*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 24 Nov 2010 15:02:47 +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/Nov/24/t12906108708otqnpnaews2tg7.htm/, Retrieved Wed, 24 Nov 2010 16:01:10 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/24/t12906108708otqnpnaews2tg7.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 «

24 14 11 12 24 26 237.588 25 11 7 8 25 23 164.083 17 6 17 8 30 25 278.261 18 12 10 8 19 23 220.36 18 8 12 9 22 19 253.967 16 10 12 7 22 29 422.31 20 10 11 4 25 25 136.921 16 11 11 11 23 21 143.495 18 16 12 7 17 22 189.785 17 11 13 7 21 25 219.529 23 13 14 12 19 24 217.761 30 12 16 10 19 18 221.754 23 8 11 10 15 22 159.854 18 12 10 8 16 15 209.464 15 11 11 8 23 22 174.283 12 4 15 4 27 28 154.55 21 9 9 9 22 20 153.024 15 8 11 8 14 12 162.49 20 8 17 7 22 24 154.462 31 14 17 11 23 20 249.671 27 15 11 9 23 21 259.473 34 16 18 11 21 20 155.337 21 9 14 13 19 21 151.289 31 14 10 8 18 23 276.614 19 11 11 8 20 28 188.214 16 8 15 9 23 24 181.098 20 9 15 6 25 24 240.898 21 9 13 9 19 24 244.551 22 9 16 9 24 23 250.238 17 9 13 6 22 23 183.129 24 10 9 6 25 29 310.331 25 16 18 16 26 24 281.942 26 11 18 5 29 18 230.343 25 8 12 7 32 25 161.563 17 9 17 9 25 21 392.527 32 16 9 6 29 26 1077.414 33 11 9 6 28 22 248.275 13 16 12 5 17 22 557.386 32 12 18 12 28 22 731.874 25 12 12 7 29 23 301.42 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation PS[t] = + 7.49421672000384 + 0.328566099942966CM[t] -0.367928837189673D[t] + 0.183960797094827PE[t] + 0.0231775389634428PC[t] + 0.400279254796218O[t] + 0.000246245385480168Time[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) 7.49421672000384 2.256315 3.3214 0.001122 0.000561 CM 0.328566099942966 0.055712 5.8975 0 0 D -0.367928837189673 0.108331 -3.3963 0.000872 0.000436 PE 0.183960797094827 0.101668 1.8094 0.072361 0.03618 PC 0.0231775389634428 0.128986 0.1797 0.857635 0.428817 O 0.400279254796218 0.072026 5.5574 0 0 Time 0.000246245385480168 0.000664 0.3707 0.7114 0.3557 Multiple Linear Regression - Regression Statistics Multiple R 0.60633034651225 R-squared 0.367636489101665 Adjusted R-squared 0.342674771566204 F-TEST (value) 14.7280125487920 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 3.17190718135407e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.41892436043040 Sum Squared Residuals 1776.73465491636 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 22.9962642069312 1.00373579306882 2 25 22.3811254427617 2.61887455723832 3 30 24.2605231153304 5.73947688466962 4 19 20.2789742488144 -1.27897424881439 5 22 20.5489472802111 1.45105271978886 6 22 23.1538485629090 -1.15384856290904 7 25 22.5432268051941 2.45677319480592 8 23 19.4237781389559 3.57622186104408 9 17 18.7441947478246 -1.74419474782463 10 21 21.6473957180592 -0.647395718059238 11 19 22.782068518612 -3.78206851861198 12 19 23.3708343007121 -4.3708343007121 13 15 23.2086573942195 -8.20865739421955 14 16 17.0740571207245 -1.07405712072445 15 23 19.433540079847 3.56645992015300 16 27 24.063293041457 2.93670695854302 17 22 20.9902568584156 1.00974314158442 18 14 16.5316300716229 -2.53163007162287 19 22 24.0564220145432 -2.05642201454321 20 23 23.9781140043529 -0.978114004352875 21 23 21.5484938589602 1.45150614103982 22 21 24.3886861147034 -3.38868611470337 23 19 22.4026230187959 -3.40262301879589 24 18 23.8283281616084 -5.8283281616084 25 20 23.1529104528613 -3.1529104528613 26 23 22.4271500905962 0.572849909403776 27 25 23.3186785103398 1.6813214896602 28 19 23.3497551673766 -4.3497551673766 29 24 23.8313248013151 0.168675198684945 30 22 21.5505540118512 0.449445988148773 31 25 25.1797431201842 -0.179743120184167 32 26 23.1797718262475 2.82022817375252 33 29 22.6786476391182 6.32135236088176 34 32 25.1814763720624 6.81852362793758 35 25 21.6069345987572 3.3930654012428 36 29 24.5887517812315 4.41124821876851 37 28 24.9516733952663 3.0483266047337 38 17 17.1455292201308 -0.145529220130813 39 28 26.1689748879406 1.83102511205941 40 29 22.9436438707969 6.05635612920314 41 26 27.4788173843796 -1.47881738437958 42 25 23.4547304446488 1.54526955535121 43 14 19.5175237491656 -5.51752374916558 44 25 22.0881209893503 2.91187901064969 45 26 21.6701564357049 4.32984356429514 46 20 20.3197264124031 -0.319726412403089 47 18 21.3671547222272 -3.36715472222716 48 32 24.6433670747050 7.35663292529504 49 25 25.0016361320139 -0.00163613201390608 50 25 21.7203585993336 3.27964140066644 51 23 20.8060346700993 2.19396532990071 52 21 22.1492356754625 -1.14923567546245 53 20 24.0299933640438 -4.02999336404385 54 15 16.5442987740029 -1.54429877400293 55 30 26.7137918866851 3.2862081133149 56 24 25.3300162522617 -1.33001625226169 57 26 24.3094954671993 1.69050453280074 58 24 21.7460901356922 2.25390986430777 59 22 21.5386621916241 0.461337808375948 60 14 15.6507000971806 -1.65070009718056 61 24 22.2400416508248 1.7599583491752 62 24 22.9193513522898 1.08064864771015 63 24 23.3132390401273 0.68676095987275 64 24 19.9847646016855 4.01523539831449 65 19 18.5362706691139 0.463729330886069 66 31 26.8120887294192 4.18791127058078 67 22 26.6055871493741 -4.60558714937407 68 27 21.4729775347493 5.5270224652507 69 19 17.6955673571701 1.30443264282986 70 25 22.2984211526827 2.70157884731732 71 20 25.0122922063225 -5.01229220632251 72 21 21.5762342604157 -0.576234260415737 73 27 27.4556169963108 -0.455616996310772 74 23 24.3037504827979 -1.30375048279792 75 25 25.6728958132087 -0.672895813208659 76 20 22.2299078147637 -2.2299078147637 77 21 19.1981960583815 1.80180394161847 78 22 22.417505141978 -0.417505141978007 79 23 23.0204165951386 -0.0204165951386168 80 25 24.0533155072195 0.946684492780452 81 25 23.4189332648042 1.58106673519578 82 17 23.8763795816059 -6.8763795816059 83 19 21.4424520620989 -2.44245206209886 84 25 23.9653388818638 1.03466111813623 85 19 22.3636478391902 -3.36364783919022 86 20 23.1563781126177 -3.1563781126177 87 26 22.5190116148012 3.48098838519878 88 23 20.7769259189403 2.22307408105969 89 27 24.392222416458 2.60777758354202 90 17 20.8995279474386 -3.89952794743858 91 17 23.3043464837684 -6.30434648376844 92 19 20.2150781936552 -1.21507819365519 93 17 19.7149683814551 -2.71496838145506 94 22 22.06731290046 -0.0673129004599782 95 21 23.5448525940642 -2.54485259406416 96 32 28.5872719187446 3.41272808125542 97 21 25.0868789369244 -4.08687893692439 98 21 24.2853818863904 -3.28538188639035 99 18 21.2932588686096 -3.29325886860963 100 18 21.2820264382490 -3.28202643824897 101 23 22.8180415895634 0.181958410436570 102 19 20.6573878892702 -1.65738788927018 103 20 20.8995953382737 -0.899595338273686 104 21 22.3335305420844 -1.33353054208437 