*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: Wed, 01 Dec 2010 10:51:41 +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/01/t1291200677u2m0tw6al81sj7b.htm/, Retrieved Wed, 01 Dec 2010 11:51:28 +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/01/t1291200677u2m0tw6al81sj7b.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 «

5 22 0 15 4 2 1 0 7 0 0 3 7 4 0 2 5 14 5 3 5 2 0 12 4 0 4 3 4 4 4 0 6 6 0 12 5 25 0 15 1 0 0 0 5 25 5 10 4 0 0 12 6 2 2 20 7 30 3 20 7 1 0 2 2 0 0 3 6 0 0 16 4 8 0 4 3 0 4 2 6 0 0 4 6 0 8 16 5 6 0 0 4 0 0 0 6 6 0 15 4 12 3 9 3 1 0 1 4 20 24 15 5 5 15 5 6 0 0 4 6 21 12 15 4 3 0 4 6 5 0 12 6 8 0 2 5 10 4 4 6 5 1 2 4 8 0 4 6 6 16 8 7 15 9 30 5 9 0 6 6 14 8 6 6 9 10 7 5 5 0 4 7 9 6 17 6 10 0 5 3 12 0 0 4 9 15 3 5 7 0 4 4 15 0 15 3 14 0 0 5 16 0 8 5 6 0 10 4 6 0 4 5 2 0 0 1 8 10 6 2 0 7 11 3 6 2 10 4 4 0 0 3 15 2 0 7 0 0 0 2 12 3 0 4 0 12 0 2 13 0 0 5 18 3 0 6 4 0 7 6 9 0 4 6 12 0 12 6 14 8 6 6 0 0 12 6 4 7 10 6 12 0 9 4 15 18 6 4 0 0 0 5 30 13 16 6 0 0 2 6 0 0 0 7 3 0 0 4 2 0 1 6 15 0 10 6 3 2 10 6 4 0 14 3 12 9 12 5 8 16 12 6 12 10 12 4 18 0 5 5 15 7 0 6 3 8 4 6 0 0 3 3 0 0 0 6 21 0 14 5 10 0 4 6 5 1 3 4 0 0 0 7 1 0 12 5 0 0 12 6 6 0 15 6 12 0 0 6 10 20 8 7 0 9 6 6 25 0 14 6 3 0 5 6 15 0 10 6 10 0 16 2 15 4 4 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 satisfaction[t] = + 4.57408744603602 -0.00206177040274046Walked[t] -0.0182799519706426Cycled[t] + 0.0871931717568843`Other `[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) 4.57408744603602 0.179503 25.482 0 0 Walked -0.00206177040274046 0.014809 -0.1392 0.889453 0.444727 Cycled -0.0182799519706426 0.019634 -0.931 0.353273 0.176637 `Other ` 0.0871931717568843 0.018162 4.8009 4e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.374085962411091 R-squared 0.139940307273032 Adjusted R-squared 0.123400697797514 F-TEST (value) 8.46091967770866 F-TEST (DF numerator) 3 F-TEST (DF denominator) 156 p-value 3.03942628936404e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.33960726636346 Sum Squared Residuals 279.949429982628 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5 5.836626073529 -0.836626073529005 2 4 4.5516839532599 -0.551683953259895 3 7 4.83566696130668 2.16433303869332 4 7 4.74022670793883 2.25977329206117 5 5 4.71540241581509 0.284597584184906 6 5 5.61628196631315 -0.616281966313151 7 4 4.7625471534241 -0.762547153424103 8 4 4.49272055654249 -0.492720556542488 9 6 5.60803488470219 0.391965115297811 10 5 5.83044076232077 -0.830440762320774 11 1 4.57408744603602 -3.57408744603602 12 5 5.30307514368314 -0.303075143683139 13 4 5.62040550711863 -1.62040550711863 14 6 6.27726743642694 -0.27726743642694 15 7 6.20125791317956 0.798742086820435 16 7 4.74641201914705 2.25358798085295 17 2 4.83566696130667 -2.83566696130667 18 6 5.96917819414617 0.0308218058538309 19 4 4.90636596984163 -0.906365969841634 20 3 4.67535398166722 -1.67535398166722 21 6 4.92286013306356 1.07713986693644 22 6 5.82293857838103 0.177061421618972 23 5 4.56171682361958 0.438283176380422 24 4 4.57408744603602 -0.57408744603602 25 6 5.86961439997284 0.130385600027158 26 4 5.27924489110317 -1.27924489110317 27 3 4.65921884739016 -1.65921884739016 28 4 5.40203076703905 -1.40203076703905 29 5 4.7255451732471 0.2744548267529 