*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: Thu, 02 Dec 2010 22:52:33 +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/02/t12913302288v0tyc4n66wwhj2.htm/, Retrieved Thu, 02 Dec 2010 23:50:40 +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/02/t12913302288v0tyc4n66wwhj2.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 «

9 41 38 13 12 14 12 53 32 9 39 32 16 11 18 11 83 51 9 30 35 19 15 11 14 66 42 9 31 33 15 6 12 12 67 41 9 34 37 14 13 16 21 76 46 9 35 29 13 10 18 12 78 47 9 39 31 19 12 14 22 53 37 9 34 36 15 14 14 11 80 49 9 36 35 14 12 15 10 74 45 9 37 38 15 9 15 13 76 47 9 38 31 16 10 17 10 79 49 9 36 34 16 12 19 8 54 33 9 38 35 16 12 10 15 67 42 9 39 38 16 11 16 14 54 33 9 33 37 17 15 18 10 87 53 9 32 33 15 12 14 14 58 36 9 36 32 15 10 14 14 75 45 9 38 38 20 12 17 11 88 54 9 39 38 18 11 14 10 64 41 9 32 32 16 12 16 13 57 36 9 32 33 16 11 18 9.5 66 41 9 31 31 16 12 11 14 68 44 9 39 38 19 13 14 12 54 33 9 37 39 16 11 12 14 56 37 9 39 32 17 12 17 11 86 52 9 41 32 17 13 9 9 80 47 9 36 35 16 10 16 11 76 43 9 33 37 15 14 14 15 69 44 9 33 33 16 12 15 14 78 45 9 34 33 14 10 11 13 67 44 9 31 31 15 12 16 9 80 49 9 27 32 12 8 13 15 54 33 9 37 31 14 10 17 10 71 43 9 34 37 16 12 15 11 84 54 9 34 30 14 12 14 13 74 42 9 32 33 10 7 16 8 71 44 9 29 31 10 9 9 20 63 37 9 36 33 14 12 15 12 71 43 9 29 31 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 16 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 4.00445406989737 + 0.161768138570369month[t] + 0.0339720452340411Connected[t] + 0.0426648655196235Separate[t] + 0.553914374083271Software[t] + 0.0693843908517855Happiness[t] -0.0309724601101621Depression[t] + 0.0210589104920521Belonging[t] -0.0218367544310276Belonging_Final[t] -0.00651732044274797t + 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) 4.00445406989737 3.893744 1.0284 0.304725 0.152362 month 0.161768138570369 0.408738 0.3958 0.692604 0.346302 Connected 0.0339720452340411 0.034675 0.9797 0.328147 0.164074 Separate 0.0426648655196235 0.035196 1.2122 0.226558 0.113279 Software 0.553914374083271 0.054661 10.1337 0 0 Happiness 0.0693843908517855 0.058102 1.1942 0.233522 0.116761 Depression -0.0309724601101621 0.042456 -0.7295 0.466353 0.233176 Belonging 0.0210589104920521 0.037979 0.5545 0.57973 0.289865 Belonging_Final -0.0218367544310276 0.056419 -0.387 0.699047 0.349524 t -0.00651732044274797 0.004332 -1.5043 0.13374 0.06687 Multiple Linear Regression - Regression Statistics Multiple R 0.667804237836336 R-squared 0.445962500072170 Adjusted R-squared 0.426331250074727 F-TEST (value) 22.7169691247506 F-TEST (DF numerator) 9 F-TEST (DF denominator) 254 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.86017625008154 Sum Squared Residuals 878.904943067328 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.131999294817 -3.13199929481699 2 16 15.773013320795 0.226986679205006 3 19 17.0643208813592 1.93567911864081 4 15 12.195441484357 2.80455851564301 5 14 16.4180322249668 -2.41803222496677 6 13 14.8802268925994 -1.88022689259937 7 19 15.3073888497988 3.69261115020122 8 15 17.0994109702753 -2.09941097027535 9 14 16.0716945323483 -2.07169453234826 10 15 14.4709276632402 0.529072336759826 11 16 15.0048320881255 0.995167911874469 12 16 16.1898230324591 -0.189823032459148 13 16 15.5298829760843 0.47011702391567 14 16 15.5014616820547 0.498538317945331 15 17 17.9849723007825 -0.984972300782522 16 15 15.4711693679876 -0.471169367987593 17 15 14.6115173032805 0.388482696719519 18 20 16.4150676139934 3.58493238600663 