*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 11:31:15 +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/t1291375827zpiqtf1vzfzz6g2.htm/, Retrieved Fri, 03 Dec 2010 12:30:39 +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/t1291375827zpiqtf1vzfzz6g2.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 «

4 4 5 4 4 4 4 4 4 4 4 3 4 4 5 5 4 4 5 5 4 3 3 2 3 4 4 3 2 3 2 3 2 4 3 5 4 3 3 4 5 4 4 3 3 3 3 4 4 2 3 4 4 2 4 2 4 4 3 4 4 5 3 4 3 2 3 2 2 3 4 3 2 4 4 4 4 2 3 2 4 2 3 2 5 4 2 5 5 5 4 3 4 2 3 3 4 4 4 3 4 4 4 4 4 4 3 3 4 4 5 4 3 2 3 3 3 3 3 4 4 4 4 4 4 4 2 3 2 2 2 4 2 4 2 4 4 3 4 4 3 3 2 4 4 4 3 3 2 4 4 2 3 4 4 4 2 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 3 4 3 5 4 4 4 4 4 4 3 4 3 2 4 4 4 1 4 4 4 4 4 4 4 2 4 4 4 3 4 4 2 4 4 4 4 4 3 4 3 2 4 4 4 3 2 4 4 4 3 4 4 5 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 3 2 3 3 5 4 4 4 2 4 4 4 4 4 3 3 3 3 4 4 4 4 3 4 3 4 4 3 3 4 4 3 3 3 4 4 4 4 3 4 4 2 3 2 3 2 3 2 2 2 4 2 2 5 2 4 3 4 4 4 5 4 4 4 4 4 2 4 4 5 4 4 4 4 5 5 4 3 2 4 4 4 4 4 3 3 4 3 4 3 4 4 2 4 4 4 4 5 4 2 4 4 4 4 3 3 4 3 3 4 3 2 2 4 2 1 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 3 2 3 4 4 2 4 3 2 2 5 2 2 4 2 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 3 4 4 3 4 4 3 4 4 4 3 4 4 2 3 2 3 1 4 3 4 4 4 4 4 4 4 5 3 4 4 2 4 4 4 4 3 4 4 4 4 5 4 4 5 5 5 5 4 4 2 4 3 4 4 3 3 2 3 3 4 3 3 3 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 16 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 0.653455385234217 + 0.0261778726526484x1[t] + 0.228695811251476x2[t] + 0.164523727475987x3[t] + 0.101091007906319x4[t] + 0.197018661004521x5[t] + 0.0540437767073316x6[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) 0.653455385234217 0.412787 1.583 0.115592 0.057796 x1 0.0261778726526484 0.061873 0.4231 0.672858 0.336429 x2 0.228695811251476 0.072759 3.1432 0.002027 0.001014 x3 0.164523727475987 0.065636 2.5066 0.013293 0.006647 x4 0.101091007906319 0.081426 1.2415 0.216425 0.108212 x5 0.197018661004521 0.073942 2.6645 0.008584 0.004292 x6 0.0540437767073316 0.062317 0.8672 0.387244 0.193622 Multiple Linear Regression - Regression Statistics Multiple R 0.55649571399397 R-squared 0.309687479693659 Adjusted R-squared 0.281122823680983 F-TEST (value) 10.8416316848426 F-TEST (DF numerator) 6 F-TEST (DF denominator) 145 p-value 5.9757754300449e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.643938914498158 Sum Squared Residuals 60.1253122127345 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 3.96835462447888 0.0316453755211221 2 4 3.63856780532104 0.361432194678961 3 5 4.06394635479085 0.936053645209152 4 3 3.03752181388844 -0.0375218138884397 5 2 2.83533979807580 -0.835339798075795 6 5 3.54345793550441 1.45654206449559 7 4 3.21917039394092 0.780829606059077 8 2 3.4032113713474 -1.40321137134740 9 4 3.65393788627307 0.346062113726933 10 4 2.44130247606675 1.55869752393325 11 4 3.25608931807175 0.743910681928247 12 2 2.74880108783993 -0.74880108783993 13 5 3.74490058711123 1.25509941288877 14 3 3.01665245534209 -0.0166524553420947 15 4 3.71348094057471 0.286519059425295 16 4 3.68180379032775 0.31819620967225 17 3 2.94193008357642 0.0580699164235791 18 4 3.73965881322735 0.260341186772646 19 2 2.61677229389248 -0.616772293892475 20 4 3.58621206001574 0.413787939984263 21 3 3.20204554136442 -0.202045541364422 22 3 3.2881023911049 -0.288102391104897 23 4 3.2822671907244 0.717732809275598 24 4 3.51096300197588 0.489036998024122 25 4 3.73965881322735 0.260341186772646 26 4 3.32965034470958 0.670349655290422 27 5 3.73965881322735 1.26034118677265 28 3 3.1819155470239 -0.181915547023902 29 1 3.73965881322735 -2.73965881322735 30 4 3.49028440691754 0.509715593082464 31 4 3.68730306792206 0.312696932077943 32 3 3.1819155470239 -0.181915547023902 33 3 3.49028440691754 -0.490284406917536 34 4 3.86692769378632 0.133072306213678 35 4 3.73965881322735 0.260341186772646 36 4 3.79370258993469 0.206297410065314 37 3 3.39517453710091 -0.395174537100912 38 4 3.68730306792206 0.312696932077943 39 3 3.32026140184724 -0.320261401847241 40 4 3.49491343639139 0.505086563608614 41 3 3.27702541684053 -0.277025416840526 42 4 3.46704753233670 0.532952467663297 43 3 2.52634391838858 0.47365608161142 44 2 2.66027342166970 -0.660273421669704 45 3 3.84074982113367 -0.840749821133673 46 4 3.46465513498271 0.53534486501729 47 4 4.03776848213819 -0.0377684821381942 48 3 3.68730306792206 -0.687303067922057 49 3 3.3519385520942 -0.351938552094197 50 4 3.74134684462939 0.258653155370612 51 4 3.63325929121473 0.366740708785275 52 3 3.04133306008071 -0.0413330600807061 53 2 2.78869600829644 -0.788696008296438 54 4 3.73965881322735 0.260341186772646 55 4 3.40837472615552 0.591625273844479 56 3 3.10550514385619 -0.105505143856194 57 2 2.58536028641603 -0.585360286416033 58 4 3.73965881322735 0.260341186772646 59 3 3.73965881322735 -0.739658813227354 60 3 3.52109130904403 -0.521091309044034 61 4 3.46704753233670 0.532952467663297 62 3 2.76801741323810 0.231982586761904 63 4 3.79370258993469 0.206297410065314 64 3 3.41061135827538 -0.410611358275378 65 4 3.76752471728204 0.232475282717963 66 4 4.43098802086566 -0.430988020865658 67 4 3.46873556373874 0.531264436261263 68 3 3.04302109148274 -0.0430210914827404 69 3 2.63443147180324 0.365568528196756 70 3 3.68561503652002 -0.685615036520023 71 4 2.6797906716002 1.32020932839980 72 3 2.55951833654957 0.440481663450427 73 2 2.45278289175076 -0.452782891750756 74 4 3.84243785253571 0.157562147464292 75 4 3.90587057210538 0.0941294278946235 76 4 4.06394635479084 -0.063946354790843 77 3 2.5121351825644 0.487864817435603 78 5 4.10120120170786 0.898798798292137 79 3 3.30421183626275 -0.304211836262749 80 2 2.94193008357642 -0.941930083576421 81 3 3.31394434097136 -0.313944340971357 82 3 3.34643927449989 -0.34643927449989 83 4 3.35656758156805 0.643432418431954 84 4 3.14942061349537 0.85057938650463 85 3 3.40456347996325 -0.404563479963249 86 2 2.28825916427477 -0.288259164274768 87 4 3.45765858947437 0.542341410525634 88 4 3.07932727120355 0.920672728796455 89 3 2.72539417264141 0.274605827358593 90 4 3.46873556373874 0.531264436261263 91 3 3.1819155470239 -0.181915547023902 92 2 3.05431074367875 -1.05431074367875 93 3 3.46241850286285 -0.462418502862853 94 3 3.09537683678804 -0.0953768367880378 95 3 2.82513307193188 0.174866928068119 96 4 3.28776646831871 0.712233531681291 97 4 3.71729218676698 0.282707813233022 98 4 2.96253025955900 1.03746974044100 99 3 3.05431074367875 -0.0543107436787454 100 4 3.73266226771901 0.26733773228099 101 4 3.12324274084272 0.87675725915728 102 3 2.55918241376338 0.440817586236615 103 4 3.78839407582838 0.211605924171624 104 3 3.70409199771237 -0.704091997712368 105 