time effect

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 23 Nov 2010 21:38:35 +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/23/t1290548219lx541v2k2f70luq.htm/, Retrieved Tue, 23 Nov 2010 22:37:09 +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/23/t1290548219lx541v2k2f70luq.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 9 23 26 9 15 6 11 13 4 18 9 21 20 9 15 6 12 16 4 11 9 21 21 9 14 13 15 19 6 12 9 21 31 14 10 8 10 15 8 16 9 24 21 8 10 7 12 14 8 18 9 22 18 8 12 9 11 13 4 14 9 21 26 11 18 5 5 19 4 14 9 22 22 10 12 8 16 15 5 15 9 21 22 9 14 9 11 14 5 15 9 20 29 15 18 11 15 15 8 17 9 22 15 14 9 8 12 16 4 19 9 21 16 11 11 11 9 16 4 10 9 21 24 14 11 12 11 16 4 18 9 23 17 6 17 8 15 17 4 14 9 22 19 20 8 7 12 15 4 14 9 23 22 9 16 9 16 15 8 17 9 22 31 10 21 12 14 20 4 14 9 24 28 8 24 20 11 18 4 16 9 23 38 11 21 7 10 16 4 18 9 21 26 14 14 8 7 16 4 14 9 23 25 11 7 8 11 19 8 12 9 23 25 16 18 16 10 16 3 17 9 21 29 14 18 10 11 17 4 9 9 20 28 11 13 6 16 17 4 16 9 32 15 11 11 8 14 16 4 14 9 22 18 12 13 9 12 15 10 11 9 21 21 9 13 9 12 14 5 16 9 21 25 7 18 11 11 15 4 13 9 21 23 13 14 12 6 12 4 17 9 22 23 10 12 8 14 14 4 15 9 21 19 9 9 7 9 16 4 14 9 21 18 9 12 8 15 14 4 16 9 21 18 13 8 9 12 7 10 9 9 22 26 16 5 4 12 10 4 15 9 21 18 12 10 8 9 14 8 17 9 21 18 6 11 8 13 16 4 13 9 21 28 14 11 8 15 16 4 15 9 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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Happiness[t] = + 16.8555988203748 -0.0786345448628769Month[t] + 0.0176147950614903Age[t] -0.0124312897250591Concern_over_mistakes[t] -0.249744352622465Doubts_about_actions[t] + 0.0885995494564707Parental_expectations[t] -0.0926244834865925Parental_criticism[t] + 0.0351359704360569Popularity[t] + 0.0421600459244758Perceived_learning_competence[t] -0.142798650718867Amotivation[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) 16.8555988203748 4.614883 3.6524 0.000372 0.000186 Month -0.0786345448628769 0.384686 -0.2044 0.838341 0.419171 Age 0.0176147950614903 0.062789 0.2805 0.779497 0.389748 Concern_over_mistakes -0.0124312897250591 0.038788 -0.3205 0.749091 0.374545 Doubts_about_actions -0.249744352622465 0.07832 -3.1888 0.001779 0.000889 Parental_expectations 0.0885995494564707 0.069585 1.2733 0.205132 0.102566 Parental_criticism -0.0926244834865925 0.086807 -1.067 0.287883 0.143941 Popularity 0.0351359704360569 0.063796 0.5508 0.582718 0.291359 Perceived_learning_competence 0.0421600459244758 0.089618 0.4704 0.638805 0.319402 Amotivation -0.142798650718867 0.073836 -1.934 0.055223 0.027611 Multiple Linear Regression - Regression Statistics Multiple R 0.419882877183372 R-squared 0.176301630551787 Adjusted R-squared 0.120978605738101 F-TEST (value) 3.18676773631822 F-TEST (DF numerator) 9 F-TEST (DF denominator) 134 p-value 0.00159616503008553 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.23501532220863 Sum Squared Residuals 669.369327727986 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 15.1187435064363 -1.11874350643635 2 18 15.3197177628732 2.68028223712679 3 11 14.5166062869294 -3.51660628692941 4 12 12.6223785088577 -0.622378508857652 5 16 14.4187382854617 1.58126171453826 6 18 14.9066512829686 3.09334871703138 7 14 14.9845927958550 -0.984592795854973 8 14 14.5672631956204 -0.567263195620417 9 15 14.6661274705030 0.33387252949702 10 15 12.9864847379961 2.01351526200391 11 17 13.4339209797357 3.56607902026433 12 19 13.9470256899615 5.05297431003849 13 10 