W10- MR

*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: Sat, 11 Dec 2010 18:14:08 +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/11/t1292091261h386v94umfj3alf.htm/, Retrieved Sat, 11 Dec 2010 19:14:24 +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/11/t1292091261h386v94umfj3alf.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 «

0 24 14 11 12 24 26 0 25 11 7 8 25 23 0 17 6 17 8 30 25 1 18 12 10 8 19 23 1 18 8 12 9 22 19 1 16 10 12 7 22 29 1 20 10 11 4 25 25 1 16 11 11 11 23 21 1 18 16 12 7 17 22 1 17 11 13 7 21 25 0 23 13 14 12 19 24 0 30 12 16 10 19 18 1 23 8 11 10 15 22 1 18 12 10 8 16 15 1 15 11 11 8 23 22 1 12 4 15 4 27 28 0 21 9 9 9 22 20 1 15 8 11 8 14 12 1 20 8 17 7 22 24 0 31 14 17 11 23 20 0 27 15 11 9 23 21 1 34 16 18 11 21 20 1 21 9 14 13 19 21 1 31 14 10 8 18 23 1 19 11 11 8 20 28 0 16 8 15 9 23 24 1 20 9 15 6 25 24 1 21 9 13 9 19 24 1 22 9 16 9 24 23 1 17 9 13 6 22 23 1 24 10 9 6 25 29 0 25 16 18 16 26 24 0 26 11 18 5 29 18 1 25 8 12 7 32 25 1 17 9 17 9 25 21 1 32 16 9 6 29 26 1 33 11 9 6 28 22 1 13 16 12 5 17 22 1 32 12 18 12 28 22 1 25 12 12 7 29 23 1 29 14 18 10 26 30 1 22 9 14 9 25 23 1 18 10 15 8 14 17 1 17 9 16 5 25 23 0 20 10 10 8 26 23 1 15 12 11 8 20 25 1 20 14 14 10 18 24 1 33 14 9 6 32 24 0 29 10 12 8 25 23 1 23 14 17 7 25 21 0 26 16 5 4 23 24 1 18 9 12 8 21 2 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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation ConcernoverMistakes[t] = + 3.44754667768642 + 0.0228923811027678gender[t] + 0.347538866580637Doubtsaboutactions[t] + 0.0806235164920517ParentalExpectations[t] -0.196292046597524ParentalCriticism[t] + 0.264624519633298PersonalStandards[t] + 0.391705515091531`Organization `[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) 3.44754667768642 2.492217 1.3833 0.168594 0.084297 gender 0.0228923811027678 0.074163 0.3087 0.757991 0.378995 Doubtsaboutactions 0.347538866580637 0.111381 3.1203 0.002163 0.001081 ParentalExpectations 0.0806235164920517 0.116227 0.6937 0.488947 0.244473 ParentalCriticism -0.196292046597524 0.098197 -1.999 0.047396 0.023698 PersonalStandards 0.264624519633298 0.080284 3.2961 0.00122 0.00061 `Organization ` 0.391705515091531 0.08232 4.7583 5e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.816486891416717 R-squared 0.666650843855334 Adjusted R-squared 0.653492324533834 F-TEST (value) 50.663059236922 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.9152072013772 Sum Squared Residuals 2329.98480931682 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.3797767956366 0.620223204363412 2 25 21.8893422906752 3.11065770932475 3 17 23.0644167510421 -6.06441675104214 4 18 20.913896970035 -2.91389697003503 5 18 18.7157479886328 -0.715747988632833 6 16 23.7204649659045 -7.72046496590446 7 20 23.4557690877388 -3.45576908773875 8 16 20.333192528504 -4.333192528504 9 18 21.7406369615811 -3.74063696158107 10 17 22.3171807689777 -5.31718076897773 11 23 21.1675748501825 1.83242514981746 12 30 19.0236340192319 10.9763659807681 13 23 17.7615773333848 5.23842266661524 14 18 16.9863792904029 1.01362070959711 15 15 21.3137741833881 -6.3137741833881 16 12 23.3973955387643 -11.3973955387643 17 21 19.1902294397261 1.80977056027392 18 15 13.9724817560312 1.0275182439688 19 20 21.4699772397458 -1.46997723974579 20 31 21.4449523310039 9.55504766899608 21 27 22.0930397069188 4.90696029308117 22 34 21.7142969224934 12.2857030775066 23 21 18.4289031730906 2.57109682690936 24 31 21.344350183563 9.655649816437 25 19 22.8701337150374 -3.87013371503739 26 16 21.1578782520972 -5.15787825209717 