4 3.59750171221174 0.402498287788257 106 4 4.06563438619288 -0.0656343861928771 107 3 3.54895721309872 -0.548957213098717 108 3 3.49028440691754 -0.490284406917536 109 3 3.46873556373874 -0.468735563738737 110 3 3.41469178703141 -0.414691787031405 111 3 3.01549111021425 -0.0154911102142459 112 2 2.55918241376338 -0.559182413763385 113 4 3.54827772846626 0.451722271533743 114 2 2.74015150918341 -0.740151509183413 115 3 3.1819155470239 -0.181915547023902 116 3 3.3519385520942 -0.351938552094197 117 3 3.12324274084272 -0.123242740842721 118 4 3.77215374675589 0.227846253244113 119 4 3.16512661723359 0.83487338276641 120 3 2.93254114071408 0.067458859285916 121 4 3.65943716386737 0.340562836132626 122 3 3.02846879381229 -0.0284687938122853 123 3 3.54895721309872 -0.548957213098717 124 3 3.44753028240621 -0.447530282406210 125 4 3.70648439506636 0.293515604933639 126 2 3.04451835939678 -1.04451835939678 127 4 3.50157405911354 0.498425940886459 128 3 3.46873556373874 -0.468735563738737 129 3 3.01052615795421 -0.0105261579542077 130 4 3.75536481696558 0.244635183034425 131 4 3.21917039394092 0.780829606059078 132 4 3.65943716386737 0.340562836132626 133 3 3.23727643409322 -0.237276434093219 134 2 2.21402551365356 -0.214025513653557 135 4 3.73965881322735 0.260341186772646 136 2 3.63157125981269 -1.63157125981269 137 3 3.32026140184724 -0.320261401847241 138 4 3.62218231695035 0.377817683049646 139 3 3.211356065151 -0.211356065151001 140 3 3.01134394123578 -0.0113439412357851 141 3 3.35656758156805 -0.356567581568046 142 3 3.54264015222283 -0.542640152222834 143 4 3.73965881322735 0.260341186772646 144 3 3.68730306792206 -0.687303067922057 145 3 3.56813854024302 -0.568138540243022 146 2 2.98584555321560 -0.985845553215596 147 2 3.73965881322735 -1.73965881322735 148 3 3.09074780731419 -0.090747807314188 149 4 3.63325929121473 0.366740708785275 150 3 3.26621762513991 -0.26621762513991 151 4 3.5768231171534 0.423176882846600 152 3 4.45716589351831 -1.45716589351831 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.827499504489573 0.345000991020855 0.172500495510427 11 0.733948042078901 0.532103915842198 0.266051957921099 12 0.63740793968802 0.725184120623962 0.362592060311981 13 0.585202766433549 0.829594467132903 0.414797233566451 14 0.800708957861648 0.398582084276705 0.199291042138352 15 0.727720058252465 0.544559883495069 0.272279941747535 16 0.648864460814805 0.70227107837039 0.351135539185195 17 0.555492287646862 0.889015424706277 0.444507712353138 18 0.512612472697588 0.974775054604824 0.487387527302412 19 0.432826958004582 0.865653916009163 0.567173041995418 20 0.413126767184344 0.826253534368688 0.586873232815656 21 0.386370506897769 0.772741013795538 0.613629493102231 22 0.331315906611843 0.662631813223686 0.668684093388157 23 0.293553651999874 0.587107303999748 0.706446348000126 24 0.252983640319836 0.505967280639672 0.747016359680164 25 0.213621141023804 0.427242282047607 0.786378858976196 26 0.299332201576741 0.598664403153482 0.700667798423259 27 0.350261740544991 0.700523481089981 0.64973825945501 28 0.446103675660155 0.89220735132031 0.553896324339845 29 0.9992604280613 0.00147914387739965 0.000739571938699827 30 0.998885020227328 0.00222995954534459 0.00111497977267230 31 0.998270662649638 0.00345867470072382 0.00172933735036191 32 0.997707017058046 0.00458596588390891 