Multiple Regression Analysis

*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: Wed, 15 Dec 2010 20:12:00 +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/15/t129244398720b7p5dhx85aa7g.htm/, Retrieved Wed, 15 Dec 2010 21:13:10 +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/15/t129244398720b7p5dhx85aa7g.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 «

13 26 9 15 25 25 16 20 9 15 25 24 19 21 9 14 19 21 15 31 14 10 18 23 14 21 8 10 18 17 13 18 8 12 22 19 19 26 11 18 29 18 15 22 10 12 26 27 14 22 9 14 25 23 15 29 15 18 23 23 16 15 14 9 23 29 16 16 11 11 23 21 16 24 14 11 24 26 17 17 6 17 30 25 15 19 20 8 19 25 15 22 9 16 24 23 20 31 10 21 32 26 18 28 8 24 30 20 16 38 11 21 29 29 16 26 14 14 17 24 19 25 11 7 25 23 16 25 16 18 26 24 17 29 14 18 26 30 17 28 11 13 25 22 16 15 11 11 23 22 15 18 12 13 21 13 14 21 9 13 19 24 15 25 7 18 35 17 12 23 13 14 19 24 14 23 10 12 20 21 16 19 9 9 21 23 14 18 9 12 21 24 7 18 13 8 24 24 10 26 16 5 23 24 14 18 12 10 19 23 16 18 6 11 17 26 16 28 14 11 24 24 16 17 14 12 15 21 14 29 10 12 25 23 20 12 4 15 27 28 14 25 12 12 29 23 14 28 12 16 27 22 11 20 14 14 18 24 15 17 9 17 25 21 16 17 9 13 22 23 14 20 10 10 26 23 16 31 14 17 23 20 14 21 10 12 16 23 12 19 9 13 27 21 16 23 14 13 25 27 9 15 8 11 14 12 14 24 9 13 19 15 16 28 8 12 20 22 16 16 9 12 16 21 15 19 9 12 18 21 16 21 9 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 13.1917916230188 + 0.00507035408271898Concern[t] -0.278495426258174Doubts[t] + 0.102339576505264Expectations[t] + 0.0218241062211261Standards[t] + 0.149071998317463Organization[t] -0.00581208015894894t + 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) 13.1917916230188 1.538649 8.5736 0 0 Concern 0.00507035408271898 0.037499 0.1352 0.892634 0.446317 Doubts -0.278495426258174 0.068266 -4.0796 7.5e-05 3.7e-05 Expectations 0.102339576505264 0.054077 1.8925 0.060448 0.030224 Standards 0.0218241062211261 0.048563 0.4494 0.653824 0.326912 Organization 0.149071998317463 0.048734 3.0589 0.002653 0.001327 t -0.00581208015894894 0.003953 -1.4702 0.143708 0.071854 Multiple Linear Regression - Regression Statistics Multiple R 0.467941938785642 R-squared 0.218969658074466 Adjusted R-squared 0.186199154217451 F-TEST (value) 6.6819130712752 F-TEST (DF numerator) 6 F-TEST (DF denominator) 143 p-value 2.98374156970649e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.05042365740092 Sum Squared Residuals 601.205916000599 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.6188461737307 -3.6188461737307 2 16 16.433539970758 -0.433539970757996 3 19 15.7522980358974 3.24770196410265 4 15 14.2716739496675 0.72832605033253 5 14 14.9916988963256 -0.991698896325595 6 13 15.5607953284484 -2.56079532844845 7 19 15.3777940064387 3.62220599356127 8 15 16.2923341433693 -1.29233414336929 9 14 16.1515845429881 -2.15158454298806 10 15 14.8760024774379 0.123997522562093 11 16 15.0510766677365 0.94892333226353 12 16 14.8979243869056 1.10207561309442 13 16 14.8643729584423 1.13562704155769 14 17 17.6469419078106 -0.646941907810596 15 15 12.5912132112229 2.40878678877711 16 15 16.2937550286648 -1.29375502866482 17 20 17.1885874362399 2.81141256376011 18 18 17.0934936735179 0.906506326482109 19 16 17.3157040045319 -1.31570400453186 20 16 14.6899350948281 1.31006490517191 21 19 14.8236827552756 4.17631724472436 22 16 14.7220249899223 1.27797501007769 23 17 16.1879171685154 0.812082831484633 24 17 15.2864230377611 1.71357696223893 25 16 14.966368989074 1.03363101092601 26 15 13.5166555006161 1.48334449938387 27 14 15.9576845305297 -1.95768453052971 28 15 16.3465243130601 -1.34652431306008 29 12 14.9445589498498 -2.94455894984981 30 14 15.1441621067236 -1.1441621067236 31 16 15.4095134098322 0.590486590167794 32 14 15.8547217034238 -1.85472170342379 33 7 14.3910419308745 -7.39104193087447 34 10 13.2614635688658 -3.26146356886583 35 14 14.6043998204022 -0.60439982040218 36 16 16.7754676568077 -0.775467656807679 37 16 14.4470204543235 1.55297954567652 38 16 13.8441411048174 2.15585889518264 39 14 15.5295400375299 -1.52954003752993 40 20 18.2045314290592 1.79546857094084 41 14 15.0279400332493 -1.02794003324931 42 14 15.2539771105999 -1.25397711059986 43 11 14.5476592328971 -3.54765923289707 44 15 15.9316846998921 -0.93168469989212 45 16 15.7491859916837 0.250814008316335 46 14 15.2603672428834 -1.26036724288341 47 16 14.4000360745228 1.59996392547725 48 14 15.2402515274475 -1.2402515274475 49 12 15.547054913684 -3.54705491368401 50 16 15.0198308960276 0.980169103972404 51 9 13.9636042445511 -4.96360424455107 52 14 14.485945603947 -0.485945603946969 53 16 15.7418988843152 0.258101115684824 54 16 15.1603787057035 0.839621294296542 55 15 15.2134259002349 -0.213425900234918 56 16 14.8489602252927 1.15103977470734 57 12 13.5419603216229 -1.54196032162286 58 16 16.5257657424622 -0.525765742462179 59 16 16.176343502517 -0.176343502517003 60 14 16.3951085305603 -2.39510853056028 61 16 12.6004479962679 3.39955200373214 62 17 15.9847966636491 1.01520333635086 63 18 14.7078404748236 3.29215952517635 64 18 15.4226482646647 2.57735173533533 65 12 14.5023541910462 -2.50235419104622 66 16 15.8665849409177 0.133415059082348 67 10 14.3924286389481 -4.3924286389481 68 14 12.7112276902394 1.28877230976062 69 18 15.4161695346175 2.58383046538255 70 18 16.2668456023684 1.73315439763157 71 16 15.5325781083834 0.46742189161659 72 16 15.4879126256698 0.512087374330196 73 16 14.7250400708633 1.27495992913671 74 13 14.6772848128695 -1.67728481286954 75 16 15.0606743409731 0.939325659026948 76 16 14.7732011509984 1.22679884900157 77 20 15.9431248688009 4.05687513119906 78 16 15.2376733072732 0.762326692726783 79 15 12.8109606543201 2.18903934567988 80 15 15.2901684502364 -0.290168450236375 81 16 15.7942574990226 0.205742500977424 82 14 14.0343154660725 -0.0343154660724661 83 15 13.2233972099907 1.77660279000925 84 12 14.9075084558678 -2.90750845586783 85 17 15.95269709246 1.04730290753996 86 16 15.1280480771863 0.871951922813655 87 15 13.0441233469337 1.95587665306625 88 13 14.3138981661038 -1.31389816610381 89 16 15.8659455128691 0.134054487130918 90 16 15.2069714224284 0.793028577571585 91 16 16.1308306340966 -0.130830634096586 92 16 15.7698914529362 0.23010854706376 93 14 15.5511003966015 -1.55110039660146 94 16 14.0704389152734 1.92956108472664 95 16 15.0448349275519 0.95516507244812 96 20 16.2680394385802 3.73196056141977 97 15 15.3971403052019 -0.397140305201947 98 16 13.9957666010059 2.00423339899415 99 13 14.2975629042617 -1.29756290426171 100 17 15.7656094215713 1.23439057842874 101 16 14.0703127913228 1.92968720867717 102 12 13.2268880271215 -1.22688802712149 103 16 14.9164048446782 1.08359515532182 104 16 15.1404128163076 0.859587183692447 105 17 15.3499887707194 1.65001122928063 106 13 13.0643675959213 -0.064367595921327 107 12 15.7061858506417 -3.70618585064166 108 18 15.6473858898329 2.35261411016713 109 14 13.5421025031089 0.457897496891092 110 14 14.3383780014259 -0.338378001425947 111 13 13.641649460122 -0.641649460122025 112 16 15.2750991868165 0.724900813183524 113 13 12.4956745715902 0.504325428409848 114 16 15.1191819234747 