27 20 22.6464346788397 -2.64643467883974 28 21 20.3085643882633 0.691435611736723 29 22 21.4818520208144 0.518147979185607 30 17 21.2996085718642 -4.29960857186421 31 24 24.4687600219257 -0.468760021925722 32 25 23.5998889669356 1.40011103306436 33 26 22.4650476149559 3.53495238504406 34 25 24.10481036871 0.895189631289954 35 17 21.0436890267567 -4.04368902675668 36 32 26.4373747546681 5.56262524533186 37 33 22.8682338417655 10.1317661582345 38 13 22.1332210547761 -9.13322105477612 39 32 22.7636320771895 9.2363679228105 40 25 23.9176812459496 1.08231875405036 41 29 26.4556889850115 2.54431101498853 42 22 21.5852295074636 0.414770492536412 43 18 16.9485811306183 1.05141886938166 44 17 22.5316447268378 -5.53164472683779 45 20 22.0482984932041 -2.04829849320407 46 15 22.0425560363434 -7.04255603634344 47 20 21.6659656714277 -1.66596567142769 48 33 25.7527595502237 7.2472404497763 49 29 21.9449210065549 7.05507899344512 50 23 23.1739674528549 -0.173967452854913 51 26 24.1134142528094 1.88658574719064 52 18 20.9534819576353 -2.95348195763535 53 20 22.580325983846 -2.58032598384604 54 6 7.78840726553034 -1.78840726553034 55 8 13.837370986172 -5.83737098617201 56 13 11.8213050682875 1.17869493171248 57 10 11.1996079265063 -1.19960792650633 58 8 10.2967327011067 -2.29673270110669 59 7 9.96028842263066 -2.96028842263066 60 15 10.8086425874688 4.19135741253117 61 9 11.029104591413 -2.02910459141299 62 10 10.9617179132952 -0.961717913295248 63 12 12.4025936126956 -0.402593612695594 64 13 9.00551147146839 3.99448852853161 65 10 10.2593306697743 -0.259330669774269 66 11 9.88778077091991 1.11221922908009 67 8 10.6576896022493 -2.65768960224927 68 9 9.69443048538135 -0.694430485381348 69 13 10.890477492941 2.10952250705896 70 11 10.4733273050511 0.526672694948916 71 8 10.719262862958 -2.71926286295801 72 9 9.53894730632696 -0.538947306326961 73 9 11.6533650102401 -2.65336501024008 74 15 12.8256308893535 2.17436911064647 75 9 11.4478845099146 -2.4478845099146 76 10 10.8125054693945 -0.812505469394451 77 14 11.632079523899 2.36792047610102 78 12 11.9437114225471 0.0562885774529119 79 12 11.5539782290959 0.446021770904078 80 11 10.3964234951505 0.603576504849498 81 14 11.9275782537714 2.07242174622864 82 6 11.8707979201675 -5.87079792016751 83 12 11.5751761400004 0.424823859999625 84 8 12.1076441513051 -4.10764415130507 85 14 10.9645186179931 3.03548138200694 86 11 12.8701262159193 -1.87012621591931 87 10 9.79343257044687 0.206567429553125 88 14 11.1148698381042 2.88513016189578 89 12 11.6914441336338 0.308555866366223 90 10 11.2291885682839 -1.2291885682839 91 14 12.9590100445565 1.0409899554435 92 5 9.56196210615771 -4.56196210615771 93 11 10.4858968315162 0.514103168483819 94 10 11.0137740422211 -1.01377404222114 95 9 11.9260991825891 -2.92609918258911 96 10 13.0219009073152 -3.0219009073152 97 16 12.6335517998056 3.36644820019441 98 13 12.769589459774 0.23041054022597 99 9 11.0328965216864 -2.03289652168638 100 10 11.0004870088008 -1.00048700880077 101 10 11.0357874472364 -1.03578744723636 102 7 10.2727059190942 -3.2727059190942 103 9 12.0147248269682 -3.01472482696822 104 8 11.9702396696424 -3.9702396696424 105 14 12.7432097928643 1.25679020713569 106 14 9.27000983753598 4.72999016246402 107 8 9.32510547219745 -1.32510547219745 108 9 9.9527286788597 -0.952728678859693 109 14 11.750193287623 2.249806712377 110 14 11.4953643827814 2.50463561721864 111 8 11.1514613821933 -3.15146138219327 112 8 13.4343690442025 -5.43436904420246 113 8 8.91618195089977 -0.916181950899767 114 7 8.79080968797238 -1.79080968797238 115 6 