workshop 7

*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 13:55:37 +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/t1291384459bby3xkhp0vge1gq.htm/, Retrieved Fri, 03 Dec 2010 14:54:30 +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/t1291384459bby3xkhp0vge1gq.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 1 4 5 4 2 1 4 4 4 3 2 5 5 4 2 1 3 4 4 2 2 4 3 5 2 1 3 5 4 1 3 4 4 3 1 1 3 4 4 1 1 2 4 4 2 1 4 4 4 2 2 2 4 4 2 4 2 4 4 2 2 2 4 2 2 1 1 3 3 1 1 4 4 4 3 3 4 5 3 2 2 2 4 2 2 2 2 2 4 2 3 3 4 3 2 3 3 4 3 3 1 3 4 4 4 2 4 4 3 2 2 3 4 3 2 2 2 4 4 2 2 2 5 4 1 3 4 4 4 2 2 4 4 4 2 2 3 4 4 2 2 4 4 4 2 2 2 4 5 4 2 4 5 4 2 3 4 4 4 4 2 5 2 4 3 2 5 5 3 1 2 4 4 4 4 2 4 5 3 3 2 4 4 4 2 1 2 4 4 4 2 4 4 3 2 1 4 4 5 3 2 4 5 4 3 2 3 4 3 2 2 2 4 3 1 2 3 5 3 2 2 4 4 4 1 3 3 4 4 2 2 2 4 4 4 2 4 4 4 2 2 4 4 4 2 4 3 4 4 2 1 4 4 4 2 2 3 4 5 2 2 4 5 3 1 1 2 3 3 2 5 4 4 5 3 2 4 5 5 2 2 4 5 4 2 2 4 4 4 1 1 3 5 3 1 2 1 2 4 2 2 3 4 4 2 2 3 4 5 1 2 4 4 4 2 2 2 4 4 1 1 3 4 5 4 1 5 5 4 4 2 4 4 3 1 2 4 4 4 1 1 3 4 4 3 2 4 4 4 4 2 2 3 4 2 1 3 4 4 4 3 4 5 4 4 3 3 5 4 3 3 4 4 3 4 2 4 4 4 2 2 3 5 3 2 2 3 4 5 2 1 2 5 4 2 4 4 3 5 2 3 3 4 5 2 2 2 4 4 2 2 2 4 4 1 2 3 4 4 3 1 2 5 4 3 2 2 4 4 2 3 4 4 5 4 1 4 5 4 4 2 4 3 3 2 2 2 4 4 2 2 2 4 3 1 1 4 5 4 1 1 2 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 12 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 neat[t] = + 1.27617742427754 + 0.237668039388989fail[t] -0.191182456604179performance[t] + 0.0507848541828642goals[t] + 0.466836776775649`organized `[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) 1.27617742427754 0.465991 2.7386 0.006897 0.003449 fail 0.237668039388989 0.075336 3.1548 0.001932 0.000966 performance -0.191182456604179 0.0754 -2.5356 0.012223 0.006111 goals 0.0507848541828642 0.076144 0.667 0.505797 0.252898 `organized ` 0.466836776775649 0.089433 5.22 1e-06 0 Multiple Linear Regression - Regression Statistics Multiple R 0.520144238515198 R-squared 0.270550028860555 Adjusted R-squared 0.251603276363426 F-TEST (value) 14.2794934858393 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 6.16247053386587e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.88938019219216 Sum Squared Residuals 121.813557444620 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.57299042583907 -0.572990425839068 2 4 3.63081757028539 0.369182429714611 3 4 4.19492478402872 -0.194924784028715 4 4 3.58003271610253 0.419967283897474 5 4 2.97279833690556 1.02720166309444 6 5 4.04686949287818 0.953130507121824 7 4 3.01078461768804 0.989215382311956 8 3 3.34236467671354 -0.342364676713538 9 4 3.29157982253067 0.708420177469326 10 4 3.63081757028539 0.369182429714608 11 4 3.33806540531548 0.661934594684516 12 4 2.95570049210713 1.04429950789287 13 4 3.33806540531548 0.661934594684516 14 2 3.01162623096115 -1.01162623096115 15 3 3.3931495308964 -0.393149530896403 16 4 3.95295747324167 0.0470425267583285 17 3 3.33806540531548 -0.338065405315484 18 2 2.40439185176419 -0.404391851764187 19 4 3.19766780289417 0.802332197105831 20 3 3.19766780289417 -0.197667802894169 21 3 3.81770075549152 -0.817700755491517 22 4 3.91497119245919 0.0850288075408088 23 3 3.38885025949835 -0.388850259498348 24 3 3.33806540531548 -0.338065405315484 25 4 3.80490218209113 0.195097817908867 26 4 3.01078461768804 0.989215382311956 27 4 3.43963511368121 0.560364886318787 28 4 3.38885025949835 0.611149740501652 29 4 3.43963511368121 0.560364886318787 30 4 3.33806540531548 0.661934594684516 31 5 4.38180796923484 0.61819203076516 32 4 3.24845265707703 0.751547342922967 33 4 