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 07:22:36 -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/t1258468650y5zbytbt83k24f8.htm/, Retrieved Tue, 17 Nov 2009 15:37:42 +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/t1258468650y5zbytbt83k24f8.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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 516.289908256881 + 121.810091743119X[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) 516.289908256881 10.333793 49.9613 0 0 X 121.810091743119 39.519158 3.0823 0.002571 0.001286 Multiple Linear Regression - Regression Statistics Multiple R 0.276242092860516 R-squared 0.076309693867958 Adjusted R-squared 0.0682776042494186 F-TEST (value) 9.50060289315269 F-TEST (DF numerator) 1 F-TEST (DF denominator) 115 p-value 0.00257126214987702 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 107.887964388953 Sum Squared Residuals 1338578.47889908 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 395.3 516.289908256882 -120.989908256882 2 395.1 516.289908256881 -121.189908256881 3 403.5 516.289908256881 -112.789908256881 4 403.3 516.289908256881 -112.989908256881 5 405.7 516.289908256881 -110.589908256881 6 406.7 516.289908256881 -109.589908256881 7 407.2 516.289908256881 -109.089908256881 8 412.4 516.289908256881 -103.889908256881 9 415.9 516.289908256881 -100.389908256881 10 414 516.289908256881 -102.289908256881 11 411.8 516.289908256881 -104.489908256881 12 409.9 516.289908256881 -106.389908256881 13 412.4 516.289908256881 -103.889908256881 14 415.9 516.289908256881 -100.389908256881 15 416.3 516.289908256881 -99.9899082568807 16 417.2 516.289908256881 -99.0899082568807 17 421.8 516.289908256881 -94.4899082568807 18 421.4 516.289908256881 -94.8899082568807 19 415.1 516.289908256881 -101.189908256881 20 412.4 516.289908256881 -103.889908256881 21 411.8 516.289908256881 -104.489908256881 22 408.8 516.289908256881 -107.489908256881 23 404.5 516.289908256881 -111.789908256881 24 402.5 516.289908256881 -113.789908256881 25 409.4 516.289908256881 -106.889908256881 26 410.7 516.289908256881 -105.589908256881 27 413.4 516.289908256881 -102.889908256881 28 415.2 516.289908256881 -101.089908256881 29 417.7 516.289908256881 -98.5899082568807 30 417.8 516.289908256881 -98.4899082568807 31 417.9 516.289908256881 -98.3899082568807 32 418.4 516.289908256881 -97.8899082568807 33 418.2 516.289908256881 -98.0899082568807 34 416.6 516.289908256881 -99.6899082568807 35 418.9 516.289908256881 -97.3899082568807 36 421 516.289908256881 -95.2899082568807 37 423.5 516.289908256881 -92.7899082568807 38 432.3 516.289908256881 -83.9899082568807 39 432.3 516.289908256881 -83.9899082568807 40 428.6 516.289908256881 -87.6899082568807 41 426.7 516.289908256881 -89.5899082568807 42 427.3 516.289908256881 -88.9899082568807 43 428.5 516.289908256881 -87.7899082568807 44 437 516.289908256881 -79.2899082568807 45 442 516.289908256881 -74.2899082568807 46 444.9 516.289908256881 -71.3899082568807 47 441.4 516.289908256881 -74.8899082568807 48 440.3 516.289908256881 -75.9899082568807 49 447.1 516.289908256881 -69.1899082568807 50 455.3 516.289908256881 -60.9899082568807 51 478.6 516.289908256881 -37.6899082568807 52 486.5 516.289908256881 -29.7899082568807 53 487.8 516.289908256881 -28.4899082568807 54 485.9 516.289908256881 -30.3899082568808 55 483.8 516.289908256881 -32.4899082568807 56 488.4 516.289908256881 -27.8899082568808 57 494 516.289908256881 -22.2899082568807 58 493.6 516.289908256881 -22.6899082568807 59 487.3 516.289908256881 -28.9899082568807 60 482.1 516.289908256881 -34.1899082568807 61 484.2 516.289908256881 -32.0899082568807 62 496.8 516.289908256881 -19.4899082568807 63 501.1 516.289908256881 -15.1899082568807 64 499.8 516.289908256881 -16.4899082568807 65 495.5 516.289908256881 -20.7899082568807 66 498.1 516.289908256881 -18.1899082568807 67 503.8 516.289908256881 -12.4899082568807 68 516.2 516.289908256881 -0.0899082568806833 69 526.1 516.289908256881 9.8100917431193 70 527.1 516.289908256881 10.8100917431193 71 525.1 516.289908256881 8.8100917431193 72 528.9 516.289908256881 12.6100917431192 73 540.1 516.289908256881 23.8100917431193 74 549 516.289908256881 32.7100917431193 75 556 516.289908256881 39.7100917431193 76 568.9 516.289908256881 52.6100917431192 77 589.1 516.289908256881 72.8100917431193 78 590.3 516.289908256881 74.0100917431192 79 603.3 516.289908256881 87.0100917431192 80 638.8 516.289908256881 122.510091743119 81 643 516.289908256881 126.710091743119 82 656.7 516.289908256881 140.410091743119 83 656.1 516.289908256881 139.810091743119 84 654.1 516.289908256881 137.810091743119 85 659.9 516.289908256881 143.610091743119 86 662.1 516.289908256881 145.810091743119 87 669.2 516.289908256881 152.910091743119 88 673.1 516.289908256881 156.810091743119 89 678.3 516.289908256881 162.010091743119 90 677.4 516.289908256881 161.110091743119 91 678.5 516.289908256881 162.210091743119 92 672.4 516.289908256881 156.110091743119 93 665.3 516.289908256881 149.010091743119 94 667.9 516.289908256881 151.610091743119 95 672.1 516.289908256881 155.810091743119 96 662.5 516.289908256881 146.210091743119 97 682.3 516.289908256881 166.010091743119 98 692.1 516.289908256881 175.810091743119 99 702.7 516.289908256881 186.410091743119 100 721.4 516.289908256881 205.110091743119 101 733.2 516.289908256881 216.910091743119 102 747.7 516.289908256881 231.410091743119 103 737.6 516.289908256881 221.310091743119 104 729.3 516.289908256881 213.010091743119 105 706.1 516.289908256881 189.810091743119 106 674.3 516.289908256881 158.010091743119 107 659 516.289908256881 142.710091743119 108 645.7 516.289908256881 129.410091743119 109 646.1 516.289908256881 129.810091743119 110 633 638.1 -5.09999999999999 111 622.3 638.1 -15.8000000000000 112 628.2 638.1 -9.89999999999995 113 637.3 638.1 -0.80000000000004 114 639.6 638.1 1.50000000000003 115 638.5 638.1 0.400000000000006 116 650.5 638.1 12.4 117 655.4 638.1 17.3 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.000215854676623502 0.000431709353247005 0.999784145323376 6 1.64807411532695e-05 3.29614823065390e-05 0.999983519258847 7 1.21591717907825e-06 2.43183435815651e-06 0.99999878408282 8 2.13637548064001e-07 4.27275096128003e-07 0.999999786362452 9 5.31805738106365e-08 1.06361147621273e-07 0.999999946819426 10 6.89822643182639e-09 1.37964528636528e-08 0.999999993101774 11 6.27107798508578e-10 1.25421559701716e-09 0.999999999372892 12 4.68168980977308e-11 9.36337961954617e-11 0.999999999953183 13 4.184376634378e-12 8.368753268756e-12 0.999999999995816 14 5.75403257940686e-13 1.15080651588137e-12 0.999999999999425 15 7.69772821937148e-14 1.53954564387430e-13 0.999999999999923 16 1.09489170470793e-14 2.18978340941586e-14 0.99999999999999 17 3.22872443093611e-15 6.45744886187222e-15 0.999999999999997 18 7.18917829030674e-16 1.43783565806135e-15 1 19 6.88014452965067e-17 1.37602890593013e-16 