*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: Sun, 05 Dec 2010 18:56:24 +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/05/t12915753173exdlr28pzmeq77.htm/, Retrieved Sun, 05 Dec 2010 19:55:29 +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/05/t12915753173exdlr28pzmeq77.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 «

1 1 41 38 13 12 14 1 1 39 32 16 11 18 1 1 30 35 19 15 11 1 0 31 33 15 6 12 1 1 34 37 14 13 16 1 1 35 29 13 10 18 1 1 39 31 19 12 14 1 1 34 36 15 14 14 1 1 36 35 14 12 15 1 1 37 38 15 9 15 1 0 38 31 16 10 17 1 1 36 34 16 12 19 1 0 38 35 16 12 10 1 1 39 38 16 11 16 1 1 33 37 17 15 18 1 0 32 33 15 12 14 1 0 36 32 15 10 14 1 1 38 38 20 12 17 1 0 39 38 18 11 14 1 1 32 32 16 12 16 1 0 32 33 16 11 18 1 1 31 31 16 12 11 1 1 39 38 19 13 14 1 1 37 39 16 11 12 1 0 39 32 17 12 17 1 1 41 32 17 13 9 1 0 36 35 16 10 16 1 1 33 37 15 14 14 1 1 33 33 16 12 15 1 0 34 33 14 10 11 1 1 31 31 15 12 16 1 0 27 32 12 8 13 1 1 37 31 14 10 17 1 1 34 37 16 12 15 1 0 34 30 14 12 14 1 0 32 33 10 7 16 1 0 29 31 10 9 9 1 0 36 33 14 12 15 1 1 29 31 16 10 17 1 0 35 33 16 10 13 1 0 37 32 16 10 15 1 1 34 33 14 12 16 1 0 38 32 20 15 16 1 0 35 33 14 10 12 1 1 38 28 14 10 15 1 1 37 35 11 12 11 1 1 38 39 14 13 15 1 1 33 34 15 11 15 1 1 36 38 16 11 17 1 0 38 32 14 12 13 1 1 32 38 16 14 16 1 0 32 30 1 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 17 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 1.94933228525291 + 0.653493146925311Pop[t] + 0.0305177066962255Gender[t] + 0.0700025359624751Connected[t] + 0.0563924721194771Separate[t] + 0.623309096789488Software[t] + 0.0764750221538199Happiness[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) 1.94933228525291 1.246266 1.5641 0.118911 0.059455 Pop 0.653493146925311 0.248484 2.6299 0.009011 0.004506 Gender 0.0305177066962255 0.234546 0.1301 0.896569 0.448285 Connected 0.0700025359624751 0.03288 2.1291 0.034119 0.017059 Separate 0.0563924721194771 0.034285 1.6448 0.101126 0.050563 Software 0.623309096789488 0.051672 12.0627 0 0 Happiness 0.0764750221538199 0.047615 1.6061 0.109373 0.054687 Multiple Linear Regression - Regression Statistics Multiple R 0.697110633887777 R-squared 0.485963235879418 Adjusted R-squared 0.47498736191243 F-TEST (value) 44.2755845540013 F-TEST (DF numerator) 6 F-TEST (DF denominator) 281 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.89915449290688 Sum Squared Residuals 1013.50736840787 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.1967205255037 -3.19672052550372 2 16 15.4009516126874 0.599048387312637 3 19 16.8980174374648 2.10198256253522 4 15 11.2914104735405 3.70858952645952 5 14 16.4265694427437 -2.42656944274373 6 13 14.3284549556896 -1.32845495568956 7 19 15.6619681487421 3.33803185125788 8 15 16.8405360231061 -1.84053602310610 9 14 15.7540054514864 -1.75400545148642 10 15 14.1232581134389 0.876741886561137 11 16 14.5442547789659 1.45574522103410 12 16 16.0035130679822 -0.0035130679822237 13 16 15.4811177059460 0.518882294053957 14 16 15.5863564010966 0.413643598903391 15 17 17.7561351446679 -0.756135144667874 16 15 15.2542176345475 -0.254217634547518 17 15 14.2312171126990 0.768782887301035 18 20 16.2161379840774 3.78386201592256 19 18 15.4028886500927 2.59711134990726 20 16 15.3812929134319 0.618707086568091 21 16 14.9368086263733 1.06319137362669 22 16 14.8725227945809 1.12747720541914 23 19 16.6800245503679 2.31997544963205 24 16 15.1968437126759 0.803156287324143 25 17 15.9172679806268 1.08273201937317 26 17 16.0992996788069 0.900700321193066 27 16 14.5533445733650 1.44665542663496 28 15 16.8269259592631 -1.82692595926311 29 16 15.4312128993600 0.568787100639958 30 14 13.9181794464320 0.0818205535679676 31 15 15.2548979053500 -0.254897905349957 32 12 12.2781010733039 -0.278101073303894 33 14 14.5047699496997 -0.504769949699651 34 16 15.7267853238004 0.273214676199575 35 14 15.2250452901140 -1.22504529011404 36 10 12.2906221949077 -2.29062219490772 37 10 12.6791226812836 -2.67912268128358 38 14 15.6107028005512 -1.61070280055124 