Multiple Regression Seasonal & Linear

*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, 28 Dec 2010 17:17:53 +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/28/t1293556546t54nsjzosmxm85i.htm/, Retrieved Tue, 28 Dec 2010 18:15:58 +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/28/t1293556546t54nsjzosmxm85i.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 «

621 0 0 587 0 0 655 0 0 517 0 0 646 0 0 657 0 0 382 0 0 345 0 0 625 0 0 654 0 0 606 0 0 510 0 0 614 0 0 647 0 0 580 0 0 614 0 0 636 0 0 388 0 0 356 0 0 639 0 0 753 0 0 611 0 0 639 0 0 630 0 0 586 0 0 695 0 0 552 0 0 619 0 0 681 0 0 421 0 0 307 0 0 754 0 0 690 0 0 644 0 0 643 0 0 608 0 0 651 0 0 691 0 0 627 0 0 634 0 0 731 0 0 475 0 0 337 0 0 803 0 0 722 0 0 590 0 0 724 0 0 627 0 0 696 0 0 825 0 0 677 0 0 656 0 0 785 0 0 412 0 0 352 0 0 839 0 0 729 0 0 696 0 0 641 0 0 695 0 0 638 0 0 762 0 0 635 0 0 721 0 0 854 0 0 418 0 0 367 0 0 824 0 0 687 0 0 601 0 0 676 0 0 740 0 0 691 0 0 683 0 0 594 0 0 729 0 0 731 0 0 386 0 0 331 0 0 706 0 0 715 0 0 657 0 0 653 0 0 642 0 0 643 0 0 718 0 0 654 0 0 632 0 0 731 0 0 392 0 0 344 0 0 792 0 0 852 0 0 649 0 0 629 0 0 685 0 0 617 0 0 715 0 0 715 0 0 629 0 0 916 0 0 531 1 0 357 1 0 917 1 0 828 1 0 708 1 0 858 1 0 775 1 0 785 1 0 1006 1 0 789 1 0 734 1 0 906 1 0 532 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 12 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 592.912200071315 + 79.5171987934752X1[t] + 36.6461688935752X2[t] + 0.644046307447164M1[t] + 88.0982926213765M2[t] -8.62927924651185M3[t] -6.9023056598549M4[t] + 108.642849744984M5[t] -204.677194740493M6[t] -319.041130244745M7[t] + 101.627100715224M8[t] + 71.4449833927896M9[t] -3.37349756600782M10[t] + 13.5093900497066M11[t] + 0.909390049706563t + 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) 592.912200071315 24.935326 23.778 0 0 X1 79.5171987934752 23.651293 3.3621 0.001051 0.000526 X2 36.6461688935752 25.684038 1.4268 0.156345 0.078172 M1 0.644046307447164 29.728512 0.0217 0.982753 0.491377 M2 88.0982926213765 29.722513 2.964 0.003692 0.001846 M3 -8.62927924651185 29.718321 -0.2904 0.772057 0.386028 M4 -6.9023056598549 29.715935 -0.2323 0.816736 0.408368 M5 108.642849744984 29.715357 3.6561 0.000388 0.000194 M6 -204.677194740493 29.771283 -6.875 0 0 M7 -319.041130244745 29.764845 -10.7187 0 0 M8 101.627100715224 29.764264 3.4144 0.000884 0.000442 M9 71.4449833927896 29.75908 2.4008 0.017964 0.008982 M10 -3.37349756600782 29.7557 -0.1134 0.909932 0.454966 M11 13.5093900497066 30.414308 0.4442 0.657748 0.328874 t 0.909390049706563 0.231751 3.924 0.000149 7.4e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.909827481322315 R-squared 0.827786045769308 Adjusted R-squared 0.806820868732528 F-TEST (value) 39.4838566980424 F-TEST (DF numerator) 14 F-TEST (DF denominator) 115 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 68.0064865853553 Sum Squared Residuals 531861.455033673 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 621 594.465636428463 26.534363571537 2 587 682.829272792104 -95.8292727921036 3 655 587.011090973922 67.9889090260779 4 517 589.647454610286 -72.6474546102858 5 646 706.102000064831 -60.102000064831 6 657 393.691345629061 263.308654370939 7 382 280.236800174515 101.763199825485 8 345 701.81442118419 -356.81442118419 9 625 672.541693911463 -47.5416939114627 10 654 598.632603002372 55.3673969976278 11 606 616.424880667793 -10.4248806677933 12 510 603.824880667793 -93.8248806677929 13 614 605.378317024947 8.62168297505329 14 647 693.741953388583 -46.7419533885827 15 580 597.9237715704 -17.9237715704007 16 614 600.560135206764 13.4398647932356 17 636 717.01468066131 -81.01468066131 18 388 404.604026225539 -16.6040262255394 19 356 291.149480770994 64.850519229006 20 639 712.727101780669 -73.7271017806691 21 753 683.454374507942 69.5456254920583 22 611 609.545283598851 1.45471640114920 23 639 627.337561264272 11.6624387357282 24 630 614.737561264272 15.2624387357283 