Workshop 7 – Multiple Linear 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: Thu, 02 Dec 2010 09:57:21 +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/t1291283823kfs6k5mbr5h4oob.htm/, Retrieved Thu, 02 Dec 2010 10:57:14 +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/t1291283823kfs6k5mbr5h4oob.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:

Meber of Sports clu (provison & illness)

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 5 1 1 4 1 1 7 1 1 7 1 2 5 1 2 5 1 1 4 1 2 4 2 1 6 1 2 5 1 1 1 1 2 5 1 1 4 2 2 6 1 2 7 1 2 7 1 1 2 1 1 6 1 1 3 1 2 6 1 2 6 1 1 5 1 2 6 1 2 4 2 2 3 2 2 4 1 2 5 2 2 6 2 1 6 2 1 4 1 2 6 1 1 6 1 2 5 1 2 6 1 2 4 1 1 6 1 2 7 1 1 5 1 1 6 1 2 6 2 1 5 2 2 7 1 2 6 1 1 3 1 1 4 1 2 5 1 2 4 2 1 3 1 2 5 1 2 5 1 1 4 1 1 5 1 2 1 1 2 2 2 2 3 1 1 4 1 1 3 1 1 7 1 1 2 1 1 4 1 1 2 1 2 5 1 2 6 1 2 6 1 2 6 1 1 6 1 2 6 1 2 6 1 1 6 1 1 4 1 1 4 1 2 5 1 1 6 1 1 6 1 1 7 1 1 6 1 2 6 2 1 6 1 2 3 1 2 5 1 2 6 1 2 4 1 1 5 1 2 6 1 2 6 1 1 3 1 2 6 1 2 5 1 1 6 1 1 4 1 2 7 1 2 5 1 2 6 1 1 6 1 2 6 1 1 7 2 2 6 1 1 6 1 1 6 1 2 6 1 2 2 1 1 4 1 2 4 1 2 6 1 1 5 1 1 6 1 1 6 1 1 2 2 2 7 1 1 1 1 1 4 1 1 1 1 1 6 1 2 6 1 1 6 1 2 7 1 1 6 1 2 4 1 2 4 1 1 6 1 1 5 2 2 7 1 2 4 1 1 4 1 2 6 1 2 7 1 2 5 1 2 6 1 1 6 2 2 6 1 2 5 1 2 7 1 2 4 1 1 6 1 1 6 1 2 7 1 2 6 1 2 6 1 2 5 1 1 5 1 2 5 1 2 6 1 2 6 2 1 7 2 1 4 1 2 6 1 2 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Member[t] = + 1.08303758464254 + 0.0762639060674089Provision[t] + 0.069728040161896Illness[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) 1.08303758464254 0.201833 5.366 0 0 Provision 0.0762639060674089 0.027323 2.7912 0.005917 0.002958 Illness 0.069728040161896 0.117296 0.5945 0.553077 0.276538 Multiple Linear Regression - Regression Statistics Multiple R 0.222116181409657 R-squared 0.0493355980440077 Adjusted R-squared 0.0369893071095143 F-TEST (value) 3.99598537777629 F-TEST (DF numerator) 2 F-TEST (DF denominator) 154 p-value 0.0203281030586162 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.489341530112215 Sum Squared Residuals 36.8760904962548 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 1.53408515514144 0.465914844858558 2 1 1.45782124907406 -0.457821249074063 3 1 1.68661296727630 -0.686612967276297 4 1 1.68661296727629 -0.686612967276294 5 2 1.53408515514148 0.465914844858524 6 2 1.53408515514148 0.465914844858524 7 1 1.45782124907407 -0.457821249074067 8 2 1.52754928923596 0.472450710764038 9 1 1.61034906120889 -0.610349061208885 10 2 1.53408515514148 0.465914844858524 11 1 1.22902953087184 -0.229029530871840 12 2 1.53408515514148 0.465914844858524 13 1 1.52754928923596 -0.527549289235962 14 2 1.61034906120888 0.389650938791115 15 2 1.68661296727629 0.313387032723706 16 2 1.68661296727629 0.313387032723706 17 1 1.30529343693925 -0.305293436939249 18 1 1.61034906120889 -0.610349061208885 19 1 1.38155734300666 -0.381557343006658 20 2 1.61034906120888 0.389650938791115 21 2 1.61034906120888 0.389650938791115 22 1 1.53408515514148 -0.534085155141476 23 2 1.61034906120888 0.389650938791115 24 2 1.52754928923596 0.472450710764038 25 2 1.45128538316855 0.548714616831447 26 2 1.45782124907407 0.542178750925933 27 2 1.60381319530337 0.396186804696629 28 2 1.68007710137078 0.31992289862922 29 1 1.68007710137078 -0.68007710137078 30 1 1.45782124907407 -0.457821249074067 31 2 1.61034906120888 0.389650938791115 32 1 1.61034906120889 -0.610349061208885 33 2 