0.880818076525294 115 13 14.6838321886214 -1.68383218862135 116 16 15.6399320422475 0.360067957752462 117 15 14.5191263454622 0.48087365453776 118 16 15.0922962476339 0.907703752366064 119 15 14.7349526834103 0.26504731658967 120 17 15.4236879666569 1.5763120333431 121 15 15.6132150879246 -0.613215087924564 122 12 13.474489808847 -1.47448980884695 123 16 14.2153036955599 1.78469630444011 124 10 13.9470944444123 -3.9470944444123 125 16 14.176633965939 1.82336603406102 126 14 14.5004486764702 -0.500448676470243 127 15 16.0995257007937 -1.09952570079375 128 13 14.2370341590664 -1.23703415906641 129 15 15.1067256678637 -0.106725667863693 130 11 13.4595577191945 -2.45955771919452 131 12 13.97596184158 -1.97596184157998 132 8 14.245371870554 -6.24537187055398 133 16 15.940786561813 0.0592134381870081 134 15 14.5159604751947 0.484039524805347 135 17 15.0284964332569 1.97150356674313 136 16 15.0960197764248 0.903980223575158 137 10 14.6532788396021 -4.65327883960213 138 18 13.6310895836648 4.3689104163352 139 13 13.5200642166552 -0.520064216655248 140 15 13.9636875153357 1.0363124846643 141 16 14.2921676906359 1.70783230936408 142 16 14.6216209286447 1.3783790713553 143 14 13.0783340759605 0.921665924039515 144 10 12.7902445582836 -2.79024455828365 145 17 15.6039722829231 1.3960277170769 146 13 13.9902062596416 -0.990206259641559 147 15 15.4621010037919 -0.462101003791891 148 16 15.5512146995837 0.448785300416284 149 12 14.9214999964229 -2.92149999642287 150 13 13.2788983865779 -0.278898386577896 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.909866210603569 0.180267578792862 0.0901337893964308 11 0.833524475390171 0.332951049219657 0.166475524609829 12 0.736812850201841 0.526374299596318 0.263187149798159 13 0.673421575736842 0.653156848526316 0.326578424263158 14 0.65525573597948 0.689488528041039 0.344744264020519 15 0.601544102856176 0.796911794287649 0.398455897143824 16 0.509632673105515 0.980734653788971 0.490367326894485 17 0.5839202416549 0.8321595166902 0.4160797583451 18 0.503097938665911 0.993804122668178 0.496902061334089 19 0.428330325125642 0.856660650251285 0.571669674874358 20 0.357004086007692 0.714008172015383 0.642995913992308 21 0.454309695119821 0.908619390239643 0.545690304880179 22 0.423955991326476 0.847911982652951 0.576044008673524 23 0.354405242433203 0.708810484866406 0.645594757566797 24 0.29854982181586 0.59709964363172 0.70145017818414 25 0.246771594392438 0.493543188784876 0.753228405607562 26 0.242200814108075 0.484401628216149 0.757799185891925 27 0.206665769472337 0.413331538944674 0.793334230527663 28 0.294888974899528 0.589777949799055 0.705111025100472 29 0.370328881146278 0.740657762292555 0.629671118853722 30 0.314596942012666 0.629193884025332 0.685403057987334 31 0.282522322214606 0.565044644429212 0.717477677785394 32 0.239554620504843 0.479109241009685 0.760445379495157 33 0.889243268407149 0.221513463185703 0.110756731592851 34 0.91691534157029 0.166169316859422 0.0830846584297108 35 0.896622490066763 0.206755019866474 0.103377509933237 36 0.895892152327348 0.208215695345303 0.104107847672652 37 0.891463219497908 0.217073561004185 0.108536780502092 38 0.890319313701304 0.219361372597392 0.109680686298696 39 0.867997221219926 0.264005557560149 0.132002778780074 40 0.904899171435692 0.190201657128616 0.095100828564308 41 0.882160404962097 0.235679190075806 0.117839595037903 42 0.861673616823244 0.276652766353512 0.138326383176756 43 0.906244883379505 0.187510233240991 0.0937551166204954 44 0.884300213959072 0.231399572081856 0.115699786040928 