1 20 5.67716850457109e-18 1.13543370091422e-17 1 21 4.57214132233776e-19 9.14428264467551e-19 1 22 3.76449677491932e-20 7.52899354983863e-20 1 23 4.29966457470694e-21 8.59932914941388e-21 1 24 6.32171994565715e-22 1.26434398913143e-21 1 25 5.25674342644445e-23 1.05134868528889e-22 1 26 4.36955144606109e-24 8.73910289212219e-24 1 27 4.04685621221371e-25 8.09371242442741e-25 1 28 4.38652391470248e-26 8.77304782940496e-26 1 29 6.54117706638642e-27 1.30823541327728e-26 1 30 9.80204016986107e-28 1.96040803397221e-27 1 31 1.48339429083147e-28 2.96678858166293e-28 1 32 2.41312040807779e-29 4.82624081615557e-29 1 33 3.82344056394588e-30 7.64688112789176e-30 1 34 5.0641019737419e-31 1.01282039474838e-30 1 35 9.14561919695966e-32 1.82912383939193e-31 1 36 2.35933833103317e-32 4.71867666206634e-32 1 37 9.88292578396888e-33 1.97658515679378e-32 1 38 4.12243261655865e-32 8.2448652331173e-32 1 39 9.99167652199906e-32 1.99833530439981e-31 1 40 7.6437757575562e-32 1.52875515151124e-31 1 41 3.92200798148844e-32 7.84401596297689e-32 1 42 2.2122950652129e-32 4.4245901304258e-32 1 43 1.51863872100385e-32 3.03727744200770e-32 1 44 5.46334847562186e-32 1.09266969512437e-31 1 45 4.56286983617537e-31 9.12573967235074e-31 1 46 4.5175481725295e-30 9.035096345059e-30 1 47 1.51201424132605e-29 3.02402848265211e-29 1 48 3.74106555839698e-29 7.48213111679395e-29 1 49 2.48005158493425e-28 4.96010316986849e-28 1 50 5.15622022793929e-27 1.03124404558786e-26 1 51 5.01838327639068e-24 1.00367665527814e-23 1 52 2.40016230937660e-21 4.80032461875321e-21 1 53 2.51679643232849e-19 5.03359286465697e-19 1 54 7.68673778369329e-18 1.53734755673866e-17 1 55 1.11031770672159e-16 2.22063541344317e-16 1 56 1.59613808529198e-15 3.19227617058397e-15 0.999999999999998 57 2.37169437235536e-14 4.74338874471072e-14 0.999999999999976 58 2.46223930794818e-13 4.92447861589637e-13 0.999999999999754 59 1.56952528541959e-12 3.13905057083918e-12 0.99999999999843 60 8.08397132030437e-12 1.61679426406087e-11 0.999999999991916 61 4.57055532653194e-11 9.14111065306389e-11 0.999999999954294 62 3.68943325095777e-10 7.37886650191554e-10 0.999999999631057 63 3.09776467556148e-09 6.19552935112296e-09 0.999999996902235 64 2.35530616060263e-08 4.71061232120526e-08 0.999999976446938 65 1.68543352411099e-07 3.37086704822198e-07 0.999999831456648 66 1.30306132460379e-06 2.60612264920757e-06 0.999998696938675 67 1.08160935530978e-05 2.16321871061955e-05 0.999989183906447 68 9.2414117118286e-05 0.000184828234236572 0.999907585882882 69 0.000715913491860645 0.00143182698372129 0.99928408650814 70 0.00456052373907773 0.00912104747815546 0.995439476260922 71 0.0243135785881895 0.0486271571763789 0.97568642141181 72 0.103009138790898 0.206018277581796 0.896990861209102 73 0.305627213126341 0.611254426252682 0.694372786873659 74 0.615487016524533 0.769025966950934 0.384512983475467 75 0.874563462507507 0.250873074984985 0.125436537492493 76 0.977330638808823 0.0453387223823545 0.0226693611911772 77 0.997027864643628 0.00594427071274433 0.00297213535637217 78 0.999791949738726 0.000416100522548955 0.000208050261274477 79 0.999988133337831 2.37333243371322e-05 1.18666621685661e-05 80 0.999998150964626 3.69807074837933e-06 1.84903537418967e-06 81 0.99999962294059 7.54118818990046e-07 3.77059409495023e-07 82 0.999999877214427 2.45571145520027e-07 1.22785572760013e-07 83 0.999999950047372 9.99052561396703e-08 4.99526280698351e-08 84 0.999999976815732 4.63685362009822e-08 