3.03208249309076 0.967917506909242 34 4 4.19492478402872 -0.194924784028715 35 3 3.20196707429222 -0.201967074292223 36 4 4.38180796923484 -0.38180796923484 37 3 3.6773031530702 -0.677303153070202 38 4 3.52924786191966 0.470752138080337 39 4 3.91497119245919 0.0850288075408088 40 3 3.63081757028539 -0.630817570285392 41 5 4.14413992984585 0.85586007015415 42 4 3.62651829888734 0.373481701112662 43 3 3.33806540531548 -0.338065405315484 44 3 3.61801899688501 -0.618018996885008 45 3 3.43963511368121 -0.439635113681213 46 4 2.95999976350518 1.04000023649482 47 4 3.33806540531548 0.661934594684516 48 4 3.91497119245919 0.0850288075408088 49 4 3.43963511368121 0.560364886318787 50 4 3.00648534628999 0.99351465371001 51 4 3.63081757028539 0.369182429714608 52 4 3.38885025949835 0.611149740501652 53 5 3.90647189045686 1.09352810954314 54 3 2.82474304575503 0.175256954244975 55 3 2.86608774386867 0.133912256131325 56 5 4.14413992984585 0.85586007015415 57 5 3.90647189045686 1.09352810954314 58 4 3.43963511368121 0.560364886318787 59 4 3.80920145348919 0.190798546510813 60 3 2.11593895819233 0.884061041807667 61 4 3.38885025949835 0.611149740501652 62 4 3.38885025949835 0.611149740501652 63 5 3.20196707429222 1.79803292570778 64 4 3.33806540531548 0.661934594684516 65 4 3.34236467671354 0.657635323286462 66 5 4.62377528002188 0.376224719978117 67 4 3.91497119245919 0.0850288075408088 68 3 3.20196707429222 -0.201967074292223 69 4 3.34236467671354 0.657635323286462 70 4 3.6773031530702 0.322696846929798 71 4 3.34656470731781 0.653435292682186 72 4 3.58003271610253 0.419967283897472 73 4 4.19062551263066 -0.190625512630661 74 4 4.1398406584478 -0.139840658447796 75 4 3.48612069646602 0.513879303533977 76 3 3.91497119245919 -0.914971192459191 77 4 3.855687036274 0.144312963726003 78 3 3.38885025949835 -0.388850259498348 79 5 3.99608463869531 1.00391536130469 80 4 2.59043342369721 1.40956657630279 81 5 3.19766780289417 1.80233219710583 82 5 3.33806540531548 1.66193459468452 83 4 3.33806540531548 0.661934594684516 84 4 3.15118222010936 0.84881777989064 85 4 4.2337526780843 -0.233752678084301 86 4 3.57573344470447 0.424266555295527 87 4 3.24845265707703 0.751547342922967 88 5 4.57299042583902 0.427009574160981 89 4 3.44813441568354 0.551865584316458 90 3 3.33806540531548 -0.338065405315484 91 4 3.33806540531548 0.661934594684516 92 3 3.85998630767205 -0.859986307672051 93 4 3.29157982253067 0.708420177469326 94 4 2.68434544333371 1.31565455666629 95 4 3.855687036274 0.144312963726003 96 4 3.57489183143137 0.425108168568633 97 4 4.09335507566299 -0.0933550756629864 98 3 3.53260627925083 -0.532606279250833 99 3 3.58003271610253 -0.580032716102528 100 3 3.14688294871130 -0.146882948711305 101 3 3.91497119245919 -0.914971192459191 102 3 3.38885025949835 -0.388850259498348 103 2 2.31047983212768 -0.310479832127682 104 3 3.19766780289417 -0.197667802894169 105 5 3.90647189045686 1.09352810954314 106 2 3.02012553296348 -1.02012553296348 107 2 3.11319593932688 -1.11319593932688 108 3 2.64205989115318 0.357940108846824 109 3 3.19766780289417 -0.197667802894169 110 2 3.43963511368121 -1.43963511368121 111 2 3.15118222010936 -1.15118222010936 112 4 2.97279833690556 1.02720166309444 113 3 2.12359664692156 0.876403353078443 114 1 2.34846611291016 -1.34846611291016 115 1 2.67920455866255 -1.67920455866255 116 1 2.31477910352574 -1.31477910352574 117 2 3.19336853149611 -1.19336853149611 118 2 3.00648534628999 -1.00648534628999 119 3 2.31477910352574 0.685220896474264 120 1 2.63356058915085 -1.63356058915085 121 3 