*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, 06 Dec 2010 13:56:53 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49.htm/, Retrieved Mon, 06 Dec 2010 14:57:21 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49.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:

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3484,74 13830,14 9349,44 7977 -5,6 6 1 2,77 3411,13 14153,22 9327,78 8241 -6,2 3 1 2,76 3288,18 15418,03 9753,63 8444 -7,1 2 1,2 2,76 3280,37 16666,97 10443,5 8490 -1,4 2 1,2 2,46 3173,95 16505,21 10853,87 8388 -0,1 2 0,8 2,46 3165,26 17135,96 10704,02 8099 -0,9 -8 0,7 2,47 3092,71 18033,25 11052,23 7984 0 0 0,7 2,71 3053,05 17671 10935,47 7786 0,1 -2 0,9 2,8 3181,96 17544,22 10714,03 8086 2,6 3 1,2 2,89 2999,93 17677,9 10394,48 9315 6 5 1,3 3,36 3249,57 18470,97 10817,9 9113 6,4 8 1,5 3,31 3210,52 18409,96 11251,2 9023 8,6 8 1,9 3,5 3030,29 18941,6 11281,26 9026 6,4 9 1,8 3,51 2803,47 19685,53 10539,68 9787 7,7 11 1,9 3,71 2767,63 19834,71 10483,39 9536 9,2 13 2,2 3,71 2882,6 19598,93 10947,43 9490 8,6 12 2,1 3,71 2863,36 17039,97 10580,27 9736 7,4 13 2,2 4,21 2897,06 16969,28 10582,92 9694 8,6 15 2,7 4,21 3012,61 16973,38 10654,41 9647 6,2 13 2,8 4,21 3142,95 16329,89 11014,51 9753 6 16 2,9 4,5 3032,93 16153,34 10967,87 10070 6,6 10 3,4 4,51 3045,78 15311,7 10433,56 10137 5,1 14 3 4,51 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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation BEL_20[t] = -2047.16188772809 + 0.0723275143762075Nikkei[t] + 0.386310468950729DJ_Indust[t] + 0.00586235663459956Goudprijs[t] + 1.0731471514904Conjunct_Seizoenzuiver[t] -7.03174420326656Cons_vertrouw[t] -14.6090054577671Alg_consumptie_index_BE[t] -12.9375414285237Gem_rente_kasbon_1j[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) -2047.16188772809 360.12577 -5.6846 0 0 Nikkei 0.0723275143762075 0.017005 4.2532 4.1e-05 2.1e-05 DJ_Indust 0.386310468950729 0.038277 10.0925 0 0 Goudprijs 0.00586235663459956 0.009282 0.6316 0.528817 0.264408 Conjunct_Seizoenzuiver 1.0731471514904 7.624152 0.1408 0.888291 0.444145 Cons_vertrouw -7.03174420326656 6.497973 -1.0821 0.281288 0.140644 Alg_consumptie_index_BE -14.6090054577671 29.85171 -0.4894 0.625433 0.312717 Gem_rente_kasbon_1j -12.9375414285237 43.028156 -0.3007 0.764165 0.382082 Multiple Linear Regression - Regression Statistics Multiple R 0.927078632287769 R-squared 0.85947479044456 Adjusted R-squared 0.851541915711591 F-TEST (value) 108.3434214425 F-TEST (DF numerator) 7 F-TEST (DF denominator) 124 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 290.116655497996 Sum Squared Residuals 10436791.5508705 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3484.74 2513.04224716505 971.69775283495 2 3411.13 2550.17071763697 860.959282363034 3 3288.18 2810.49576337 477.684236630001 4 3280.37 3177.6003619873 102.769638012696 5 3173.95 3331.07162350843 -157.121623508434 6 3165.26 3387.89980780453 -222.639807804526 7 3092.71 3528.24842942687 -435.53842942687 8 3053.05 3465.86605367731 -412.816053677312 9 3181.96 3334.88755464712 -152.927554647124 10 2999.93 3210.359289611 -210.429289611004 11 3249.57 3407.16655639094 -157.59655639094 12 3210.52 3563.67375751684 -353.153757516838 13 3030.29 3605.69489422131 -575.404894221313 14 2803.47 3360.76583188458 -557.295831884577 15 2767.63 3331.50231335007 -563.87231335007 16 2882.6 3501.2915300753 -618.691530075303 17 2863.36 3159.56350979423 -296.203509794231 18 2897.06 3135.14796701341 -238.087967013415 19 3012.61 3172.813349183 -160.203349182998 20 3142.95 3239.48047702933 -96.530477029331 21 3032.93 3245.95237651484 -213.022376514843 22 3045.78 2955.16878318751 90.6112168124899 23 3110.52 3002.25053557194 108.269464428064 24 3013.24 2983.37369174739 29.8663082526084 25 2987.1 2953.76157872875 33.3384212712537 26 2995.55 2989.55263045666 5.99736954334172 27 2833.18 2680.18362452632 152.996375473685 28 2848.96 2805.92013571683 43.0398642831692 29 2794.83 2971.91891963235 -177.088919632346 30 2845.26 2983.64029736613 -138.380297366134 31 2915.02 2802.26327507224 112.756724927764 32 2892.63 2735.39858379642 157.231416203582 33 2604.42 2168.88679605968 435.533203940322 34 2641.65 2339.59194808802 302.058051911981 35 2659.81 2569.98227185514 89.827728144863 36 2638.53 2598.06382120476 40.4661787952357 37 2720.25 2507.6437578261 212.606242173902 38 2745.88 2463.79141445968 282.088585540318 39 2735.7 2796.55898772855 -60.8589877285517 40 2811.7 2696.93745250031 114.762547499694 41 2799.43 2685.32327400572 114.106725994275 42 2555.28 2415.46146891726 139.818531082738 43 2304.98 2030.33596231522 274.644037684781 44 2214.95 2029.43955394705 185.510446052952 45 2065.81 1801.27367517313 264.536324826869 46 1940.49 1715.51599287712 224.974007122883 47 2042 1950.18925085621 91.8107491437909 48 1995.37 1929.37217140869 65.9978285913104 49 1946.81 1913.19615150551 33.6138484944906 50 1765.9 1718.78346093438 47.1165390656171 51 1635.25 1742.97103504667 -107.721035046669 52 1833.42 1812.90394305156 20.5160569484361 53 1910.43 1941.12543797604 -30.6954379760365 54 1959.67 2176.45845413851 -216.78845413851 55 1969.6 2279.63578461636 -310.035784616361 56 2061.41 2330.11408802713 -268.704088027127 57 2093.48 2428.85394532106 -335.373945321062 58 2120.88 2578.37668418935 -457.496684189354 59 2174.56 2509.00753533109 -334.447535331088 60 2196.72 2659.11311376011 -462.393113760114 61 2350.44 2842.00345895263 -491.563458952635 62 2440.25 2838.67345150581 -398.423451505808 63 2408.64 2811.33513337478 -402.695133374777 64 2472.81 2884.35598635747 -411.545986357472 65 2407.6 2692.87348592586 -285.273485925856 66 2454.62 2794.75149363828 -340.131493638285 67 2448.05 2731.04832255857 -282.99832255857 68 2497.84 2644.75810256734 -146.918102567335 69 2645.64 2720.58733136742 -74.9473313674172 70 2756.76 2654.00316572147 102.756834278535 71 2849.27 2817.91262000126 31.3573799987422 72 2921.44 2919.85110940607 1.58889059393404 73 2981.85 2892.12542303066 89.7245769693375 74 3080.58 2946.75347184702 133.826528152979 75 3106.22 2935.14288332766 171.077116672341 76 3119.31 2774.36786522877 344.942134771225 77 3061.26 2834.25836767093 227.001632329068 78 3097.31 2899.13047084474 198.179529155257 79 3161.69 2941.73345391272 219.956546087279 80 3257.16 2974.9579793867 282.202020613305 81 3277.01 3056.56814410221 220.441855897789 82 3295.32 2978.61527504628 316.704724953718 83 3363.99 3199.05761616041 164.932383839592 84 3494.17 3313.23561621932 180.93438378068 85 3667.03 3343.49975080762 323.530249192376 86 3813.06 3401.84898408881 411.211015911192 87 3917.96 3506.95114359578 411.008856404218 88 3895.51 3601.65842015465 293.851579845351 89 3801.06 3593.51885913975 207.541140860253 90 3570.12 3327.82072543168 242.299274568322 91 3701.61 3365.67253968774 335.937460312255 92 3862.27 3494.15960261278 368.110397387219 93 3970.1 3611.27802547262 