13.0759897716792 -3.07598977167917 14 18 16.2809923692112 1.71900763078882 15 14 11.8475945932063 2.15240540679370 16 14 14.6680001054871 -0.668000105487062 17 17 15.1656065387259 1.83439346127412 18 14 15.0726934805885 -1.07269348058852 19 16 15.0003963050803 0.999603694919672 20 18 13.5468798928006 4.4531201071994 21 14 13.4194064009629 0.58059359903707 22 12 12.9566609593639 -0.956660959363893 23 17 13.8614391821468 3.13856081785317 24 9 14.7086687735221 -5.70866877352209 25 16 14.6067730280030 1.39322697199697 26 14 13.2589375799070 0.741062420092959 27 11 14.6250951812076 -3.62509518120762 28 16 15.4824302340688 0.517569765931228 29 13 13.2596440265179 -0.259644026517915 30 17 14.5851985698176 2.41480143018237 31 15 14.6025193610647 0.397480638935307 32 14 14.9146205464400 -0.914620546439961 33 16 12.2113003175449 3.78869968245507 34 9 12.5608275480887 -3.56082754808873 35 15 13.2061779641678 1.79382203583218 36 17 15.5893022058277 1.41069779417228 37 13 13.5373064284695 -0.537306428469528 38 15 13.8073552501306 1.19264474986939 39 16 13.9592857926279 2.04071420737206 40 16 17.0569149648932 -1.05691496489316 41 12 13.9100914487873 -1.91009144878734 42 11 13.4714638472947 -2.47146384729472 43 15 15.2844491754492 -0.284449175449200 44 17 14.9468723775083 2.05312762249165 45 13 14.3551518351716 -1.35515183517163 46 16 11.8117219792692 4.18827802073083 47 14 14.2388318808711 -0.238831880871055 48 11 13.5181277155191 -2.51812771551909 49 12 13.2180225913502 -1.21802259135017 50 12 14.0125858833841 -2.01258588338413 51 15 14.0645261074146 0.935473892585384 52 16 15.1643394313368 0.835660568663244 53 15 14.8656445409333 0.134355459066687 54 12 15.0194526107514 -3.01945261075140 55 12 14.4780397816004 -2.47803978160035 56 8 12.8834643798061 -4.88346437980607 57 13 15.4410597590180 -2.44105975901798 58 11 14.9545700845368 -3.95457008453676 59 14 14.726401615604 -0.726401615604001 60 15 13.2075779158707 1.79242208412926 61 10 14.0220843152958 -4.02208431529579 62 11 12.741917967334 -1.74191796733400 63 12 13.8374257407787 -1.83742574077869 64 15 13.1224673399753 1.87753266002472 65 15 14.4842436573547 0.515756342645343 66 14 13.7531639125390 0.246836087460958 67 16 13.1925020617359 2.80749793826409 68 15 14.9277012822455 0.0722987177544991 69 15 15.2427298471073 -0.242729847107324 70 13 14.8170685028367 -1.81706850283673 71 17 14.8375496606220 2.16245033937797 72 13 13.3745828755644 -0.37458287556444 73 15 13.7439756906725 1.25602430932753 74 13 14.554042127295 -1.55404212729500 75 15 14.0671102094667 0.932889790533274 76 16 14.5215787074808 1.47842129251923 77 15 14.5461563228556 0.453843677144362 78 16 14.2117358221213 1.78826417787872 79 15 14.3180395985345 0.681960401465486 80 14 14.7377088005423 -0.737708800542279 81 15 12.2990048976007 2.70099510239928 82 7 11.6715508490726 -4.67155084907257 83 17 14.9805113422822 2.0194886577178 84 13 14.5147066422741 -1.51470664227414 85 15 13.6307527450909 1.36924725490912 86 14 13.8463059794131 0.153694020586945 87 13 13.7154514978716 -0.715451497871638 88 16 15.2664000925737 0.733599907426265 89 12 14.1509407882566 -2.15094078825657 90 14 15.5285006361618 -1.52850063616180 91 17 14.6738923371139 2.32610766288613 92 15 15.4878392217852 -0.487839221785187 93 17 13.2265010734638 3.77349892653621 94 12 13.9346446367192 -1.93464463671918 95 16 15.3600481944662 0.639951805533752 96 11 14.0844254755203 -3.08442547552025 97 15 13.2341424332127 1.76585756678735 98 9 14.0630057963438 -5.06300579634381 99 16 14.722995177714 1.27700482228601 100 10 13.0708203937425 -3.07082039374252 101 10 13.2045645870976 -3.20456458709756 102 15 14.8764284007164 0.123571599283556 103 11 13.9252878062601 -2.92528780626008 104 13 15.1863686071566 -2.18636860715656 105 14 13.225325560287 0.774674439713003 106 18 14.6184280211542 3.38157197884583 107 16 15.0834959090075 0.916504090992459 108 14 12.3008999283921 1.69910007160793 109 14 13.1771891454181 0.82281085458187 110 14 13.1981807063311 0.801819293668948 111 14 14.3127438182216 -0.312743818221648 112 12 13.7001098309657 -1.70010983096573 113 14 14.4638814051687 -0.463881405168717 114 15 14.3118047763015 0.68819522369848 115 15 14.9646733966296 0.0353266033704079 116 13 13.5736718031087 -0.573671803108669 117 17 14.8819899432468 2.11801005675318 118 17 15.3550100799349 1.64498992006510 119 19 14.9387016044131 4.06129839558688 120 15 13.8607229834053 1.13927701659474 121 13 14.0527081029942 -1.05270810299424 122 9 12.1771991614099 -3.17719916140986 123 15 15.0418790087624 -0.0418790087624142 124 15 14.5587721624333 0.441227837566655 125 16 13.8499906545279 2.15000934547209 126 11 13.2810069511133 -2.28100695111328 127 14 14.5860703071595 -0.58607030715945 128 11 12.6338756957475 -1.63387569574755 129 15 13.3679284248399 1.63207157516014 130 13 13.3853231292893 -0.385323129289257 131 16 12.6870887460228 3.31291125397724 132 14 14.6631349353270 -0.663134935327046 133 15 14.7954102298823 0.204589770117651 134 16 13.0148193934049 2.98518060659512 135 16 15.4402781789436 0.559721821056384 136 11 12.4000225370024 -1.4000225370024 137 13 13.9992080202958 -0.999208020295785 138 16 14.6067730280030 1.39322697199697 139 12 13.9855072458696 -1.98550724586963 140 9 11.4645641357693 -2.46456413576929 141 13 11.4594581978043 1.54054180219571 142 13 14.5147066422741 -1.51470664227414 143 19 14.9387016044131 4.06129839558688 144 13 15.4912077042297 -2.49120770422968 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.332278062883377 0.664556125766754 0.667721937116623 14 0.295505094733614 0.591010189467229 0.704494905266386 15 0.228416901523891 0.456833803047782 0.771583098476109 16 0.261121833634578 0.522243667269157 0.738878166365422 17 0.884431059973162 0.231137880053677 0.115568940026838 18 0.843921394026472 0.312157211947055 0.156078605973528 19 0.824776882105781 0.350446235788438 0.175223117894219 20 0.860960494113242 0.278079011773517 0.139039505886758 21 0.843748075539599 0.312503848920803 0.156251924460402 22 0.82654426363689 0.346911472726218 0.173455736363109 23 0.836077440852032 0.327845118295936 0.163922559147968 24 0.924246692022634 0.151506615954733 0.0757533079773663 25 0.901739028678314 0.196521942643371 0.0982609713216856 26 0.898535233509654 0.202929532980691 0.101464766490346 27 0.943489967583227 0.113020064833546 0.0565100324167729 28 0.922590784666578 0.154818430666843 0.0774092153334216 29 0.912634920089224 0.174730159821552 0.0873650799107759 30 0.925164844196968 0.149670311606065 0.0748351558030323 31 0.900628869249186 0.198742261501628 0.0993711307508142 32 0.874256879583196 0.251486240833608 0.125743120416804 33 0.885792935024182 0.228414129951637 0.114207064975819 34 0.906320118824906 0.187359762350187 0.0936798811750935 35 0.891506398545788 0.216987202908424 0.108493601454212 36 0.880855517417588 0.238288965164824 0.119144482582412 37 0.855898870610863 0.288202258778273 0.144101129389137 38 0.840426252433594 0.319147495132812 