W8 Regressiemodel

*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, 26 Nov 2010 11:00:47 +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/Nov/26/t1290769162i0q02xiz9ggbc3n.htm/, Retrieved Fri, 26 Nov 2010 11:59:23 +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/Nov/26/t1290769162i0q02xiz9ggbc3n.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 «

14.458 13.594 17.814 20.235 21.811 21.439 21.393 19.831 20.468 21.080 21.600 17.390 17848 19592 21092 20889 25890 24965 22225 20977 22897 22785 22769 19637 20203 20450 23083 21738 26766 25280 22574 22729 21378 22902 24989 21116 15169 15846 20927 18273 22538 15596 14034 11366 14861 15149 13577 13026 13190 13196 15826 14733 16307 15703 14589 12043 15057 14053 12698 10888 10045 11549 13767 12424 13116 14211 12266 12602 15714 13742 12745 10491 10057 10900 11771 11992 11993 14504 11727 11477 13578 11555 11846 11397 10066 10269 14279 13870 13695 14420 11424 9704 12464 14301 13464 9893 11572 12380 16692 16052 16459 14761 13654 13480 18068 16560 14530 10650 11651 13735 13360 17818 20613 16231 13862 12004 17734 15034 12609 12320 10833 11350 13648 14890 16325 18045 15616 11926 16855 15083 12520 12355

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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Pas[t] = + 11516.7062045455 -32.8866979166674M1[t] + 745.405183712119M2[t] + 3028.25015625000M3[t] + 2861.47703787879M4[t] + 4766.35437405303M5[t] + 3852.05461931818M6[t] + 1868.78450094697M7[t] + 620.103837121209M8[t] + 3368.07762784091M9[t] + 2685.14005492424M10[t] + 1822.64866382575M11[t] + 6.44775473484847t + 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) 11516.7062045455 2087.765023 5.5163 0 0 M1 -32.8866979166674 2594.083062 -0.0127 0.989906 0.494953 M2 745.405183712119 2593.29756 0.2874 0.774279 0.387139 M3 3028.25015625000 2592.586662 1.168 0.245125 0.122562 M4 2861.47703787879 2591.950431 1.104 0.271827 0.135913 M5 4766.35437405303 2591.388921 1.8393 0.068363 0.034182 M6 3852.05461931818 2590.90218 1.4868 0.139722 0.069861 M7 1868.78450094697 2590.490251 0.7214 0.472077 0.236039 M8 620.103837121209 2590.153169 0.2394 0.811201 0.4056 M9 3368.07762784091 2589.890964 1.3005 0.195953 0.097976 M10 2685.14005492424 2589.703659 1.0369 0.301907 0.150954 M11 1822.64866382575 2589.591269 0.7038 0.48291 0.241455 t 6.44775473484847 13.929582 0.4629 0.644294 0.322147 Multiple Linear Regression - Regression Statistics Multiple R 0.253366532834073 R-squared 0.0641945999603596 Adjusted R-squared -0.0301723311360749 F-TEST (value) 0.680265843283159 F-TEST (DF numerator) 12 F-TEST (DF denominator) 119 p-value 0.767537094382899 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6073.04198876287 Sum Squared Residuals 4388938840.67594 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14.458 11490.2672613636 -11475.8092613636 2 13.594 12275.0068977273 -12261.4128977273 3 17.814 14564.299625 -14546.485625 4 20.235 14403.9742613636 -14383.7392613636 5 21.811 16315.2993522727 -16293.4883522727 6 21.439 15407.4473522727 -15386.0083522727 7 21.393 13430.6249886364 -13409.2319886364 8 19.831 12188.3920795455 -12168.5610795455 9 20.468 14942.813625 -14922.345625 10 21.08 14266.3238068182 -14245.2438068182 11 21.6 13410.2801704545 -13388.6801704545 12 17.39 11594.0792613636 -11576.6892613636 13 17848 11567.6403181818 6280.35968181818 14 19592 12352.3799545455 7239.62004545455 15 21092 14641.6726818182 6450.32731818182 16 20889 14481.3473181818 6407.65268181818 17 25890 16392.6724090909 9497.32759090909 18 24965 15484.8204090909 9480.1795909091 19 22225 13507.9980454545 8717.00195454545 20 20977 12265.7651363636 8711.23486363637 21 22897 15020.1866818182 7876.81331818181 22 22785 14343.6968636364 8441.30313636363 23 22769 13487.6532272727 9281.34677272727 24 19637 11671.4523181818 7965.54768181818 25 20203 11645.013375 8557.986625 26 20450 12429.7530113636 8020.24698863637 27 23083 14719.0457386364 