105 20 23.8127345742175 -3.81273457421754 106 17 18.7686083422305 -1.76860834223047 107 18 20.3002417700377 -2.30024177003772 108 19 20.7495092255928 -1.74950922559285 109 22 22.0366239387346 -0.0366239387345734 110 15 18.7407712497276 -3.74077124972764 111 14 18.8355296791659 -4.83552967916586 112 18 26.6291025639715 -8.62910256397148 113 24 21.5505509898711 2.44944901012894 114 35 23.5633972054291 11.4366027945709 115 29 19.2039535019427 9.79604649805726 116 21 21.967868257756 -0.967868257756001 117 25 20.5021838260721 4.49781617392795 118 20 18.4812793547594 1.51872064524063 119 22 23.1946468951034 -1.19464689510339 120 13 16.8291807695812 -3.82918076958117 121 26 23.2344953166909 2.76550468330912 122 17 16.8733506318130 0.12664936818703 123 25 20.0720113696827 4.92798863031729 124 20 20.7767361587495 -0.776736158749502 125 19 18.0601762336538 0.939823766346184 126 21 22.5959450671439 -1.59594506714386 127 22 21.0689785113094 0.931021488690564 128 24 22.6905984418058 1.30940155819417 129 21 22.982097229875 -1.982097229875 130 26 25.5178091406303 0.482190859369658 131 24 20.5703782637555 3.42962173624446 132 16 20.3122802923847 -4.31228029238474 133 23 22.3629503695323 0.637049630467728 134 18 20.8149317488686 -2.81493174886861 135 16 22.3642469310098 -6.36424693100983 136 26 24.0302321620341 1.96976783796592 137 19 19.0871712491341 -0.0871712491341471 138 21 16.8582901590141 4.14170984098589 139 21 22.2021942974782 -1.20219429747818 140 22 18.4932588273828 3.50674117261723 141 23 19.7298333834010 3.27016661659905 142 29 24.7920678538949 4.20793214610507 143 21 19.17187081109 1.82812918891002 144 21 19.9285190316639 1.07148096833607 145 23 23.0163143430536 -0.0163143430536237 146 27 22.9393206891251 4.06067931087485 147 25 25.3596759096072 -0.359675909607165 148 21 20.9918076532554 0.00819234674459343 149 10 17.1263926997398 -7.12639269973983 150 20 22.6678186162857 -2.6678186162857 151 26 22.5737736927436 3.42622630725645 152 24 23.5995633031397 0.400436696860332 153 29 31.612147522841 -2.61214752284098 154 19 18.9708868931160 0.0291131068840264 155 24 22.0494535679128 1.95054643208716 156 19 20.7482599647819 -1.74825996478193 157 24 23.419837637952 0.580162362047991 158 22 21.7948537513373 0.205146248662671 159 17 23.6833853837874 -6.68338538378743 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.111826554309661 0.223653108619321 0.88817344569034 11 0.312023218759579 0.624046437519159 0.68797678124042 12 0.192339400052152 0.384678800104304 0.807660599947848 13 0.904219024549064 0.191561950901872 0.095780975450936 14 0.849641488857788 0.300717022284424 0.150358511142212 15 0.799604632407437 0.400790735185126 0.200395367592563 16 0.754654552119464 0.490690895761071 0.245345447880536 17 0.679008324136573 0.641983351726855 0.320991675863427 18 0.644380953876067 0.711238092247866 0.355619046123933 19 0.585643133009941 0.828713733980119 0.414356866990059 20 0.581757570265131 0.836484859469738 0.418242429734869 21 0.562501662946044 0.874996674107911 0.437498337053956 22 0.493090472662342 0.986180945324683 0.506909527337658 23 0.444621239753454 0.889242479506908 0.555378760246546 24 0.489029153775672 0.978058307551345 0.510970846224328 25 0.502087969291693 0.995824061416615 0.497912030708307 26 0.431246973008219 0.862493946016437 