0.159573747566406 39 0.84207409826136 0.315851803477281 0.157925901738640 40 0.837475990488177 0.325048019023646 0.162524009511823 41 0.805920422317453 0.388159155365094 0.194079577682547 42 0.834945394105331 0.330109211789338 0.165054605894669 43 0.801186426351701 0.397627147296597 0.198813573648299 44 0.79435379379866 0.41129241240268 0.20564620620134 45 0.754491407692555 0.49101718461489 0.245508592307445 46 0.819080862136607 0.361838275726786 0.180919137863393 47 0.799173564935804 0.401652870128391 0.200826435064195 48 0.892226016548225 0.215547966903549 0.107773983451775 49 0.879757641557083 0.240484716885833 0.120242358442917 50 0.87990299974386 0.240194000512280 0.120097000256140 51 0.868398696380083 0.263202607239833 0.131601303619917 52 0.857658415489145 0.284683169021709 0.142341584510855 53 0.839327503092114 0.321344993815772 0.160672496907886 54 0.842816682998975 0.314366634002050 0.157183317001025 55 0.826099425844712 0.347801148310576 0.173900574155288 56 0.910381742128437 0.179236515743127 0.0896182578715633 57 0.917085760533073 0.165828478933855 0.0829142394669274 58 0.944988871811837 0.110022256376326 0.0550111281881629 59 0.93238184747905 0.135236305041900 0.0676181525209498 60 0.927572558546979 0.144854882906042 0.072427441453021 61 0.937782115615568 0.124435768768863 0.0622178843844316 62 0.920651465742824 0.158697068514352 0.0793485342571758 63 0.908431510228342 0.183136979543316 0.0915684897716579 64 0.940854480285124 0.118291039429753 0.0591455197148765 65 0.932229649946383 0.135540700107234 0.0677703500536172 66 0.916984455513197 0.166031088973605 0.0830155444868027 67 0.932598346573652 0.134803306852696 0.0674016534263478 68 0.91969883244119 0.160602335117620 0.0803011675588101 69 0.899387258213529 0.201225483572942 0.100612741786471 70 0.891899662513842 0.216200674972317 0.108100337486158 71 0.892126967880445 0.215746064239109 0.107873032119555 72 0.867820450648947 0.264359098702107 0.132179549351053 73 0.852301858326413 0.295396283347174 0.147698141673587 74 0.844643314403429 0.310713371193142 0.155356685596571 75 0.818948091770497 0.362103816459005 0.181051908229503 76 0.807130665022627 0.385738669954745 0.192869334977373 77 0.771359269855301 0.457281460289398 0.228640730144699 78 0.752492149474444 0.495015701051112 0.247507850525556 79 0.712436002554289 0.575127994891422 0.287563997445711 80 0.672959108075029 0.654081783849943 0.327040891924971 81 0.700061118112297 0.599877763775406 0.299938881887703 82 0.807544175119132 0.384911649761737 0.192455824880868 83 0.793712724519645 0.41257455096071 0.206287275480355 84 0.773534561777308 0.452930876445385 0.226465438222692 85 0.747685614415519 0.504628771168962 0.252314385584481 86 0.704196134917091 0.591607730165818 0.295803865082909 87 0.663140050183279 0.673719899633442 0.336859949816721 88 0.628883910644597 0.742232178710806 0.371116089355403 89 0.620765658591415 0.75846868281717 0.379234341408585 90 0.597005118575495 0.805989762849009 0.402994881424505 91 0.597801551007749 0.804396897984503 0.402198448992251 92 0.55132156124337 0.89735687751326 0.44867843875663 93 0.713061860297512 0.573876279404977 0.286938139702488 94 0.692747603692481 0.614504792615038 0.307252396307519 95 0.657547700722988 0.684904598554023 0.342452299277012 96 0.68922083076564 0.621558338468722 0.310779169234361 97 0.69662568658985 0.6067486268203 0.303374313410150 98 0.892004909359708 0.215990181280584 0.107995090640292 99 0.875642516759372 0.248714966481255 