8363.95426136363 28 21738 14558.720375 7179.279625 29 26766 16470.0454659091 10295.9545340909 30 25280 15562.1934659091 9717.8065340909 31 22574 13585.3711022727 8988.62889772727 32 22729 12343.1381931818 10385.8618068182 33 21378 15097.5597386364 6280.44026136364 34 22902 14421.0699204545 8480.93007954545 35 24989 13565.0262840909 11423.9737159091 36 21116 11748.825375 9367.174625 37 15169 11722.3864318182 3446.61356818182 38 15846 12507.1260681818 3338.87393181818 39 20927 14796.4187954545 6130.58120454545 40 18273 14636.0934318182 3636.90656818182 41 22538 16547.4185227273 5990.58147727273 42 15596 15639.5665227273 -43.5665227272722 43 14034 13662.7441590909 371.255840909091 44 11366 12420.51125 -1054.51125000000 45 14861 15174.9327954545 -313.932795454544 46 15149 14498.4429772727 650.557022727276 47 13577 13642.3993409091 -65.3993409090896 48 13026 11826.1984318182 1199.80156818181 49 13190 11799.7594886364 1390.24051136363 50 13196 12584.499125 611.500875 51 15826 14873.7918522727 952.208147727272 52 14733 14713.4664886364 19.5335113636345 53 16307 16624.7915795455 -317.791579545453 54 15703 15716.9395795455 -13.9395795454540 55 14589 13740.1172159091 848.88278409091 56 12043 12497.8843068182 -454.884306818183 57 15057 15252.3058522727 -195.305852272726 58 14053 14575.8160340909 -522.816034090907 59 12698 13719.7723977273 -1021.77239772727 60 10888 11903.5714886364 -1015.57148863637 61 10045 11877.1325454545 -1832.13254545455 62 11549 12661.8721818182 -1112.87218181818 63 13767 14951.1649090909 -1184.16490909091 64 12424 14790.8395454545 -2366.83954545455 65 13116 16702.1646363636 -3586.16463636363 66 14211 15794.3126363636 -1583.31263636364 67 12266 13817.4902727273 -1551.49027272727 68 12602 12575.2573636364 26.7426363636362 69 15714 15329.6789090909 384.321090909093 70 13742 14653.1890909091 -911.18909090909 71 12745 13797.1454545455 -1052.14545454545 72 10491 11980.9445454545 -1489.94454545455 73 10057 11954.5056022727 -1897.50560227273 74 10900 12739.2452386364 -1839.24523863636 75 11771 15028.5379659091 -3257.53796590909 76 11992 14868.2126022727 -2876.21260227273 77 11993 16779.5376931818 -4786.53769318182 78 14504 15871.6856931818 -1367.68569318182 79 11727 13894.8633295455 -2167.86332954546 80 11477 12652.6304204545 -1175.63042045455 81 13578 15407.0519659091 -1829.05196590909 82 11555 14730.5621477273 -3175.56214772727 83 11846 13874.5185113636 -2028.51851136364 84 11397 12058.3176022727 -661.31760227273 85 10066 12031.8786590909 -1965.87865909091 86 10269 12816.6182954545 -2547.61829545454 87 14279 15105.9110227273 -826.911022727272 88 13870 14945.5856590909 -1075.58565909091 89 13695 16856.91075 -3161.91075 90 14420 15949.05875 -1529.05875 91 11424 13972.2363863636 -2548.23638636364 92 9704 12730.0034772727 -3026.00347727273 93 12464 15484.4250227273 -3020.42502272727 94 14301 14807.9352045455 -506.935204545452 95 13464 13951.8915681818 -487.891568181817 96 9893 12135.6906590909 -2242.69065909091 97 11572 12109.2517159091 -537.251715909092 98 12380 12893.9913522727 -513.991352272726 99 16692 15183.2840795455 1508.71592045455 100 16052 15022.9587159091 1029.04128409091 101 16459 16934.2838068182 -475.28380681818 102 14761 16026.4318068182 -1265.43180681818 103 13654 14049.6094431818 -395.609443181818 104 13480 12807.3765340909 672.623465909092 105 18068 15561.7980795455 2506.20192045455 106 16560 14885.3082613636 1674.69173863637 107 14530 14029.264625 500.735375000003 108 10650 12213.0637159091 -1563.06371590909 109 11651 12186.6247727273 -535.624772727274 110 13735 12971.3644090909 763.635590909092 111 13360 15260.6571363636 -1900.65713636364 112 17818 15100.3317727273 2717.66822727273 113 20613 17011.6568636364 3601.34313636364 114 16231 16103.8048636364 127.195136363638 115 13862 14126.9825 -264.982499999999 116 12004 12884.7495909091 -880.749590909091 117 17734 15639.1711363636 2094.82886363637 118 15034 14962.6813181818 71.3186818181851 