Mini tutorial - Multiple Linear Regression

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 02 Dec 2010 11:31:15 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q.htm/, Retrieved Thu, 02 Dec 2010 12:57:23 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q.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:

Not popular test

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 13 13 14 13 3 5 3 12 12 8 13 5 3 3 15 10 12 16 6 0 3 12 9 7 12 6 7 3 10 10 10 11 5 4 3 12 12 7 12 3 1 2 15 13 16 18 8 6 3 9 12 11 11 4 3 3 12 12 14 14 4 12 4 11 6 6 9 4 0 3 11 5 16 14 6 5 3 11 12 11 12 6 6 2 15 11 16 11 5 6 3 7 14 12 12 4 6 3 11 14 7 13 6 2 3 11 12 13 11 4 1 3 10 12 11 12 6 5 3 14 11 15 16 6 7 2 10 11 7 9 4 3 4 6 7 9 11 4 3 3 11 9 7 13 2 3 2 15 11 14 15 7 7 3 11 11 15 10 5 8 3 12 12 7 11 4 6 2 14 12 15 13 6 3 2 15 11 17 16 6 5 4 9 11 15 15 7 5 2 13 8 14 14 5 10 3 13 9 14 14 6 2 2 16 12 8 14 4 6 4 13 10 8 8 4 4 3 12 10 14 13 7 6 2 14 12 14 15 7 8 3 11 8 8 13 4 4 3 9 12 11 11 4 5 1 16 11 16 15 6 10 3 12 12 10 15 6 6 3 10 7 8 9 5 7 3 13 11 14 13 6 4 2 16 11 16 16 7 10 3 14 12 13 13 6 4 15 9 5 11 3 3 5 5 15 8 12 3 3 4 8 11 10 12 4 3 3 11 11 8 12 6 3 2 16 11 13 14 7 7 2 17 11 15 14 5 15 3 9 15 6 8 4 0 4 9 11 12 13 5 0 2 13 12 16 16 6 4 3 10 12 5 13 6 5 4 6 9 15 11 6 5 3 12 12 12 14 5 2 4 8 12 8 13 4 3 3 14 13 13 13 5 0 3 12 11 14 13 5 9 4 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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation NotPopular[t] = + 2.98670740628656 -0.0111064541653232Popularity[t] + 0.496005575693039FindingFriends[t] + 0.560172927756955KnowingPeople[t] -0.80285171304812Liked[t] + 0.137898841611536Celebrity[t] -0.293925773283954WeightedSum[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) 2.98670740628656 1.645463 1.8151 0.071517 0.035759 Popularity -0.0111064541653232 0.118792 -0.0935 0.925636 0.462818 FindingFriends 0.496005575693039 0.076239 6.5059 0 0 KnowingPeople 0.560172927756955 0.090529 6.1878 0 0 Liked -0.80285171304812 0.071574 -11.2171 0 0 Celebrity 0.137898841611536 0.078246 1.7624 0.080056 0.040028 WeightedSum -0.293925773283954 0.141543 -2.0766 0.039558 0.019779 Multiple Linear Regression - Regression Statistics Multiple R 0.84624116396135 R-squared 0.716124107582662 Adjusted R-squared 0.704692863592702 F-TEST (value) 62.6462096523909 F-TEST (DF numerator) 6 F-TEST (DF denominator) 149 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.65918914845553 Sum Squared Residuals 1053.62175216228 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 5.63981236353336 -3.63981236353336 2 3 2.65752490525503 0.342475094744966 3 3 2.48400712471986 0.515992875280144 4 3 0.374382711942808 2.62561728805719 5 3 4.11985017052585 -1.11985017052585 6 3 3.21225755389104 -0.212257553891044 7 2 3.1192551802499 -1.11925518024990 8 3 5.83916763550658 -2.83916763550658 9 3 2.43247995758153 0.567520042418473 10 4 2.52753738018102 1.47246261981898 11 3 2.42517133362024 0.574828666379757 12 3 4.40812337749902 -1.40812337749902 13 2 7.33350949536604 -5.33350949536604 14 3 5.72893559008028 -2.72893559008028 15 3 3.53229419794498 -0.532294197944976 16 3 7.52515212925775 -4.52515212925775 17 3 4.7131556049483 -1.7131556049483 18 3 2.6141575248614 0.3858424751386 19 2 4.69706732071663 -2.69706732071663 20 4 2.27211326402345 1.72788673597655 21 3 0.206745179749689 2.79325482025031 22 2 2.98362869759878 -0.983628697598777 23 3 7.0327625507506 -4.03276255075059 24 3 2.68337924213092 0.316620757869077 25 2 6.69442133283461 -4.69442133283461 26 2 4.3112484727779 -2.31124847277790 27 4 4.19829189691558 -0.198291896915585 28 2 1.16310158882349 0.836898411176508 29 3 4.1484121923997 -1.14841219239970 30 2 0.790571214082226 1.20942878591777 31 4 5.23684125004874 -1.23684125004874 32 3 