ws3

*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: Tue, 17 Nov 2009 08:02:21 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg.htm/, Retrieved Tue, 17 Nov 2009 16:03:26 +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/2009/Nov/17/t1258470193s51uyvfj3lnf4dg.htm/}, year = {2009}, } @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 = {2009}, 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 «

395.3 0 395.1 0 403.5 0 403.3 0 405.7 0 406.7 0 407.2 0 412.4 0 415.9 0 414.0 0 411.8 0 409.9 0 412.4 0 415.9 0 416.3 0 417.2 0 421.8 0 421.4 0 415.1 0 412.4 0 411.8 0 408.8 0 404.5 0 402.5 0 409.4 0 410.7 0 413.4 0 415.2 0 417.7 0 417.8 0 417.9 0 418.4 0 418.2 0 416.6 0 418.9 0 421.0 0 423.5 0 432.3 0 432.3 0 428.6 0 426.7 0 427.3 0 428.5 0 437.0 0 442.0 0 444.9 0 441.4 0 440.3 0 447.1 0 455.3 0 478.6 0 486.5 0 487.8 0 485.9 0 483.8 0 488.4 0 494.0 0 493.6 0 487.3 0 482.1 0 484.2 0 496.8 0 501.1 0 499.8 0 495.5 0 498.1 0 503.8 0 516.2 0 526.1 0 527.1 0 525.1 0 528.9 0 540.1 0 549.0 0 556.0 0 568.9 0 589.1 0 590.3 0 603.3 0 638.8 0 643.0 0 656.7 0 656.1 0 654.1 0 659.9 0 662.1 0 669.2 0 673.1 0 678.3 0 677.4 0 678.5 0 672.4 0 665.3 0 667.9 0 672.1 0 662.5 0 682.3 0 692.1 0 702.7 0 721.4 0 733.2 0 747.7 0 737.6 0 729.3 0 706.1 0 674.3 0 659.0 0 645.7 0 646.1 0 633.0 1 622.3 1 628.2 1 637.3 1 639.6 1 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 334.951619017219 -71.0679068117941X[t] + 3.29705980435749t + 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) 334.951619017219 7.338996 45.64 0 0 X -71.0679068117941 15.498156 -4.5856 1.2e-05 6e-06 t 3.29705980435749 0.115817 28.4678 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.941323218705861 R-squared 0.886089402074763 Adjusted R-squared 0.884090970532215 F-TEST (value) 443.392422111688 F-TEST (DF numerator) 2 F-TEST (DF denominator) 114 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 38.0529531418478 Sum Squared Residuals 165075.105680986 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 395.3 338.248678821577 57.0513211784233 2 395.1 341.545738625933 53.5542613740666 3 403.5 344.842798430291 58.6572015697091 4 403.3 348.139858234649 55.1601417653514 5 405.7 351.436918039006 54.2630819609939 6 406.7 354.733977843364 51.9660221566364 7 407.2 358.031037647721 49.1689623522789 8 412.4 361.328097452079 51.0719025479214 9 415.9 364.625157256436 51.2748427435639 10 414 367.922217060794 46.0777829392064 11 411.8 371.219276865151 40.5807231348489 12 409.9 374.516336669509 35.3836633304914 13 412.4 377.813396473866 34.5866035261339 14 415.9 381.110456278224 34.7895437217764 15 416.3 384.407516082581 31.8924839174190 16 417.2 387.704575886939 29.4954241130615 17 421.8 391.001635691296 30.798364308704 18 421.4 394.298695495654 27.1013045043465 19 415.1 397.595755300011 17.504244699989 20 412.4 400.892815104368 11.5071848956315 21 411.8 404.189874908726 7.61012509127402 22 408.8 407.486934713083 1.31306528691652 23 404.5 410.783994517441 -6.28399451744097 24 402.5 414.081054321798 -11.5810543217985 25 409.4 417.378114126156 -7.97811412615599 26 410.7 420.675173930513 -9.97517393051347 27 413.4 423.972233734871 -10.5722337348710 28 415.2 427.269293539228 -12.0692935392285 29 417.7 430.566353343586 -12.8663533435859 30 417.8 433.863413147943 -16.0634131479434 31 417.9 437.160472952301 -19.2604729523009 32 418.4 440.457532756658 -22.0575327566584 33 418.2 443.754592561016 -25.5545925610159 34 416.6 447.051652365373 -30.4516523653734 35 418.9 450.348712169731 -31.4487121697309 36 421 453.645771974088 -32.6457719740884 37 423.5 456.942831778446 -33.4428317784459 38 432.3 460.239891582803 -27.9398915828033 39 432.3 463.536951387161 -31.2369513871608 40 428.6 466.834011191518 -38.2340111915183 