1.53408515514148 0.465914844858524 34 2 1.61034906120888 0.389650938791115 35 2 1.45782124907407 0.542178750925933 36 1 1.61034906120889 -0.610349061208885 37 2 1.68661296727629 0.313387032723706 38 1 1.53408515514148 -0.534085155141476 39 1 1.61034906120889 -0.610349061208885 40 2 1.68007710137078 0.31992289862922 41 1 1.60381319530337 -0.603813195303371 42 2 1.68661296727629 0.313387032723706 43 2 1.61034906120888 0.389650938791115 44 1 1.38155734300666 -0.381557343006658 45 1 1.45782124907407 -0.457821249074067 46 2 1.53408515514148 0.465914844858524 47 2 1.52754928923596 0.472450710764038 48 1 1.38155734300666 -0.381557343006658 49 2 1.53408515514148 0.465914844858524 50 2 1.53408515514148 0.465914844858524 51 1 1.45782124907407 -0.457821249074067 52 1 1.53408515514148 -0.534085155141476 53 2 1.22902953087184 0.77097046912816 54 2 1.37502147710114 0.624978522898856 55 2 1.38155734300666 0.618442656993342 56 1 1.45782124907407 -0.457821249074067 57 1 1.38155734300666 -0.381557343006658 58 1 1.68661296727629 -0.686612967276294 59 1 1.30529343693925 -0.305293436939249 60 1 1.45782124907407 -0.457821249074067 61 1 1.30529343693925 -0.305293436939249 62 2 1.53408515514148 0.465914844858524 63 2 1.61034906120888 0.389650938791115 64 2 1.61034906120888 0.389650938791115 65 2 1.61034906120888 0.389650938791115 66 1 1.61034906120889 -0.610349061208885 67 2 1.61034906120888 0.389650938791115 68 2 1.61034906120888 0.389650938791115 69 1 1.61034906120889 -0.610349061208885 70 1 1.45782124907407 -0.457821249074067 71 1 1.45782124907407 -0.457821249074067 72 2 1.53408515514148 0.465914844858524 73 1 1.61034906120889 -0.610349061208885 74 1 1.61034906120889 -0.610349061208885 75 1 1.68661296727629 -0.686612967276294 76 1 1.61034906120889 -0.610349061208885 77 2 1.68007710137078 0.31992289862922 78 1 1.61034906120889 -0.610349061208885 79 2 1.38155734300666 0.618442656993342 80 2 1.53408515514148 0.465914844858524 81 2 1.61034906120888 0.389650938791115 82 2 1.45782124907407 0.542178750925933 83 1 1.53408515514148 -0.534085155141476 84 2 1.61034906120888 0.389650938791115 85 2 1.61034906120888 0.389650938791115 86 1 1.38155734300666 -0.381557343006658 87 2 1.61034906120888 0.389650938791115 88 2 1.53408515514148 0.465914844858524 89 1 1.61034906120889 -0.610349061208885 90 1 1.45782124907407 -0.457821249074067 91 2 1.68661296727629 0.313387032723706 92 2 1.53408515514148 0.465914844858524 93 2 1.61034906120888 0.389650938791115 94 1 1.61034906120889 -0.610349061208885 95 2 1.61034906120888 0.389650938791115 96 1 1.75634100743819 -0.75634100743819 97 2 1.61034906120888 0.389650938791115 98 1 1.61034906120889 -0.610349061208885 99 1 1.61034906120889 -0.610349061208885 100 2 1.61034906120888 0.389650938791115 101 2 1.30529343693925 0.694706563060751 102 1 1.45782124907407 -0.457821249074067 103 2 1.45782124907407 0.542178750925933 104 2 1.61034906120888 0.389650938791115 105 1 1.53408515514148 -0.534085155141476 106 1 1.61034906120889 -0.610349061208885 107 1 1.61034906120889 -0.610349061208885 108 1 1.37502147710114 -0.375021477101144 109 2 1.68661296727629 0.313387032723706 110 1 1.22902953087184 -0.229029530871840 111 1 1.45782124907407 -0.457821249074067 112 1 1.22902953087184 -0.229029530871840 113 1 1.61034906120889 -0.610349061208885 114 2 1.61034906120888 0.389650938791115 115 1 1.61034906120889 -0.610349061208885 116 2 1.68661296727629 0.313387032723706 117 1 