30 6 4.92286013306356 1.07713986693644 31 6 5.61932842028402 0.380671579715976 32 4 4.91667482185534 -0.916674821855336 33 6 5.61009665510493 0.389903344895070 34 6 4.73197962632787 1.26802037367213 35 5 4.82912262115358 0.170877378846417 36 6 4.71988498556544 1.28011501443456 37 4 4.90636596984163 -0.906365969841634 38 6 4.96678296614437 1.03321703385563 39 7 6.99443647496566 0.00556352503434097 40 5 5.07869054295266 -0.0786905429526623 41 6 4.92214207517382 1.07785792482618 42 6 4.98308419500312 1.01691580499688 43 5 4.91255128104986 0.0874487189501445 44 7 5.92813572045453 1.07186427954547 45 6 4.98943560079304 1.01056439920696 46 3 4.54934620120314 -1.54934620120314 47 4 4.54291174812237 -0.54291174812237 48 5 4.90842774024437 0.0915722597556254 49 4 5.85105846634818 -1.85105846634818 50 3 4.54522266039765 -1.54522266039765 51 5 5.23864449364725 -0.238644493647248 52 5 5.43364854118842 -0.433648541188421 53 4 4.91048951064711 -0.910489510647115 54 5 4.56996390523054 0.43003609476946 55 1 4.89795279364898 -3.89795279364898 56 2 5.40525267156725 -3.40525267156725 57 3 5.39708863724714 -2.39708863724714 58 4 4.56584036442506 -0.565840364425059 59 3 4.50660098605363 -1.50660098605363 60 7 4.57408744603602 2.42591255396398 61 2 4.49450634529121 -2.49450634529121 62 4 4.35472802238831 -0.354728022388309 63 2 4.54728443080039 -2.54728443080039 64 5 4.48213572287476 0.517864277125235 65 6 5.17619256672325 0.823807433276751 66 6 4.90430419943889 1.09569580056111 67 6 5.59566426228575 0.404335737714253 68 6 4.92214207517382 1.07785792482618 69 6 5.62040550711863 0.379594492881368 70 6 5.3098124181994 0.690187581800597 71 6 5.33408474701509 0.665915252984906 72 4 4.73728078506465 -0.737280785064652 73 4 4.57408744603602 -0.57408744603602 74 5 5.6696857064456 -0.669685706445602 75 6 4.74847378954979 1.25152621045021 76 6 4.57408744603602 1.42591255396398 77 7 4.5679021348278 2.4320978651722 78 4 4.65715707698742 -0.657157076987424 79 6 5.41509260756376 0.584907392436243 80 6 5.40327394845536 0.596726051544643 81 6 5.78654476902144 0.213455230978561 82 3 5.43114469454996 -2.43114469454996 83 5 5.31143211236643 -0.311432112366426 84 6 5.41286474257932 0.58713525742068 85 4 4.97294143757111 -0.972941437571114 86 5 4.41520122620042 0.584798773799584 87 6 4.77043520609020 1.22956479390980 88 6 4.83566696130667 1.16433303869333 89 3 4.57408744603602 -1.57408744603602 90 6 5.75149467217485 0.248505327825149 91 5 4.90224242903615 0.0977575709638468 92 6 4.80707815732233 1.19292184267767 93 4 4.57408744603602 -0.57408744603602 94 7 5.61834373671589 1.38165626328411 95 5 5.62040550711863 -0.620405507118632 96 6 5.86961439997284 0.130385600027158 97 6 4.54934620120314 1.45065379879686 98 6 4.88541607665084 1.11458392334916 99 7 4.93272690884154 2.06727309115846 100 6 5.74324759056389 0.256752409436111 101 6 5.00386799361222 0.99613200638778 102 6 5.41509260756376 0.584907392436243 103 6 5.94856049011876 0.0514395098812352 104 2 4.81881376913988 -2.81881376913988 105 4 4.56584036442506 -0.565840364425059 106 4 5.2144552121224 -1.21445521212241 107 6 5.61628196631315 0.383718033686849 108 5 5.07250523174444 -0.072505231744441 109 6 4.90430419943889 1.09569580056111 110 6 5.80405045559297 0.195949544407028 111 2 4.56584036442506 -2.56584036442506 112 7 5.70347513807004 1.29652486192996 113 1 4.57408744603602 -3.57408744603602 114 4 4.57202567563328 -0.57202567563328 115 1 4.57408744603602 -3.57408744603602 116 6 4.57408744603602 1.42591255396398 117 6 5.44601916360486 0.553980836395137 118 6 4.87733508962157 1.12266491037843 119 7 5.96299288293795 1.03700711706205 120 6 5.08487585416088 0.915124145839116 121 4 4.28160821450574 -0.281608214505738 122 4 4.5516839532599 -0.551683953259897 123 6 4.73181353174617 1.26818646825383 124 5 5.32789943580687 -0.327899435806872 125 7 6.04400074348661 0.95599925651339 126 4 5.28435311547678 -1.28435311547678 127 4 4.64668213039203 -0.646682130392026 128 6 5.060134609328 0.939865390672002 129 7 5.25101511606369 1.74898488393631 130 5 4.83566696130667 0.164333038693327 131 6 5.13344735157374 0.866552648426258 132 6 4.51924759012409 1.48075240987591 133 6 5.327540406862 0.672459593137997 134 5 4.80295461651685 0.197045383483152 135 7 4.49272055654249 2.50727944345751 136 4 5.24070626404999 -1.24070626404999 137 6 4.56377859402232 1.43622140597768 138 6 4.74775573166005 1.25224426833995 139 7 5.68491920444537 1.31508079555463 140 6 5.57092301745286 0.429076982547139 141 6 5.81001599265654 0.189984007343457 142 5 6.3179508811737 -1.31795088117371 143 5 6.24015556917761 -1.24015556917761 144 5 6.3804028080977 -1.38040280809771 145 6 5.43158677078568 0.56841322921432 146 6 5.7947918506324 0.205208149367600 147 7 5.5626759358419 1.4373240641581 148 4 5.8572437775564 -1.8572437775564 149 6 4.83434073259952 1.16565926740048 150 6 4.92286013306356 1.07713986693644 151 7 5.18408061938934 1.81591938061066 152 6 4.55759328281410 1.44240671718590 153 7 5.6457455667933 1.35425443320670 154 4 4.54522266039765 -0.545222660397654 155 6 6.39895874172237 -0.398958741722369 156 4 4.54962218285716 -0.549622182857157 157 4 4.66128061779290 -0.661280617792905 158 7 5.86513183022249 1.13486816977751 159 4 5.62040550711863 -1.62040550711863 160 7 4.72579431511964 2.27420568488035 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.663073242670396 0.673853514659209 0.336926757329604 8 0.534966068117771 0.930067863764458 0.465033931882229 9 0.422873218243762 0.845746436487523 0.577126781756238 10 0.313817626601812 0.627635253203624 0.686182373398188 11 0.945356001649768 0.109287996700463 0.0546439983502315 12 0.912491286822479 0.175017426355042 0.087508713177521 13 0.898128051316108 0.203743897367784 0.101871948683892 14 0.857805507031091 0.284388985937818 0.142194492968909 15 0.828200756155478 0.343598487689044 0.171799243844522 16 0.899371105470608 0.201257789058784 0.100628894529392 17 0.955063536720604 0.0898729265587922 0.0449364632793961 18 0.936343844626097 0.127312310747806 0.063656155373903 19 0.915978995030377 0.168042009939246 0.084021004969623 20 0.909848504039668 0.180302991920665 0.0901514959603323 21 0.906683609448593 0.186632781102814 0.0933163905514069 22 0.880856358830032 0.238287282339935 0.119143641169968 23 0.852100972662617 0.295798054674766 0.147899027337383 24 0.812774884226552 0.374450231546896 0.187225115773448 25 0.767325884401459 0.465348231197082 0.232674115598541 26 0.747350358556431 0.505299282887137 0.252649641443569 27 0.7456495344534 0.5087009310932 0.2543504655466 28 