*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 16:04:07 +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/t1290528232ewo56fymx517bmk.htm/, Retrieved Tue, 23 Nov 2010 17:04:05 +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/t1290528232ewo56fymx517bmk.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 11 12 11 12 6 6 53 6 18 12 12 8 13 5 3 86 6 11 15 10 12 16 6 0 66 13 12 10 10 10 11 5 4 67 8 16 12 9 7 12 6 7 76 7 18 11 6 6 9 4 0 78 9 14 5 15 8 12 3 3 53 5 14 16 11 16 16 7 10 80 8 15 11 11 8 12 6 3 74 9 15 15 13 16 18 8 6 76 11 17 12 12 7 12 3 1 79 8 19 9 12 11 11 4 3 54 11 10 11 5 16 14 6 5 67 12 18 15 11 16 11 5 6 87 8 14 12 13 12 12 6 6 58 7 14 16 11 13 14 7 7 75 9 17 14 9 19 12 6 2 88 12 14 11 14 7 13 6 2 64 20 16 10 12 8 11 4 0 57 7 18 7 14 12 12 4 6 66 8 14 11 12 13 11 4 1 54 8 12 10 12 11 12 6 5 56 16 17 11 8 8 13 4 4 86 10 9 16 9 16 16 6 7 80 6 16 14 11 15 16 6 7 76 8 14 12 7 11 15 5 2 69 9 11 12 12 12 14 5 2 67 9 16 11 9 7 13 2 3 80 11 13 6 7 9 11 4 3 54 12 17 14 12 15 13 6 3 71 8 15 9 9 6 12 5 8 84 7 14 15 11 14 15 7 7 74 8 16 12 10 14 13 7 6 71 9 9 12 12 7 11 4 6 63 4 15 9 11 15 15 7 5 71 8 17 13 8 14 14 5 10 76 8 13 15 11 17 16 6 5 69 8 15 11 8 14 15 5 5 74 6 16 10 12 5 13 6 5 75 8 16 13 9 14 14 6 2 54 4 12 16 12 8 14 4 6 69 14 11 13 10 8 8 4 4 68 10 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 14 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Happiness[t] = + 7.35959823099505 -0.0312731524219015Popularity[t] + 0.125401376884334FindingFriends[t] + 0.0641716190319723KnowingPeople[t] + 0.0499017519535321Liked[t] + 0.0373567347735441Celebrity[t] -0.220050387130058WeightedSum[t] + 0.0785349987054337BelongingtoSports[t] -0.043444033219829ParentalCriticism[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) 7.35959823099505 2.118078 3.4747 0.000687 0.000343 Popularity -0.0312731524219015 0.090652 -0.345 0.730642 0.365321 FindingFriends 0.125401376884334 0.105545 1.1881 0.23685 0.118425 KnowingPeople 0.0641716190319723 0.074493 0.8614 0.390509 0.195254 Liked 0.0499017519535321 0.10854 0.4598 0.646427 0.323213 Celebrity 0.0373567347735441 0.187595 0.1991 0.842455 0.421227 WeightedSum -0.220050387130058 0.064136 -3.431 0.000797 0.000398 BelongingtoSports 0.0785349987054337 0.018313 4.2884 3.4e-05 1.7e-05 ParentalCriticism -0.043444033219829 0.075098 -0.5785 0.563883 0.281942 Multiple Linear Regression - Regression Statistics Multiple R 0.432247937595427 R-squared 0.186838279555500 Adjusted R-squared 0.139005237176411 F-TEST (value) 3.90605050949429 F-TEST (DF numerator) 8 F-TEST (DF denominator) 136 p-value 0.000352998523401538 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.20429805773299 Sum Squared Residuals 660.814470116257 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 12.6306477276902 1.36935227230984 2 18 15.6712108540218 2.3287891459782 3 11 14.5556800644922 -3.55568006449215 4 12 13.7123907102809 -1.71239071028086 5 16 13.5092945183624 2.49070548163755 6 18 14.4863078365733 3.51369216342671 7 14 13.593500906068 0.40649909393199 8 14 14.0600577765307 -0.0600577765306574 9 15 14.4917855282547 0.508214471745308 10 15 14.9150233754408 0.0849766245591556 11 17 15.2858917303716 1.71410826962837 12 19 13.0900448050298 5.90995519497021 13 10 13.2323758582539 -3.23237585825389 14 18 15.1970552390961 2.80294476090392 15 14 13.1381785314919 0.861821468508111 16 14 13.9917715501709 0.00822844982914775 17 17 16.0422593959187 0.957740604081346 18 14 