39 16 13.9447496619999 2.05525033800015 40 16 14.1411320267021 1.85886797329785 41 16 14.3776946708153 1.62230532918474 42 14 15.5776904574763 -1.57769045747634 43 20 17.640717712879 2.35928228712101 44 14 14.0646570045483 -0.0646570045483274 45 14 14.2526450249961 -0.252645024996055 46 11 15.5181078988336 -4.51810789883362 47 14 16.7428895086788 -2.74288950867877 48 15 14.8642962746900 0.135703725309969 49 16 15.452823815363 0.547176184636996 50 14 15.5413653560491 -1.54136535604907 51 16 16.9662659397277 -0.966265939727748 52 14 13.8384220246101 0.161577975389889 53 12 15.0247925680861 -3.02479256808606 54 16 16.1770618262479 -0.177061826247930 55 9 10.6817114405940 -1.68171144059399 56 14 12.0841534067120 1.91584659328803 57 16 15.9840956094082 0.015904390591811 58 16 15.2075952276296 0.792404772370382 59 15 14.9971485896212 0.00285141037880324 60 16 14.1515671833640 1.84843281663597 61 12 11.2568545851548 0.743145414845177 62 16 15.6541503002880 0.345849699711975 63 16 16.5547184845252 -0.554718484525167 64 14 14.7042086527307 -0.704208652730738 65 16 15.3884304910836 0.611569508916438 66 17 16.0072041390871 0.99279586091294 67 18 16.6947235564501 1.30527644354988 68 18 13.9995985888086 4.00040141119142 69 12 16.2459754199712 -4.24597541997123 70 16 15.7662701530667 0.233729846933329 71 10 13.3501738795228 -3.35017387952285 72 14 15.0263361133968 -1.02633611339681 73 18 17.0861884616184 0.913811538381645 74 18 17.448465843011 0.551534156989019 75 16 14.9793928516018 1.02060714839821 76 17 13.5826983419465 3.41730165805346 77 16 16.7130520727850 -0.713052072784978 78 16 14.6121713499864 1.38782865001357 79 13 14.9378975686125 -1.93789756861248 80 16 15.1894004594892 0.81059954051079 81 16 15.5698726090222 0.430127390977756 82 16 15.7967878597629 0.2032121402371 83 15 15.7571803586675 -0.757180358667533 84 15 14.7942937387276 0.205706261272445 85 16 13.9953347393883 2.00466526061171 86 14 14.2191354148246 -0.219135414824587 87 16 15.4111303493257 0.588869650674301 88 16 14.9418602390830 1.05813976091698 89 15 14.8194127221295 0.180587277870518 90 12 13.7434079977327 -1.7434079977327 91 17 17.3018052811888 -0.301805281188814 92 16 16.0223577482408 -0.0223577482408084 93 15 15.0027729806464 -0.00277298064636092 94 13 14.8290752948441 -1.82907529484407 95 16 14.8502623600682 1.14973763993183 96 16 16.2178920177769 -0.217892017776924 97 16 13.5120307145238 2.48796928547625 98 16 15.8900478529408 0.109952147059170 99 14 14.2532518794808 -0.253251879480793 100 16 17.3499712334175 -1.34997123341746 101 16 14.9407561175017 1.05924388249828 102 20 17.8131927082477 2.18680729175234 103 15 14.1195211106992 0.880478889300815 104 16 15.1462586352874 0.853741364712584 105 13 15.3754703393587 -2.37547033935874 106 17 15.9704855455652 1.02951445443481 107 16 16.2990703130805 -0.299070313080476 108 16 14.7178035372316 1.28219646276840 109 12 13.1398499133435 -1.13984991334355 110 16 15.2775977635921 0.722402236407907 111 16 16.2319259323988 -0.231925932398788 112 17 15.0360909992563 1.96390900074374 113 12 14.7504223882119 -2.75042238821190 114 18 16.3240969833375 1.67590301666246 115 14 16.3727942788320 -2.37279427883205 116 14 13.3262513308471 0.673748669152915 117 13 14.8442137246557 -1.84421372465569 118 16 15.8739279733770 0.126072026622972 119 13 14.7735309178908 -1.77353091789077 120 16 15.4996870693539 0.500312930646103 121 13 16.1195804118893 -3.11958041188928 122 16 17.2398035973863 -1.23980359738630 123 15 16.151744659798 -1.151744659798 124 16 17.0081850734959 -1.00818507349592 125 15 14.6706497870479 0.32935021295215 126 17 16.0692365751823 0.930763424817718 127 15 14.0363631139653 0.963636886034711 128 12 14.9479088744955 -2.94790887449550 129 16 13.9311244188147 2.06887558118528 130 10 13.9121308110196 -3.91213081101955 131 16 13.6535641524173 2.34643584758268 132 12 14.1881934637410 -2.18819346374104 133 14 15.9626676971111 -1.9626676971111 134 15 15.2121154970735 -0.212115497073478 135 13 12.2545379405534 0.745462059446554 136 15 