Multiple Regression (invoer) (monthly dummies, linear trend)

*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: Mon, 14 Dec 2009 04:40:33 -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/Dec/14/t1260790992bdwhzyucii417we.htm/, Retrieved Mon, 14 Dec 2009 12:43:29 +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/Dec/14/t1260790992bdwhzyucii417we.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 «

7787.0 0 8474.2 0 9154.7 0 8557.2 0 7951.1 0 9156.7 0 7865.7 0 7337.4 0 9131.7 0 8814.6 0 8598.8 0 8439.6 0 7451.8 0 8016.2 0 9544.1 0 8270.7 0 8102.2 0 9369.0 0 7657.7 0 7816.6 0 9391.3 0 9445.4 0 9533.1 0 10068.7 0 8955.5 0 10423.9 0 11617.2 0 9391.1 0 10872.0 0 10230.4 0 9221.0 0 9428.6 0 10934.5 0 10986.0 0 11724.6 0 11180.9 0 11163.2 0 11240.9 0 12107.1 0 10762.3 0 11340.4 0 11266.8 0 9542.7 0 9227.7 0 10571.9 1 10774.4 1 10392.8 1 9920.2 1 9884.9 1 10174.5 1 11395.4 1 10760.2 1 10570.1 1 10536.0 1 9902.6 1 8889.0 1 10837.3 1 11624.1 1 10509.0 1 10984.9 1 10649.1 1 10855.7 1 11677.4 1 10760.2 1 10046.2 1 10772.8 1 9987.7 1 8638.7 1 11063.7 1 11855.7 1 10684.5 1 11337.4 1 10478.0 1 11123.9 1 12909.3 1 11339.9 1 10462.2 1 12733.5 1 10519.2 1 10414.9 1 12476.8 1 12384.6 1 12266.7 1 12919.9 1 11497.3 1 12142.0 1 13919.4 1 12656.8 1 120 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 Invoer[t] = + 7685.635 -1757.34375000000Dummie[t] -120.158503787875M1[t] + 249.857196969693M2[t] + 1508.58198863636M3[t] + 103.397689393936M4[t] -11.0957007575741M5[t] + 727.13818181818M6[t] -843.927935606062M7[t] -1367.89405303030M8[t] + 563.171079545452M9[t] + 686.09587121212M10[t] + 259.502481060605M11[t] + 74.6206628787879t + 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) 7685.635 252.046352 30.4929 0 0 Dummie -1757.34375000000 235.443694 -7.464 0 0 M1 -120.158503787875 313.207938 -0.3836 0.701937 0.350969 M2 249.857196969693 313.086022 0.798 0.426447 0.213223 M3 1508.58198863636 312.991166 4.8199 4e-06 2e-06 M4 103.397689393936 312.923394 0.3304 0.741665 0.370832 M5 -11.0957007575741 312.882724 -0.0355 0.971771 0.485885 M6 727.13818181818 312.869166 2.3241 0.021831 0.010916 M7 -843.927935606062 312.882724 -2.6973 0.008015 0.004008 M8 -1367.89405303030 312.923394 -4.3713 2.7e-05 1.3e-05 M9 563.171079545452 312.747118 1.8007 0.074301 0.03715 M10 686.09587121212 312.679294 2.1942 0.030177 0.015088 M11 259.502481060605 312.638592 0.83 0.408192 0.204096 t 74.6206628787879 2.912712 25.619 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.95796555587297 R-squared 0.917698006239009 Adjusted R-squared 0.908630837434832 F-TEST (value) 101.211086509854 F-TEST (DF numerator) 13 F-TEST (DF denominator) 118 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 733.170667831002 Sum Squared Residuals 63429628.9237955 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7787 7640.09715909086 146.902840909142 2 8474.2 8084.7335227273 389.466477272701 3 9154.7 9418.07897727273 -263.378977272727 4 8557.2 8087.5153409091 469.684659090908 5 7951.1 8047.64261363636 -96.542613636356 6 9156.7 8860.4971590909 296.202840909097 7 7865.7 7364.05170454546 501.648295454538 8 7337.4 6914.70625 422.693749999999 9 9131.7 8920.39204545455 211.307954545451 10 8814.6 9117.9375 -303.337499999999 11 8598.8 8765.96477272727 -167.164772727272 12 8439.6 8581.08295454546 -141.482954545456 13 7451.8 8535.54511363637 -1083.74511363637 14 8016.2 8980.18147727272 -963.981477272725 15 9544.1 10313.5269318182 -769.426931818182 16 8270.7 8982.96329545455 -712.263295454546 17 8102.2 8943.09056818182 -840.89056818182 18 9369 9755.94511363636 -386.945113636365 19 7657.7 8259.4996590909 -601.799659090909 20 7816.6 7810.15420454546 6.4457954545444 21 9391.3 9815.84 -424.540000000001 22 9445.4 10013.3854545455 -567.985454545456 23 9533.1 9661.41272727273 -128.312727272728 24 10068.7 9476.5309090909 592.16909090909 25 8955.5 9430.99306818182 -475.493068181824 26 10423.9 9875.62943181818 548.27056818182 27 11617.2 11208.9748863636 408.225113636364 28 9391.1 9878.41125 -487.31125 29 10872 9838.53852272727 1033.46147727273 30 10230.4 10651.3930681818 -420.993068181819 31 9221 9154.94761363636 66.052386363637 32 