8.10634783699819 -2.10634783699819 116 8 11.3555086310819 -3.35550863108193 117 6 9.62479840746586 -3.62479840746586 118 11 8.94203851078523 2.05796148921476 119 14 12.3828198135388 1.6171801864612 120 11 8.28822696291168 2.71177303708832 121 11 7.97654359718782 3.02345640281218 122 11 9.79160406460357 1.20839593539643 123 14 10.2158520986749 3.78414790132511 124 8 9.04967875154605 -1.04967875154605 125 20 10.5049470872995 9.4950529127005 126 11 12.4227741365669 -1.42277413656687 127 8 10.0130840871477 -2.01308408714768 128 11 10.9342438712819 0.0657561287180931 129 10 12.6005753651029 -2.6005753651029 130 14 10.5746362127895 3.42536378721046 131 11 9.79998075905849 1.20001924094152 132 9 11.4374269880652 -2.43742698806517 133 9 10.819988225095 -1.81998822509497 134 8 9.81727575333507 -1.81727575333508 135 10 11.6894324177541 -1.68943241775408 136 13 12.9096128183801 0.090387181619895 137 13 10.4684640578607 2.53153594213926 138 12 8.81291774328939 3.18708225671061 139 8 11.3533562115723 -3.35335621157227 140 13 9.2123994597571 3.7876005402429 141 14 7.17780576154678 6.82219423845322 142 12 10.6746118700954 1.32538812990458 143 14 12.8661846848057 1.13381531519433 144 15 9.38473733711195 5.61526266288805 145 13 12.422033969409 0.57796603059102 146 16 9.86090308916355 6.13909691083645 147 9 11.3032530953576 -2.30325309535761 148 9 9.4630438616911 -0.463043861691107 149 9 10.1871011119845 -1.18710111198445 150 8 11.3813133348038 -3.38131333480376 151 7 9.56378521604572 -2.56378521604572 152 16 12.3258282137406 3.67417178625936 153 11 14.1617796912668 -3.16177969126679 154 9 9.1381151583667 -0.138115158366692 155 11 12.4857586200766 -1.48575862007657 156 9 11.0577350629719 -2.0577350629719 157 14 10.5881338808375 3.41186611916255 158 13 11.4738116323644 1.52618836763558 159 16 14.0059508212852 1.99404917871479 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.12927196236873 0.258543924737461 0.87072803763127 11 0.0814002005426561 0.162800401085312 0.918599799457344 12 0.2450983791157 0.4901967582314 0.7549016208843 13 0.177490734799599 0.354981469599198 0.822509265200401 14 0.273779649130806 0.547559298261612 0.726220350869194 15 0.205893020944205 0.411786041888409 0.794106979055795 16 0.206828058959321 0.413656117918641 0.79317194104068 17 0.275513153125338 0.551026306250676 0.724486846874662 18 0.343135284671248 0.686270569342497 0.656864715328752 19 0.353323902511736 0.706647805023472 0.646676097488264 20 0.492688840811306 0.985377681622613 0.507311159188694 21 0.43362923614526 0.86725847229052 0.56637076385474 22 0.824312272821643 0.351375454356715 0.175687727178357 23 0.778220577090909 0.443558845818182 0.221779422909091 24 0.970397708395917 0.0592045832081665 0.0296022916040833 25 0.960606483256659 0.0787870334866826 0.0393935167433413 26 0.973700995392942 0.0525980092141152 0.0262990046070576 27 0.967628706658617 0.0647425866827651 0.0323712933413825 28 0.95972616772877 0.0805476645424584 0.0402738322712292 29 0.9482667154448 0.103466569110401 0.0517332845552005 30 0.940608116383384 0.118783767233231 0.0593918836166157 31 0.968870809095504 0.0622583818089914 0.0311291909044957 32 0.977725244699414 0.044549510601172 0.022274755300586 33 0.972012762247953 0.0559744755040949 0.0279872377520474 34 0.982821529715652 0.0343569405686952 0.0171784702843476 35 0.984577534146675 0.0308449317066497 0.0154224658533248 36 0.988618832313738 0.0227623353725235 0.0113811676862618 37 0.9988365729116 0.00232685417680037 0.00116342708840019 38 0.999930790248883 0.000138419502234548 6.92097511172742e-05 39 0.99998449205764 