4.4205716837819 -1.4205716837819 33 2 3.19681495417318 -1.19681495417318 34 3 0.25278444175272 2.74721555824728 35 3 5.25131608893867 -2.25131608893867 36 1 3.07319193748396 -2.07319193748396 37 3 1.42828885643239 1.57171114356761 38 3 2.23541369417715 0.76458630582285 39 3 5.35542351026599 -2.35542351026599 40 2 2.40823906604738 -0.408239066047379 41 3 5.28014970403675 -2.28014970403675 42 15 8.06419192186081 6.93580807813919 43 5 10.3396686249889 -5.33966862498889 44 8 10.8671796532721 -2.8671796532721 45 11 8.56339084907374 2.43660915092626 46 16 11.9125082364509 4.08749176354913 47 17 15.3194877735415 1.68051222645849 48 9 5.89041752469227 3.10958247530773 49 9 11.4967412678164 -2.49674126781636 50 13 14.6049937798081 -1.60499377980813 51 10 7.31238673224142 2.68761326775858 52 6 11.4793417694378 -5.47934176943782 53 12 11.7337538780632 0.266246121936845 54 8 10.4242349754777 -2.42423497547765 55 14 11.6766081618948 2.3233918381052 56 12 13.1419904471384 -1.14199044713835 57 11 12.0374306446612 -1.03743064466125 58 16 14.7580838938548 1.24191610614525 59 8 14.9989230023693 -6.9989230023693 60 15 11.1086971646971 3.89130283530288 61 7 10.5471430092182 -3.54714300921817 62 16 14.3120409739634 1.68795902603657 63 14 13.9037662484163 0.096233751583721 64 16 12.6502196299958 3.34978037000419 65 9 8.79201275384015 0.207987246159846 66 14 12.5151076657293 1.48489233427067 67 11 12.8335883843680 -1.83358838436802 68 13 8.8591305322635 4.1408694677365 69 15 11.6941278626203 3.30587213737967 70 5 6.24994206653401 -1.24994206653401 71 15 13.4359162204223 1.56408377957769 72 13 12.6348784172800 0.365121582720013 73 11 12.6640993527726 -1.66409935277256 74 11 14.7913896476171 -3.79138964761709 75 12 11.3763621269304 0.623637873069637 76 12 12.7042671040673 -0.704267104067294 77 12 12.3019350178886 -0.301935017888561 78 12 12.5776615724515 -0.577661572451516 79 14 11.1041786547853 2.89582134521474 80 6 9.62365562138995 -3.62365562138995 81 7 9.52408340370008 -2.52408340370008 82 14 12.3400405728694 1.65995942713063 83 14 13.3857531000565 0.614246899943477 84 10 10.8472376533054 -0.847237653305417 85 13 10.0062900833589 2.99370991664108 86 12 10.6449709950659 1.3550290049341 87 9 9.03062032959518 -0.0306203295951838 88 12 12.4413050475216 -0.441305047521602 89 16 11.1642869554502 4.83571304454977 90 10 10.9227694440252 -0.922769444025204 91 14 11.4840398481428 2.5159601518572 92 10 13.1376340356444 -3.13763403564441 93 16 14.5097643648786 1.49023563512143 94 15 13.4982832713141 1.50171672868595 95 12 10.9740300407516 1.02596995924837 96 10 8.89019259512914 1.10980740487086 97 8 6.32031806092886 1.67968193907114 98 8 9.60917933190357 -1.60917933190357 99 11 14.0379860719860 -3.03798607198605 100 13 10.8762717329676 2.12372826703244 101 16 15.0168763947369 0.983123605263068 102 16 13.1596600881446 2.84033991185538 103 14 15.7854357778498 -1.78543577784982 104 11 9.1734313232094 1.82656867679060 105 4 8.81943483875701 -4.81943483875701 106 14 10.2698200385505 3.73017996144948 107 9 13.1510128487701 -4.15101284877014 108 14 11.9360902143663 2.06390978563366 109 8 12.3696590611040 -4.36965906110396 110 8 11.9582198358997 -3.95821983589969 111 11 12.1877914012893 -1.18779140128929 112 12 11.5321446828459 0.467855317154133 113 11 7.90882944885377 3.09117055114623 114 14 12.5749322150329 1.42506778496706 115 15 12.6636409037180 2.33635909628205 116 16 13.3492643668036 2.65073563319644 117 16 12.2349671797460 3.76503282025405 118 11 11.3626995624433 -0.362699562443263 119 14 13.9720623299428 0.0279376700571903 120 14 12.2728873294928 1.72711267050722 121 12 12.8219538030844 -0.821953803084415 122 14 12.7464356210983 1.25356437890174 123 8 11.1985671272483 -3.19856712724827 124 13 13.6851581925544 -0.685158192554415 125 16 