*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: Fri, 24 Dec 2010 17:56:21 +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/24/t1293213262ng44fsibcl3bdz5.htm/, Retrieved Fri, 24 Dec 2010 18:54:25 +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/24/t1293213262ng44fsibcl3bdz5.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 10 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 1.94933228525292 + 0.653493146925309Pop[t] + 0.0305177066962302Gender[t] + 0.0700025359624756Connected[t] + 0.0563924721194769Separate[t] + 0.623309096789489Software[t] + 0.0764750221538192Happiness[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) 1.94933228525292 1.246266 1.5641 0.118911 0.059455 Pop 0.653493146925309 0.248484 2.6299 0.009011 0.004506 Gender 0.0305177066962302 0.234546 0.1301 0.896569 0.448285 Connected 0.0700025359624756 0.03288 2.1291 0.034119 0.017059 Separate 0.0563924721194769 0.034285 1.6448 0.101126 0.050563 Software 0.623309096789489 0.051672 12.0627 0 0 Happiness 0.0764750221538192 0.047615 1.6061 0.109373 0.054687 Multiple Linear Regression - Regression Statistics Multiple R 0.697110633887777 R-squared 0.485963235879419 Adjusted R-squared 0.474987361912431 F-TEST (value) 44.2755845540015 F-TEST (DF numerator) 6 F-TEST (DF denominator) 281 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.89915449290687 Sum Squared Residuals 1013.50736840787 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.1967205255034 -3.1967205255034 2 16 15.4009516126874 0.599048387312609 3 19 16.8980174374648 2.10198256253524 4 15 11.2914104735405 3.70858952645953 5 14 16.4265694427437 -2.42656944274373 6 13 14.3284549556896 -1.32845495568957 7 19 15.6619681487421 3.33803185125788 8 15 16.8405360231061 -1.84053602310611 9 14 15.7540054514864 -1.75400545148642 10 15 14.1232581134389 0.876741886561136 11 16 14.5442547789659 1.4557452210341 12 16 16.0035130679822 -0.00351306798222419 13 16 15.481117705946 0.518882294053951 14 16 15.5863564010966 0.413643598903388 15 17 17.7561351446679 -0.756135144667875 16 15 15.2542176345475 -0.254217634547519 17 15 14.231217112699 0.768782887301034 18 20 16.2161379840774 3.78386201592256 19 18 15.4028886500927 2.59711134990726 20 16 15.3812929134319 0.61870708656809 21 16 14.9368086263733 1.06319137362669 22 16 14.8725227945809 1.12747720541914 23 19 16.6800245503679 2.31997544963205 24 16 15.1968437126759 0.80315628732414 25 17 15.9172679806268 1.08273201937317 26 17 16.0992996788069 0.900700321193055 27 16 14.553344573365 1.44665542663496 28 15 16.8269259592631 -1.82692595926311 29 16 15.43121289936 0.568787100639956 30 14 13.918179446432 0.0818205535679651 31 15 15.25489790535 -0.254897905349958 32 12 12.2781010733039 -0.27810107330389 33 14 14.5047699496997 -0.504769949699653 34 16 15.7267853238004 0.273214676199573 35 14 15.225045290114 -1.22504529011404 36 10 12.2906221949077 -2.29062219490771 37 10 12.6791226812836 -2.67912268128358 38 14 15.6107028005512 -1.61070280055124 39 16 13.9447496619998 2.05525033800015 40 16 14.1411320267021 1.85886797329785 41 16 14.3776946708153 1.62230532918474 42 14 15.5776904574763 -1.57769045747634 43 20 17.640717712879 2.359282287121 44 14 14.0646570045483 -0.0646570045483297 45 14 14.2526450249961 -0.25264502499606 46 11 15.5181078988336 -4.51810789883362 47 14 16.7428895086788 -2.74288950867877 48 15 14.86429627469 0.135703725309968 49 16 15.452823815363 0.547176184636995 50 14 15.5413653560491 -1.54136535604908 51 16 16.9662659397277 -0.96626593972775 52 14 13.8384220246101 0.161577975389889 53 12 15.0247925680861 -3.02479256808606 54 16 16.1770618262479 -0.177061826247935 55 9 10.681711440594 -1.68171144059398 56 14 12.084153406712 1.91584659328803 57 16 15.9840956094082 0.0159043905918067 58 16 15.2075952276296 0.792404772370382 59 15 14.9971485896212 0.00285141037879988 60 