0.707407562047616 0.585184875904768 0.292592437952384 29 0.681769515683013 0.636460968633975 0.318230484316987 30 0.67630786444445 0.647384271111099 0.323692135555550 31 0.635665935975648 0.728668128048705 0.364334064024352 32 0.594325021487284 0.811349957025431 0.405674978512716 33 0.545167667182542 0.909664665634917 0.454832332817458 34 0.55223707917266 0.89552584165468 0.44776292082734 35 0.498993199891822 0.997986399783644 0.501006800108178 36 0.503127272287116 0.993745455425767 0.496872727712884 37 0.468361987484471 0.936723974968943 0.531638012515529 38 0.464982228886603 0.929964457773207 0.535017771113397 39 0.410880376469702 0.821760752939404 0.589119623530298 40 0.358429631736608 0.716859263473216 0.641570368263392 41 0.345071839237035 0.690143678474069 0.654928160762965 42 0.3264856866145 0.652971373229 0.6735143133855 43 0.280393669975866 0.560787339951731 0.719606330024134 44 0.267262053515532 0.534524107031065 0.732737946484468 45 0.251099527902353 0.502199055804705 0.748900472097647 46 0.262258672357279 0.524517344714558 0.73774132764272 47 0.227670123585576 0.455340247171152 0.772329876414424 48 0.191136298108600 0.382272596217200 0.8088637018914 49 0.221544787182425 0.443089574364851 0.778455212817575 50 0.225032949094204 0.450065898188408 0.774967050905796 51 0.189340648859429 0.378681297718858 0.81065935114057 52 0.159125707286352 0.318251414572703 0.840874292713648 53 0.140211557600561 0.280423115201122 0.859788442399439 54 0.119040755431062 0.238081510862124 0.880959244568938 55 0.387438500442585 0.774877000885171 0.612561499557415 56 0.625527217071259 0.748945565857482 0.374472782928741 57 0.707193645802945 0.58561270839411 0.292806354197055 58 0.67053630998443 0.658927380031139 0.329463690015569 59 0.673956724950896 0.652086550098208 0.326043275049104 60 0.77564071809297 0.448718563814059 0.224359281907029 61 0.843352048610091 0.313295902779818 0.156647951389909 62 0.816812261877665 0.366375476244671 0.183187738122335 63 0.880672217804026 0.238655564391947 0.119327782195974 64 0.865228352476992 0.269543295046016 0.134771647523008 65 0.851123028043954 0.297753943912092 0.148876971956046 66 0.845397430655335 0.309205138689330 0.154602569344665 67 0.820260541329539 0.359478917340922 0.179739458670461 68 0.81455771360069 0.37088457279862 0.18544228639931 69 0.785204316088836 0.429591367822328 0.214795683911164 70 0.761490785099676 0.477018429800647 0.238509214900324 71 0.735367383202514 0.529265233594973 0.264632616797486 72 0.710039965114845 0.579920069770309 0.289960034885155 73 0.678314396601308 0.643371206797383 0.321685603398692 74 0.648164600229082 0.703670799541836 0.351835399770918 75 0.644223154085361 0.711553691829278 0.355776845914639 76 0.650502697375138 0.698994605249724 0.349497302624862 77 0.741952694532389 0.516094610935222 0.258047305467611 78 0.713532213781797 0.572935572436405 0.286467786218203 79 0.681683029960066 0.636633940079868 0.318316970039934 80 0.647875626575742 0.704248746848516 0.352124373424258 81 0.605245124543746 0.789509750912507 0.394754875456254 82 0.706256198911094 0.587487602177811 0.293743801088906 83 0.673917556923504 0.652164886152993 0.326082443076496 84 0.641652985669805 0.71669402866039 0.358347014330195 85 0.62479364785158 0.75041270429684 0.37520635214842 