13.5402377150473 2.45976228495268 126 12 9.06977428724976 2.93022571275024 127 16 12.4209757271604 3.57902427283958 128 12 11.8768740543981 0.123125945601918 129 11 10.9059392948890 0.0940607051109729 130 4 4.31532253938963 -0.315322539389629 131 16 13.6801933917251 2.31980660827488 132 15 11.0894579895420 3.91054201045803 133 10 12.5547064637049 -2.55470646370489 134 13 12.1052818858668 0.894718114133203 135 15 11.9966311972151 3.0033688027849 136 12 10.7823417095592 1.21765829044084 137 14 12.9816207127056 1.01837928729438 138 7 13.7347931858019 -6.73479318580192 139 19 13.9806398912536 5.01936010874637 140 12 13.7132698290606 -1.71326982906063 141 12 14.6973118084712 -2.69731180847124 142 13 12.6486637045806 0.351336295419442 143 15 14.3731649147882 0.62683508521181 144 8 8.48254043217644 -0.482540432176445 145 12 11.5541449684753 0.445855031524733 146 10 6.39157817754845 3.60842182245155 147 8 10.7694077367544 -2.7694077367544 148 10 14.6368147368153 -4.63681473681533 149 15 14.2033766765781 0.796623323421898 150 16 9.90349975673664 6.09650024326336 151 13 10.7184308913893 2.28156910861066 152 16 13.8577318575131 2.14226814248689 153 9 9.95747755274446 -0.957477552744455 154 14 12.0830114576097 1.91698854239033 155 14 12.2107904212288 1.78920957877123 156 12 14.6589579670823 -2.65895796708231 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.000429388122947294 0.000858776245894588 0.999570611877053 11 0.000730527467289361 0.00146105493457872 0.99926947253271 12 0.000138557620338037 0.000277115240676075 0.999861442379662 13 1.79910848727217e-05 3.59821697454433e-05 0.999982008915127 14 2.12852836940137e-06 4.25705673880274e-06 0.99999787147163 15 2.25805436844015e-07 4.51610873688031e-07 0.999999774194563 16 5.01683168676068e-08 1.00336633735214e-07 0.999999949831683 17 5.51575124385806e-09 1.10315024877161e-08 0.999999994484249 18 2.43208360751691e-09 4.86416721503383e-09 0.999999997567916 19 2.21510726346730e-08 4.43021452693460e-08 0.999999977848927 20 3.37144747107402e-09 6.74289494214805e-09 0.999999996628553 21 9.41760948767846e-10 1.88352189753569e-09 0.99999999905824 22 2.3334810497393e-10 4.6669620994786e-10 0.999999999766652 23 7.85517199778525e-11 1.57103439955705e-10 0.999999999921448 24 1.37859176788035e-11 2.75718353576069e-11 0.999999999986214 25 3.57235974493121e-12 7.14471948986243e-12 0.999999999996428 26 7.8881926041566e-13 1.57763852083132e-12 0.999999999999211 27 6.32062223754689e-13 1.26412444750938e-12 0.999999999999368 28 3.79816315907879e-13 7.59632631815759e-13 0.99999999999962 29 7.40780612979165e-14 1.48156122595833e-13 0.999999999999926 30 1.20067499811604e-14 2.40134999623207e-14 0.999999999999988 31 1.03416084774483e-13 2.06832169548966e-13 0.999999999999897 32 2.17651337368183e-14 4.35302674736367e-14 0.999999999999978 33 6.13804271494524e-15 1.22760854298905e-14 0.999999999999994 34 1.22119633916234e-15 2.44239267832467e-15 0.999999999999999 35 2.75990869642768e-16 5.51981739285537e-16 1 36 3.86687701497779e-16 7.73375402995558e-16 1 37 8.89025431016517e-17 1.77805086203303e-16 1 38 2.27582297035992e-17 4.55164594071984e-17 1 39 1.30450771407335e-17 2.60901542814669e-17 1 40 3.721601180822e-17 7.443202361644e-17 1 41 1.96523337595439e-15 3.93046675190878e-15 0.999999999999998 42 0.0514726740767212 0.102945348153442 0.948527325923279 43 0.0859224545816991 0.171844909163398 0.9140775454183 44 0.0828927811935519 0.165785562387104 0.917107218806448 45 0.199750734674156 0.399501469348313 0.800249265325844 46 0.8338572395161 0.332285520967800 0.166142760483900 47 0.833407891031713 0.333184217936575 0.166592108968287 48 0.854039172889335 0.29192165422133 0.145960827110665 49 0.854658420808766 0.290683158382468 0.145341579191234 50 0.888172639032306 0.223654721935387 