WS07-Multiple Regression - Lineaire 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: Fri, 20 Nov 2009 18:45:11 -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/21/t1258768038fem10au147ba8c2.htm/, Retrieved Sat, 21 Nov 2009 02:47:30 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2.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 «

423.4 0 404.1 0 500 0 472.6 0 496.1 0 562 0 434.8 0 538.2 0 577.6 0 518.1 0 625.2 0 561.2 0 523.3 0 536.1 0 607.3 0 637.3 0 606.9 0 652.9 0 617.2 0 670.4 0 729.9 0 677.2 0 710 0 844.3 0 748.2 0 653.9 0 742.6 0 854.2 0 808.4 0 1819 1 1936.5 1 1966.1 1 2083.1 1 1620.1 1 1527.6 1 1795 1 1685.1 1 1851.8 1 2164.4 1 1981.8 1 1726.5 1 2144.6 1 1758.2 1 1672.9 1 1837.3 1 1596.1 1 1446 1 1898.4 1 1964.1 1 1755.9 1 2255.3 1 1881.2 1 2117.9 1 1656.5 1 1544.1 1 2098.9 1 2133.3 1 1963.5 1 1801.2 1 2365.4 1 1936.5 1 1667.6 1 1983.5 1 2058.6 1 2448.3 1 1858.1 1 1625.4 1 2130.6 1 2515.7 1 2230.2 1 2086.9 1 2235 1 2100.2 1 2288.6 1 2490 1 2573.7 1 2543.8 1 2004.7 1 2390 1 2338.4 1 2724.5 1 2292.5 1 2386 1 2477.9 1 2337 1 2605.1 1 2560.8 1 2839.3 1 2407.2 1 2085.2 1 2735.6 1 2798.7 1 3053.2 1 2405 1 2471.9 1 2727.3 1 2790.7 1 2385.4 1 3206.6 1 2705.6 1 3518.4 1 1954.9 1 2584.3 1 2535.8 1 2685.9 1 2866 1 2236.6 1 2934.9 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(Export_farma_prod)[t] = + 404.662125621084 + 851.445963643862`X(sprong)`[t] + 13.7889617402036t + 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) 404.662125621084 46.189006 8.761 0 0 `X(sprong)` 851.445963643862 75.35168 11.2996 0 0 t 13.7889617402036 0.931228 14.8073 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.95848144298342 R-squared 0.91868667654358 Adjusted R-squared 0.917296705202444 F-TEST (value) 660.93929375058 F-TEST (DF numerator) 2 F-TEST (DF denominator) 117 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 237.088429825369 Sum Squared Residuals 6576678.05617589 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 423.4 418.451087361289 4.9489126387107 2 404.1 432.240049101483 -28.1400491014832 3 500 446.029010841694 53.9709891583062 4 472.6 459.817972581898 12.7820274181020 5 496.1 473.606934322102 22.4930656778984 6 562 487.395896062305 74.6041039376946 7 434.8 501.184857802509 -66.384857802509 8 538.2 514.973819542713 23.2261804572874 9 577.6 528.762781282916 48.8372187170838 10 518.1 542.55174302312 -24.4517430231198 11 625.2 556.340704763324 68.8592952366765 12 561.2 570.129666503527 -8.92966650352717 13 523.3 583.918628243731 -60.6186282437309 14 536.1 597.707589983934 -61.6075899839344 15 607.3 611.496551724138 -4.19655172413818 16 637.3 625.285513464342 12.0144865356582 17 606.9 639.074475204545 -32.1744752045455 18 652.9 652.863436944749 0.0365630552508093 19 617.2 666.652398684953 -49.4523986849527 20 670.4 680.441360425156 -10.0413604251565 21 729.9 694.23032216536 35.6696778346399 22 677.2 708.019283905564 -30.8192839055636 23 710 721.808245645767 -11.8082456457673 24 844.3 735.597207385971 108.702792614029 25 748.2 749.386169126175 -1.18616912617449 26 653.9 763.175130866378 -109.275130866378 27 742.6 776.964092606582 -34.3640926065818 28 854.2 790.753054346785 63.4469456532146 29 808.4 804.542016086989 3.85798391301089 30 1819 1669.77694147106 149.223058528944 31 1936.5 1683.56590321126 252.934096788740 32 1966.1 1697.35486495146 268.745135048537 33 2083.1 1711.14382669167 371.956173308333 34 1620.1 1724.93278843187 -104.832788431871 35 1527.6 1738.72175017207 -211.121750172074 36 1795 1752.51071191228 42.4892880877222 37 1685.1 1766.29967365248 -81.1996736524815 38 1851.8 1780.08863539269 71.711364607315 39 2164.4 1793.87759713289 370.522402867111 40 1981.8 1807.66655887309 174.133441126908 41 1726.5 1821.45552061330 -94.955520613296 42 2144.6 1835.2444823535 309.3555176465 43 1758.2 1849.03344409370 -90.8334440937033 44 1672.9 1862.82240583391 -189.922405833907 45 1837.3 1876.61136757411 -39.3113675741107 46 1596.1 1890.40032931431 -294.300329314314 47 1446 1904.18929105452 -458.189291054518 48 1898.4 1917.97825279472 -19.5782527947214 49 1964.1 1931.76721453493 32.3327854650748 50 1755.9 1945.55617627513 -189.656176275129 51 2255.3 1959.34513801533 295.954861984668 52 1881.2 1973.13409975554 -91.934099755536 53 2117.9 1986.92306149574 130.976938504260 54 1656.5 2000.71202323594 -344.212023235943 55 1544.1 2014.50098497615 -470.400984976147 56 2098.9 2028.28994671635 70.6100532836495 57 2133.3 2042.07890845655 91.221091543446 58 1963.5 2055.86787019676 -92.367870196758 59 1801.2 2069.65683193696 -268.456831936962 60 2365.4 2083.44579367717 281.954206322835 61 1936.5 2097.23475541737 -160.734755417369 62 1667.6 2111.02371715757 -443.423717157573 63 1983.5 2124.81267889778 -141.312678897776 64 2058.6 2138.60164063798 -80.0016406379799 65 2448.3 2152.39060237818 295.909397621817 66 1858.1 2166.17956411839 -308.079564118387 67 1625.4 2179.96852585859 -554.568525858591 68 2130.6 2193.75748759879 -63.1574875987944 69 2515.7 2207.546449339 308.153550661002 70 2230.2 2221.3354110792 8.86458892079823 71 2086.9 2235.12437281941 -148.224372819405 72 2235 2248.91333455961 -13.9133345596089 73 2100.2 2262.70229629981 -162.502296299813 74 2288.6 2276.49125804002 12.1087419599838 75 2490 2290.28021978022 199.719780219780 76 2573.7 2304.06918152042 269.630818479576 77 2543.8 2317.85814326063 225.941856739373 78 2004.7 2331.64710500083 -326.947105000831 79 2390 2345.43606674103 44.5639332589656 80 2338.4 2359.22502848124 -20.8250284812379 81 2724.5 2373.01399022144 351.486009778558 82 2292.5 2386.80295196165 -94.3029519616453 83 2386 2400.59191370185 -14.5919137018489 84 2477.9 2414.38087544205 63.5191245579475 85 2337 2428.16983718226 -91.1698371822562 86 2605.1 2441.95879892246 163.14120107754 87 2560.8 2455.74776066266 105.052239337337 88 2839.3 2469.53672240287 369.763277597133 89 2407.2 2483.32568414307 -76.1256841430709 90 2085.2 2497.11464588327 -411.914645883275 91 2735.6 2510.90360762348 224.696392376522 92 2798.7 2524.69256936368 274.007430636318 93 3053.2 2538.48153110389 514.718468896114 94 2405 2552.27049284409 -147.270492844089 95 2471.9 2566.05945458429 -94.1594545842925 96 2727.3 2579.84841632450 147.451583675504 97 2790.7 2593.6373780647 197.0626219353 98 2385.4 2607.42633980490 -222.026339804903 99 3206.6 2621.21530154511 585.384698454893 100 2705.6 2635.00426328531 70.5957367146891 101 3518.4 2648.79322502551 869.606774974486 102 1954.9 2662.58218676572 -707.682186765718 103 2584.3 2676.37114850592 -92.0711485059215 104 2535.8 2690.16011024613 -154.360110246125 105 2685.9 2703.94907198633 -18.0490719863289 106 2866 2717.73803372653 148.261966273467 107 2236.6 2731.52699546674 -494.926995466736 108 2934.9 2745.31595720694 189.584042793060 109 2668.6 2759.10491894714 -90.5049189471436 110 2371.2 2772.89388068735 -401.693880687347 111 3165.9 2786.68284242755 379.217157572449 112 2887.2 2800.47180416775 86.7281958322454 113 3112.2 2814.26076590796 297.939234092042 114 2671.2 2828.04972764816 -156.849727648162 115 2432.6 2841.83868938837 -409.238689388365 116 2812.3 2855.62765112857 -43.3276511285687 117 3095.7 2869.41661286877 226.283387131227 118 2862.9 2883.20557460898 -20.3055746089762 119 2607.3 2896.99453634918 -289.69453634918 120 2862.5 2910.78349808938 -48.2834980893835 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.00403893683906052 0.00807787367812103 0.99596106316094 7 0.00605287077577423 0.0121057415515485 0.993947129224226 8 0.00125441255020573 0.00250882510041147 0.998745587449794 9 0.000274736051710429 0.000549472103420859 0.99972526394829 10 7.30037311247695e-05 0.000146007462249539 0.999926996268875 11 2.16553660637136e-05 4.33107321274272e-05 0.999978344633936 12 4.93742349283792e-06 9.87484698567583e-06 0.999995062576507 13 2.38801384060602e-06 4.77602768121204e-06 0.99999761198616 14 7.24255585130209e-07 