46.0257693337217 -12.0257693337217 138 62 59.7205724873639 2.27942751263615 139 47 41.1693177752797 5.83068222472034 140 52 61.9505538819357 -9.95055388193572 141 37 55.7354121533853 -18.7354121533853 142 46 46.7480622059432 -0.7480622059432 143 61 61.360280699653 -0.360280699653013 144 70 61.4438534895153 8.55614651048474 145 63 60.6660355254088 2.33396447459117 146 34 43.1891486725199 -9.18914867251991 147 46 43.5998650868783 2.40013491312169 148 40 48.7033994366018 -8.70339943660178 149 30 45.4828278407567 -15.4828278407567 150 35 50.4044652122142 -15.4044652122142 151 51 56.2836574009237 -5.28365740092368 152 56 44.4397843198291 11.5602156801709 153 44 54.0667091554162 -10.0667091554162 154 58 47.73362366363 10.2663763363700 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.25421968105371 0.50843936210742 0.74578031894629 11 0.411604796700695 0.82320959340139 0.588395203299305 12 0.272196079137742 0.544392158275484 0.727803920862258 13 0.380005420847302 0.760010841694604 0.619994579152698 14 0.387161950601279 0.774323901202558 0.612838049398721 15 0.338355935349171 0.676711870698343 0.661644064650829 16 0.261740361328081 0.523480722656162 0.738259638671919 17 0.222247714199627 0.444495428399253 0.777752285800373 18 0.218278544254667 0.436557088509335 0.781721455745333 19 0.252951801545719 0.505903603091439 0.747048198454281 20 0.397615561381966 0.795231122763932 0.602384438618034 21 0.319105033864973 0.638210067729945 0.680894966135027 22 0.263210443008280 0.526420886016559 0.73678955699172 23 0.510487729182694 0.979024541634613 0.489512270817306 24 0.762933168502891 0.474133662994218 0.237066831497109 25 0.74752326932658 0.504953461346841 0.252476730673421 26 0.763753559233545 0.47249288153291 0.236246440766455 27 0.789215015855602 0.421569968288796 0.210784984144398 28 0.778065166198304 0.443869667603392 0.221934833801696 29 0.770913355860769 0.458173288278462 0.229086644139231 30 0.729663642093462 0.540672715813076 0.270336357906538 31 0.676130423023314 0.647739153953371 0.323869576976685 32 0.619172178891776 0.761655642216448 0.380827821108224 33 0.558714865354158 0.882570269291683 0.441285134645842 34 0.521329858905409 0.957340282189183 0.478670141094591 35 0.487192843896362 0.974385687792725 0.512807156103638 36 0.516700682871238 0.966598634257523 0.483299317128762 37 0.463616777412819 0.927233554825639 0.53638322258718 38 0.628834389593437 0.742331220813125 0.371165610406563 39 0.590465796299476 0.819068407401047 0.409534203700524 40 0.567841220577627 0.864317558844747 0.432158779422373 41 0.517325109303862 0.965349781392275 0.482674890696138 42 0.480186761204069 0.960373522408138 0.519813238795931 43 0.42554502406296 0.85109004812592 0.57445497593704 44 0.54245063649352 0.91509872701296 0.45754936350648 45 0.620146041620497 0.759707916759006 0.379853958379503 46 0.655144195042761 0.689711609914478 0.344855804957239 47 0.624890076751215 0.75021984649757 0.375109923248785 48 0.583971656986577 0.832056686026846 0.416028343013423 49 0.599245181762974 0.801509636474052 0.400754818237026 50 0.565732720721478 0.868534558557044 0.434267279278522 51 0.754888462623763 0.490223074752474 0.245111537376237 52 0.780091989232849 0.439816021534302 0.219908010767151 53 0.816946369009242 0.366107261981516 0.183053630990758 54 0.802656675807309 0.394686648385383 0.197343324192691 55 0.78776645284949 0.424467094301022 0.212233547150511 56 0.90178971733219 0.19642056533562 0.09821028266781 57 0.881648230849435 0.23670353830113 0.118351769150565 58 0.904156184728685 0.19168763054263 0.095843815271315 59 0.948330827763835 0.103338344472331 0.0516691722361654 60 0.985215959102233 0.0295680817955339 0.0147840408977669 61 0.981625531373165 0.0367489372536695 0.0183744686268347 62 0.975580449085367 0.0488391018292661 0.0244195509146331 63 0.968109733966123 0.0637805320677546 0.0318902660338773 64 0.961473111573097 0.0770537768538053 0.0385268884269026 65 0.951984415893215 0.0960311682135692 0.0480155841067846 66 0.956684005874656 0.0866319882506881 0.0433159941253440 67 0.96837776473039 0.0632444705392188 0.0316222352696094 68 0.962126152778295 0.0757476944434104 0.0378738472217052 69 0.958033948011067 0.0839321039778654 0.0419660519889327 70 0.949326428745284 0.101347142509433 0.0506735712547163 71 0.942358654106729 0.115282691786542 0.0576413458932711 72 0.941295345185573 0.117409309628854 0.0587046548144269 73 0.932647593980657 0.134704812038685 0.0673524060193426 74 0.927345385296159 0.145309229407683 0.0726546147038413 75 0.994370900621626 0.0112581987567479 0.00562909937837395 76 0.99311913979319 0.0137617204136214 0.00688086020681072 77 0.992226514986008 0.0155469700279836 0.0077734850139918 78 0.989349803742493 0.0213003925150136 0.0106501962575068 79 0.99005365899567 0.0198926820086615 0.00994634100433076 80 0.98647196175414 0.0270560764917207 0.0135280382458604 81 0.985379456317566 0.0292410873648676 0.0146205436824338 82 0.981978251416798 0.0360434971664047 0.0180217485832024 83 0.97671566161686 0.0465686767662817 0.0232843383831408 84 0.971861462511263 0.0562770749774737 