119 12609 14106.6376818182 -1497.63768181818 120 12320 12290.4367727273 29.5632272727255 121 10833 12263.9978295455 -1430.99782954546 122 11350 13048.7374659091 -1698.73746590909 123 13648 15338.0301931818 -1690.03019318182 124 14890 15177.7048295455 -287.704829545454 125 16325 17089.0299204545 -764.029920454543 126 18045 16181.1779204545 1863.82207954546 127 15616 14204.3555568182 1411.64444318182 128 11926 12962.1226477273 -1036.12264772727 129 16855 15716.5441931818 1138.45580681818 130 15083 15040.054375 42.9456250000042 131 12520 14184.0107386364 -1664.01073863636 132 12355 12367.8098295455 -12.8098295454563 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0446694702171001 0.0893389404342002 0.9553305297829 17 0.217795139174473 0.435590278348946 0.782204860825527 18 0.206948424615960 0.413896849231920 0.79305157538404 19 0.123002155567594 0.246004311135189 0.876997844432406 20 0.0713426550017686 0.142685310003537 0.928657344998231 21 0.0408406913809466 0.0816813827618932 0.959159308619053 22 0.0225191683580043 0.0450383367160085 0.977480831641996 23 0.0124562644601262 0.0249125289202524 0.987543735539874 24 0.00920881500578142 0.0184176300115628 0.990791184994219 25 0.989571375209978 0.0208572495800439 0.0104286247900220 26 0.99988700383339 0.000225992333219593 0.000112996166609796 27 0.999988354674786 2.32906504274421e-05 1.16453252137211e-05 28 0.999998132574066 3.73485186844505e-06 1.86742593422252e-06 29 0.999999574468331 8.51063337608523e-07 4.25531668804261e-07 30 0.999999914148836 1.71702327833412e-07 8.58511639167061e-08 31 0.999999985300168 2.93996636958791e-08 1.46998318479396e-08 32 0.999999998926972 2.14605675328575e-09 1.07302837664287e-09 33 0.99999999964541 7.09180906061965e-10 3.54590453030983e-10 34 0.999999999945367 1.09265111156789e-10 5.46325555783946e-11 35 0.999999999999762 4.7653891972433e-13 2.38269459862165e-13 36 1 1.91329174150928e-15 9.56645870754638e-16 37 1 7.8066204954338e-19 3.9033102477169e-19 38 1 3.69556328537189e-21 1.84778164268595e-21 39 1 9.86093781566029e-24 4.93046890783014e-24 40 1 4.36821141735872e-25 2.18410570867936e-25 41 1 1.05992621743059e-28 5.29963108715296e-29 42 1 1.30134624421135e-29 6.50673122105673e-30 43 1 3.13412898732319e-30 1.56706449366159e-30 44 1 8.66840979567252e-31 4.33420489783626e-31 45 1 1.06822080726673e-30 5.34110403633363e-31 46 1 1.05786641852041e-30 5.28933209260205e-31 47 1 8.13912135642193e-31 4.06956067821096e-31 48 1 4.52487437541523e-31 2.26243718770762e-31 49 1 1.01984837220099e-31 5.09924186100497e-32 50 1 6.0865066063739e-32 3.04325330318695e-32 51 1 2.80563036045276e-32 1.40281518022638e-32 52 1 5.37436586866497e-32 2.68718293433248e-32 53 1 5.04670452763168e-32 2.52335226381584e-32 54 1 1.02214817307039e-31 5.11074086535195e-32 55 1 8.05388788693352e-32 4.02694394346676e-32 56 1 1.63607705432227e-31 8.18038527161135e-32 57 1 6.50564532722289e-31 3.25282266361145e-31 58 1 1.96841100336608e-30 9.84205501683039e-31 59 1 4.96832028371087e-30 2.48416014185543e-30 60 1 1.31415574018369e-29 6.57077870091843e-30 61 1 3.99781116601239e-29 1.99890558300620e-29 62 1 1.12334424053747e-28 5.61672120268735e-29 63 1 3.18940627190774e-28 1.59470313595387e-28 64 1 1.18240212709421e-27 5.91201063547105e-28 65 1 3.31436246355277e-27 1.65718123177638e-27 66 1 1.56223291974110e-26 7.81116459870548e-27 67 1 6.87657093711081e-26 3.43828546855541e-26 68 1 1.13190559507520e-25 5.65952797537598e-26 69 1 3.63200832673205e-25 1.81600416336602e-25 70 1 1.51292993941597e-24 7.56464969707984e-25 71 1 4.54038756860062e-24 2.27019378430031e-24 72 1 1.73569558207494e-23 8.67847791037469e-24 73 1 7.46037915896143e-23 3.73018957948071e-23 74 1 3.27516659137081e-22 1.63758329568541e-22 75 1 1.25688207486982e-21 6.2844103743491e-22 76 1 3.24029247958044e-21 1.62014623979022e-21 77 1 2.47537819770185e-21 1.23768909885092e-21 78 1 1.29641431436841e-20 6.48207157184203e-21 79 1 6.29727439672095e-20 