16 14.151567183364 1.84843281663596 61 12 11.2568545851548 0.743145414845176 62 16 15.654150300288 0.34584969971197 63 16 16.5547184845252 -0.554718484525173 64 14 14.7042086527307 -0.704208652730738 65 16 15.3884304910836 0.611569508916434 66 17 16.0072041390871 0.992795860912935 67 18 16.6947235564501 1.30527644354988 68 18 13.9995985888086 4.00040141119142 69 12 16.2459754199712 -4.24597541997124 70 16 15.7662701530667 0.233729846933328 71 10 13.3501738795228 -3.35017387952285 72 14 15.0263361133968 -1.02633611339681 73 18 17.0861884616184 0.913811538381642 74 18 17.448465843011 0.551534156989017 75 16 14.9793928516018 1.02060714839821 76 17 13.5826983419465 3.41730165805346 77 16 16.713052072785 -0.713052072784981 78 16 14.6121713499864 1.38782865001356 79 13 14.9378975686125 -1.93789756861248 80 16 15.1894004594892 0.810599540510784 81 16 15.5698726090222 0.430127390977756 82 16 15.7967878597629 0.203212140237098 83 15 15.7571803586675 -0.757180358667535 84 15 14.7942937387276 0.205706261272444 85 16 13.9953347393883 2.00466526061171 86 14 14.2191354148246 -0.219135414824587 87 16 15.4111303493257 0.588869650674299 88 16 14.941860239083 1.05813976091697 89 15 14.8194127221295 0.18058727787051 90 12 13.7434079977327 -1.7434079977327 91 17 17.3018052811888 -0.30180528118882 92 16 16.0223577482408 -0.0223577482408098 93 15 15.0027729806464 -0.00277298064636416 94 13 14.8290752948441 -1.82907529484407 95 16 14.8502623600682 1.14973763993183 96 16 16.2178920177769 -0.217892017776931 97 16 13.5120307145238 2.48796928547624 98 16 15.8900478529408 0.109952147059169 99 14 14.2532518794808 -0.253251879480791 100 16 17.3499712334175 -1.34997123341747 101 16 14.9407561175017 1.05924388249828 102 20 17.8131927082477 2.18680729175234 103 15 14.1195211106992 0.880478889300812 104 16 15.1462586352874 0.853741364712584 105 13 15.3754703393588 -2.37547033935875 106 17 15.9704855455652 1.02951445443481 107 16 16.2990703130805 -0.29907031308048 108 16 14.7178035372316 1.28219646276839 109 12 13.1398499133436 -1.13984991334355 110 16 15.2775977635921 0.722402236407906 111 16 16.2319259323988 -0.231925932398793 112 17 15.0360909992563 1.96390900074374 113 12 14.7504223882119 -2.7504223882119 114 18 16.3240969833375 1.67590301666245 115 14 16.3727942788321 -2.37279427883205 116 14 13.3262513308471 0.673748669152917 117 13 14.8442137246557 -1.84421372465569 118 16 15.873927973377 0.126072026622967 119 13 14.7735309178908 -1.77353091789077 120 16 15.4996870693539 0.500312930646099 121 13 16.1195804118893 -3.11958041188928 122 16 17.2398035973863 -1.23980359738631 123 15 16.151744659798 -1.15174465979801 124 16 17.0081850734959 -1.00818507349592 125 15 14.6706497870479 0.329350212952149 126 17 16.0692365751823 0.930763424817714 127 15 14.0363631139653 0.963636886034715 128 12 14.9479088744955 -2.94790887449551 129 16 13.9311244188147 2.06887558118528 130 10 13.9121308110196 -3.91213081101955 131 16 13.6535641524173 2.34643584758267 132 12 14.188193463741 -2.18819346374104 133 14 15.9626676971111 -1.9626676971111 134 15 15.2121154970735 -0.21211549707348 135 13 12.2545379405534 0.745462059446553 136 15 14.8836985539219 0.116301446078065 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 13.6228052050396 1.37719479496035 142 17 17.1274425039262 -0.127442503926217 143 16 14.0734563027546 1.9265436972454 144 10 13.3916843418543 -3.39168434185428 145 18 15.722639649624 2.27736035037599 146 13 15.4739801282944 -2.47398012829439 147 16 14.9884826460009 1.01151735399907 148 13 13.1555303691779 -0.155530369177906 149 10 13.0795099500957 -3.07950995009566 150 15 16.7571646639821 -1.75716466398208 151 16 13.959207821009 2.04079217899097 152 16 11.9402931568035 4.05970684319653 153 14 12.885531531211 1.11446846878897 154 10 12.6722415236555 -2.6722415236555 155 13 11.7704506489847 1.22954935101528 