2.35276538430822 0.647234615691784 122 1 2.9220134827227 -1.9220134827227 123 2 3.24845265707703 -1.24845265707703 124 1 3.20196707429222 -2.20196707429222 125 2 3.43963511368121 -1.43963511368121 126 2 3.21046637629455 -1.21046637629455 127 3 2.87038701526673 0.129612984733271 128 2 3.10805505465572 -1.10805505465572 129 2 3.10805505465572 -1.10805505465572 130 4 2.17438150110442 1.82561849889558 131 2 3.24845265707703 -1.24845265707703 132 3 3.90647189045686 -0.906471890456861 133 2 2.87038701526673 -0.87038701526673 134 1 3.01078461768804 -2.01078461768804 135 2 3.43963511368121 -1.43963511368121 136 3 3.06576950247518 -0.065769502475184 137 1 1.84794232675009 -0.847942326750087 138 2 3.14688294871131 -1.14688294871131 139 2 2.78161588030139 -0.781615880301385 140 3 2.68004617193566 0.319953828064344 141 3 2.73083102611852 0.269168973881480 142 3 1.65675987014591 1.34324012985409 143 4 3.42673729948705 0.57326270051295 144 4 3.66880385106787 0.331196148932128 145 2 3.86418633827633 -1.86418633827633 146 3 2.59043342369721 0.409566576302794 147 3 3.48612069646602 -0.486120696466023 148 2 2.78161588030139 -0.781615880301385 149 1 3.4784630077368 -2.4784630077368 150 2 3.33806540531548 -1.33806540531548 151 2 2.81960216108387 -0.819602161083865 152 4 3.5241069772485 0.475893022751497 153 4 2.69620316266721 1.30379683733279 154 2 2.87122862853984 -0.871228628539835 155 3 2.72653175472047 0.273468245279534 156 2 3.24845265707703 -1.24845265707703 157 4 3.43963511368121 0.560364886318787 158 2 2.59043342369721 -0.590433423697206 159 4 3.91497119245919 0.0850288075408088 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.394575567795316 0.789151135590632 0.605424432204684 9 0.239537719918183 0.479075439836365 0.760462280081817 10 0.145495354134054 0.290990708268109 0.854504645865946 11 0.0843373438701368 0.168674687740274 0.915662656129863 12 0.0456486057247868 0.0912972114495735 0.954351394275213 13 0.0221796354593606 0.0443592709187213 0.97782036454064 14 0.0772135603167922 0.154427120633584 0.922786439683208 15 0.0910082454648711 0.182016490929742 0.908991754535129 16 0.0736243258388617 0.147248651677723 0.926375674161138 17 0.0650548398035237 0.130109679607047 0.934945160196476 18 0.0445290152754172 0.0890580305508344 0.955470984724583 19 0.0283349959052103 0.0566699918104205 0.97166500409479 20 0.0295425878639823 0.0590851757279645 0.970457412136018 21 0.0215233578269678 0.0430467156539356 0.978476642173032 22 0.0158931659186065 0.0317863318372130 0.984106834081394 23 0.0138996243885405 0.0277992487770809 0.98610037561146 24 0.0101704035789484 0.0203408071578968 0.989829596421052 25 0.00597145500197897 0.0119429100039579 0.994028544998021 26 0.00366645893876691 0.00733291787753382 0.996333541061233 27 0.00221575598367115 0.0044315119673423 0.997784244016329 28 0.00148836705296107 0.00297673410592215 0.998511632947039 29 0.000867617146543367 0.00173523429308673 0.999132382853457 30 0.000686180497539771 0.00137236099507954 0.99931381950246 31 0.000654057096619972 0.00130811419323994 0.99934594290338 32 0.000375159661876243 0.000750319323752486 0.999624840338124 33 0.000593274164088893 0.00118654832817779 0.99940672583591 34 0.000490722985477348 0.000981445970954696 0.999509277014523 35 0.000505438847583918 0.00101087769516784 0.999494561152416 36 0.000344527322521216 0.000689054645042433 0.999655472677479 37 0.000443111444320663 0.000886222888641325 0.99955688855568 38 0.000374236019419817 0.000748472038839634 0.99962576398058 39 0.000211553839995693 0.000423107679991386 