358.82197452738 94 4138.52 3791.72011426174 346.799885738257 95 4199.75 3852.66270698186 347.087293018141 96 4290.89 4036.4790102024 254.410989797599 97 4443.91 4072.54221845797 371.367781542027 98 4502.64 4137.42282898134 365.217171018658 99 4356.98 3962.65876349701 394.321236502991 100 4591.27 4156.85844065085 434.411559349153 101 4696.96 4426.09333882031 270.866661179692 102 4621.4 4485.9714253816 135.428574618402 103 4562.84 4568.23672396381 -5.39672396381288 104 4202.52 4300.95790338994 -98.4379033899365 105 4296.49 4406.2607467519 -109.770746751903 106 4435.23 4571.34253545309 -136.112535453087 107 4105.18 4245.83162809351 -140.651628093511 108 4116.68 4291.75368311439 -175.073683114394 109 3844.49 3843.3452010813 1.14479891869715 110 3720.98 3768.77387935548 -47.7938793554795 111 3674.4 3603.45597932261 70.9440206773902 112 3857.62 3851.76542482941 5.85457517059325 113 3801.06 3955.5299365064 -154.469936506402 114 3504.37 3668.29571027602 -163.925710276023 115 3032.6 3331.01404974883 -298.414049748829 116 3047.03 3384.30478666795 -337.274786667948 117 2962.34 3141.46433135622 -179.124331356217 118 2197.82 2245.42290890139 -47.602908901391 119 2014.45 2032.05379814711 -17.6037981471105 120 1862.83 2049.36098603662 -186.530986036618 121 1905.41 1953.22083825645 -47.810838256453 122 1810.99 1687.76757234031 123.222427659686 123 1670.07 1539.2419717546 130.828028245398 124 1864.44 1888.76129141735 -24.3212914173478 125 2052.02 2081.65021075726 -29.6302107572624 126 2029.6 2201.32254681594 -171.722546815938 127 2070.83 2226.49667183747 -155.666671837467 128 2293.41 2500.17498406255 -206.764984062554 129 2443.27 2601.61720593431 -158.347205934307 130 2513.17 2684.26042005449 -171.090420054495 131 2466.92 2789.33277902907 -322.412779029072 132 2502.66 2937.74226763193 -435.082267631931 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.0875093044736154 0.175018608947231 0.912490695526385 12 0.0335760341507567 0.0671520683015133 0.966423965849243 13 0.0161027002297789 0.0322054004595579 0.98389729977022 14 0.0152190577885078 0.0304381155770156 0.984780942211492 15 0.0147186419205087 0.0294372838410175 0.985281358079491 16 0.0108863946581355 0.021772789316271 0.989113605341864 17 0.0283987821438733 0.0567975642877466 0.971601217856127 18 0.028080835878263 0.056161671756526 0.971919164121737 19 0.0200504336031821 0.0401008672063641 0.979949566396818 20 0.0169852835421988 0.0339705670843975 0.9830147164578 21 0.0126071003944452 0.0252142007888905 0.987392899605555 22 0.00737698932687835 0.0147539786537567 0.992623010673122 23 0.00411851519345512 0.00823703038691024 0.995881484806545 24 0.00495613960568621 0.00991227921137242 0.995043860394314 25 0.0106368931623135 0.0212737863246271 0.989363106837686 26 0.0112780157341248 0.0225560314682496 0.988721984265875 27 0.0304101249502902 0.0608202499005803 0.96958987504971 28 0.0648687210989556 0.129737442197911 0.935131278901044 29 0.0783765980077411 0.156753196015482 0.921623401992259 30 0.0730037159455102 0.14600743189102 0.92699628405449 31 0.0532875962726844 0.106575192545369 0.946712403727316 32 0.037140973576223 0.074281947152446 0.962859026423777 33 0.0612311677610991 0.122462335522198 0.9387688322389 34 0.0499611935351499 0.0999223870702999 0.95003880646485 35 0.0432218038171936 0.0864436076343871 0.956778196182806 36 0.0385626186724981 0.0771252373449962 0.961437381327502 37 0.031630221112162 0.0632604422243241 