0.0281385374887368 85 0.965241292672562 0.0695174146548753 0.0347587073274376 86 0.960143514108308 0.0797129717833837 0.0398564858916919 87 0.951092166773996 0.0978156664520071 0.0489078332260036 88 0.941906118830384 0.116187762339231 0.0580938811696157 89 0.946468722912434 0.107062554175133 0.0535312770875663 90 0.945030281027256 0.109939437945488 0.0549697189727441 91 0.936100217631118 0.127799564737764 0.0638997823688821 92 0.921139243016987 0.157721513966025 0.0788607569830127 93 0.901711143034457 0.196577713931086 0.098288856965543 94 0.898789238214546 0.202421523570907 0.101210761785454 95 0.889903218629698 0.220193562740603 0.110096781370302 96 0.913571243349707 0.172857513300585 0.0864287566502927 97 0.891991014633025 0.216017970733949 0.108008985366975 98 0.877090919023563 0.245818161952875 0.122909080976437 99 0.849418410500686 0.301163178998628 0.150581589499314 100 0.833507664993427 0.332984670013147 0.166492335006573 101 0.827393769014873 0.345212461970254 0.172606230985127 102 0.806712144042974 0.386575711914052 0.193287855957026 103 0.786222570080427 0.427554859839147 0.213777429919573 104 0.746018568320931 0.507962863358137 0.253981431679069 105 0.809901930206025 0.380196139587951 0.190098069793975 106 0.772626404342078 0.454747191315845 0.227373595657922 107 0.73023493750314 0.53953012499372 0.26976506249686 108 0.769855967471541 0.460288065056918 0.230144032528459 109 0.74026776587287 0.51946446825426 0.25973223412713 110 0.710104917213827 0.579790165572347 0.289895082786173 111 0.672416831410564 0.655166337178873 0.327583168589436 112 0.640365872790853 0.719268254418295 0.359634127209147 113 0.643013739091105 0.71397252181779 0.356986260908895 114 0.63116056232319 0.73767887535362 0.36883943767681 115 0.760552706138483 0.478894587723034 0.239447293861517 116 0.758171394481162 0.483657211037676 0.241828605518838 117 0.741447981202704 0.517104037594592 0.258552018797296 118 0.714992891228186 0.570014217543627 0.285007108771814 119 0.671450400572188 0.657099198855624 0.328549599427812 120 0.688660534723914 0.622678930552172 0.311339465276086 121 0.705548989660785 0.588902020678431 0.294451010339215 122 0.699717149274181 0.600565701451637 0.300282850725819 123 0.747848313293219 0.504303373413563 0.252151686706781 124 0.707024870258699 0.585950259482603 0.292975129741301 125 0.657743938587118 0.684512122825765 0.342256061412882 126 0.702263669603366 0.595472660793268 0.297736330396634 127 0.763137543427554 0.473724913144891 0.236862456572446 128 0.713686035564906 0.572627928870189 0.286313964435094 129 0.688263275132206 0.623473449735588 0.311736724867794 130 0.627096877501266 0.745806244997467 0.372903122498734 131 0.739960108354014 0.520079783291971 0.260039891645986 132 0.758222160253096 0.483555679493809 0.241777839746904 133 0.691018129598634 0.617963740802732 0.308981870401366 134 0.640394644850922 0.719210710298155 0.359605355149078 135 0.561564150687768 0.876871698624463 0.438435849312232 136 0.642626347829949 0.714747304340101 0.357373652170051 137 0.602296861904399 0.795406276191203 0.397703138095601 138 0.511544505103714 0.976910989792572 0.488455494896286 139 0.730111574364794 0.539776851270413 0.269888425635206 140 0.63388580076043 0.732228398479139 0.366114199239570 141 0.599297370530086 0.801405258939828 0.400702629469914 142 0.473918607466531 0.947837214933063 0.526081392533469 143 0.335323407284504 0.670646814569008 0.664676592715496 144 0.352786363008558 0.705572726017116 0.647213636991442 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 12 0.0888888888888889 NOK 10% type I error level 23 0.170370370370370 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/10u8sb1290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/10u8sb1290422018.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/1gyu21290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/1gyu21290422018.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/2gyu21290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/2gyu21290422018.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/3gyu21290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/3gyu21290422018.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/49pb51290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/49pb51290422018.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/59pb51290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/59pb51290422018.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/69pb51290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/69pb51290422018.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/72ht81290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/72ht81290422018.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/8u8sb1290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/8u8sb1290422018.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/9u8sb1290422018.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290422038wh8ha6fqhnbpe5k/9u8sb1290422018.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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