2.31842681004911e-08 85 0.999999985915375 2.81692497392974e-08 1.40846248696487e-08 86 0.999999989758994 2.04820118193421e-08 1.02410059096711e-08 87 0.999999990490512 1.90189751493123e-08 9.50948757465615e-09 88 0.999999989539383 2.09212334751242e-08 1.04606167375621e-08 89 0.99999998660059 2.67988202275636e-08 1.33994101137818e-08 90 0.999999981058754 3.78824925947177e-08 1.89412462973589e-08 91 0.999999970612415 5.8775169801245e-08 2.93875849006225e-08 92 0.999999954174464 9.16510728957403e-08 4.58255364478701e-08 93 0.999999935262035 1.29475929580598e-07 6.47379647902991e-08 94 0.999999901311645 1.97376709766211e-07 9.86883548831053e-08 95 0.99999983267539 3.34649220093995e-07 1.67324610046998e-07 96 0.999999784286504 4.31426992885191e-07 2.15713496442595e-07 97 0.999999554052646 8.91894708227204e-07 4.45947354113602e-07 98 0.999998960581953 2.07883609450927e-06 1.03941804725464e-06 99 0.99999751296796 4.97406408124844e-06 2.48703204062422e-06 100 0.999995375040132 9.249919735495e-06 4.6249598677475e-06 101 0.999994236241354 1.15275172920555e-05 5.76375864602777e-06 102 0.999997572116119 4.85576776256499e-06 2.42788388128250e-06 103 0.99999918823615 1.6235276980218e-06 8.117638490109e-07 104 0.999999919686762 1.60626476200699e-07 8.03132381003495e-08 105 0.99999999450275 1.09945003912364e-08 5.49725019561818e-09 106 0.999999990994174 1.80116518479478e-08 9.00582592397388e-09 107 0.999999943505276 1.12989448670926e-07 5.64947243354631e-08 108 0.999999389050932 1.22189813673235e-06 6.10949068366174e-07 109 0.999993730631205 1.2538737589268e-05 6.269368794634e-06 110 0.999943026641626 0.000113946716748002 5.69733583740012e-05 111 0.999806874138193 0.000386251723614204 0.000193125861807102 112 0.999137885716748 0.00172422856650356 0.000862114283251778 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 102 0.944444444444444 NOK 5% type I error level 104 0.962962962962963 NOK 10% type I error level 104 0.962962962962963 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/10tnxt1258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/10tnxt1258467749.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/1y3fd1258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/1y3fd1258467749.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/2pqwk1258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/2pqwk1258467749.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/3ikwp1258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/3ikwp1258467749.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/4m4ow1258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/4m4ow1258467749.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/5vgb71258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/5vgb71258467749.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/6se6p1258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/6se6p1258467749.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/7egek1258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/7egek1258467749.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/839k81258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/839k81258467749.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/9o9t61258467749.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/17/t1258468650y5zbytbt83k24f8/9o9t61258467749.ps (open in new window)

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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