0.00229298294195445 33 0.997775698857804 0.00444860228439215 0.00222430114219608 34 0.996686180142432 0.00662763971513504 0.00331381985756752 35 0.99516025754758 0.00967948490483908 0.00483974245241954 36 0.993832563658303 0.0123348726833944 0.00616743634169719 37 0.993255636987188 0.0134887260256234 0.00674436301281172 38 0.990877464411527 0.0182450711769455 0.00912253558847276 39 0.988931446250827 0.0221371074983455 0.0110685537491727 40 0.990979833941727 0.0180403321165466 0.00902016605827328 41 0.987948245095376 0.0241035098092473 0.0120517549046237 42 0.99024479417113 0.0195104116577411 0.00975520582887057 43 0.989500326715926 0.0209993465681472 0.0104996732840736 44 0.992654166511312 0.0146916669773752 0.0073458334886876 45 0.99494634947856 0.0101073010428807 0.00505365052144033 46 0.993917355801222 0.0121652883975552 0.00608264419877758 47 0.99176227978467 0.0164754404306582 0.0082377202153291 48 0.992290122809025 0.0154197543819509 0.00770987719097547 49 0.99010219351347 0.0197956129730591 0.00989780648652953 50 0.986693872831584 0.0266122543368315 0.0133061271684158 51 0.983897160846946 0.0322056783061085 0.0161028391530542 52 0.978193428881253 0.0436131422374941 0.0218065711187471 53 0.980571200815026 0.0388575983699486 0.0194287991849743 54 0.975039226979904 0.049921546040192 0.024960773020096 55 0.974266397877726 0.0514672042445475 0.0257336021222737 56 0.966869909259656 0.0662601814806887 0.0331300907403443 57 0.964178178855292 0.0716436422894156 0.0358218211447078 58 0.955356479932238 0.089287040135524 0.044643520067762 59 0.959668855875318 0.0806622882493636 0.0403311441246818 60 0.954935542850706 0.090128914298587 0.0450644571492935 61 0.95171993485195 0.0965601302960993 0.0482800651480496 62 0.941866230652898 0.116267538694204 0.0581337693471018 63 0.928557111130621 0.142885777738757 0.0714428888693786 64 0.917569845026846 0.164860309946308 0.0824301549731538 65 0.901128028938075 0.197743942123850 0.0988719710619248 66 0.89317776855981 0.213644462880378 0.106822231440189 67 0.884994671234071 0.230010657531858 0.115005328765929 68 0.860199641307763 0.279600717384475 0.139800358692237 69 0.842483493540261 0.315033012919478 0.157516506459739 70 0.843781677591291 0.312436644817417 0.156218322408709 71 0.916004392730153 0.167991214539693 0.0839956072698466 72 0.906147400733441 0.187705198533118 0.093852599266559 73 0.898557583344475 0.202884833311050 0.101442416655525 74 0.878158864612354 0.243682270775291 0.121841135387646 75 0.856315340425334 0.287369319149333 0.143684659574666 76 0.828322648048068 0.343354703903864 0.171677351951932 77 0.813621731888202 0.372756536223597 0.186378268111798 78 0.86113034282475 0.277739314350500 0.138869657175250 79 0.840711737499146 0.318576525001708 0.159288262500854 80 0.872559814747873 0.254880370504255 0.127440185252127 81 0.852887134198 0.294225731604001 0.147112865802001 82 0.830308656560613 0.339382686878775 0.169691343439387 83 0.830140607735088 0.339718784529824 0.169859392264912 84 0.858789000117917 0.282421999764167 0.141210999882083 85 0.839921460440978 0.320157079118044 0.160078539559022 86 0.826399083196087 0.347201833607827 0.173600916803913 87 0.816491601091038 0.367016797817925 0.183508398908962 88 0.839721975875816 0.320556048248369 0.160278024124184 89 0.813309903178064 0.373380193643872 0.186690096821936 