0.968369778887838 38 0.0284264486625495 0.056852897325099 0.97157355133745 39 0.0206466265207482 0.0412932530414964 0.979353373479252 40 0.01924295347535 0.0384859069507 0.98075704652465 41 0.0136438644621503 0.0272877289243006 0.98635613553785 42 0.0138779544800885 0.027755908960177 0.986122045519912 43 0.0473855309850013 0.0947710619700026 0.952614469014999 44 0.093668040446088 0.187336080892176 0.906331959553912 45 0.117210975401526 0.234421950803052 0.882789024598474 46 0.173169280887331 0.346338561774663 0.826830719112668 47 0.208701134726393 0.417402269452787 0.791298865273607 48 0.192991054881407 0.385982109762813 0.807008945118593 49 0.178885770489806 0.357771540979612 0.821114229510194 50 0.152984205724443 0.305968411448887 0.847015794275557 51 0.150801803785728 0.301603607571456 0.849198196214272 52 0.272337181775393 0.544674363550786 0.727662818224607 53 0.349649547743651 0.699299095487301 0.65035045225635 54 0.409701101342564 0.819402202685127 0.590298898657436 55 0.407462717180001 0.814925434360003 0.592537282819999 56 0.376273290997003 0.752546581994006 0.623726709002997 57 0.398009949503583 0.796019899007167 0.601990050496417 58 0.46221741693315 0.924434833866299 0.53778258306685 59 0.48659109592812 0.97318219185624 0.51340890407188 60 0.501008722727964 0.997982554544071 0.498991277272036 61 0.546449992750308 0.907100014499384 0.453550007249692 62 0.546215729222555 0.90756854155489 0.453784270777445 63 0.647870402321688 0.704259195356625 0.352129597678312 64 0.868235523848527 0.263528952302947 0.131764476151473 65 0.937231687261455 0.125536625477089 0.0627683127385445 66 0.98045447510779 0.0390910497844212 0.0195455248922106 67 0.995137090200594 0.00972581959881287 0.00486290979940643 68 0.99845353923005 0.00309292153989755 0.00154646076994877 69 0.999524550132695 0.00095089973461071 0.000475449867305355 70 0.99987262021895 0.000254759562098626 0.000127379781049313 71 0.999942475313145 0.000115049373709868 5.7524686854934e-05 72 0.99996300670436 7.39865912818429e-05 3.69932956409214e-05 73 0.999975853870006 4.82922599885831e-05 2.41461299942916e-05 74 0.999983284802715 3.34303945696871e-05 1.67151972848435e-05 75 0.999989960265864 2.00794682716592e-05 1.00397341358296e-05 76 0.999992910392062 1.4179215875988e-05 7.08960793799402e-06 77 0.99999442858421 1.11428315800221e-05 5.57141579001103e-06 78 0.999995889992927 8.22001414596243e-06 4.11000707298122e-06 79 0.999996079718208 7.84056358475542e-06 3.92028179237771e-06 80 0.999996822498 6.3550040000917e-06 3.17750200004585e-06 81 0.999998224009727 3.55198054537045e-06 1.77599027268522e-06 82 0.999999104719815 1.79056037082588e-06 8.9528018541294e-07 83 0.999998828116842 2.34376631524907e-06 1.17188315762453e-06 84 0.99999875747742 2.48504515847819e-06 1.2425225792391e-06 85 0.999998957966425 2.08406714998244e-06 1.04203357499122e-06 86 0.999998629796582 2.74040683598103e-06 1.37020341799051e-06 87 0.999997952608002 4.09478399580471e-06 2.04739199790236e-06 88 0.99999736770658 5.26458684149547e-06 2.63229342074773e-06 89 0.999995485495563 9.02900887351383e-06 4.51450443675692e-06 90 0.9999945031339 1.09937322002118e-05 5.49686610010591e-06 91 0.999989817985782 2.0364028435404e-05 1.0182014217702e-05 92 0.999980982188265 3.80356234691745e-05 1.90178117345872e-05 93 0.999964669791917 7.06604161658346e-05 3.53302080829173e-05 94 0.999946465586445 0.000107068827110446 5.35344135552229e-05 95 0.999895311493606 