0.124357483240628 100 0.87071551816381 0.258568963672382 0.129284481836191 101 0.878420926066322 0.243158147867355 0.121579073933678 102 0.845658568751792 0.308682862496416 0.154341431248208 103 0.87024353047592 0.259512939048161 0.129756469524080 104 0.900482731424374 0.199034537151253 0.0995172685756264 105 0.891792211055875 0.216415577888250 0.108207788944125 106 0.894855860948435 0.21028827810313 0.105144139051565 107 0.875135934749661 0.249728130500679 0.124864065250339 108 0.907712113682479 0.184575772635042 0.092287886317521 109 0.884350719660121 0.231298560679758 0.115649280339879 110 0.889643851268033 0.220712297463934 0.110356148731967 111 0.85856910446366 0.28286179107268 0.14143089553634 112 0.840803532972898 0.318392934054203 0.159196467027101 113 0.799621730450113 0.400756539099774 0.200378269549887 114 0.747514767842477 0.504970464315045 0.252485232157523 115 0.705217094645946 0.589565810708109 0.294782905354054 116 0.639214549676832 0.721570900646335 0.360785450323168 117 0.702154641374285 0.595690717251431 0.297845358625716 118 0.731722811242165 0.536554377515670 0.268277188757835 119 0.732951866394142 0.534096267211715 0.267048133605858 120 0.744571664272433 0.510856671455133 0.255428335727567 121 0.745066899254621 0.509866201490757 0.254933100745379 122 0.69973076191612 0.600538476167759 0.300269238083879 123 0.629417056057465 0.74116588788507 0.370582943942535 124 0.544788343120138 0.910423313759723 0.455211656879862 125 0.504397976868921 0.991204046262158 0.495602023131079 126 0.419394281792616 0.838788563585232 0.580605718207384 127 0.327636924176015 0.65527384835203 0.672363075823985 128 0.298051624859243 0.596103249718486 0.701948375140757 129 0.221925946962777 0.443851893925553 0.778074053037223 130 0.229217071237245 0.45843414247449 0.770782928762755 131 0.981168985904672 0.0376620281906566 0.0188310140953283 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 1 0.00840336134453781 OK 10% type I error level 1 0.00840336134453781 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/109ay01290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/109ay01290548303.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/1k91o1290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/1k91o1290548303.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/2k91o1290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/2k91o1290548303.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/3k91o1290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/3k91o1290548303.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/4d0191290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/4d0191290548303.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/5d0191290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/5d0191290548303.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/6d0191290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/6d0191290548303.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/7590u1290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/7590u1290548303.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/8g0hf1290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/8g0hf1290548303.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/9g0hf1290548303.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290548219lx541v2k2f70luq/9g0hf1290548303.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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