14.8836985539219 0.116301446078066 137 11 13.7814719535173 -2.78147195351732 138 12 13.1343740562465 -1.13437405624652 139 11 13.3505977303017 -2.35059773030171 140 16 12.9243664483591 3.07563355164091 141 15 13.6228052050397 1.37719479496035 142 17 17.1274425039262 -0.127442503926215 143 16 14.0734563027546 1.92654369724540 144 10 13.3916843418543 -3.39168434185428 145 18 15.722639649624 2.27736035037599 146 13 15.4739801282944 -2.47398012829439 147 16 14.9884826460009 1.01151735399908 148 13 13.1555303691779 -0.155530369177903 149 10 13.0795099500957 -3.07950995009566 150 15 16.7571646639821 -1.75716466398207 151 16 13.9592078210090 2.04079217899097 152 16 11.9402931568035 4.05970684319653 153 14 12.8855315312110 1.11446846878898 154 10 12.6722415236555 -2.67224152365550 155 13 11.7704506489847 1.22954935101527 156 15 14.0363631139653 0.963636886034711 157 16 14.6685638221059 1.33143617789409 158 12 12.9205112703755 -0.92051127037554 159 13 12.3034462207792 0.69655377922076 160 12 11.6427382596654 0.357261740334557 161 17 16.4203079412837 0.579692058716324 162 15 13.557083816766 1.44291618323400 163 10 11.1488653299446 -1.14886532994457 164 14 13.8374103189078 0.162589681092228 165 11 13.6071371572801 -2.60713715728013 166 13 14.6708345160717 -1.67083451607167 167 16 14.0939065855186 1.90609341448136 168 12 10.2453634792078 1.75463652079224 169 16 15.2897722709539 0.710227729046113 170 12 13.7145389511754 -1.71453895117536 171 9 10.7770743033739 -1.77707430337394 172 12 14.7822400218786 -2.78224002187859 173 15 14.0137253129179 0.986274687082144 174 12 12.1056433762038 -0.105643376203762 175 12 12.2686646646627 -0.268664664662725 176 14 13.3547865648457 0.645213435154327 177 12 13.1774749417413 -1.17747494174127 178 16 15.0804297545268 0.91957024547323 179 11 10.8252250762605 0.174774923739544 180 19 16.6463016805405 2.35369831945955 181 15 14.9643472312776 0.0356527687224169 182 8 13.8022045184039 -5.80220451840394 183 16 14.7239445885231 1.27605541147695 184 17 14.3138180068021 2.6861819931979 185 12 11.9684045400232 0.0315954599768104 186 11 10.8457314770737 0.154268522926336 187 11 10.1773131599928 0.822686840007234 188 14 14.5709945442154 -0.57099454421541 189 16 15.4460047149296 0.553995285070372 190 12 9.09793534536687 2.90206465463313 191 16 14.2140855274328 1.78591447256718 192 13 13.4047065507738 -0.404706550773805 193 15 15.0797494837243 -0.0797494837243312 194 16 12.7885350316360 3.21146496836403 195 16 14.9268146187588 1.07318538124118 196 14 12.3419496002933 1.6580503997067 197 16 13.9091668885697 2.09083311143027 198 14 12.7013836121388 1.29861638786118 199 11 12.9874423914012 -1.9874423914012 200 12 14.6078620652739 -2.60786206527386 201 15 12.3408758373963 2.65912416260374 202 15 14.3935906079662 0.606409392033848 203 16 14.4435105938943 1.55648940610572 204 16 15.1328595561757 0.867140443824294 205 11 13.5576414157393 -2.55764141573931 206 15 13.6470614102758 1.35293858972418 207 12 14.3888721554743 -2.38887215547429 208 12 16.0040145489064 -4.00401454890637 209 15 14.0863451570881 0.913654842911875 210 15 11.6051904678046 3.39480953219545 211 16 14.7246096799834 1.27539032001664 212 14 12.6994313953913 1.30056860460866 213 17 14.4201456441918 2.57985435580816 214 14 13.9310342245963 0.0689657754037351 215 13 12.0414330556302 0.958566944369807 216 15 15.3260821930390 -0.326082193039021 217 13 14.5813070290482 -1.58130702904818 218 14 14.0962489704842 -0.0962489704841555 219 15 14.3389521695462 0.661047830453843 220 12 12.6808772113256 -0.680877211325614 221 8 11.2135150742476 -3.21351507424758 222 14 13.6100863967304 0.389913603269619 223 14 12.7042421610281 1.29575783897194 224 11 12.4119521362558 -1.41195213625578 225 12 12.7541621469562 -0.75416214695619 226 13 10.8622152691480 2.13778473085197 227 10 13.323696079834 -3.32369607983399 228 16 10.9937374011586 5.00626259884142 229 18 16.4314081894059 1.56859181059413 230 13 13.6211866448526 -0.621186644852575 231 11 13.2919064271927 -2.29190642719272 232 4 10.8887551260316 -6.88875512603159 233 13 14.4659047766014 -1.46590477660143 234 16 14.0025495535768 1.99745044642322 235 10 11.4355892006673 -1.43558920066725 236 12 11.5481329042248 0.451867095775234 237 12 13.8413578100362 -1.84135781003618 238 10 8.2760200677619 1.72397993223811 239 13 10.9179274704651 2.08207252953493 240 12 11.7808403703543 0.219159629645673 241 14 12.7671071193389 1.23289288066112 242 10 12.9849325756804 -2.98493257568040 243 12 10.2453630855993 1.75463691440069 244 12 11.1052348265019 0.894765173498093 245 11 11.5470439619856 -0.547043961985592 246 10 11.4213140453639 -1.42131404536395 247 12 11.1513152073971 0.848684792602932 248 16 12.6984499456392 3.30155005436085 249 12 13.5511689295480 -1.55116892954797 250 14 13.9644704184500 0.0355295815499680 251 16 14.6539268732184 1.34607312678156 252 14 11.6292356883094 2.37076431169057 253 13 14.4908132716146 -1.49081327161462 254 4 8.75639042612676 -4.75639042612676 255 15 13.4887430013581 1.51125699864186 256 11 15.0991669422984 -4.09916694229837 257 11 11.6780515526563 -0.678051552656262 258 14 12.4643971172468 1.53560288275316 259 15 14.6182820425936 0.381717957406382 260 14 11.9721107904702 2.02788920952984 261 13 12.7925576403748 0.207442359625186 262 11 12.2546307500409 -1.25463075004086 263 15 13.7845566664800 1.21544333352003 264 11 11.2830630071385 -0.28306300713848 265 13 11.6540215114935 1.34597848850649 266 13 11.5831708803649 1.41682911963515 267 16 13.5116841002817 2.48831589971828 268 13 12.2235554443713 0.776444555628686 269 16 14.9339521964105 1.06604780358953 270 16 15.8343977088185 0.165602291181504 271 12 11.4401587256225 0.559841274377467 272 7 10.8122952832199 -3.8122952832199 273 16 13.9145504325219 2.0854495674781 274 5 9.20467165419334 -4.20467165419334 275 16 13.1462921435847 2.85370785641526 276 4 8.64172838275076 -4.64172838275076 277 12 13.3400723794214 -1.34007237942137 278 15 14.1310305266007 0.86896947339933 279 14 14.8341122245542 -0.83411222455421 280 11 13.0205622269631 -2.02056222696309 281 16 14.9844297813119 1.01557021868807 282 15 13.6374140169034 1.36258598309663 283 12 12.0787396068096 -0.0787396068096423 284 6 8.99807980056002 -2.99807980056002 285 16 14.5182164030065 1.48178359699351 286 10 13.3329348017697 -3.33293480176972 287 15 16.0797337890389 -1.07973378903887 288 14 14.4912371223935 -0.491237122393488 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.81408626134769 0.371827477304618 0.185913738652309 11 0.761229325523223 0.477541348953555 0.238770674476777 12 0.784144665799992 0.431710668400016 0.215855334200008 13 0.719161450846134 0.561677098307732 0.280838549153866 14 0.712411879221667 0.575176241556666 0.287588120778333 15 0.669044511839594 0.661910976320811 0.330955488160405 16 0.612600387080064 0.774799225839873 0.387399612919936 17 0.524822802404638 0.950354395190725 0.475177197595362 18 0.855741154814498 0.288517690371005 0.144258845185502 19 0.849998819513108 0.300002360973783 0.150001180486892 20 0.80200281047647 0.395994379047061 0.197997189523530 21 0.745897869930954 0.508204260138092 0.254102130069046 22 0.684099119237835 0.63180176152433 0.315900880762165 23 0.703792204183171 0.592415591633657 0.296207795816829 24 0.640615637606269 0.718768724787462 0.359384362393731 25 0.577482789177759 0.845034421644483 0.422517210822241 26 0.510840199927044 0.978319600145911 0.489159800072956 27 0.447186101972807 0.894372203945614 0.552813898027193 28 0.4304026560373 0.8608053120746 0.5695973439627 29 0.369874070903403 0.739748141806805 0.630125929096597 30 0.356279887151216 0.712559774302432 0.643720112848784 31 0.300856874206313 0.601713748412626 0.699143125793687 32 0.285203192192067 0.570406384384134 0.714796807807933 33 0.251839765907608 0.503679531815215 0.748160234092392 34 0.207049743900599 0.414099487801198 0.792950256099401 35 0.205931838932882 0.411863677865765 0.794068161067118 36 0.294191589926571 0.588383179853141 0.705808410073429 37 0.381722839826487 0.763445679652975 0.618277160173513 38 0.383989808759571 0.767979617519143 