19 18 15.4898912080503 2.51010879194969 20 16 15.5511175520187 0.448882447981341 21 16 15.3608695373747 0.639130462625267 22 16 15.1405055659748 0.859494434025239 23 19 16.4738106847532 2.52618931524677 24 16 15.0882424925316 0.911757507468418 25 17 16.1489849108884 0.851015089111614 26 17 16.2540261576059 0.745973842394144 27 16 14.9707572768000 1.02924272319996 28 15 16.7314032980079 -1.73140329800789 29 16 15.7144480582795 0.28555194172051 30 14 14.1776976706257 -0.177697670625716 31 15 15.7271570905493 -0.727157090549255 32 12 12.8196274232436 -0.81962742324364 33 14 14.7900282358008 -0.790028235800783 34 16 15.9092330167818 0.0907669832181634 35 14 15.5241842748814 -1.52418427488142 36 10 12.9949264320293 -2.99492643202928 37 10 13.0360177328080 -3.03601773280804 38 14 15.7159143656349 -1.71591436563490 39 16 14.5189322404391 1.48106775956085 40 16 14.4639740033125 1.53602599668751 41 16 14.6922614387991 1.30773856120088 42 14 15.6917393515645 -1.69173935156446 43 20 17.4239904078573 2.57600959214275 44 14 14.1268333106255 -0.126833310625486 45 14 14.4277755307962 -0.427775530796168 46 11 15.4769010866658 -4.47690108666582 47 14 16.5016700566974 -2.50167005669743 48 15 15.0872733557269 -0.087273355726934 49 16 15.4344986815598 0.565501318440216 50 14 15.5957515567831 -1.59575155678312 51 16 16.9470055618408 -0.947005561840803 52 14 14.1029056640276 -0.102905664027613 53 12 14.9814432966391 -2.98144329663915 54 16 15.785793299267 0.214206700732997 55 9 11.3563715377051 -2.35637153770508 56 14 12.3349345138998 1.66506548610016 57 16 15.7945814318002 0.205418568199844 58 16 15.4209469984546 0.579053001545421 59 15 15.0830124726959 -0.0830124726959017 60 16 14.1512679246356 1.84873207536441 61 12 11.5069610190735 0.493038980926456 62 16 15.6140188033833 0.385981196616663 63 16 16.4810046021701 -0.481004602170093 64 14 14.6386116076605 -0.638611607660451 65 16 15.2160664980086 0.7839335019914 66 17 16.1283594964296 0.871640503570416 67 18 16.3659810285842 1.63401897141582 68 18 14.5460652096084 3.45393479039163 69 12 15.9859557929281 -3.98595579292812 70 16 15.7235896801084 0.276410319891618 71 10 13.4364628729273 -3.43646287292727 72 14 14.9824764129632 -0.982476412963164 73 18 17.0158830121805 0.984116987819492 74 18 17.2454880935873 0.754511906412746 75 16 15.3257205980238 0.674279401976158 76 17 13.5757520187901 3.42424798120991 77 16 16.4687902994353 -0.468790299435257 78 16 14.5522158332352 1.44778416676477 79 13 15.2614002582591 -2.26140025825906 80 16 15.1964525622985 0.803547437701546 81 16 15.7574496667773 0.242550333222654 82 16 15.7768516930372 0.223148306962762 83 15 15.7298773413515 -0.729877341351537 84 15 14.9299702304001 0.0700297695999293 85 16 14.2149434227545 1.78505657724555 86 14 14.2366309572854 -0.236630957285364 87 16 15.4094170749233 0.590582925076748 88 16 14.9000272038213 1.09997279617871 89 15 14.5575243875150 0.442475612484963 90 12 13.9195769686057 -1.91957696860565 91 17 16.7800226813811 0.219977318618857 92 16 15.8629648187689 0.137035181231110 93 15 15.130179843395 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0.82856258629681 118 13 14.7890480129649 -1.78904801296490 119 16 15.5214947103640 0.478505289635981 120 13 14.4173866932526 -1.41738669325258 121 16 15.3732648403476 0.626735159652424 122 13 15.8239894208261 -2.82398942082606 123 16 16.8206727627472 -0.820672762747186 124 15 15.8151943614052 -0.815194361405174 125 16 16.7758864663847 -0.775886466384696 126 15 14.6563176955803 0.343682304419720 127 