0.999788446160004 40 0.000193648604793772 0.000387297209587545 0.999806351395206 41 0.000197433691414870 0.000394867382829739 0.999802566308585 42 0.000120374060760541 0.000240748121521081 0.99987962593924 43 8.78279734878803e-05 0.000175655946975761 0.999912172026512 44 0.000116059096819980 0.000232118193639959 0.99988394090318 45 0.000109377463280954 0.000218754926561909 0.999890622536719 46 8.6541263606332e-05 0.000173082527212664 0.999913458736394 47 6.6506798025166e-05 0.000133013596050332 0.999933493201975 48 3.71144383431998e-05 7.42288766863996e-05 0.999962885561657 49 2.32317195437311e-05 4.64634390874622e-05 0.999976768280456 50 1.53716439815283e-05 3.07432879630566e-05 0.999984628356019 51 9.9920480194896e-06 1.99840960389792e-05 0.99999000795198 52 6.66297475627693e-06 1.33259495125539e-05 0.999993337025244 53 9.11324777437129e-06 1.82264955487426e-05 0.999990886752226 54 5.07782718166808e-06 1.01556543633362e-05 0.999994922172818 55 7.54678800433379e-06 1.50935760086676e-05 0.999992453211996 56 7.48803992864586e-06 1.49760798572917e-05 0.999992511960071 57 9.39506845062826e-06 1.87901369012565e-05 0.99999060493155 58 5.92005185221844e-06 1.18401037044369e-05 0.999994079948148 59 3.35366167872601e-06 6.70732335745202e-06 0.999996646338321 60 3.13613778421466e-06 6.27227556842931e-06 0.999996863862216 61 2.11147218697081e-06 4.22294437394161e-06 0.999997888527813 62 1.41848518353778e-06 2.83697036707557e-06 0.999998581514816 63 8.0320330368929e-06 1.60640660737858e-05 0.999991967966963 64 6.24925277931202e-06 1.24985055586240e-05 0.99999375074722 65 4.92312557777087e-06 9.84625115554175e-06 0.999995076874422 66 3.49220297400520e-06 6.98440594801039e-06 0.999996507797026 67 1.94513179529554e-06 3.89026359059109e-06 0.999998054868205 68 1.86640457540459e-06 3.73280915080918e-06 0.999998133595425 69 1.53850558414448e-06 3.07701116828895e-06 0.999998461494416 70 9.06753993850674e-07 1.81350798770135e-06 0.999999093246006 71 8.0028170235294e-07 1.60056340470588e-06 0.999999199718298 72 5.48989913205184e-07 1.09797982641037e-06 0.999999451010087 73 3.64519053103312e-07 7.29038106206624e-07 0.999999635480947 74 2.13263201289525e-07 4.26526402579049e-07 0.999999786736799 75 1.28941554950695e-07 2.57883109901390e-07 0.999999871058445 76 1.99836599440161e-07 3.99673198880322e-07 0.9999998001634 77 1.17428939642933e-07 2.34857879285865e-07 0.99999988257106 78 9.94621335313256e-08 1.98924267062651e-07 0.999999900537866 79 2.22850509113330e-07 4.45701018226659e-07 0.99999977714949 80 3.32962942065282e-07 6.65925884130564e-07 0.999999667037058 81 2.38318763583848e-06 4.76637527167696e-06 0.999997616812364 82 1.74399580483271e-05 3.48799160966542e-05 0.999982560041952 83 1.69351320944401e-05 3.38702641888802e-05 0.999983064867906 84 2.13241412360098e-05 4.26482824720195e-05 0.999978675858764 85 1.40654288902314e-05 2.81308577804628e-05 0.99998593457111 86 1.1486792406358e-05 2.2973584812716e-05 0.999988513207594 87 1.06458979016536e-05 2.12917958033073e-05 0.999989354102098 88 1.08774030185536e-05 2.17548060371072e-05 0.999989122596981 89 8.77071227284339e-06 1.75414245456868e-05 0.999991229287727 90 7.63629623074312e-06 1.52725924614862e-05 0.99999236370377 91 9.65878912110816e-06 1.93175782422163e-05 0.999990341210879 92 1.35481600014219e-05 2.70963200028437e-05 0.999986451839999 93 3.00541278291332e-05 6.01082556582664e-05 0.999969945872171 94 0.000124775929442531 0.000249551858885061 0.999875224070558 95 0.000138200267603502 0.000276400535207004 0.999861799732396 96 0.000123276943774198 