41 426.7 470.131070995876 -43.4310709958759 42 427.3 473.428130800233 -46.1281308002333 43 428.5 476.725190604591 -48.2251906045908 44 437 480.022250408948 -43.0222504089483 45 442 483.319310213306 -41.3193102133058 46 444.9 486.616370017663 -41.7163700176633 47 441.4 489.913429822021 -48.5134298220208 48 440.3 493.210489626378 -52.9104896263783 49 447.1 496.507549430736 -49.4075494307357 50 455.3 499.804609235093 -44.5046092350933 51 478.6 503.101669039451 -24.5016690394507 52 486.5 506.398728843808 -19.8987288438083 53 487.8 509.695788648166 -21.8957886481657 54 485.9 512.992848452523 -27.0928484525233 55 483.8 516.289908256881 -32.4899082568807 56 488.4 519.586968061238 -31.1869680612383 57 494 522.884027865596 -28.8840278655957 58 493.6 526.181087669953 -32.5810876699532 59 487.3 529.478147474311 -42.1781474743107 60 482.1 532.775207278668 -50.6752072786682 61 484.2 536.072267083026 -51.8722670830257 62 496.8 539.369326887383 -42.5693268873832 63 501.1 542.666386691741 -41.5663866917407 64 499.8 545.963446496098 -46.1634464960982 65 495.5 549.260506300456 -53.7605063004557 66 498.1 552.557566104813 -54.4575661048131 67 503.8 555.854625909171 -52.0546259091706 68 516.2 559.151685713528 -42.9516857135281 69 526.1 562.448745517886 -36.3487455178856 70 527.1 565.745805322243 -38.6458053222431 71 525.1 569.042865126601 -43.9428651266006 72 528.9 572.339924930958 -43.4399249309581 73 540.1 575.636984735316 -35.5369847353156 74 549 578.934044539673 -29.9340445396731 75 556 582.23110434403 -26.2311043440306 76 568.9 585.528164148388 -16.6281641483881 77 589.1 588.825223952746 0.274776047254456 78 590.3 592.122283757103 -1.82228375710310 79 603.3 595.41934356146 7.8806564385394 80 638.8 598.716403365818 40.0835966341819 81 643 602.013463170176 40.9865368298245 82 656.7 605.310522974533 51.389477025467 83 656.1 608.607582778891 47.4924172211095 84 654.1 611.904642583248 42.195357416752 85 659.9 615.201702387606 44.6982976123945 86 662.1 618.498762191963 43.601237808037 87 669.2 621.79582199632 47.4041780036796 88 673.1 625.092881800678 48.007118199322 89 678.3 628.389941605035 49.9100583949645 90 677.4 631.687001409393 45.712998590607 91 678.5 634.98406121375 43.5159387862495 92 672.4 638.281121018108 34.118878981892 93 665.3 641.578180822465 23.7218191775345 94 667.9 644.875240626823 23.024759373177 95 672.1 648.17230043118 23.9276995688196 96 662.5 651.469360235538 11.0306397644621 97 682.3 654.766420039895 27.5335799601045 98 692.1 658.063479844253 34.0365201557471 99 702.7 661.36053964861 41.3394603513896 100 721.4 664.657599452968 56.7424005470321 101 733.2 667.954659257325 65.2453407426747 102 747.7 671.251719061683 76.4482809383172 103 737.6 674.54877886604 63.0512211339596 104 729.3 677.845838670398 51.4541613296021 105 706.1 681.142898474755 24.9571015252447 106 674.3 684.439958279113 -10.1399582791129 107 659 687.73701808347 -28.7370180834703 108 645.7 691.034077887828 -45.3340778878278 109 646.1 694.331137692185 -48.2311376921853 110 633 626.560290684749 6.43970931525123 111 622.3 629.857350489106 -7.55735048910632 112 628.2 633.154410293464 -4.95441029346372 113 637.3 636.451470097821 0.8485299021787 114 639.6 639.748529902179 -0.148529902178725 115 638.5 643.045589706536 -4.54558970653624 116 650.5 646.342649510894 4.15735048910627 117 655.4 649.639709315251 5.76029068474875 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.000466496409112765 0.00093299281822553 0.999533503590887 7 4.67225613695761e-05 9.34451227391522e-05 0.99995327743863 8 3.26775694149021e-06 6.53551388298042e-06 0.999996732243059 9 2.65011113019184e-07 5.30022226038367e-07 0.999999734988887 10 3.34438975567698e-08 6.68877951135396e-08 0.999999966556102 11 2.4690428822045e-08 