0.111827360967694 51 0.868973626683891 0.262052746632218 0.131026373316109 52 0.957687390417254 0.0846252191654912 0.0423126095827456 53 0.96333884527627 0.0733223094474613 0.0366611547237306 54 0.965274000641586 0.0694519987168273 0.0347259993584136 55 0.987792405188837 0.0244151896223259 0.0122075948111630 56 0.984286254865396 0.0314274902692074 0.0157137451346037 57 0.979846343762142 0.0403073124757166 0.0201536562378583 58 0.985484905823214 0.0290301883535715 0.0145150941767857 59 0.996464957038868 0.00707008592226502 0.00353504296113251 60 0.999148759112026 0.00170248177594788 0.000851240887973938 61 0.999237535248951 0.00152492950209756 0.000762464751048781 62 0.999349134668226 0.00130173066354768 0.00065086533177384 63 0.999176839931601 0.00164632013679696 0.000823160068398482 64 0.999622199184614 0.00075560163077251 0.000377800815386255 65 0.999426792322648 0.00114641535470463 0.000573207677352313 66 0.999356990507936 0.00128601898412752 0.000643009492063762 67 0.999403897614371 0.00119220477125828 0.000596102385629139 68 0.99973193948126 0.000536121037478694 0.000268060518739347 69 0.999773511379993 0.000452977240012923 0.000226488620006462 70 0.999729337274968 0.000541325450064904 0.000270662725032452 71 0.999724122590696 0.000551754818607428 0.000275877409303714 72 0.999582026969936 0.000835946060127548 0.000417973030063774 73 0.999405639259463 0.00118872148107334 0.000594360740536668 74 0.99955965094066 0.00088069811868029 0.000440349059340145 75 0.999366225100581 0.00126754979883792 0.00063377489941896 76 0.999223095380364 0.00155380923927295 0.000776904619636477 77 0.998869368432236 0.00226126313552829 0.00113063156776414 78 0.99837531495697 0.00324937008605889 0.00162468504302944 79 0.998871026619255 0.00225794676149053 0.00112897338074526 80 0.999143373845068 0.00171325230986342 0.000856626154931712 81 0.999116965852018 0.0017660682959646 0.0008830341479823 82 0.999204162762134 0.00159167447573277 0.000795837237866387 83 0.998891549467514 0.00221690106497189 0.00110845053248595 84 0.99847233733729 0.00305532532541955 0.00152766266270978 85 0.999569622848842 0.000860754302317045 0.000430377151158522 86 0.999422381994566 0.00115523601086851 0.000577618005434254 87 0.999121414854953 0.00175717029009320 0.000878585145046599 88 0.998866124140725 0.00226775171855093 0.00113387585927547 89 0.99924640632927 0.00150718734146044 0.000753593670730222 90 0.998883221426636 0.00223355714672796 0.00111677857336398 91 0.9986896791631 0.00262064167379977 0.00131032083689988 92 0.999137852388177 0.001724295223646 0.000862147611823 93 0.998881939259347 0.00223612148130677 0.00111806074065339 94 0.998550779996895 0.00289844000620975 0.00144922000310487 95 0.99794169768387 0.00411660463225813 0.00205830231612906 96 0.99707708569029 0.00584582861941968 0.00292291430970984 97 0.996049724387556 0.00790055122488862 0.00395027561244431 98 0.994614777312794 0.010770445374413 0.0053852226872065 99 0.99417087725071 0.0116582454985784 0.00582912274928922 100 0.992867016128795 0.0142659677424096 0.00713298387120479 101 0.990460349886322 0.0190793002273551 0.00953965011367755 102 0.989086074206443 0.0218278515871149 0.0109139257935575 103 0.991589404522872 0.0168211909542554 0.00841059547712768 104 0.992780000587399 0.0144399988252024 0.0072199994126012 105 0.993469678681714 0.0130606426365712 0.00653032131828561 106 0.993121774626668 0.0137564507466643 0.00687822537333217 107 0.992453297195778 0.0150934056084445 0.00754670280422226 108 0.993336488650858 0.0133270226982834 0.0066635113491417 109 0.994805618849024 0.0103887623019524 0.00519438115097622 110 0.995828473475053 0.00834305304989435 0.00417152652494717 111 0.995004458093604 0.00999108381279153 0.00499554190639576 112 0.996738565126588 0.00652286974682496 