17 15.5135458446765 1.48645415532348 128 15 13.9561905870924 1.04380941290757 129 12 14.6649696205487 -2.66496962054875 130 16 13.9484125272074 2.05158747279264 131 10 13.6993457863953 -3.69934578639529 132 16 13.4787326491481 2.52126735085192 133 12 14.1171191044060 -2.11711910440598 134 14 15.4969825827167 -1.49698258271669 135 15 15.0228514514540 -0.0228514514539678 136 13 12.0782835373044 0.921716462695573 137 15 14.4179752062836 0.582024793716389 138 11 13.4148843246345 -2.41488432463447 139 12 12.9615388133991 -0.961538813399098 140 11 13.3294291078386 -2.32942910783858 141 16 12.8198286730183 3.18017132698169 142 15 13.6114765181638 1.38852348183617 143 17 16.7647361618203 0.235263838179739 144 16 14.0972664814835 1.90273351851650 145 10 13.2326063570416 -3.23260635704162 146 18 15.4231808220058 2.57681917799422 147 13 14.8643149057299 -1.86431490572987 148 16 14.7811040097575 1.21889599024249 149 13 12.7593738938659 0.240626106134064 150 10 12.8479456212172 -2.8479456212172 151 15 15.8571245856987 -0.85712458569868 152 16 13.8243203686565 2.17567963134345 153 16 11.817790540179 4.18220945982101 154 14 12.1796252670648 1.8203747329352 155 10 12.3603674449609 -2.3603674449609 156 17 16.3563968526025 0.643603147397474 157 13 11.6399592761047 1.36004072389525 158 15 13.76067097381 1.23932902619001 159 16 14.4777838001372 1.52221619986284 160 12 12.6712686826820 -0.671268682682037 161 13 12.5501583930836 0.449841606916437 162 13 12.6951856659235 0.304814334076526 163 12 12.5325265824158 -0.532526582415784 164 17 16.2944365499899 0.705563450010119 165 15 13.7802694966019 1.21973050339809 166 10 11.6960484317299 -1.69604843172991 167 14 14.4098138706111 -0.409813870611069 168 11 14.2824014929904 -3.28240149299045 169 13 14.8696564507497 -1.86965645074970 170 16 14.5277256233795 1.4722743766205 171 12 10.5781596972200 1.42184030277997 172 16 15.4053957124387 0.594604287561291 173 12 13.9507326026571 -1.95073260265711 174 9 11.4327559786395 -2.43275597863949 175 12 14.9708875013237 -2.97088750132369 176 15 14.6153118153365 0.384688184663523 177 12 12.3484847331071 -0.348484733107104 178 12 12.7410235452396 -0.741023545239609 179 14 13.8482569329381 0.151743067061868 180 12 13.4363825724819 -1.43638257248190 181 16 15.0574225512253 0.94257744877469 182 11 11.5290900782481 -0.52909007824815 183 19 16.7023934664027 2.29760653359726 184 15 15.1861080347248 -0.186108034724758 185 8 14.6098477634635 -6.60984776346354 186 16 14.7948754284262 1.20512457157383 187 17 14.4889678086466 2.51103219135342 188 12 12.4492788886035 -0.449278888603544 189 11 11.5258253233485 -0.525825323348466 190 11 10.4839919409227 0.51600805907726 191 14 14.7297291026958 -0.72972910269576 192 16 15.4573408606036 0.542659139396387 193 12 9.79494997958053 2.20505002041947 194 16 14.0582376070539 1.94176239294607 195 13 13.6671267744826 -0.667126774482572 196 15 15.0059615481752 -0.00596154817517691 197 16 12.9612756487799 3.03872435122008 198 16 15.0216959506926 0.978304049307385 199 14 12.4654951689653 1.53450483103466 200 16 14.5360348798980 1.46396512010202 201 16 14.0101773215679 1.98982267843206 202 14 13.3505146449400 0.64948535505996 203 11 13.4248894641780 -2.42488946417804 204 12 14.4629453484512 -2.46294534845120 205 15 12.7281807329234 2.27181926707665 206 15 14.4392077029054 0.560792297094569 207 16 14.4841958335770 1.51580416642298 208 16 14.8639174831779 1.13608251682205 209 11 13.5735507320522 -2.57355073205221 210 15 13.9329916342196 1.06700836578037 211 12 