13.8105358264869 0.189464173513147 19 16 13.9357890858978 2.06421091410224 20 18 13.9300681573623 4.06993184263772 21 14 13.7262746121695 0.273725387830465 22 12 12.6831359311601 -0.683135931160116 23 17 14.7696952441234 2.23030475587655 24 9 14.5189375158183 -5.51893751581828 25 16 14.3670868941374 1.63291310586262 26 14 14.0911456400813 -0.0911456400813096 27 11 14.5753523941706 -3.57535239417055 28 16 14.4616078941063 1.53839210589365 29 13 12.3850701065901 0.614929893409949 30 17 14.8303095701542 2.16969042984582 31 15 13.9098152243360 1.09018477566396 32 14 14.1020271080927 -0.102027108092653 33 16 13.9116430423609 2.08835695763911 34 9 13.0903109311337 -4.09031093113373 35 15 14.5583334197998 0.44166658020015 36 17 13.1606728968035 3.83932710319648 37 13 14.3545127631015 -1.35451276310150 38 15 14.3031909582799 0.696809041720058 39 16 14.1877252100837 1.81227478991631 40 16 13.5298402668616 2.47015973313835 41 12 13.215864856373 -1.21586485637300 42 11 13.2948129565828 -2.29481295658285 43 15 15.2925161847293 -0.292516184729268 44 17 14.1255393167085 2.87446068329151 45 13 13.5801242962764 -0.580124296276409 46 16 14.0635740074675 1.93642599253252 47 14 12.1677691978031 1.83223080219689 48 11 13.0135840392906 -2.01358403929058 49 12 13.2179470675665 -1.21794706756645 50 12 12.1337486814449 -0.133748681444940 51 15 14.8384437828057 0.161556217194319 52 16 14.7310083688659 1.26899163113415 53 15 14.1792164389136 0.820783561086443 54 12 14.6824299755909 -2.68242997559088 55 12 13.4472633566066 -1.44726335660660 56 8 13.1637759141025 -5.16377591410246 57 13 15.6359178491568 -2.63591784915680 58 11 12.4976831330759 -1.49768313307586 59 14 13.8428325827167 0.157167417283339 60 15 13.4768701991264 1.52312980087361 61 10 15.0015334687176 -5.00153346871761 62 11 13.5281970684520 -2.52819706845204 63 12 14.6511036793256 -2.65110367932557 64 15 12.7173438318843 2.28265616811568 65 15 14.170127471217 0.829872528783 66 14 15.2229102072091 -1.22291020720913 67 16 13.1157502273080 2.88424977269197 68 15 16.3805412291863 -1.38054122918627 69 15 15.1149056444681 -0.114905644468148 70 13 14.4493269759958 -1.44932697599577 71 17 15.2133356817351 1.78666431826486 72 13 13.6736123056363 -0.673612305636337 73 15 13.6719222370981 1.32807776290185 74 13 12.7955242059414 0.204475794058628 75 15 13.3658722428453 1.63412775715468 76 16 11.3244608371187 4.67553916288129 77 15 13.4835531775784 1.51644682242161 78 16 13.5377503495359 2.46224965046407 79 15 13.3303393629675 1.66966063703248 80 14 13.8033463859710 0.19665361402898 81 15 13.7250302175393 1.27496978246073 82 7 14.1976137481222 -7.19761374812221 83 17 14.3418239380411 2.6581760619589 84 13 12.9612992942113 0.0387007057887043 85 15 14.4767099997257 0.523290000274294 86 14 15.5170480641489 -1.51704806414889 87 13 14.4464043795154 -1.44640437951538 88 16 15.0908668632488 0.909133136751205 89 12 13.5123923112252 -1.51239231122517 90 14 14.0184543050635 -0.0184543050635022 91 17 14.7134506619271 2.28654933807286 92 15 14.2429214338353 0.75707856616466 93 17 15.1939180135887 1.80608198641128 94 12 14.5707264754630 -2.57072647546302 95 16 14.9321417944473 1.06785820555272 96 11 13.3548781289606 -2.35487812896058 97 15 14.5916024696945 0.408397530305549 98 9 13.2045493226285 -4.20454932262847 99 16 14.5314703199834 1.46852968001657 100 10 12.1996838587030 -2.19968385870295 101 10 11.6404511988986 -1.64045119889855 102 15 15.1155685243875 -0.11556852438751 103 11 12.5692849764924 -1.56928497649244 104 13 15.3163729002433 -2.3163729002433 105 14 13.4377422383947 0.562257761605252 106 18 14.0648065687236 3.93519343127644 107 16 15.1994141847324 0.80058581526756 108 14 12.4587578251036 1.54124217489639 109 14 14.0538509401887 -0.053850940188737 110 14 14.5339876395488 -0.533987639548811 111 14 15.6563292165257 -1.65632921652571 112 12 12.3230772073644 -0.323077207364429 113 14 14.6040619296622 -0.60406192966222 114 15 16.4688541909947 -1.46885419099471 115 15 14.0425625759276 0.957437424072445 116 13 14.9055139128044 -1.90551391280445 117 17 16.3043184006375 0.695681599362526 118 17 15.9623881653838 1.03761183461622 119 19 16.1555505134566 2.84444948654337 120 15 14.0874554188901 0.91254458110993 121 13 13.6902410989869 -0.690241098986853 122 9 12.8002569554608 -3.80025695546077 123 15 14.6860055346038 0.313994465396165 124 15 13.9964621109498 1.00353788905025 125 16 15.8084484348203 0.191551565179657 126 11 12.3320729711756 -1.33207297117563 127 14 13.9530121789983 0.046987821001694 128 11 12.2086825899907 -1.20868258999070 129 15 13.5635798824317 1.43642011756828 130 13 14.0662310454359 -1.06623104543591 131 16 13.9845490291049 2.01545097089508 132 14 14.8209861057312 -0.820986105731151 133 15 14.6093128092856 0.390687190714361 134 16 16.0856483530275 -0.0856483530275327 135 16 14.8132095976584 1.18679040234155 136 11 13.9799157282784 -2.97991572827842 137 13 15.0929140244885 -2.09291402448847 138 16 14.3670868941374 1.63291310586262 139 12 15.4450075085444 -3.4450075085444 140 9 13.3108996936204 -4.31089969362043 141 13 14.1870981451331 -1.18709814513312 142 13 12.9612992942113 0.0387007057887043 143 14 13.2868303320654 0.713169667934567 144 19 16.1555505134566 2.84444948654337 145 13 15.1224291434151 -2.12242914341513 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.902254625636545 0.19549074872691 0.097745374363455 13 0.829710707006944 0.340578585986111 0.170289292993056 14 0.761563568937873 0.476872862124254 0.238436431062127 15 0.671388381096139 0.657223237807723 0.328611618903861 16 0.593801669251122 0.812396661497756 0.406198330748878 17 0.488507942223145 0.977015884446289 0.511492057776855 18 0.597000033812908 0.805999932374185 0.402999966187092 19 0.518305726563826 0.963388546872347 0.481694273436174 20 0.496275243047289 0.992550486094579 0.503724756952711 21 0.425754556558919 0.851509113117838 0.574245443441081 22 0.385710954598167 0.771421909196333 0.614289045401833 23 0.324298322058728 0.648596644117456 0.675701677941272 24 0.574428041453988 0.851143917092023 0.425571958546012 25 0.611818091579303 0.776363816841395 0.388181908420697 26 0.601894371522166 0.796211256955668 0.398105628477834 27 0.693698248029931 0.612603503940138 0.306301751970069 28 0.636126315638223 0.727747368723554 0.363873684361777 29 0.569656886130811 0.860686227738377 0.430343113869189 30 0.56837220533284 0.86325558933432 0.43162779466716 31 0.537625598457733 0.924748803084535 0.462374401542267 32 0.474704454463118 0.949408908926235 0.525295545536882 33 0.458390259689095 0.916780519378191 0.541609740310905 34 0.72397749478046 0.55204501043908 0.27602250521954 35 0.672834802360713 0.654330395278573 0.327165197639287 36 0.771546604811608 0.456906790376784 0.228453395188392 37 0.729808394462186 0.540383211075628 0.270191605537814 38 0.688264664448475 0.62347067110305 0.311735335551525 39 0.653039991309791 0.693920017380418 0.346960008690209 40 0.762571293122957 0.474857413754086 0.237428706877043 41 