0.616010191240429 39 0.412444714595412 0.824889429190823 0.587555285404588 40 0.391693744234272 0.783387488468545 0.608306255765728 41 0.357991618691334 0.715983237382668 0.642008381308666 42 0.344927714219763 0.689855428439526 0.655072285780237 43 0.357907768525071 0.715815537050142 0.642092231474929 44 0.317195445568800 0.634390891137599 0.6828045544312 45 0.281112065180269 0.562224130360538 0.718887934819731 46 0.516421228254308 0.967157543491384 0.483578771745692 47 0.567873751768147 0.864252496463707 0.432126248231853 48 0.521401393801848 0.957197212396304 0.478598606198152 49 0.477155337160499 0.954310674320998 0.522844662839501 50 0.480679222342281 0.961358444684563 0.519320777657719 51 0.438573970753701 0.877147941507401 0.561426029246299 52 0.393324924345819 0.786649848691637 0.606675075654181 53 0.446961455047453 0.893922910094906 0.553038544952547 54 0.404471451454385 0.80894290290877 0.595528548545615 55 0.406474981449883 0.812949962899766 0.593525018550117 56 0.390812560784678 0.781625121569357 0.609187439215322 57 0.349516667635936 0.699033335271873 0.650483332364064 58 0.326711949330064 0.653423898660129 0.673288050669936 59 0.287653471802315 0.57530694360463 0.712346528197685 60 0.289704324453997 0.579408648907994 0.710295675546003 61 0.260293166371497 0.520586332742994 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0.68339009285512 264 0.259566944219748 0.519133888439495 0.740433055780252 265 0.257080674000104 0.514161348000209 0.742919325999896 266 0.368586064858854 0.737172129717707 0.631413935141146 267 0.613750884771851 0.772498230456298 0.386249115228149 268 0.552043750471296 0.895912499057408 0.447956249528704 269 0.503051090380986 0.993897819238027 0.496948909619014 270 0.51366135445178 0.97267729109644 0.48633864554822 271 0.441941819414827 0.883883638829655 0.558058180585173 272 0.418639515243933 0.837279030487865 0.581360484756067 273 0.364864530929152 0.729729061858304 0.635135469070848 274 0.288946915103501 0.577893830207001 0.711053084896499 275 0.425595101421128 0.851190202842256 0.574404898578872 276 0.376777275592881 0.753554551185763 0.623222724407119 277 0.266605613017509 0.533211226035017 0.733394386982491 278 0.171092306073470 0.342184612146941 0.82890769392653 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.0223048327137546 NOK 5% type I error level 107 0.397769516728625 NOK 10% type I error level 131 0.486988847583643 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/10pr5c1291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/10pr5c1291575365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/1b0731291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/1b0731291575365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/2b0731291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/2b0731291575365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/3b0731291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/3b0731291575365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/449661291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/449661291575365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/549661291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/549661291575365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/649661291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/649661291575365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/7win91291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/7win91291575365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/8win91291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/8win91291575365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/9pr5c1291575365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t12915753173exdlr28pzmeq77/9pr5c1291575365.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = equal ; par3 = 2 ; par4 = no ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = no ;

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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