9428.6 8705.60215909091 722.99784090909 33 10934.5 10711.2879545455 223.212045454545 34 10986 10908.8334090909 77.1665909090907 35 11724.6 10556.8606818182 1167.73931818182 36 11180.9 10371.9788636364 808.921136363635 37 11163.2 10326.4410227273 836.758977272721 38 11240.9 10771.0773863636 469.822613636365 39 12107.1 12104.4228409091 2.67715909090909 40 10762.3 10773.8592045455 -11.5592045454567 41 11340.4 10733.9864772727 606.41352272727 42 11266.8 11546.8410227273 -280.041022727275 43 9542.7 10050.3955681818 -507.695568181817 44 9227.7 9601.05011363637 -373.350113636365 45 10571.9 9849.3921590909 722.507840909091 46 10774.4 10046.9376136364 727.462386363636 47 10392.8 9694.96488636364 697.835113636363 48 9920.2 9510.08306818182 410.116931818182 49 9884.9 9464.54522727273 420.354772727268 50 10174.5 9909.18159090909 265.318409090912 51 11395.4 11242.5270454545 152.872954545454 52 10760.2 9911.9634090909 848.236590909092 53 10570.1 9872.09068181818 698.009318181817 54 10536 10684.9452272727 -148.945227272727 55 9902.6 9188.49977272727 714.100227272728 56 8889 8739.15431818182 149.845681818182 57 10837.3 10744.8401136364 92.4598863636357 58 11624.1 10942.3855681818 681.714431818183 59 10509 10590.4128409091 -81.4128409090913 60 10984.9 10405.5310227273 579.368977272726 61 10649.1 10359.9931818182 289.106818181814 62 10855.7 10804.6295454545 51.070454545458 63 11677.4 12137.975 -460.575 64 10760.2 10807.4113636364 -47.2113636363623 65 10046.2 10767.5386363636 -721.338636363636 66 10772.8 11580.3931818182 -807.593181818183 67 9987.7 10083.9477272727 -96.2477272727258 68 8638.7 9634.60227272727 -995.902272727273 69 11063.7 11640.2880681818 -576.588068181817 70 11855.7 11837.8335227273 17.8664772727284 71 10684.5 11485.8607954545 -801.360795454545 72 11337.4 11300.9789772727 36.4210227272715 73 10478 11255.4411363636 -777.44113636364 74 11123.9 11700.0775 -576.177499999997 75 12909.3 13033.4229545455 -124.122954545455 76 11339.9 11702.8593181818 -362.959318181818 77 10462.2 11662.9865909091 -1200.78659090909 78 12733.5 12475.8411363636 257.658863636363 79 10519.2 10979.3956818182 -460.19568181818 80 10414.9 10530.0502272727 -115.150227272728 81 12476.8 12535.7360227273 -58.936022727273 82 12384.6 12733.2814772727 -348.681477272727 83 12266.7 12381.30875 -114.608749999999 84 12919.9 12196.4269318182 723.473068181817 85 11497.3 12150.8890909091 -653.589090909097 86 12142 12595.5254545455 -453.525454545451 87 13919.4 13928.8709090909 -9.4709090909087 88 12656.8 12598.3072727273 58.492727272727 89 12034.1 12558.4345454545 -524.334545454545 90 13199.7 13371.2890909091 -171.58909090909 91 10881.3 11874.8436363636 -993.543636363636 92 11301.2 11425.4981818182 -124.298181818181 93 13643.9 13431.1839772727 212.716022727273 94 12517 13628.7294318182 -1111.72943181818 95 13981.1 13276.7567045455 704.343295454546 96 14275.7 13091.8748863636 1183.82511363636 97 13435 13046.3370454545 388.66295454545 98 13565.7 13490.9734090909 74.726590909095 99 16216.3 14824.3188636364 1391.98113636364 100 12970 13493.7552272727 -523.755227272727 101 14079.9 13453.8825 626.017499999999 102 14235 14266.7370454545 -31.7370454545456 103 12213.4 12770.2915909091 -556.89159090909 104 12581 12320.9461363636 260.053863636364 105 14130.4 14326.6319318182 -196.231931818182 106 14210.8 14524.1773863636 -313.377386363637 107 14378.5 14172.2046590909 206.295340909091 108 13142.8 13987.3228409091 -844.522840909092 109 13714.7 13941.785 -227.085000000004 110 13621.9 14386.4213636364 -764.521363636361 111 15379.8 15719.7668181818 -339.966818181818 112 13306.3 14389.2031818182 -1082.90318181818 113 14391.2 14349.3304545455 41.8695454545459 114 14909.9 15162.185 -252.285000000001 115 14025.4 13665.7395454545 359.660454545455 116 12951.2 13216.3940909091 -265.19409090909 117 14344.3 15222.0798863636 -877.779886363636 118 16093.4 15419.6253409091 673.774659090909 119 15413.6 15067.6526136364 345.947386363637 120 14705.7 14882.7707954545 -177.070795454545 121 15972.8 14837.2329545455 1135.56704545454 122 16241.4 15281.8693181818 959.530681818185 123 16626.4 16615.2147727273 11.1852272727283 124 17136.2 15284.6511363636 