25 586 616.290997621426 -30.2909976214254 26 695 704.654633985062 -9.6546339850615 27 552 608.83645216688 -56.8364521668795 28 619 611.472815803243 7.52718419675683 29 681 727.927361257789 -46.9273612577886 30 421 415.516706822018 5.48329317798185 31 307 302.062161367473 4.93783863252729 32 754 723.639782377148 30.3602176228522 33 690 694.36705510442 -4.36705510442049 34 644 620.45796419533 23.5420358046704 35 643 638.25024186075 4.74975813924948 36 608 625.65024186075 -17.6502418607505 37 651 627.203678217904 23.7963217820958 38 691 715.56731458154 -24.5673145815402 39 627 619.749132763358 7.25086723664173 40 634 622.385496399722 11.6145036002781 41 731 738.840041854267 -7.84004185426742 42 475 426.429387418497 48.5706125815031 43 337 312.974841963951 24.0251580360485 44 803 734.552462973627 68.4475370263734 45 722 705.279735700899 16.7202642991008 46 590 631.370644791808 -41.3706447918083 47 724 649.16292245723 74.8370775427707 48 627 636.56292245723 -9.56292245722924 49 696 638.116358814383 57.883641185617 50 825 726.479995178019 98.520004821981 51 677 630.661813359837 46.338186640163 52 656 633.298176996201 22.7018230037993 53 785 749.752722450746 35.2472775492538 54 412 437.342068014976 -25.3420680149757 55 352 323.88752256043 28.1124774395697 56 839 745.465143570105 93.5348564298947 57 729 716.192416297378 12.807583702622 58 696 642.283325388287 53.716674611713 59 641 660.075603053708 -19.0756030537080 60 695 647.475603053708 47.524396946292 61 638 649.029039410862 -11.0290394108617 62 762 737.392675774498 24.6073242255023 63 635 641.574493956316 -6.57449395631577 64 721 644.21085759268 76.7891424073205 65 854 760.665403047225 93.334596952775 66 418 448.254748611454 -30.2547486114544 67 367 334.800203156909 32.199796843091 68 824 756.377824166584 67.622175833416 69 687 727.105096893857 -40.1050968938568 70 601 653.196005984766 -52.1960059847658 71 676 670.988283650187 5.01171634981322 72 740 658.388283650187 81.6117163498132 73 691 659.94172000734 31.0582799926595 74 683 748.305356370976 -65.3053563709765 75 594 652.487174552794 -58.4871745527945 76 729 655.123538189158 73.8764618108418 77 731 771.578083643704 -40.5780836437036 78 386 459.167429207933 -73.1674292079332 79 331 345.712883753388 -14.7128837533877 80 706 767.290504763063 -61.2905047630628 81 715 738.017777490335 -23.0177774903355 82 657 664.108686581245 -7.10868658124455 83 653 681.900964246666 -28.9009642466655 84 642 669.300964246666 -27.3009642466655 85 643 670.854400603819 -27.8544006038192 86 718 759.218036967455 -41.2180369674552 87 654 663.399855149273 -9.39985514927324 88 632 666.036218785637 -34.0362187856370 89 731 782.490764240182 -51.4907642401824 90 392 470.080109804412 -78.080109804412 91 344 356.625564349866 -12.6255643498665 92 792 778.203185359542 13.7968146404584 93 852 748.930458086814 103.069541913186 94 649 675.021367177723 -26.0213671777233 95 629 692.813644843144 -63.8136448431443 96 685 680.213644843144 4.78635515685576 97 617 681.767081200298 -64.767081200298 98 715 770.130717563934 -55.130717563934 99 715 674.312535745752 40.687464254248 100 629 676.948899382116 -47.9488993821157 101 916 793.403444836661 122.596555163339 102 531 560.509989194366 -29.509989194366 103 357 447.055443739821 -90.0554437398206 104 917 868.633064749496 48.3669352505043 105 828 839.360337476768 -11.3603374767683 106 708 765.451246567677 -57.4512465676774 107 858 783.243524233098 74.7564757669016 108 775 770.643524233098 4.35647576690166 109 785 772.196960590252 12.8030394097479 110 1006 860.560596953888 145.439403046112 111 789 764.742415135706 24.2575848642939 112 734 767.37877877207 -33.3787787720698 113 906 883.833324226615 22.1666757733847 114 532 571.422669790845 -39.4226697908447 115 387 457.968124336299 -70.9681243362994 116 991 916.19191423955 74.8080857604505 117 841 886.919186966822 -45.9191869668222 118 892 813.010096057731 78.9899039422687 119 782 830.802373723152 -48.8023737231523 120 813 