156 15 14.0363631139653 0.963636886034715 157 16 14.6685638221059 1.33143617789408 158 12 12.9205112703755 -0.92051127037554 159 13 12.3034462207792 0.69655377922076 160 12 11.6427382596654 0.357261740334559 161 17 16.4203079412837 0.57969205871632 162 15 13.557083816766 1.442916183234 163 10 11.1488653299446 -1.14886532994456 164 14 13.8374103189078 0.16258968109223 165 11 13.6071371572801 -2.60713715728013 166 13 14.6708345160717 -1.67083451607168 167 16 14.0939065855186 1.90609341448136 168 12 10.2453634792078 1.75463652079224 169 16 15.2897722709539 0.710227729046111 170 12 13.7145389511754 -1.71453895117537 171 9 10.7770743033739 -1.77707430337393 172 12 14.7822400218786 -2.7822400218786 173 15 14.0137253129179 0.986274687082144 174 12 12.1056433762038 -0.105643376203767 175 12 12.2686646646627 -0.268664664662723 176 14 13.3547865648457 0.645213435154328 177 12 13.1774749417413 -1.17747494174128 178 16 15.0804297545268 0.919570245473227 179 11 10.8252250762605 0.174774923739546 180 19 16.6463016805405 2.35369831945955 181 15 14.9643472312776 0.0356527687224139 182 8 13.8022045184039 -5.80220451840394 183 16 14.7239445885231 1.27605541147695 184 17 14.3138180068021 2.6861819931979 185 12 11.9684045400232 0.0315954599768089 186 11 10.8457314770737 0.15426852292634 187 11 10.1773131599928 0.822686840007238 188 14 14.5709945442154 -0.570994544215413 189 16 15.4460047149296 0.553995285070368 190 12 9.09793534536686 2.90206465463314 191 16 14.2140855274328 1.78591447256717 192 13 13.4047065507738 -0.404706550773805 193 15 15.0797494837243 -0.0797494837243335 194 16 12.788535031636 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 0.606409392033847 203 16 14.4435105938943 1.55648940610571 204 16 15.1328595561757 0.867140443824294 205 11 13.5576414157393 -2.55764141573932 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 1.30056860460867 213 17 14.4201456441918 2.57985435580816 214 14 13.9310342245963 0.0689657754037312 215 13 12.0414330556302 0.958566944369804 216 15 15.326082193039 -0.326082193039023 217 13 14.5813070290482 -1.58130702904818 218 14 14.0962489704842 -0.0962489704841552 219 15 14.3389521695462 0.661047830453838 220 12 12.6808772113256 -0.68087721132561 221 8 11.2135150742476 -3.21351507424758 222 14 13.6100863967304 0.389913603269624 223 14 12.7042421610281 1.29575783897194 224 11 12.4119521362558 -1.41195213625578 225 12 12.7541621469562 -0.754162146956191 226 13 10.862215269148 2.13778473085197 227 10 13.323696079834 -3.323696079834 228 16 10.9937374011586 5.00626259884143 229 18 16.4314081894059 1.56859181059412 230 13 13.6211866448526 -0.621186644852575 231 11 13.2919064271927 -2.29190642719272 232 4 10.8887551260316 -6.88875512603158 233 13 14.4659047766014 -1.46590477660143 234 16 14.0025495535768 1.99745044642322 235 10 11.4355892006673 -1.43558920066726 236 12 11.5481329042248 0.451867095775238 237 12 13.8413578100362 -1.84135781003619 238 10 8.27602006776189 1.72397993223811 239 13 10.9179274704651 2.08207252953493 240 12 11.7808403703543 0.219159629645675 241 14 12.7671071193389 1.23289288066112 242 10 12.9849325756804 -2.9849325756804 243 12 10.2453630855993 1.7546369144007 244 12 11.1052348265019 0.894765173498096 245 11 11.5470439619856 -0.547043961985587 246 10 11.4213140453639 -1.42131404536395 247 12 11.1513152073971 0.848684792602932 248 16 12.6984499456392 3.30155005436085 249 12 13.551168929548 -1.55116892954797 250 14 13.96447041845 0.0355295815499662 251 16 14.6539268732184 1.34607312678155 252 14 11.6292356883094 2.37076431169056 253 13 14.4908132716146 -1.49081327161463 254 4 8.75639042612676 -4.75639042612676 255 15 13.4887430013581 1.51125699864186 256 11 15.0991669422984 -4.09916694229836 257 11 11.6780515526563 -0.678051552656267 258 14 12.4643971172468 1.53560288275316 259 15 14.6182820425936 0.381717957406375 