14.1909393598993 -2.19093935989935 212 12 15.7003657756719 -3.7003657756719 213 15 14.0984721484565 0.90152785154354 214 15 12.0898039545762 2.9101960454238 215 16 14.4861173675814 1.51388263241863 216 14 13.0447911555702 0.955208844429784 217 17 14.5703847036008 2.42961529639919 218 14 13.8898769613098 0.110123038690205 219 13 11.8763407163770 1.12365928362303 220 15 15.0824598206262 -0.0824598206262444 221 13 14.5750556822787 -1.57505568227875 222 14 13.9860332277979 0.0139667722021436 223 15 14.1866032608968 0.813396739103202 224 12 13.0451003628764 -1.04510036287638 225 13 12.5277927132757 0.472207286724271 226 8 11.6960459918855 -3.69604599188549 227 14 13.6561993287026 0.34380067129741 228 14 12.9000716996087 1.09992830039132 229 11 12.1551096302894 -1.15510963028936 230 12 12.8141987020800 -0.814198702080019 231 13 11.1927984749469 1.80720152505309 232 10 13.1324013386614 -3.13240133866138 233 16 11.3238724214746 4.67612757852538 234 18 15.7016623752784 2.29833762472164 235 13 13.6986247386433 -0.698624738643332 236 11 13.1953213217862 -2.19532132178623 237 4 10.9144168771812 -6.91441687718123 238 13 14.0863865432717 -1.08638654327175 239 16 14.1114446024490 1.88855539755096 240 10 11.5810420842532 -1.58104208425324 241 12 12.1457895056583 -0.145789505658296 242 12 13.3223330284657 -1.32233302846566 243 10 8.80195508184795 1.19804491815205 244 13 10.9675970396727 2.03240296032730 245 15 13.4825144280370 1.51748557196297 246 12 11.7701175979104 0.229882402089584 247 14 12.6701662045844 1.32983379541564 248 10 12.2934478887145 -2.29344788871453 249 12 10.6014073663047 1.39859263369527 250 12 11.5045860621479 0.495413937852056 251 11 11.6933270811220 -0.693327081122031 252 10 11.4970254698553 -1.49702546985534 253 12 11.2277722925804 0.772227707419619 254 16 12.6330294634868 3.36697053651322 255 12 13.1033064447535 -1.10330644475347 256 14 13.6115101268512 0.388489873148829 257 16 14.1380220385243 1.86197796147568 258 14 11.4512965204411 2.54870347955891 259 13 13.9883658481621 -0.988365848162086 260 4 9.27855351815033 -5.27855351815033 261 15 13.4908178141533 1.50918218584669 262 11 14.7054478781160 -3.70544787811602 263 11 11.1003815456158 -0.100381545615756 264 14 12.5759984379471 1.42400156205287 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.309807656286817 0.619615312573634 0.690192343713183 14 0.2982458895084 0.5964917790168 0.7017541104916 15 0.180880645654023 0.361761291308045 0.819119354345977 16 0.137959527969735 0.275919055939470 0.862040472030265 17 0.143729595500073 0.287459191000146 0.856270404499927 18 0.295672611917276 0.591345223834551 0.704327388082725 19 0.245953051754568 0.491906103509136 0.754046948245432 20 0.197531582642351 0.395063165284702 0.802468417357649 21 0.154638598434060 0.309277196868121 0.84536140156594 22 0.181179794070588 0.362359588141176 0.818820205929412 23 0.292370722019794 0.584741444039587 0.707629277980206 24 0.413563053247267 0.827126106494533 0.586436946752734 25 0.343871514454900 0.687743028909799 0.6561284855451 26 0.292745395722881 0.585490791445763 0.707254604277119 27 0.280275008418916 0.560550016837832 0.719724991581084 28 0.396379429891148 0.792758859782295 0.603620570108852 29 0.342705495061225 0.68541099012245 0.657294504938775 30 0.453590892318243 0.907181784636485 0.546409107681757 31 0.4098203042314 0.8196406084628 0.5901796957686 32 0.379700407782805 0.75940081556561 0.620299592217195 33 0.362199175090739 0.724398350181479 0.637800824909261 34 0.323061419276707 0.646122838553414 