45 0.863840809003296 0.272318381993409 0.136159190996704 46 0.839234248615915 0.321531502768171 0.160765751384085 47 0.825862226527356 0.348275546945287 0.174137773472644 48 0.798361629013855 0.40327674197229 0.201638370986145 49 0.83919869252127 0.32160261495746 0.16080130747873 50 0.822818954015804 0.354362091968392 0.177181045984196 51 0.92039986205842 0.159200275883159 0.0796001379415793 52 0.909673296710763 0.180653406578474 0.0903267032892368 53 0.902946427672464 0.194107144655072 0.0970535723275361 54 0.896764842612183 0.206470314775634 0.103235157387817 55 0.880469800437468 0.239060399125064 0.119530199562532 56 0.878994906016144 0.242010187967712 0.121005093983856 57 0.868178003535675 0.26364399292865 0.131821996464325 58 0.845519340700573 0.308961318598854 0.154480659299427 59 0.820175873300697 0.359648253398605 0.179824126699303 60 0.836405491566855 0.32718901686629 0.163594508433145 61 0.877915498704494 0.244169002591011 0.122084501295506 62 0.863695387169896 0.272609225660207 0.136304612830104 63 0.896855201153344 0.206289597693311 0.103144798846656 64 0.909881210121303 0.180237579757395 0.0901187898786975 65 0.928039152438182 0.143921695123635 0.0719608475618177 66 0.912921372022981 0.174157255954037 0.0870786279770186 67 0.968633147984988 0.0627337040300236 0.0313668520150118 68 0.961260901638187 0.0774781967236264 0.0387390983618132 69 0.968550294380607 0.062899411238785 0.0314497056193925 70 0.966936408738449 0.0661271825231027 0.0330635912615513 71 0.957700611587494 0.0845987768250116 0.0422993884125058 72 0.94680327179107 0.106393456417858 0.0531967282089289 73 0.934752249293285 0.130495501413429 0.0652477507067145 74 0.940537412032094 0.118925175935812 0.0594625879679058 75 0.928948073938857 0.142103852122286 0.0710519260611432 76 0.914218404689837 0.171563190620325 0.0857815953101626 77 0.94605977983531 0.107880440329379 0.0539402201646893 78 0.93145697752695 0.137086044946102 0.0685430224730511 79 0.924484163043414 0.151031673913172 0.0755158369565861 80 0.90927380188742 0.181452396225159 0.0907261981125796 81 0.888029411568446 0.223941176863108 0.111970588431554 82 0.86526203435746 0.269475931285081 0.134737965642541 83 0.852768092578754 0.294463814842491 0.147231907421246 84 0.900639178956048 0.198721642087904 0.0993608210439518 85 0.884914732033992 0.230170535932016 0.115085267966008 86 0.859685898769045 0.280628202461911 0.140314101230955 87 0.842992720105906 0.314014559788188 0.157007279894094 88 0.836244753142422 0.327510493715156 0.163755246857578 89 0.807681624856724 0.384636750286552 0.192318375143276 90 0.772128418425759 0.455743163148483 0.227871581574241 91 0.74282640937607 0.514347181247859 0.257173590623929 92 0.704677455366553 0.590645089266894 0.295322544633447 93 0.735328230459725 0.52934353908055 0.264671769540275 94 0.725222786688035 0.54955442662393 0.274777213311965 95 0.685487099936091 0.629025800127818 0.314512900063909 96 0.731782756984787 0.536434486030425 0.268217243015213 97 0.696888027299852 0.606223945400296 0.303111972700148 98 0.689294668468745 0.621410663062511 0.310705331531256 99 0.67977453030079 0.640450939398421 0.32022546969921 100 0.637390627446188 0.725218745107624 0.362609372553812 101 0.619762799479761 0.760474401040479 0.380237200520239 102 0.591646594407718 0.816706811184563 0.408353405592282 103 0.544107084854174 0.911785830291652 0.455892915145826 104 0.507732958591658 0.984534082816684 0.492267041408342 105 0.492232808545272 0.984465617090543 0.507767191454728 106 0.439845840367415 0.87969168073483 0.560154159632585 