0.721007907135754 0.557984185728492 0.278992092864246 42 0.779176524357817 0.441646951284365 0.220823475642183 43 0.73549509609132 0.529009807817359 0.264504903908679 44 0.757632165105627 0.484735669788745 0.242367834894373 45 0.71430375332109 0.571392493357822 0.285696246678911 46 0.686332773168292 0.627334453663415 0.313667226831708 47 0.68503371766299 0.629932564674021 0.314966282337011 48 0.685031141966102 0.629937716067796 0.314968858033898 49 0.643980818914443 0.712038362171114 0.356019181085557 50 0.602110299708202 0.795779400583596 0.397889700291798 51 0.550139305360479 0.899721389279042 0.449860694639521 52 0.509232595900422 0.981534808199156 0.490767404099578 53 0.461807058304095 0.92361411660819 0.538192941695905 54 0.518505058417418 0.962989883165164 0.481494941582582 55 0.477640823987335 0.95528164797467 0.522359176012665 56 0.724616848083646 0.550766303832707 0.275383151916354 57 0.822535950365763 0.354928099268475 0.177464049634237 58 0.801919251275956 0.396161497448088 0.198080748724044 59 0.765388481999536 0.469223036000929 0.234611518000464 60 0.760916829123733 0.478166341752534 0.239083170876267 61 0.923841810320448 0.152316379359105 0.0761581896795523 62 0.92667654442727 0.146646911145461 0.0733234555727303 63 0.935238071891427 0.129523856217146 0.0647619281085728 64 0.935389864187282 0.129220271625435 0.0646101358127176 65 0.920315070494282 0.159369859011436 0.0796849295057181 66 0.905505396059244 0.188989207881513 0.0944946039407564 67 0.921141917096832 0.157716165806335 0.0788580829031677 68 0.909195139076365 0.181609721847270 0.0908048609236348 69 0.88694665212673 0.226106695746539 0.113053347873269 70 0.872237017158566 0.255525965682867 0.127762982841434 71 0.865337721023961 0.269324557952078 0.134662278976039 72 0.838935809693269 0.322128380613463 0.161064190306731 73 0.819658310445945 0.360683379108111 0.180341689554055 74 0.78506618274364 0.429867634512721 0.214933817256360 75 0.77067066008665 0.458658679826701 0.229329339913351 76 0.893997594918527 0.212004810162946 0.106002405081473 77 0.885749023187944 0.228501953624112 0.114250976812056 78 0.887804819943333 0.224390360113334 0.112195180056667 79 0.88311730534255 0.2337653893149 0.11688269465745 80 0.858605917677976 0.282788164644048 0.141394082322024 81 0.843790707587463 0.312418584825075 0.156209292412537 82 0.989441476157166 0.0211170476856684 0.0105585238428342 83 0.991059534512626 0.0178809309747478 0.0089404654873739 84 0.987833256766388 0.0243334864672234 0.0121667432336117 85 0.98381130681574 0.0323773863685215 0.0161886931842607 86 0.980887433078495 0.0382251338430094 0.0191125669215047 87 0.97660219127703 0.046795617445941 0.0233978087229705 88 0.970824676899613 0.0583506462007731 0.0291753231003866 89 0.96490068222648 0.0701986355470389 0.0350993177735195 90 0.953495296906316 0.0930094061873684 0.0465047030936842 91 0.962590980326117 0.0748180393477666 0.0374090196738833 92 0.95342074407335 0.0931585118533004 0.0465792559266502 93 0.951902481028253 0.0961950379434938 0.0480975189717469 94 0.957388520496344 0.0852229590073119 0.0426114795036559 95 0.955776117764062 0.0884477644718765 0.0442238822359383 96 0.952445556317433 0.095108887365134 0.047554443682567 97 0.939084307545245 0.121831384909511 0.0609156924547554 98 0.965061870518302 0.0698762589633965 0.0349381294816982 99 0.958051737745272 0.0838965245094558 0.0419482622547279 100 0.951464179260288 0.097071641479423 0.0485358207397115 101 0.939834342625024 