818.202373723152 -5.20237372315224 121 793 819.755810080306 -26.755810080306 122 978 908.119446443942 69.880553556058 123 775 812.30126462576 -37.30126462576 124 797 814.937628262124 -17.9376282621237 125 946 931.392173716669 14.6078262833309 126 594 618.981519280899 -24.9815192808986 127 438 505.526973826353 -67.5269738263534 128 1022 927.104594836028 94.8954051639717 129 868 897.831867563301 -29.831867563301 130 795 823.92277665421 -28.9227766542100 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.998588366582717 0.00282326683456550 0.00141163341728275 19 0.996576697195653 0.00684660560869493 0.00342330280434747 20 0.999995093846648 9.81230670393486e-06 4.90615335196743e-06 21 0.99999471947096 1.05610580800388e-05 5.28052904001939e-06 22 0.999988461561507 2.30768769867344e-05 1.15384384933672e-05 23 0.999970722651859 5.85546962824801e-05 2.92773481412401e-05 24 0.99996121646564 7.75670687168802e-05 3.87835343584401e-05 25 0.99994043191173 0.000119136176539298 5.9568088269649e-05 26 0.999902323828037 0.000195352343925639 9.76761719628195e-05 27 0.999917942429583 0.000164115140833703 8.20575704168513e-05 28 0.999845871266476 0.000308257467048322 0.000154128733524161 29 0.999814944454106 0.000370111091788194 0.000185055545894097 30 0.999864272725244 0.000271454549511001 0.000135727274755501 31 0.999809093626145 0.000381812747709486 0.000190906373854743 32 0.999992165450011 1.56690999775414e-05 7.83454998877072e-06 33 0.999985119450147 2.97610997067743e-05 1.48805498533871e-05 34 0.99997008254024 5.98349195218359e-05 2.99174597609179e-05 35 0.999943014785392 0.000113970429216951 5.69852146084754e-05 36 0.99991430565127 0.000171388697461536 8.56943487307682e-05 37 0.99984120131488 0.000317597370241355 0.000158798685120678 38 0.999811178822474 0.000377642355053103 0.000188821177526551 39 0.999679324087112 0.000641351825775951 0.000320675912887976 40 0.99948004010015 0.00103991979969927 0.000519959899849637 41 0.999420602423538 0.00115879515292424 0.000579397576462118 42 0.999278975253487 0.00144204949302582 0.000721024746512908 43 0.998932349384536 0.00213530123092835 0.00106765061546417 44 0.99967034165313 0.000659316693738404 0.000329658346869202 45 0.99944573841025 0.00110852317949947 0.000554261589749734 46 0.999525042688916 0.000949914622168768 0.000474957311084384 47 0.999410200842384 0.00117959831523187 0.000589799157615933 48 0.999231699384443 0.00153660123111485 0.000768300615557424 49 0.99886554268058 0.00226891463884087 0.00113445731942043 50 0.999096192427467 0.00180761514506572 0.000903807572532859 51 0.998586297611494 0.00282740477701290 0.00141370238850645 52 0.997769985562365 0.00446002887526971 0.00223001443763486 53 0.996912415548239 0.00617516890352263 0.00308758445176131 54 0.997620493461665 0.00475901307666946 0.00237950653833473 55 0.996925617589431 0.00614876482113755 0.00307438241056878 56 0.997858972942268 0.00428205411546319 0.00214102705773160 57 0.996772101813399 0.00645579637320214 0.00322789818660107 58 0.995734051997478 0.00853189600504409 0.00426594800252204 59 0.994675821463187 0.0106483570736264 0.00532417853681321 60 0.992591732292146 0.0148165354157082 0.0074082677078541 61 0.990490563266972 0.0190188734660561 0.00950943673302805 62 0.98618120824843 0.0276375835031414 0.0138187917515707 63 0.981786141228845 0.0364277175423107 0.0182138587711553 64 0.980966228547978 0.0380675429040433 0.0190337714520216 65 0.982784824612697 0.0344303507746054 0.0172151753873027 66 0.983632955058618 0.0327340898827648 0.0163670449413824 67 0.985431316912463 0.0291373661750745 0.0145686830875373 68 0.984108023715755 0.0317839525684904 0.0158919762842452 69 0.981267672323611 0.0374646553527771 0.0187323276763885 70 0.979877154497876 0.0402456910042473 0.0201228455021237 71 0.973632674736929 0.0527346505261429 0.0263673252630715 72 0.979699782024693 0.0406004359506146 0.0203002179753073 73 0.979724703586003 0.0405505928279932 0.0202752964139966 74 0.980926611084243 