0.000246553887548396 0.999876723056226 97 0.000110384753124311 0.000220769506248621 0.999889615246876 98 0.000131153699490270 0.000262307398980540 0.99986884630051 99 0.000132633613384604 0.000265267226769208 0.999867366386615 100 0.000136717291223542 0.000273434582447085 0.999863282708776 101 0.000151642380710763 0.000303284761421526 0.99984835761929 102 0.000147949153845665 0.000295898307691330 0.999852050846154 103 0.000153043680930534 0.000306087361861067 0.99984695631907 104 0.000141668866912758 0.000283337733825515 0.999858331133087 105 0.00103933593548958 0.00207867187097915 0.99896066406451 106 0.000946404942550354 0.00189280988510071 0.99905359505745 107 0.00115754640079307 0.00231509280158614 0.998842453599207 108 0.000993791813389715 0.00198758362677943 0.99900620818661 109 0.000978638475325743 0.00195727695065149 0.999021361524674 110 0.00206418418672431 0.00412836837344863 0.997935815813276 111 0.00319562797645047 0.00639125595290095 0.99680437202355 112 0.00788070499976302 0.0157614099995260 0.992119295000237 113 0.00704428379989039 0.0140885675997808 0.99295571620011 114 0.0239327082591237 0.0478654165182474 0.976067291740876 115 0.0967461848170725 0.193492369634145 0.903253815182927 116 0.140218456351257 0.280436912702514 0.859781543648743 117 0.162340380479305 0.324680760958611 0.837659619520695 118 0.170892140803751 0.341784281607502 0.829107859196249 119 0.173999538605468 0.347999077210936 0.826000461394532 120 0.202508414022032 0.405016828044063 0.797491585977968 121 0.193815538439315 0.38763107687863 0.806184461560685 122 0.26299531578925 0.5259906315785 0.73700468421075 123 0.26816659828452 0.53633319656904 0.73183340171548 124 0.373979919953762 0.747959839907523 0.626020080046239 125 0.369474407658726 0.738948815317451 0.630525592341274 126 0.356419370014423 0.712838740028846 0.643580629985577 127 0.316136127390609 0.632272254781218 0.683863872609391 128 0.337413050522423 0.674826101044845 0.662586949477577 129 0.374947124882626 0.749894249765252 0.625052875117374 130 0.533272830273251 0.933454339453499 0.466727169726749 131 0.531192939661699 0.937614120676602 0.468807060338301 132 0.483165594724514 0.966331189449028 0.516834405275486 133 0.473022227923317 0.946044455846634 0.526977772076683 134 0.645107599100362 0.709784801799276 0.354892400899638 135 0.636597459210947 0.726805081578105 0.363402540789053 136 0.583734052046278 0.832531895907444 0.416265947953722 137 0.585280773332145 0.82943845333571 0.414719226667855 138 0.547440982989999 0.905118034020002 0.452559017010001 139 0.521411173112457 0.957177653775085 0.478588826887543 140 0.513584260844953 0.972831478310095 0.486415739155047 141 0.474602752622888 0.949205505245776 0.525397247377112 142 0.56003361238085 0.8799327752383 0.43996638761915 143 0.507941598895195 0.98411680220961 0.492058401104805 144 0.570006118975389 0.859987762049222 0.429993881024611 145 0.739130322216338 0.521739355567324 0.260869677783662 146 0.7032921706984 0.593415658603199 0.296707829301600 147 0.640880073175152 0.718239853649696 0.359119926824848 148 0.531818406408882 0.936363187182236 0.468181593591118 149 0.60330465092359 0.79339069815282 0.39669534907641 150 0.546084610770435 0.90783077845913 0.453915389229565 151 0.389965274061581 0.779930548123162 0.610034725938419 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 86 0.597222222222222 NOK 5% type I error level 95 0.659722222222222 NOK 10% type I error level 99 0.6875 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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