3.10158847181172e-05 1.55079423590586e-05 40 0.999975201227156 4.95975456878245e-05 2.47987728439122e-05 41 0.999972434910472 5.51301790567708e-05 2.75650895283854e-05 42 0.999952744343527 9.45113129462913e-05 4.72556564731457e-05 43 0.999925923093892 0.000148153812216446 7.40769061082231e-05 44 0.999946827732208 0.000106344535584969 5.31722677924845e-05 45 0.99993029273929 0.000139414521419677 6.97072607098385e-05 46 0.999985417465352 2.91650692960059e-05 1.4582534648003e-05 47 0.999981412902522 3.71741949551242e-05 1.85870974775621e-05 48 0.999992976034093 1.40479318149904e-05 7.02396590749522e-06 49 0.999998974942519 2.05011496243531e-06 1.02505748121766e-06 50 0.999998660641587 2.67871682669231e-06 1.33935841334615e-06 51 0.999999247613949 1.50477210222477e-06 7.52386051112385e-07 52 0.999998699593104 2.60081379282364e-06 1.30040689641182e-06 53 0.99999940375825 1.19248349909207e-06 5.96241749546037e-07 54 0.999999429311888 1.14137622380804e-06 5.7068811190402e-07 55 0.999999474469442 1.05106111506088e-06 5.25530557530438e-07 56 0.999999680274105 6.39451790811497e-07 3.19725895405748e-07 57 0.99999950543999 9.89120020594644e-07 4.94560010297322e-07 58 0.999999702282699 5.95434602790449e-07 2.97717301395225e-07 59 0.999999890658359 2.18683282314544e-07 1.09341641157272e-07 60 0.999999950681223 9.86375544283654e-08 4.93187772141827e-08 61 0.999999931457538 1.37084924298745e-07 6.85424621493726e-08 62 0.999999876859193 2.46281614077229e-07 1.23140807038614e-07 63 0.999999791529815 4.16940370349383e-07 2.08470185174691e-07 64 0.99999990303569 1.93928620235086e-07 9.69643101175429e-08 65 0.999999947126591 1.05746817571595e-07 5.28734087857977e-08 66 0.999999968499645 6.30007095979228e-08 3.15003547989614e-08 67 0.999999984695287 3.06094265213831e-08 1.53047132606915e-08 68 0.999999970976361 5.80472775008957e-08 2.90236387504479e-08 69 0.999999979545798 4.0908404114361e-08 2.04542020571805e-08 70 0.99999996076268 7.84746419491663e-08 3.92373209745831e-08 71 0.999999962359525 7.52809508087031e-08 3.76404754043515e-08 72 0.999999928124853 1.43750293567251e-07 7.18751467836257e-08 73 0.99999989786401 2.04271982207588e-07 1.02135991103794e-07 74 0.999999911730308 1.76539384792206e-07 8.82696923961029e-08 75 0.999999843482375 3.13035249796715e-07 1.56517624898358e-07 76 0.999999774210162 4.51579675135983e-07 2.25789837567992e-07 77 0.999999904094604 1.91810791722923e-07 9.59053958614615e-08 78 0.999999821266262 3.57467476750732e-07 1.78733738375366e-07 79 0.999999668678544 6.62642912602417e-07 3.31321456301209e-07 80 0.999999561254067 8.77491866762805e-07 4.38745933381402e-07 81 0.99999936389792 1.27220416094658e-06 6.36102080473292e-07 82 0.999999711769639 5.76460722018273e-07 2.88230361009137e-07 83 0.999999478363684 1.04327263202991e-06 5.21636316014955e-07 84 0.99999954594794 9.08104120966383e-07 4.54052060483192e-07 85 0.99999949566522 1.00866956123295e-06 5.04334780616473e-07 86 0.999999148780621 1.70243875747221e-06 8.51219378736104e-07 87 0.99999844620105 3.10759789787932e-06 1.55379894893966e-06 88 0.999998699742077 2.60051584684946e-06 1.30025792342473e-06 89 0.999997894804209 4.2103915826634e-06 2.1051957913317e-06 90 0.999996438680997 7.12263800534313e-06 3.56131900267157e-06 91 0.999994316021205 1.13679575890747e-05 5.68397879453735e-06 92 0.999994388890566 1.12222188670841e-05 5.61110943354206e-06 93 0.999990359246947 1.92815061055781e-05 9.64075305278905e-06 94 0.999983219231577 3.35615368466483e-05 1.67807684233241e-05 95 0.999982048629327 3.59027413466131e-05 1.79513706733065e-05 96 