0.0381467778315131 0.0190733889157565 75 0.979355457944532 0.0412890841109364 0.0206445420554682 76 0.98968723235645 0.0206255352870990 0.0103127676435495 77 0.986755104309932 0.0264897913801367 0.0132448956900684 78 0.986601782767456 0.0267964344650877 0.0133982172325439 79 0.98841151738913 0.0231769652217385 0.0115884826108693 80 0.990627001029722 0.0187459979405556 0.00937299897027782 81 0.986257898316071 0.0274842033678577 0.0137421016839288 82 0.980760223496422 0.0384795530071565 0.0192397765035783 83 0.973266531813864 0.053466936372272 0.026733468186136 84 0.962752458844609 0.074495082310782 0.037247541155391 85 0.951066522642662 0.097866954714676 0.048933477357338 86 0.948921776092198 0.102156447815605 0.0510782239078023 87 0.929341357395772 0.141317285208457 0.0706586426042283 88 0.909301305722173 0.181397388555654 0.0906986942778272 89 0.920168215561563 0.159663568876874 0.079831784438437 90 0.912301165909382 0.175397668181237 0.0876988340906183 91 0.909140255087395 0.181719489825211 0.0908597449126053 92 0.894730284685706 0.210539430628587 0.105269715314294 93 0.963653097217311 0.0726938055653771 0.0363469027826885 94 0.946818929408551 0.106362141182897 0.0531810705914486 95 0.940076151873339 0.119847696253322 0.059923848126661 96 0.915755071731332 0.168489856537337 0.0842449282686683 97 0.898095748953266 0.203808502093467 0.101904251046734 98 0.988239557909761 0.0235208841804770 0.0117604420902385 99 0.980297435509386 0.0394051289812281 0.0197025644906141 100 0.987531981808282 0.0249360363834370 0.0124680181917185 101 0.981995059422407 0.0360098811551871 0.0180049405775936 102 0.968578747959857 0.0628425040802868 0.0314212520401434 103 0.950312653917843 0.0993746921643137 0.0496873460821569 104 0.943808324286066 0.112383351427868 0.0561916757139342 105 0.907839456520642 0.184321086958717 0.0921605434793584 106 0.963350143966414 0.0732997120671719 0.0366498560335860 107 0.981121350936122 0.0377572981277553 0.0188786490638777 108 0.960239202308237 0.0795215953835251 0.0397607976917626 109 0.92316643587466 0.153667128250679 0.0768335641253393 110 0.915592232640757 0.168815534718486 0.0844077673592428 111 0.892322591210848 0.215354817578304 0.107677408789152 112 0.776577293786 0.446845412428 0.223422706214 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 41 0.431578947368421 NOK 5% type I error level 69 0.726315789473684 NOK 10% type I error level 78 0.821052631578947 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/10v7xh1293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/10v7xh1293556659.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/16o0n1293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/16o0n1293556659.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/26o0n1293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/26o0n1293556659.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/3zfz81293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/3zfz81293556659.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/4zfz81293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/4zfz81293556659.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/5zfz81293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/5zfz81293556659.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/6zfz81293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/6zfz81293556659.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/7rogt1293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/7rogt1293556659.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/8kgxe1293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/8kgxe1293556659.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/9kgxe1293556659.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293556546t54nsjzosmxm85i/9kgxe1293556659.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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') }

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