86 0.591869531127797 0.816260937744406 0.408130468872203 87 0.582245252925969 0.835509494148062 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0.404306363069377 0.808612726138754 0.595693636930623 106 0.402986624254929 0.805973248509857 0.597013375745071 107 0.360787891343328 0.721575782686657 0.639212108656672 108 0.318040606469498 0.636081212938996 0.681959393530502 109 0.297827821054976 0.595655642109952 0.702172178945024 110 0.256619371484922 0.513238742969844 0.743380628515078 111 0.390134521396651 0.780269042793303 0.609865478603349 112 0.391986272181245 0.783972544362491 0.608013727818755 113 0.739489460333199 0.521021079333602 0.260510539666801 114 0.719192610473613 0.561614779052775 0.280807389526387 115 0.966374640045192 0.067250719909617 0.0336253599548085 116 0.961477223628982 0.0770455527420359 0.0385227763710180 117 0.95050254266541 0.0989949146691798 0.0494974573345899 118 0.940870574608034 0.118258850783932 0.0591294253919658 119 0.941488957891128 0.117022084217744 0.0585110421088722 120 0.927930149476291 0.144139701047417 0.0720698505237087 121 0.918707905788696 0.162584188422607 0.0812920942113036 122 0.92094729622344 0.158105407553119 0.0790527037765594 123 0.908033943873343 0.183932112253315 0.0919660561266574 124 0.891325576991017 0.217348846017967 0.108674423008983 125 0.894849106203715 0.210301787592570 0.105150893796285 126 0.936376140886495 0.12724771822701 0.063623859113505 127 0.94592248223053 0.108155035538939 0.0540775177694697 128 0.929370253009057 0.141259493981886 0.070629746990943 129 0.93802444597856 0.123951108042880 0.0619755540214398 130 0.91744923002819 0.16510153994362 0.08255076997181 131 0.894937889166093 0.210124221667815 0.105062110833907 132 0.87702317324348 0.245953653513039 0.122976826756520 133 0.842206377677312 0.315587244645376 0.157793622322688 134 0.80601984375197 0.387960312496061 0.193980156248030 135 0.846755312431927 0.306489375136146 0.153244687568073 136 0.886887317906247 0.226225364187506 0.113112682093753 137 0.864412614273025 0.271174771453950 0.135587385726975 138 0.826014204638672 0.347971590722655 0.173985795361328 139 0.836685676865686 0.326628646268628 0.163314323134314 140 0.785523310391355 0.428953379217289 0.214476689608645 141 0.727441318830139 0.545117362339722 0.272558681169861 142 0.665543783673326 0.668912432653349 0.334456216326674 143 0.666626344776154 0.666747310447692 0.333373655223846 144 0.65231117277915 0.6953776544417 0.34768882722085 145 0.575423502981862 0.849152994036275 0.424576497018138 146 0.511798881679478 0.976402236641045 0.488201118320522 147 0.425111064786727 0.850222129573454 0.574888935213273 148 0.568753144086361 0.862493711827279 0.431246855913639 149 0.567109912607403 0.865780174785195 0.432890087392597 150 0.578229860254267 0.843540279491466 0.421770139745733 151 0.507589219137907 0.984821561724185 0.492410780862093 152 0.490526646498549 0.981053292997099 0.509473353501451 153 0.366607151554785 0.733214303109571 0.633392848445215 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 4 0.0272108843537415 OK

Charts produced by software:

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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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