1.44851117026042e-06 0.999999275744415 15 1.39574499368316e-07 2.79148998736631e-07 0.9999998604255 16 2.97409511059042e-08 5.94819022118085e-08 0.999999970259049 17 5.36100061829533e-09 1.07220012365907e-08 0.999999994639 18 9.80739250269553e-10 1.96147850053911e-09 0.99999999901926 19 1.90864149179582e-10 3.81728298359165e-10 0.999999999809136 20 3.24232584387388e-11 6.48465168774776e-11 0.999999999967577 21 1.24260753325050e-11 2.48521506650100e-11 0.999999999987574 22 2.01866245509098e-12 4.03732491018196e-12 0.999999999997981 23 3.14510823335748e-13 6.29021646671496e-13 0.999999999999685 24 1.86022009483782e-12 3.72044018967565e-12 0.99999999999814 25 3.20175947925155e-13 6.4035189585031e-13 0.99999999999968 26 4.32553909655502e-13 8.65107819311004e-13 0.999999999999567 27 8.10867851961252e-14 1.62173570392250e-13 0.99999999999992 28 5.06239975744726e-14 1.01247995148945e-13 0.99999999999995 29 9.49840160068214e-15 1.89968032013643e-14 0.99999999999999 30 1.75182859853469e-15 3.50365719706938e-15 0.999999999999998 31 1.04536394975491e-15 2.09072789950982e-15 0.999999999999999 32 4.10932976756265e-16 8.2186595351253e-16 1 33 2.08846405639004e-15 4.17692811278009e-15 0.999999999999998 34 2.97202125924061e-11 5.94404251848121e-11 0.99999999997028 35 1.06284082904139e-08 2.12568165808277e-08 0.999999989371592 36 4.66352777531173e-09 9.32705555062345e-09 0.999999995336472 37 5.5736629311307e-09 1.11473258622614e-08 0.999999994426337 38 2.06383201057634e-09 4.12766402115268e-09 0.999999997936168 39 1.96848871582178e-08 3.93697743164356e-08 0.999999980315113 40 1.00979001923020e-08 2.01958003846040e-08 0.9999999899021 41 1.37666728559637e-08 2.75333457119274e-08 0.999999986233327 42 2.97764487309841e-08 5.95528974619682e-08 0.999999970223551 43 3.41251728192176e-08 6.82503456384352e-08 0.999999965874827 44 9.24209914981586e-08 1.84841982996317e-07 0.999999907579008 45 5.03949460951857e-08 1.00789892190371e-07 0.999999949605054 46 2.86188081421449e-07 5.72376162842898e-07 0.999999713811919 47 7.51293450783752e-06 1.50258690156750e-05 0.999992487065492 48 3.81879285785796e-06 7.63758571571593e-06 0.999996181207142 49 2.05178430832272e-06 4.10356861664545e-06 0.999997948215692 50 1.53190766241818e-06 3.06381532483637e-06 0.999998468092338 51 5.25456543070962e-06 1.05091308614192e-05 0.99999474543457 52 2.84816527003035e-06 5.6963305400607e-06 0.99999715183473 53 2.28454075222052e-06 4.56908150444103e-06 0.999997715459248 54 5.0500284554885e-06 1.0100056910977e-05 0.999994949971545 55 2.81643346246643e-05 5.63286692493287e-05 0.999971835665375 56 2.09660996664632e-05 4.19321993329264e-05 0.999979033900334 57 1.64540992557902e-05 3.29081985115804e-05 0.999983545900744 58 9.04384906768039e-06 1.80876981353608e-05 0.999990956150932 59 8.17225261993678e-06 1.63445052398736e-05 0.99999182774738 60 2.39906860757939e-05 4.79813721515877e-05 0.999976009313924 61 1.48996425835180e-05 2.97992851670361e-05 0.999985100357417 62 4.33757661576031e-05 8.67515323152062e-05 0.999956624233842 63 2.67488117514696e-05 5.34976235029392e-05 0.999973251188249 64 1.59220166986819e-05 3.18440333973638e-05 0.999984077983301 65 4.9338488741043e-05 9.8676977482086e-05 0.99995066151126 66 5.49216275039643e-05 0.000109843255007929 0.999945078372496 67 0.00037511546840955 0.0007502309368191 0.99962488453159 68 0.000264293032689479 0.000528586065378957 0.99973570696731 69 0.000676527843434942 0.00135305568686988 0.999323472156565 70 0.000476769458436413 0.000953538916872826 0.999523230541564 71 0.000354018145368677 0.000708036290737354 0.999645981854631 72 0.000243597511550632 0.000487195023101265 0.99975640248845 73 0.000192812626106889 0.000385625252213779 0.999807187373893 74 0.000136295804894437 0.000272591609788874 0.999863704195106 75 0.000151608189887399 0.000303216379774797 0.999848391810113 76 0.000212960261150225 0.00042592052230045 0.99978703973885 77 0.000222085530977404 