1851.54886363637 125 15622.9 15244.7784090909 378.12159090909 126 18003.9 16057.6329545455 1946.26704545455 127 16136.1 14561.1875 1574.91250000000 128 14423.7 14111.8420454545 311.857954545456 129 16789.4 16117.5278409091 671.872159090912 130 16782.2 16315.0732954545 467.126704545455 131 14133.8 15963.1005681818 -1829.30056818182 132 12607 15778.21875 -3171.21875 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0718352127461591 0.143670425492318 0.928164787253841 18 0.029646313712666 0.059292627425332 0.970353686287334 19 0.00987126060766277 0.0197425212153255 0.990128739392337 20 0.00750866312277064 0.0150173262455413 0.99249133687723 21 0.00298483405847649 0.00596966811695299 0.997015165941524 22 0.00277507824699506 0.00555015649399013 0.997224921753005 23 0.00469296759759084 0.00938593519518168 0.99530703240241 24 0.0295364367649332 0.0590728735298665 0.970463563235067 25 0.0355136774176575 0.071027354835315 0.964486322582342 26 0.108561427577742 0.217122855155485 0.891438572422258 27 0.17253018677411 0.34506037354822 0.82746981322589 28 0.12644117975249 0.25288235950498 0.87355882024751 29 0.273708975520045 0.547417951040091 0.726291024479955 30 0.220742110450277 0.441484220900555 0.779257889549723 31 0.168924424548406 0.337848849096812 0.831075575451594 32 0.143815323944358 0.287630647888715 0.856184676055642 33 0.109827665628601 0.219655331257202 0.8901723343714 34 0.0877186928152014 0.175437385630403 0.912281307184799 35 0.124352673225446 0.248705346450891 0.875647326774554 36 0.103981684867844 0.207963369735689 0.896018315132156 37 0.123160960369392 0.246321920738784 0.876839039630608 38 0.0948598191413641 0.189719638282728 0.905140180858636 39 0.069172765043546 0.138345530087092 0.930827234956454 40 0.0492656227938825 0.098531245587765 0.950734377206117 41 0.0391346190147294 0.0782692380294589 0.96086538098527 42 0.0294594483309373 0.0589188966618746 0.970540551669063 43 0.0272139702181941 0.0544279404363882 0.972786029781806 44 0.0294107030297677 0.0588214060595353 0.970589296970232 45 0.0217951576926782 0.0435903153853563 0.978204842307322 46 0.0160406665437256 0.0320813330874511 0.983959333456274 47 0.0130277215830687 0.0260554431661374 0.986972278416931 48 0.0114258105928184 0.0228516211856368 0.988574189407182 49 0.00776181050128265 0.0155236210025653 0.992238189498717 50 0.0056793920162154 0.0113587840324308 0.994320607983785 51 0.00371144285313911 0.00742288570627822 0.99628855714686 52 0.00331603674841274 0.00663207349682549 0.996683963251587 53 0.00257934490158254 0.00515868980316508 0.997420655098417 54 0.00186434660104179 0.00372869320208358 0.998135653398958 55 0.00147824016849362 0.00295648033698724 0.998521759831506 56 0.0011771347401527 0.0023542694803054 0.998822865259847 57 0.000886546662133464 0.00177309332426693 0.999113453337866 58 0.00073033652751621 0.00146067305503242 0.999269663472484 59 0.000776293285701512 0.00155258657140302 0.999223706714298 60 0.000713778763757991 0.00142755752751598 0.999286221236242 61 0.000476066260287888 0.000952132520575777 0.999523933739712 62 0.000361241825667580 0.000722483651335159 0.999638758174332 63 0.000319078271541854 0.000638156543083707 0.999680921728458 64 0.000215105798722902 0.000430211597445805 0.999784894201277 65 0.000414394642998826 0.000828789285997653 0.999585605357 66 0.000468235529171614 0.000936471058343227 0.999531764470828 67 0.000304984364236119 0.000609968728472238 0.999695015635764 68 0.000635008327395726 0.00127001665479145 0.999364991672604 69 0.000580445918407545 0.00116089183681509 0.999419554081592 70 0.000376508208336271 0.000753016416672542 0.999623491791664 71 0.00048755661353232 0.00097511322706464 0.999512443386468 72 0.000388955833735967 0.000777911667471935 0.999611044166264 73 0.000365342296629274 0.000730684593258548 0.99963465770337 74 0.000278584453446869 0.000557168906893739 0.999721415546553 75 0.000165905843464987 0.000331811686929974 0.999834094156535 76 0.000101714465496341 0.000203428930992682 0.999898285534504 77 0.000192007799756771 0.000384015599513542 0.999807992200243 78 0.000144177651163378 0.000288355302326756 0.999855822348837 79 9.2514316596576e-05 