4.938085764409e-08 0.999999975309571 12 2.70635959672774e-08 5.41271919345548e-08 0.999999972936404 13 6.44626045788952e-09 1.28925209157790e-08 0.99999999355374 14 8.5947329924625e-10 1.7189465984925e-09 0.999999999140527 15 1.25420397619654e-10 2.50840795239307e-10 0.99999999987458 16 1.86994623996367e-11 3.73989247992735e-11 0.9999999999813 17 2.77581865162598e-12 5.55163730325196e-12 0.999999999997224 18 3.82549915356283e-13 7.65099830712566e-13 0.999999999999617 19 5.94414174728479e-13 1.18882834945696e-12 0.999999999999406 20 2.02226227465294e-12 4.04452454930588e-12 0.999999999997978 21 3.57476735045427e-12 7.14953470090854e-12 0.999999999996425 22 1.02949763125221e-11 2.05899526250443e-11 0.999999999989705 23 5.34240043491488e-11 1.06848008698298e-10 0.999999999946576 24 1.59524283069442e-10 3.19048566138884e-10 0.999999999840476 25 6.63304815564183e-11 1.32660963112837e-10 0.99999999993367 26 2.27221313087698e-11 4.54442626175395e-11 0.999999999977278 27 6.53825254359825e-12 1.30765050871965e-11 0.999999999993462 28 1.82190376380821e-12 3.64380752761642e-12 0.999999999998178 29 5.37709978123681e-13 1.07541995624736e-12 0.999999999999462 30 1.51133701808610e-13 3.02267403617219e-13 0.999999999999849 31 4.05372217462707e-14 8.10744434925415e-14 0.99999999999996 32 1.05374906795391e-14 2.10749813590781e-14 0.99999999999999 33 2.58553450998887e-15 5.17106901997775e-15 0.999999999999997 34 6.16509898392692e-16 1.23301979678538e-15 1 35 1.38805272018870e-16 2.77610544037741e-16 1 36 3.23664600003903e-17 6.47329200007806e-17 1 37 8.7779480060419e-18 1.75558960120838e-17 1 38 1.57074398685388e-17 3.14148797370776e-17 1 39 1.48496333492108e-17 2.96992666984216e-17 1 40 4.53382491913846e-18 9.06764983827692e-18 1 41 9.97167871601507e-19 1.99433574320301e-18 1 42 2.09745647098200e-19 4.19491294196401e-19 1 43 4.41084552149511e-20 8.82169104299021e-20 1 44 3.59826695025642e-20 7.19653390051284e-20 1 45 7.96624948624072e-20 1.59324989724814e-19 1 46 2.06310751595031e-19 4.12621503190063e-19 1 47 1.12357722407772e-19 2.24715444815545e-19 1 48 3.92590957765078e-20 7.85181915530156e-20 1 49 4.04772930607288e-20 8.09545861214576e-20 1 50 2.44662457244236e-19 4.89324914488472e-19 1 51 2.60828429831531e-15 5.21656859663062e-15 0.999999999999997 52 2.65340976645963e-12 5.30681953291926e-12 0.999999999997347 53 1.39129238181187e-10 2.78258476362374e-10 0.99999999986087 54 9.97890965677005e-10 1.99578193135401e-09 0.999999999002109 55 2.38804261368671e-09 4.77608522737342e-09 0.999999997611957 56 5.83623916318255e-09 1.16724783263651e-08 0.99999999416376 57 1.59099481347724e-08 3.18198962695449e-08 0.999999984090052 58 2.56700992173972e-08 5.13401984347944e-08 0.9999999743299 59 1.99142447851969e-08 3.98284895703937e-08 0.999999980085755 60 1.15028190178852e-08 2.30056380357704e-08 0.999999988497181 61 6.90485148372367e-09 1.38097029674473e-08 0.999999993095149 62 6.39580289518823e-09 1.27916057903765e-08 0.999999993604197 63 6.49757600376684e-09 1.29951520075337e-08 0.999999993502424 64 5.58544060450661e-09 1.11708812090132e-08 0.99999999441456 65 4.47232518507631e-09 8.94465037015262e-09 0.999999995527675 66 4.23437698258845e-09 8.4687539651769e-09 0.999999995765623 67 5.05696845564153e-09 1.01139369112831e-08 0.999999994943032 68 9.26254377702879e-09 1.85250875540576e-08 0.999999990737456 69 2.52651509139618e-08 5.05303018279236e-08 0.999999974734849 70 6.6931922376245e-08 1.3386384475249e-07 0.999999933068078 71 1.94243485314202e-07 3.88486970628405e-07 0.999999805756515 72 7.97343517219955e-07 1.59468703443991e-06 0.999999202656483 73 4.76919393781294e-06 9.53838787562587e-06 0.999995230806062 74 3.72908345343161e-05 7.45816690686321e-05 0.999962709165466 75 