1.61034906120889 -0.610349061208885 118 2 1.45782124907407 0.542178750925933 119 2 1.45782124907407 0.542178750925933 120 1 1.61034906120889 -0.610349061208885 121 1 1.60381319530337 -0.603813195303371 122 2 1.68661296727629 0.313387032723706 123 2 1.45782124907407 0.542178750925933 124 1 1.45782124907407 -0.457821249074067 125 2 1.61034906120888 0.389650938791115 126 2 1.68661296727629 0.313387032723706 127 2 1.53408515514148 0.465914844858524 128 2 1.61034906120888 0.389650938791115 129 1 1.68007710137078 -0.68007710137078 130 2 1.61034906120888 0.389650938791115 131 2 1.53408515514148 0.465914844858524 132 2 1.68661296727629 0.313387032723706 133 2 1.45782124907407 0.542178750925933 134 1 1.61034906120889 -0.610349061208885 135 1 1.61034906120889 -0.610349061208885 136 2 1.68661296727629 0.313387032723706 137 2 1.61034906120888 0.389650938791115 138 2 1.61034906120888 0.389650938791115 139 2 1.53408515514148 0.465914844858524 140 1 1.53408515514148 -0.534085155141476 141 2 1.53408515514148 0.465914844858524 142 2 1.61034906120888 0.389650938791115 143 2 1.68007710137078 0.31992289862922 144 1 1.75634100743819 -0.75634100743819 145 1 1.45782124907407 -0.457821249074067 146 2 1.61034906120888 0.389650938791115 147 2 1.61034906120888 0.389650938791115 148 2 1.68661296727629 0.313387032723706 149 1 1.61034906120889 -0.610349061208885 150 2 1.68661296727629 0.313387032723706 151 2 1.52754928923596 0.472450710764038 152 2 1.61034906120888 0.389650938791115 153 1 1.45782124907407 -0.457821249074067 154 1 1.45782124907407 -0.457821249074067 155 2 1.68661296727629 0.313387032723706 156 1 1.45782124907407 -0.457821249074067 157 2 1.75634100743819 0.243658992561811 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.828074392254746 0.343851215490509 0.171925607745255 7 0.852655999723854 0.294688000552293 0.147344000276146 8 0.765158739234083 0.469682521531834 0.234841260765917 9 0.707641131136473 0.584717737727055 0.292358868863527 10 0.713532969730992 0.572934060538016 0.286467030269008 11 0.730933804071326 0.538132391857349 0.269066195928674 12 0.742469445158622 0.515061109682757 0.257530554841378 13 0.792832324035614 0.414335351928772 0.207167675964386 14 0.781881430497189 0.436237139005622 0.218118569502811 15 0.750212863119846 0.499574273760307 0.249787136880154 16 0.70735764344756 0.58528471310488 0.29264235655244 17 0.655614756531764 0.688770486936472 0.344385243468236 18 0.6823361977779 0.635327604444199 0.317663802222099 19 0.637599337183428 0.724801325633145 0.362400662816572 20 0.613343512624439 0.773312974751122 0.386656487375561 21 0.584122456816826 0.831755086366348 0.415877543183174 22 0.585158659864497 0.829682680271006 0.414841340135503 23 0.557160194106794 0.885679611786413 0.442839805893206 24 0.537072131084912 0.925855737830175 0.462927868915088 25 0.519021110302202 0.961957779395595 0.480978889697798 26 0.543129959744731 0.913740080510537 0.456870040255269 27 0.490555258976457 0.981110517952914 0.509444741023543 28 0.434928388629526 0.869856777259051 0.565071611370474 29 0.565335905097156 0.869328189805688 0.434664094902844 30 0.553119038624852 0.893761922750295 0.446880961375148 31 0.528855477338748 0.942289045322504 0.471144522661252 32 0.559231931060304 0.881536137879392 0.440768068939696 33 0.554548881005586 0.890902237988829 0.445451118994414 34 0.530601163589491 0.938797672821017 0.469398836410509 35 0.540124352808699 0.919751294382603 