0.676938580723293 35 0.27741937114134 0.55483874228268 0.72258062885866 36 0.412599374054753 0.825198748109507 0.587400625945247 37 0.440486741081803 0.880973482163606 0.559513258918197 38 0.414751240937735 0.82950248187547 0.585248759062265 39 0.458996581775578 0.917993163551155 0.541003418224423 40 0.438077281087412 0.876154562174824 0.561922718912588 41 0.397606632447526 0.795213264895052 0.602393367552474 42 0.357011020557362 0.714022041114724 0.642988979442638 43 0.375803323977979 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229 0.00290095626256910 0.00580191252513821 0.997099043737431 230 0.00210006526868233 0.00420013053736466 0.997899934731318 231 0.00187435006150138 0.00374870012300276 0.998125649938499 232 0.00445268431966201 0.00890536863932401 0.995547315680338 233 0.0186513607143556 0.0373027214287112 0.981348639285644 234 0.0287056236663921 0.0574112473327842 0.971294376333608 235 0.0202408156875338 0.0404816313750676 0.979759184312466 236 0.0166385178465637 0.0332770356931275 0.983361482153436 237 0.158811527145599 0.317623054291199 0.8411884728544 238 0.122053659592906 0.244107319185811 0.877946340407095 239 0.0996048696320387 0.199209739264077 0.900395130367961 240 0.0750857716468304 0.150171543293661 0.92491422835317 241 0.0646426417753595 0.129285283550719 0.93535735822464 242 0.102490655553289 0.204981311106577 0.897509344446711 243 0.081491720832899 0.162983441665798 0.9185082791671 244 0.0842682626125305 0.168536525225061 0.91573173738747 245 0.0665871193041568 0.133174238608314 0.933412880695843 246 0.0544356840043543 0.108871368008709 0.945564315995646 247 0.0329907544098212 0.0659815088196424 0.967009245590179 248 0.0266391640759625 0.053278328151925 0.973360835924038 249 0.0224913576759628 0.0449827153519257 0.977508642324037 250 0.0664473388463356 0.132894677692671 0.933552661153664 251 0.0486972483238257 0.0973944966476515 0.951302751676174 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 16 0.0669456066945607 NOK 5% type I error level 98 0.410041841004184 NOK 10% type I error level 133 0.556485355648536 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/105gcb1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/105gcb1291330335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/1yxxh1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/1yxxh1291330335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/2yxxh1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/2yxxh1291330335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/39pfk1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/39pfk1291330335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/49pfk1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/49pfk1291330335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/59pfk1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/59pfk1291330335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/6jyen1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/6jyen1291330335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/7cpdq1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/7cpdq1291330335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/8cpdq1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/8cpdq1291330335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/9cpdq1291330335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913302288v0tyc4n66wwhj2/9cpdq1291330335.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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