0.000444171061954808 0.999777914469023 78 0.000364876048231005 0.000729752096462011 0.99963512395177 79 0.000243849884297926 0.000487699768595853 0.999756150115702 80 0.000160252423636538 0.000320504847273076 0.999839747576363 81 0.000278687677013039 0.000557375354026077 0.999721312322987 82 0.000197339684556456 0.000394679369112912 0.999802660315444 83 0.000125840223653263 0.000251680447306526 0.999874159776347 84 7.86026984238664e-05 0.000157205396847733 0.999921397301576 85 5.6561725597269e-05 0.000113123451194538 0.999943438274403 86 3.95175520057194e-05 7.90351040114387e-05 0.999960482447994 87 2.41246790031506e-05 4.82493580063012e-05 0.999975875320997 88 3.80672808067838e-05 7.61345616135675e-05 0.999961932719193 89 2.47669523182955e-05 4.9533904636591e-05 0.999975233047682 90 0.000122102343072062 0.000244204686144124 0.999877897656928 91 9.10335977398026e-05 0.000182067195479605 0.99990896640226 92 7.6749451256384e-05 0.000153498902512768 0.999923250548744 93 0.000261150348801434 0.000522300697602869 0.999738849651199 94 0.00021057503492691 0.00042115006985382 0.999789424965073 95 0.000149485304743368 0.000298970609486736 0.999850514695257 96 8.72756088724134e-05 0.000174551217744827 0.999912724391128 97 5.49653445283714e-05 0.000109930689056743 0.999945034655472 98 6.29157329518436e-05 0.000125831465903687 0.999937084267048 99 0.000376971827579709 0.000753943655159419 0.99962302817242 100 0.000208030097767244 0.000416060195534488 0.999791969902233 101 0.0514042960059528 0.102808592011906 0.948595703994047 102 0.247473036595586 0.494946073191173 0.752526963404414 103 0.193594495332484 0.387188990664969 0.806405504667515 104 0.156300882805829 0.312601765611658 0.843699117194171 105 0.112388228024047 0.224776456048094 0.887611771975953 106 0.0936714483857383 0.187342896771477 0.906328551614262 107 0.223521927938869 0.447043855877739 0.77647807206113 108 0.181946683500269 0.363893367000537 0.818053316499731 109 0.132537315158004 0.265074630316008 0.867462684841996 110 0.353571927134054 0.707143854268109 0.646428072865946 111 0.356415302298154 0.712830604596308 0.643584697701846 112 0.249995999986044 0.499991999972088 0.750004000013956 113 0.376973530455832 0.753947060911664 0.623026469544168 114 0.239520057716311 0.479040115432622 0.760479942283689 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 94 0.862385321100917 NOK 5% type I error level 95 0.871559633027523 NOK 10% type I error level 95 0.871559633027523 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/10d18q1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/10d18q1258767904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/1w49c1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/1w49c1258767904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/22v6k1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/22v6k1258767904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/3mahc1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/3mahc1258767904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/4jjxz1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/4jjxz1258767904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/5meol1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/5meol1258767904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/6ml2h1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/6ml2h1258767904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/7qp9x1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/7qp9x1258767904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/81cgm1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/81cgm1258767904.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/90ztl1258767904.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258768038fem10au147ba8c2/90ztl1258767904.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') }

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