0.120331314749951 0.0601656573749757 102 0.920451369739505 0.159097260520991 0.0795486302604953 103 0.905838976771938 0.188322046456123 0.0941610232280616 104 0.918697531651537 0.162604936696927 0.0813024683484635 105 0.895435396681718 0.209129206636564 0.104564603318282 106 0.952660231099157 0.0946795378016851 0.0473397689008426 107 0.94317940222377 0.11364119555246 0.05682059777623 108 0.954685134779126 0.090629730441749 0.0453148652208745 109 0.937159514770156 0.125680970459687 0.0628404852298436 110 0.91966832243393 0.160663355132141 0.0803316775660707 111 0.898691672529645 0.202616654940711 0.101308327470356 112 0.865882680344878 0.268234639310245 0.134117319655122 113 0.837757303578697 0.324485392842607 0.162242696421303 114 0.819454960089583 0.361090079820834 0.180545039910417 115 0.794306744383695 0.411386511232609 0.205693255616305 116 0.77292920184099 0.454141596318022 0.227070798159011 117 0.72614782275737 0.547704354485259 0.273852177242630 118 0.673093020315873 0.653813959368254 0.326906979684127 119 0.670052480339441 0.659895039321119 0.329947519660559 120 0.638298204379347 0.723403591241306 0.361701795620653 121 0.56364441766825 0.872711164663499 0.436355582331749 122 0.600165491183795 0.799669017632409 0.399834508816204 123 0.518115892770891 0.963768214458217 0.481884107229109 124 0.454808988729314 0.909617977458627 0.545191011270686 125 0.373553601769184 0.747107203538368 0.626446398230816 126 0.297158771015386 0.594317542030772 0.702841228984614 127 0.290537249894724 0.581074499789447 0.709462750105276 128 0.213060857333020 0.426121714666039 0.78693914266698 129 0.239243363673153 0.478486727346306 0.760756636326847 130 0.171584672081938 0.343169344163875 0.828415327918062 131 0.190942777290352 0.381885554580704 0.809057222709648 132 0.222328777773038 0.444657555546076 0.777671222226962 133 0.125795673134787 0.251591346269573 0.874204326865213 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 6 0.0491803278688525 OK 10% type I error level 20 0.163934426229508 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/109bm31290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/109bm31290528231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/1ks7s1290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/1ks7s1290528231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/2ks7s1290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/2ks7s1290528231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/3ks7s1290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/3ks7s1290528231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/4djod1290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/4djod1290528231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/5djod1290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/5djod1290528231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/6djod1290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/6djod1290528231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/75b5y1290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/75b5y1290528231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/8ykmi1290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/8ykmi1290528231.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/9ykmi1290528231.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290528232ewo56fymx517bmk/9ykmi1290528231.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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