0.459875647191301 36 0.572236496936874 0.855527006126252 0.427763503063126 37 0.537479978445643 0.925040043108714 0.462520021554357 38 0.547198534964266 0.905602930071468 0.452801465035734 39 0.573173979122673 0.853652041754655 0.426826020877327 40 0.533124405293129 0.933751189413742 0.466875594706871 41 0.57881412257553 0.842371754848939 0.421185877424469 42 0.547755130622032 0.904489738755937 0.452244869377968 43 0.52717353547312 0.94565292905376 0.47282646452688 44 0.501759293544601 0.996481412910797 0.498240706455399 45 0.489020739242466 0.978041478484932 0.510979260757534 46 0.485709185637246 0.971418371274491 0.514290814362754 47 0.475888297741228 0.951776595482455 0.524111702258772 48 0.449341641527725 0.89868328305545 0.550658358472275 49 0.445968463964824 0.891936927929649 0.554031536035176 50 0.441182716224001 0.882365432448001 0.558817283776 51 0.430920727995411 0.861841455990822 0.569079272004589 52 0.438098640169998 0.876197280339996 0.561901359830002 53 0.523644197796264 0.952711604407472 0.476355802203736 54 0.548875421878195 0.90224915624361 0.451124578121805 55 0.574854432040124 0.850291135919752 0.425145567959876 56 0.569599394474615 0.86080121105077 0.430400605525385 57 0.550911175226353 0.898177649547294 0.449088824773647 58 0.592291146057712 0.815417707884575 0.407708853942287 59 0.563311801306633 0.873376397386734 0.436688198693367 60 0.554527304292519 0.890945391414962 0.445472695707481 61 0.523517655989388 0.952964688021225 0.476482344010612 62 0.521651521364322 0.956696957271356 0.478348478635678 63 0.505532005720026 0.988935988559947 0.494467994279974 64 0.488576068823569 0.977152137647137 0.511423931176431 65 0.470953884967462 0.941907769934924 0.529046115032538 66 0.496503660679227 0.993007321358454 0.503496339320773 67 0.479185931572225 0.95837186314445 0.520814068427775 68 0.461387810163727 0.922775620327454 0.538612189836273 69 0.487264128886065 0.97452825777213 0.512735871113935 70 0.479445675422463 0.958891350844925 0.520554324577537 71 0.471718025190332 0.943436050380665 0.528281974809668 72 0.46796686314583 0.93593372629166 0.53203313685417 73 0.493210154019466 0.986420308038932 0.506789845980534 74 0.51814422619978 0.96371154760044 0.48185577380022 75 0.56269029580342 0.87461940839316 0.43730970419658 76 0.587753774232109 0.824492451535783 0.412246225767891 77 0.573286225036614 0.853427549926773 0.426713774963386 78 0.599788901345778 0.800422197308444 0.400211098654222 79 0.630107949816689 0.739784100366623 0.369892050183311 80 0.627656383291121 0.744687233417758 0.372343616708879 81 0.612146282282426 0.775707435435148 0.387853717717574 82 0.624881772627512 0.750236454744977 0.375118227372488 83 0.633648854763938 0.732702290472124 0.366351145236062 84 0.617496077515962 0.765007844968076 0.382503922484038 85 0.600747728950046 0.798504542099907 0.399252271049954 86 0.581056626843424 0.837886746313153 0.418943373156576 87 0.563456173366885 0.87308765326623 0.436543826633115 88 0.559194820254961 0.881610359490078 0.440805179745039 89 0.588175883963552 0.823648232072897 0.411824116036448 90 0.582326773651515 0.83534645269697 0.417673226348485 91 0.553209314533477 0.893581370933046 0.446790685466523 92 0.54800552369821 0.90398895260358 0.45199447630179 93 0.529075365099282 0.941849269801437 0.470924634900718 94 0.55961678566521 0.88076642866958 0.44038321433479 95 0.540174703890512 0.919650592218975 0.459825296109488 96 