0.000209377012787501 0.000104688506393751 96 0.999852331661738 0.000295336676524583 0.000147668338262292 97 0.999772066649967 0.000455866700065753 0.000227933350032877 98 0.999574977692224 0.000850044615551285 0.000425022307775643 99 0.99939190596703 0.00121618806593983 0.000608094032969913 100 0.999534499832279 0.000931000335442373 0.000465500167721187 101 0.999682266674026 0.000635466651948284 0.000317733325974142 102 0.99970616307892 0.000587673842159232 0.000293836921079616 103 0.999641694910845 0.000716610178310125 0.000358305089155063 104 0.999472737915908 0.00105452416818501 0.000527262084092506 105 0.999251374863885 0.00149725027222921 0.000748625136114606 106 0.998779199742839 0.00244160051432196 0.00122080025716098 107 0.998707080097089 0.00258583980582249 0.00129291990291124 108 0.997968901151082 0.00406219769783498 0.00203109884891749 109 0.998890845742434 0.0022183085151313 0.00110915425756565 110 0.998995504447728 0.00200899110454336 0.00100449555227168 111 0.999372527983593 0.0012549440328141 0.000627472016407048 112 0.99972791315867 0.000544173682660498 0.000272086841330249 113 0.999929087130073 0.00014182573985315 7.09128699265752e-05 114 0.999994285069936 1.14298601280183e-05 5.71493006400913e-06 115 0.999975128728984 4.9742542032518e-05 2.4871271016259e-05 116 0.999895405640248 0.000209188719504279 0.000104594359752139 117 0.999704121107972 0.000591757784055213 0.000295878892027606 118 0.998793721865895 0.0024125562682107 0.00120627813410535 119 0.999712455790022 0.000575088419955293 0.000287544209977647 120 0.998254940732999 0.00349011853400228 0.00174505926700114 121 0.98977364413465 0.0204527117307008 0.0102263558653504 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 56 0.504504504504504 NOK 5% type I error level 72 0.648648648648649 NOK 10% type I error level 83 0.747747747747748 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/10b8211291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/10b8211291643802.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/14p5p1291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/14p5p1291643802.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/2wg4s1291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/2wg4s1291643802.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/3wg4s1291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/3wg4s1291643802.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/4wg4s1291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/4wg4s1291643802.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/57p4d1291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/57p4d1291643802.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/67p4d1291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/67p4d1291643802.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/70glf1291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/70glf1291643802.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/80glf1291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/80glf1291643802.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/9b8211291643802.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/06/t12916438383b0wittuxfmkk49/9b8211291643802.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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Software written by Ed van Stee & Patrick Wessa

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