0.00326143487341248 113 0.99578636144782 0.00842727710436053 0.00421363855218027 114 0.993914818765018 0.0121703624699651 0.00608518123498253 115 0.991700049442792 0.0165999011144151 0.00829995055720754 116 0.992291751100562 0.0154164977988766 0.00770824889943831 117 0.993103528047763 0.0137929439044739 0.00689647195223694 118 0.98993891596612 0.0201221680677614 0.0100610840338807 119 0.984952385322899 0.0300952293542030 0.0150476146771015 120 0.989322211421922 0.021355577156156 0.010677788578078 121 0.98483001258123 0.0303399748375387 0.0151699874187694 122 0.977956505486933 0.0440869890261345 0.0220434945130673 123 0.97519827200154 0.0496034559969207 0.0248017279984604 124 0.96465896780478 0.07068206439044 0.03534103219522 125 0.961129271220504 0.0777414575589914 0.0388707287794957 126 0.959343875766437 0.0813122484671263 0.0406561242335632 127 0.947244946171157 0.105510107657685 0.0527550538288426 128 0.944885074908693 0.110229850182615 0.0551149250913074 129 0.962337924046218 0.0753241519075644 0.0376620759537822 130 0.95077422649332 0.0984515470133593 0.0492257735066797 131 0.932381319163265 0.13523736167347 0.067618680836735 132 0.925789565459797 0.148420869080406 0.0742104345402028 133 0.896208119098758 0.207583761802484 0.103791880901242 134 0.856107588051293 0.287784823897415 0.143892411948707 135 0.827029698050106 0.345940603899788 0.172970301949894 136 0.801501693553192 0.396996612893617 0.198498306446808 137 0.761229158207378 0.477541683585244 0.238770841792622 138 0.788723187794414 0.422553624411172 0.211276812205586 139 0.963182395090226 0.0736352098195482 0.0368176049097741 140 0.992241537816593 0.0155169243668151 0.00775846218340754 141 0.984544708711558 0.0309105825768841 0.0154552912884420 142 0.966749208105246 0.066501583789507 0.0332507918947535 143 0.93569078992425 0.128618420151501 0.0643092100757505 144 0.874374833657287 0.251250332685425 0.125625166342713 145 0.805760227110124 0.388479545779752 0.194239772889876 146 0.735273958206097 0.529452083587806 0.264726041793903 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 75 0.547445255474453 NOK 5% type I error level 103 0.751824817518248 NOK 10% type I error level 113 0.824817518248175 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/10uel61291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/10uel61291289463.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/1ndoc1291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/1ndoc1291289463.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/2ndoc1291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/2ndoc1291289463.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/3y4nf1291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/3y4nf1291289463.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/4y4nf1291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/4y4nf1291289463.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/5y4nf1291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/5y4nf1291289463.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/69wmi1291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/69wmi1291289463.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/72n431291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/72n431291289463.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/82n431291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/82n431291289463.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/92n431291289463.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291291026jg8ozfvprf7wr9q/92n431291289463.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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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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