0.000340552561681836 0.000681105123363671 0.999659447438318 76 0.00310908456082419 0.00621816912164839 0.996890915439176 77 0.0221036504195551 0.0442073008391102 0.977896349580445 78 0.0959719793953725 0.191943958790745 0.904028020604628 79 0.27413673234592 0.54827346469184 0.72586326765408 80 0.53832095672687 0.92335808654626 0.46167904327313 81 0.721327027923976 0.557345944152048 0.278672972076024 82 0.8396212633854 0.320757473229201 0.160378736614600 83 0.893791320764517 0.212417358470965 0.106208679235483 84 0.920162361152718 0.159675277694564 0.079837638847282 85 0.935449347088071 0.129101305823858 0.0645506529119289 86 0.94337863448404 0.113242731031922 0.0566213655159608 87 0.947305202943028 0.105389594113945 0.0526947970569723 88 0.947665734352654 0.104668531294693 0.0523342656473463 89 0.945471458443054 0.109057083113892 0.054528541556946 90 0.939225541927595 0.12154891614481 0.0607744580724049 91 0.929447001807295 0.14110599638541 0.070552998192705 92 0.91663852654713 0.166722946905741 0.0833614734528705 93 0.908692593577539 0.182614812844923 0.0913074064224614 94 0.904122840243269 0.191754319513463 0.0958771597567314 95 0.902779796785276 0.194440406429448 0.0972202032147241 96 0.936021040920368 0.127957918159263 0.0639789590796315 97 0.9476600326877 0.104679934624599 0.0523399673122997 98 0.954383378787106 0.0912332424257873 0.0456166212128936 99 0.953522056799018 0.0929558864019635 0.0464779432009817 100 0.937586735743645 0.124826528512709 0.0624132642563546 101 0.918006275565044 0.163987448869912 0.081993724434956 102 0.936999364212787 0.126001271574427 0.0630006357872133 103 0.965015166051788 0.0699696678964232 0.0349848339482116 104 0.994554262869554 0.0108914742608918 0.00544573713044592 105 0.99985623707105 0.000287525857900612 0.000143762928950306 106 0.999986446136788 2.71077264242438e-05 1.35538632121219e-05 107 0.999995386683298 9.22663340315218e-06 4.61331670157609e-06 108 0.99996814752129 6.37049574198638e-05 3.18524787099319e-05 109 0.999767437369917 0.000465125260165874 0.000232562630082937 110 0.999877231737074 0.000245536525852868 0.000122768262926434 111 0.99859978077724 0.00280043844551967 0.00140021922275984 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 78 0.735849056603774 NOK 5% type I error level 80 0.754716981132076 NOK 10% type I error level 83 0.783018867924528 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/10gb7u1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/10gb7u1258470133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/1xvbo1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/1xvbo1258470133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/2d29s1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/2d29s1258470133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/31wia1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/31wia1258470133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/4iw7f1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/4iw7f1258470133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/5h2zd1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/5h2zd1258470133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/6yeof1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/6yeof1258470133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/79fpz1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/79fpz1258470133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/8idho1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/8idho1258470133.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/9r6yx1258470133.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258470193s51uyvfj3lnf4dg/9r6yx1258470133.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by