3.14863719836048e-20 80 1 2.54259644977851e-19 1.27129822488926e-19 81 1 1.02208179426063e-18 5.11040897130313e-19 82 1 2.08215305619356e-18 1.04107652809678e-18 83 1 1.02484472507311e-17 5.12422362536555e-18 84 1 3.73944531377065e-17 1.86972265688533e-17 85 1 1.80495537517788e-16 9.02477687588941e-17 86 1 7.0941935887671e-16 3.54709679438355e-16 87 0.999999999999998 3.15141190595537e-15 1.57570595297769e-15 88 0.999999999999994 1.18330028544004e-14 5.91650142720019e-15 89 0.999999999999993 1.32085544240374e-14 6.6042772120187e-15 90 0.999999999999974 5.24192599970922e-14 2.62096299985461e-14 91 0.999999999999943 1.14847958459624e-13 5.74239792298119e-14 92 0.999999999999876 2.47122402176736e-13 1.23561201088368e-13 93 0.99999999999999 1.90360410643387e-14 9.51802053216936e-15 94 0.999999999999964 7.25831813073968e-14 3.62915906536984e-14 95 0.9999999999998 4.00130313613739e-13 2.00065156806869e-13 96 0.999999999999583 8.3478179288123e-13 4.17390896440615e-13 97 0.999999999997718 4.56301685163247e-12 2.28150842581624e-12 98 0.999999999988383 2.32341676778831e-11 1.16170838389415e-11 99 0.99999999998565 2.87006607660736e-11 1.43503303830368e-11 100 0.999999999925504 1.48991945792713e-10 7.44959728963564e-11 101 0.999999999843074 3.13852264540182e-10 1.56926132270091e-10 102 0.999999999831731 3.36537443494355e-10 1.68268721747177e-10 103 0.999999999527287 9.45425183683165e-10 4.72712591841582e-10 104 0.999999997505618 4.98876375657457e-09 2.49438187828728e-09 105 0.999999986133296 2.77334073040907e-08 1.38667036520454e-08 106 0.999999932517554 1.34964892834633e-07 6.74824464173167e-08 107 0.999999748705998 5.02588004602093e-07 2.51294002301047e-07 108 0.999999517051373 9.6589725301962e-07 4.8294862650981e-07 109 0.999997387718965 5.22456206978607e-06 2.61228103489303e-06 110 0.999991301296299 1.73974074028618e-05 8.69870370143092e-06 111 0.999958301496567 8.33970068654296e-05 4.16985034327148e-05 112 0.999906803214395 0.000186393571209182 9.3196785604591e-05 113 0.999992312187483 1.53756250334749e-05 7.68781251673744e-06 114 0.99997845279414 4.30944117199411e-05 2.15472058599705e-05 115 0.999993622138568 1.27557228635836e-05 6.37786143179179e-06 116 0.999844893339378 0.000310213321244287 0.000155106660622144 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 91 0.900990099009901 NOK 5% type I error level 95 0.94059405940594 NOK 10% type I error level 97 0.96039603960396 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/104dj31290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/104dj31290769236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/1fc491290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/1fc491290769236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/2fc491290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/2fc491290769236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/3q3lu1290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/3q3lu1290769236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/4q3lu1290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/4q3lu1290769236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/5q3lu1290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/5q3lu1290769236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/61c3x1290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/61c3x1290769236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/7b3k01290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/7b3k01290769236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/8b3k01290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/8b3k01290769236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/9b3k01290769236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290769162i0q02xiz9ggbc3n/9b3k01290769236.ps (open in new window)

Parameters (Session):

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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