260 14 11.9721107904702 2.02788920952984 261 13 12.7925576403748 0.207442359625191 262 11 12.2546307500409 -1.25463075004086 263 15 13.78455666648 1.21544333352003 264 11 11.2830630071385 -0.283063007138481 265 13 11.6540215114935 1.34597848850649 266 13 11.5831708803649 1.41682911963515 267 16 13.5116841002817 2.48831589971827 268 13 12.2235554443713 0.776444555628686 269 16 14.9339521964105 1.06604780358952 270 16 15.8343977088185 0.1656022911815 271 12 11.4401587256225 0.559841274377468 272 7 10.8122952832199 -3.81229528321989 273 16 13.9145504325219 2.0854495674781 274 5 9.20467165419333 -4.20467165419333 275 16 13.1462921435847 2.85370785641526 276 4 8.64172838275074 -4.64172838275074 277 12 13.3400723794214 -1.34007237942137 278 15 14.1310305266007 0.868969473399328 279 14 14.8341122245542 -0.834112224554211 280 11 13.0205622269631 -2.02056222696309 281 16 14.9844297813119 1.01557021868807 282 15 13.6374140169034 1.36258598309663 283 12 12.0787396068096 -0.0787396068096389 284 6 8.99807980056001 -2.99807980056001 285 16 14.5182164030065 1.48178359699351 286 10 13.3329348017697 -3.33293480176971 287 15 16.0797337890389 -1.07973378903888 288 14 14.4912371223935 -0.491237122393489 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.814086261347692 0.371827477304616 0.185913738652308 11 0.761229325523221 0.477541348953557 0.238770674476779 12 0.78414466579999 0.431710668400018 0.215855334200009 13 0.719161450846133 0.561677098307734 0.280838549153867 14 0.712411879221667 0.575176241556666 0.287588120778333 15 0.669044511839594 0.661910976320811 0.330955488160405 16 0.612600387080061 0.774799225839878 0.387399612919939 17 0.524822802404636 0.950354395190728 0.475177197595364 18 0.855741154814497 0.288517690371006 0.144258845185503 19 0.84999881951311 0.300002360973782 0.150001180486891 20 0.802002810476474 0.395994379047051 0.197997189523526 21 0.745897869930955 0.50820426013809 0.254102130069045 22 0.684099119237837 0.631801761524326 0.315900880762163 23 0.703792204183172 0.592415591633656 0.296207795816828 24 0.64061563760627 0.718768724787461 0.359384362393731 25 0.577482789177759 0.845034421644482 0.422517210822241 26 0.510840199927048 0.978319600145904 0.489159800072952 27 0.447186101972804 0.894372203945608 0.552813898027196 28 0.430402656037299 0.860805312074597 0.569597343962701 29 0.369874070903398 0.739748141806796 0.630125929096602 30 0.356279887151219 0.712559774302438 0.643720112848781 31 0.300856874206312 0.601713748412624 0.699143125793688 32 0.285203192192063 0.570406384384127 0.714796807807937 33 0.251839765907609 0.503679531815217 0.748160234092392 34 0.207049743900597 0.414099487801194 0.792950256099403 35 0.205931838932885 0.41186367786577 0.794068161067115 36 0.294191589926572 0.588383179853145 0.705808410073428 37 0.381722839826489 0.763445679652978 0.618277160173511 38 0.383989808759572 0.767979617519143 0.616010191240428 39 0.412444714595408 0.824889429190815 0.587555285404592 40 0.391693744234266 0.783387488468533 0.608306255765734 41 0.357991618691332 0.715983237382665 0.642008381308668 42 0.344927714219757 0.689855428439514 0.655072285780243 43 0.357907768525075 0.71581553705015 0.642092231474925 44 0.317195445568795 0.634390891137589 0.682804554431205 45 0.281112065180272 0.562224130360543 0.718887934819728 46 0.516421228254306 0.967157543491388 0.483578771745694 47 0.567873751768146 0.864252496463709 0.432126248231854 48 0.52140139380185 0.9571972123963 0.47859860619815 49 0.477155337160497 0.954310674320995 0.522844662839503 50 0.480679222342282 0.961358444684563 0.519320777657718 51 0.438573970753703 0.877147941507407 0.561426029246297 52 0.393324924345817 0.786649848691633 0.606675075654183 53 0.446961455047449 0.893922910094897 0.553038544952551 54 0.404471451454389 0.808942902908778 0.595528548545611 55 0.406474981449885 