107 0.618341846429254 0.763316307141492 0.381658153570746 108 0.606979471275439 0.786041057449123 0.393020528724561 109 0.592603038537055 0.81479392292589 0.407396961462945 110 0.540420550511882 0.919158898976235 0.459579449488118 111 0.48853312462531 0.97706624925062 0.51146687537469 112 0.432819971817275 0.86563994363455 0.567180028182725 113 0.397730274100847 0.795460548201694 0.602269725899153 114 0.358568761807934 0.717137523615867 0.641431238192066 115 0.346278443894417 0.692556887788834 0.653721556105583 116 0.292992329213789 0.585984658427578 0.707007670786211 117 0.263311693030945 0.52662338606189 0.736688306969055 118 0.265780809992912 0.531561619985823 0.734219190007088 119 0.217190759038245 0.43438151807649 0.782809240961755 120 0.191406310539477 0.382812621078954 0.808593689460523 121 0.155042888219786 0.310085776439571 0.844957111780214 122 0.139319930830981 0.278639861661962 0.860680069169019 123 0.13217585516348 0.264351710326959 0.86782414483652 124 0.176850342133763 0.353700684267527 0.823149657866237 125 0.14370897018203 0.287417940364061 0.85629102981797 126 0.116324191862826 0.232648383725653 0.883675808137174 127 0.087913151248406 0.175826302496812 0.912086848751594 128 0.0727171559416297 0.145434311883259 0.92728284405837 129 0.0508111566621314 0.101622313324263 0.949188843337869 130 0.0511974463032324 0.102394892606465 0.948802553696768 131 0.0425516557745547 0.0851033115491094 0.957448344225445 132 0.433632905851438 0.867265811702875 0.566367094148562 133 0.347660055481819 0.695320110963637 0.652339944518181 134 0.285227266883766 0.570454533767532 0.714772733116234 135 0.230400763894476 0.460801527788952 0.769599236105524 136 0.175638978979725 0.35127795795945 0.824361021020275 137 0.733713036835001 0.532573926329997 0.266286963164999 138 0.657980042471367 0.684039915057266 0.342019957528633 139 0.540068004219057 0.919863991561886 0.459931995780943 140 0.384927668935354 0.769855337870708 0.615072331064646 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 0 0 OK 10% type I error level 6 0.0458015267175573 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/10ezd01292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/10ezd01292443905.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/17gy61292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/17gy61292443905.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/27gy61292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/27gy61292443905.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/37gy61292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/37gy61292443905.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/4z7f91292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/4z7f91292443905.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/5z7f91292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/5z7f91292443905.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/6sgec1292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/6sgec1292443905.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/7sgec1292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/7sgec1292443905.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/837vx1292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/837vx1292443905.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/937vx1292443905.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t129244398720b7p5dhx85aa7g/937vx1292443905.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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