0.000185028633193152 0.999907485683403 80 5.22264516658392e-05 0.000104452903331678 0.999947773548334 81 2.92128156154956e-05 5.84256312309911e-05 0.999970787184384 82 1.66590734069114e-05 3.33181468138228e-05 0.999983340926593 83 8.99840859035728e-06 1.79968171807146e-05 0.99999100159141 84 1.61857456299184e-05 3.23714912598369e-05 0.99998381425437 85 1.19739725249743e-05 2.39479450499486e-05 0.999988026027475 86 6.82502201344623e-06 1.36500440268925e-05 0.999993174977987 87 3.83622827857981e-06 7.67245655715962e-06 0.999996163771721 88 2.06686035687334e-06 4.13372071374669e-06 0.999997933139643 89 1.28400714670026e-06 2.56801429340053e-06 0.999998715992853 90 7.42634448826283e-07 1.48526889765257e-06 0.99999925736555 91 1.13189189156568e-06 2.26378378313135e-06 0.999998868108108 92 5.5711994845652e-07 1.11423989691304e-06 0.999999442880052 93 3.11001935029188e-07 6.22003870058377e-07 0.999999688998065 94 6.10544131960679e-07 1.22108826392136e-06 0.999999389455868 95 7.78184927854118e-07 1.55636985570824e-06 0.999999221815072 96 2.07509906811323e-05 4.15019813622646e-05 0.999979249009319 97 1.42367975316513e-05 2.84735950633026e-05 0.999985763202468 98 7.49226022258124e-06 1.49845204451625e-05 0.999992507739777 99 6.64857088297332e-05 0.000132971417659466 0.99993351429117 100 4.09027104001686e-05 8.18054208003372e-05 0.9999590972896 101 3.74097275356951e-05 7.48194550713901e-05 0.999962590272464 102 2.06411751698468e-05 4.12823503396935e-05 0.99997935882483 103 2.02496997677372e-05 4.04993995354744e-05 0.999979750300232 104 1.14580267899242e-05 2.29160535798484e-05 0.99998854197321 105 5.36175453468417e-06 1.07235090693683e-05 0.999994638245465 106 2.73237635144951e-06 5.46475270289902e-06 0.999997267623649 107 3.05313110102756e-06 6.10626220205512e-06 0.999996946868899 108 9.02665603998595e-06 1.80533120799719e-05 0.99999097334396 109 4.8855531664012e-06 9.7711063328024e-06 0.999995114446834 110 4.54351967206340e-06 9.08703934412681e-06 0.999995456480328 111 1.67666140942857e-06 3.35332281885715e-06 0.99999832333859 112 2.77348885170652e-05 5.54697770341304e-05 0.999972265111483 113 1.02907352252244e-05 2.05814704504488e-05 0.999989709264775 114 7.05600279366534e-05 0.000141120055873307 0.999929439972063 115 0.000140848935547526 0.000281697871095051 0.999859151064453 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 68 0.686868686868687 NOK 5% type I error level 76 0.767676767676768 NOK 10% type I error level 84 0.848484848484849 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/10ysb01260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/10ysb01260790827.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/1jruc1260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/1jruc1260790827.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/2m7kt1260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/2m7kt1260790827.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/3zagz1260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/3zagz1260790827.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/4jg9o1260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/4jg9o1260790827.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/5hvf91260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/5hvf91260790827.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/6k0191260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/6k0191260790827.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/7ni4g1260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/7ni4g1260790827.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/85s321260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/85s321260790827.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/97ye91260790827.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260790992bdwhzyucii417we/97ye91260790827.ps (open in new window)

Parameters (Session):

par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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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Software written by Ed van Stee & Patrick Wessa

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