90 0.801944379576226 0.396111240847549 0.198055620423774 91 0.767725784991793 0.464548430016414 0.232274215008207 92 0.823846770152669 0.352306459694662 0.176153229847331 93 0.80520618537565 0.389587629248699 0.194793814624349 94 0.769396438355509 0.461207123288982 0.230603561644491 95 0.733925892275498 0.532148215449004 0.266074107724502 96 0.761080576099965 0.477838847800071 0.238919423900035 97 0.7426426686632 0.5147146626736 0.2573573313368 98 0.825195902232604 0.349608195534792 0.174804097767396 99 0.790242131518271 0.419515736963458 0.209757868481729 100 0.772871569327724 0.454256861344552 0.227128430672276 101 0.827371909175064 0.345256181649873 0.172628090824936 102 0.830991694037755 0.338016611924490 0.169008305962245 103 0.805917786791212 0.388164426417576 0.194082213208788 104 0.798934641122255 0.402130717755491 0.201065358877745 105 0.789770003678532 0.420459992642937 0.210229996321468 106 0.751296915114298 0.497406169771405 0.248703084885702 107 0.726374733725267 0.547250532549467 0.273625266274733 108 0.696122523847662 0.607754952304676 0.303877476152338 109 0.673970054825446 0.652059890349109 0.326029945174554 110 0.652592177127913 0.694815645744173 0.347407822872087 111 0.599319295513518 0.801361408972964 0.400680704486482 112 0.564354809217237 0.871290381565527 0.435645190782763 113 0.520715544121783 0.958568911756434 0.479284455878217 114 0.560736949441413 0.878526101117175 0.439263050558587 115 0.504521495194325 0.99095700961135 0.495478504805675 116 0.453918058654678 0.907836117309356 0.546081941345322 117 0.396290441920743 0.792580883841487 0.603709558079257 118 0.366058755494459 0.732117510988919 0.63394124450554 119 0.433633147830666 0.867266295661332 0.566366852169334 120 0.376501303051922 0.753002606103843 0.623498696948078 121 0.365154093739325 0.73030818747865 0.634845906260675 122 0.307999820908394 0.615999641816788 0.692000179091606 123 0.276535195812085 0.55307039162417 0.723464804187915 124 0.241263979164014 0.482527958328028 0.758736020835986 125 0.209179432699067 0.418358865398133 0.790820567300933 126 0.268697411976187 0.537394823952375 0.731302588023813 127 0.257983887821663 0.515967775643326 0.742016112178337 128 0.240166171310017 0.480332342620033 0.759833828689983 129 0.188664803184977 0.377329606369955 0.811335196815023 130 0.176502073819329 0.353004147638657 0.823497926180671 131 0.298690167754151 0.597380335508303 0.701309832245849 132 0.371020369744729 0.742040739489458 0.628979630255271 133 0.403606202701408 0.807212405402817 0.596393797298592 134 0.324625599409749 0.649251198819499 0.675374400590251 135 0.518135120232471 0.963729759535057 0.481864879767529 136 0.512603795655777 0.974792408688447 0.487396204344223 137 0.411539306259827 0.823078612519654 0.588460693740173 138 0.367739710708646 0.735479421417292 0.632260289291354 139 0.277326738180859 0.554653476361718 0.722673261819141 140 0.208180492932124 0.416360985864247 0.791819507067876 141 0.143261637909271 0.286523275818542 0.856738362090729 142 0.0822831594503916 0.164566318900783 0.917716840549608 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.0526315789473684 NOK 5% type I error level 26 0.195488721804511 NOK 10% type I error level 33 0.248120300751880 NOK

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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