0.81294996289977 0.593525018550115 56 0.390812560784675 0.78162512156935 0.609187439215325 57 0.34951666763594 0.699033335271879 0.65048333236406 58 0.326711949330067 0.653423898660134 0.673288050669933 59 0.287653471802319 0.575306943604637 0.712346528197681 60 0.289704324454 0.579408648908 0.710295675546 61 0.260293166371496 0.520586332742992 0.739706833628504 62 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0.18215975492051 0.36431950984102 0.81784024507949 248 0.278669368608705 0.55733873721741 0.721330631391295 249 0.262232421822134 0.524464843644269 0.737767578177866 250 0.222656632817523 0.445313265635047 0.777343367182477 251 0.189286491802872 0.378572983605743 0.810713508197128 252 0.212337552441341 0.424675104882682 0.787662447558659 253 0.19409584784521 0.38819169569042 0.80590415215479 254 0.258985606869741 0.517971213739481 0.74101439313026 255 0.248278849996825 0.49655769999365 0.751721150003175 256 0.50086758464725 0.9982648307055 0.49913241535275 257 0.453196418096376 0.906392836192753 0.546803581903624 258 0.461761174397253 0.923522348794506 0.538238825602747 259 0.44069371400784 0.88138742801568 0.55930628599216 260 0.463087071786501 0.926174143573002 0.536912928213499 261 0.403509463059615 0.807018926119231 0.596490536940385 262 0.354189024496567 0.708378048993134 0.645810975503433 263 0.316609907144878 0.633219814289757 0.683390092855122 264 0.259566944219752 0.519133888439505 0.740433055780248 265 0.257080674000104 0.514161348000208 0.742919325999896 266 0.368586064858861 0.737172129717722 0.631413935141139 267 0.613750884771853 0.772498230456294 0.386249115228147 268 0.552043750471305 0.89591249905739 0.447956249528695 269 0.503051090380994 0.993897819238013 0.496948909619006 270 0.513661354451781 0.972677291096438 0.486338645548219 271 0.441941819414828 0.883883638829655 0.558058180585172 272 0.418639515243928 0.837279030487857 0.581360484756072 273 0.364864530929151 0.729729061858303 0.635135469070849 274 0.288946915103503 0.577893830207006 0.711053084896497 275 0.425595101421127 0.851190202842254 0.574404898578873 276 0.376777275592881 0.753554551185763 0.623222724407119 277 0.266605613017507 0.533211226035014 0.733394386982493 278 0.17109230607347 0.34218461214694 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/24/t1293213262ng44fsibcl3bdz5/10axcz1293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/10axcz1293213365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/1t5y31293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/1t5y31293213365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/24ffo1293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/24ffo1293213365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/34ffo1293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/34ffo1293213365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/4woer1293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/4woer1293213365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/5woer1293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/5woer1293213365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/6woer1293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/6woer1293213365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/7pxvc1293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/7pxvc1293213365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/8pxvc1293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/8pxvc1293213365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/9h6dx1293213365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293213262ng44fsibcl3bdz5/9h6dx1293213365.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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

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

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