0.587664847857016 0.824670304285969 0.412335152142984 97 0.568227993571607 0.863544012856786 0.431772006428393 98 0.598752606793483 0.802494786413034 0.401247393206517 99 0.631348702708317 0.737302594583366 0.368651297291683 100 0.610897329857732 0.778205340284535 0.389102670142268 101 0.672441630409219 0.655116739181561 0.327558369590781 102 0.664211214579592 0.671577570840817 0.335788785420409 103 0.679959697106728 0.640080605786544 0.320040302893272 104 0.660578330391133 0.678843339217735 0.339421669608867 105 0.670219392613804 0.659561214772392 0.329780607386196 106 0.705786102428152 0.588427795143696 0.294213897571848 107 0.743568054544728 0.512863890910545 0.256431945455272 108 0.715981936489092 0.568036127021815 0.284018063510907 109 0.682765752800883 0.634468494398234 0.317234247199117 110 0.640406733817374 0.719186532365252 0.359593266182626 111 0.634122536570409 0.731754926859182 0.365877463429591 112 0.590449443326255 0.81910111334749 0.409550556673745 113 0.638793703081978 0.722412593836043 0.361206296918022 114 0.610963007571918 0.778073984856164 0.389036992428082 115 0.663783675830687 0.672432648338626 0.336216324169313 116 0.624074143529701 0.751851712940597 0.375925856470299 117 0.682999293272058 0.634001413455884 0.317000706727942 118 0.690848095238701 0.618303809522597 0.309151904761299 119 0.706168541248366 0.587662917503268 0.293831458751634 120 0.767041158582768 0.465917682834465 0.232958841417232 121 0.763883131284919 0.472233737430162 0.236116868715081 122 0.72402406746579 0.551951865068421 0.275975932534210 123 0.744298539596574 0.511402920806852 0.255701460403426 124 0.735024638261503 0.529950723476994 0.264975361738497 125 0.702238302176771 0.595523395646458 0.297761697823229 126 0.655077251615435 0.68984549676913 0.344922748384565 127 0.64253219538196 0.714935609236081 0.357467804618041 128 0.605935810696282 0.788128378607437 0.394064189303718 129 0.660376446264991 0.679247107470018 0.339623553735009 130 0.624280143133447 0.751439713733105 0.375719856866553 131 0.617585358027567 0.764829283944866 0.382414641972433 132 0.562842207493227 0.874315585013546 0.437157792506773 133 0.616773505449247 0.766452989101505 0.383226494550753 134 0.680179084656431 0.639641830687138 0.319820915343569 135 0.758208848787327 0.483582302425346 0.241791151212673 136 0.701144258633052 0.597711482733897 0.298855741366948 137 0.657210316536622 0.685579366926756 0.342789683463378 138 0.612440188215827 0.775119623568345 0.387559811784173 139 0.621742955318374 0.756514089363252 0.378257044681626 140 0.624856072960795 0.750287854078409 0.375143927039205 141 0.636945857818893 0.726108284362214 0.363054142181107 142 0.597312589821825 0.80537482035635 0.402687410178175 143 0.540738061666943 0.918523876666113 0.459261938333057 144 0.899168381896514 0.201663236206972 0.100831618103486 145 0.853037882133746 0.293924235732508 0.146962117866254 146 0.828690479246537 0.342619041506926 0.171309520753463 147 0.813339531922743 0.373320936154515 0.186660468077257 148 0.73550333255281 0.52899333489438 0.26449666744719 149 0.846831090967019 0.306337818065963 0.153168909032981 150 0.739665328430983 0.520669343138034 0.260334671569017 151 0.958156331427024 0.0836873371459514 0.0418436685729757 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 1 0.00684931506849315 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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