0.999973694264714 5.26114705715509e-05 2.63057352857754e-05 97 0.999970234499561 5.9531000877729e-05 2.97655004388645e-05 98 0.999950158203975 9.96835920507854e-05 4.98417960253927e-05 99 0.999930419596636 0.000139160806727652 6.9580403363826e-05 100 0.99989969066168 0.000200618676640935 0.000100309338320467 101 0.999833643818154 0.000332712363691417 0.000166356181845709 102 0.999764829509328 0.000470340981344296 0.000235170490672148 103 0.99967334865099 0.000653302698021157 0.000326651349010578 104 0.99966219366384 0.000675612672321233 0.000337806336160616 105 0.999467277414387 0.00106544517122514 0.000532722585612572 106 0.999543673054797 0.000912653890406378 0.000456326945203189 107 0.999541678035267 0.000916643929465452 0.000458321964732726 108 0.999557053519842 0.000885892960315092 0.000442946480157546 109 0.999351374335821 0.0012972513283574 0.000648625664178702 110 0.999277389131454 0.00144522173709173 0.000722610868545863 111 0.999097220686718 0.00180555862656453 0.000902779313282267 112 0.999737097079837 0.000525805840325684 0.000262902920162842 113 0.999822596848737 0.00035480630252681 0.000177403151263405 114 0.999697259294644 0.000605481410712283 0.000302740705356142 115 0.99959790368282 0.000804192634359274 0.000402096317179637 116 0.999412346487853 0.00117530702429369 0.000587653512146845 117 0.999229437159416 0.00154112568116765 0.000770562840583827 118 0.998817093248374 0.00236581350325116 0.00118290675162558 119 0.998194805560716 0.00361038887856833 0.00180519443928417 120 0.99741260130821 0.00517479738358216 0.00258739869179108 121 0.996942545797038 0.00611490840592368 0.00305745420296184 122 0.99566532487291 0.00866935025417903 0.00433467512708951 123 0.994896483633127 0.0102070327337469 0.00510351636687346 124 0.993092363644364 0.0138152727112726 0.00690763635563629 125 0.999705706470355 0.000588587059290149 0.000294293529645074 126 0.99954869218116 0.000902615637681423 0.000451307818840712 127 0.999191720437599 0.00161655912480292 0.000808279562401458 128 0.998526116721889 0.00294776655622213 0.00147388327811106 129 0.997512414808636 0.00497517038272877 0.00248758519136439 130 0.996152435477451 0.0076951290450978 0.0038475645225489 131 0.993784711922499 0.0124305761550028 0.00621528807750141 132 0.990662126906948 0.0186757461861032 0.0093378730930516 133 0.984903890179531 0.030192219640938 0.015096109820469 134 0.976204064980322 0.047591870039356 0.023795935019678 135 0.96543399419942 0.0691320116011615 0.0345660058005808 136 0.952268131344794 0.095463737310411 0.0477318686552055 137 0.949746367686682 0.100507264626636 0.0502536323133182 138 0.942382778881768 0.115234442236464 0.0576172211182322 139 0.94084856972104 0.118302860557918 0.0591514302789592 140 0.910771437752151 0.178457124495697 0.0892285622478486 141 0.888348887635494 0.223302224729013 0.111651112364506 142 0.835963421234312 0.328073157531377 0.164036578765688 143 0.81067672677776 0.378646546444479 0.18932327322224 144 0.769462794968775 0.46107441006245 0.230537205031225 145 0.702412067630627 0.595175864738745 0.297587932369373 146 0.760954624095327 0.478090751809347 0.239045375904673 147 0.69052443379002 0.618951132419959 0.309475566209979 148 0.546482339009851 0.907035321980299 0.453517660990149 149 0.399890772305037 0.799781544610073 0.600109227694963 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 92 0.657142857142857 NOK 5% type I error level 102 0.728571428571429 NOK 10% type I error level 111 0.792857142857143 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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