0.568753026991781 27 0.377457063728912 0.754914127457824 0.622542936271088 28 0.391459414209954 0.782918828419908 0.608540585790046 29 0.334415085545063 0.668830171090126 0.665584914454937 30 0.276648702510233 0.553297405020466 0.723351297489767 31 0.225256085763367 0.450512171526734 0.774743914236633 32 0.245215053104533 0.490430106209067 0.754784946895466 33 0.396015868106801 0.792031736213602 0.603984131893199 34 0.632669865507602 0.734660268984797 0.367330134492399 35 0.60669986357242 0.78660027285516 0.39330013642758 36 0.573623522029754 0.852752955940492 0.426376477970246 37 0.580443426413375 0.83911314717325 0.419556573586625 38 0.550804949340372 0.898390101319255 0.449195050659628 39 0.496764478746724 0.993528957493447 0.503235521253276 40 0.589594893611027 0.820810212777946 0.410405106388973 41 0.543438644540949 0.913122710918102 0.456561355459051 42 0.496678804851487 0.993357609702975 0.503321195148513 43 0.58224460551052 0.83551078897896 0.41775539448948 44 0.553339465535186 0.893321068929628 0.446660534464814 45 0.581097108909403 0.837805782181194 0.418902891090597 46 0.532801697246697 0.934396605506606 0.467198302753303 47 0.510841140407933 0.978317719184134 0.489158859592067 48 0.657789957721259 0.684420084557483 0.342210042278741 49 0.613769847275331 0.772460305449338 0.386230152724669 50 0.593467987099017 0.813064025801965 0.406532012900982 51 0.555560575771904 0.888878848456192 0.444439424228096 52 0.51369087886096 0.97261824227808 0.48630912113904 53 0.541205405586484 0.917589188827032 0.458794594413516 54 0.512609192476076 0.974781615047848 0.487390807523924 55 0.545338976206478 0.909322047587045 0.454661023793523 56 0.509911830771903 0.980176338456193 0.490088169228097 57 0.468893416240098 0.937786832480196 0.531106583759902 58 0.434091656542364 0.868183313084728 0.565908343457636 59 0.390602502722927 0.781205005445854 0.609397497277073 60 0.352681288257497 0.705362576514994 0.647318711742503 61 0.322718510683227 0.645437021366455 0.677281489316773 62 0.285357892404444 0.570715784808888 0.714642107595556 63 0.248339592652623 0.496679185305245 0.751660407347377 64 0.274760658556674 0.549521317113348 0.725239341443326 65 0.237424672141676 0.474849344283352 0.762575327858324 66 0.252312154407402 0.504624308814805 0.747687845592598 67 0.312207352044850 0.624414704089699 0.68779264795515 68 0.381940406072917 0.763880812145835 0.618059593927083 69 0.34859503042642 0.69719006085284 0.65140496957358 70 0.332868185802845 0.66573637160569 0.667131814197155 71 0.414771347756137 0.829542695512275 0.585228652243863 72 0.378089183316672 0.756178366633345 0.621910816683328 73 0.33598078675489 0.67196157350978 0.66401921324511 74 0.29697894643773 0.59395789287546 0.70302105356227 75 0.263721722289576 0.527443444579151 0.736278277710424 76 0.241756850656723 0.483513701313447 0.758243149343277 77 0.222453493429253 0.444906986858507 0.777546506570747 78 0.189300274558610 0.378600549117219 0.81069972544139 79 0.160459600954963 0.320919201909927 0.839540399045037 80 0.136965801232548 0.273931602465095 0.863034198767452 81 0.118144083834776 0.236288167669552 0.881855916165224 82 0.205504674632148 0.411009349264295 0.794495325367852 83 0.191026897308407 0.382053794616813 0.808973102691593 84 0.164328016825473 0.328656033650947 0.835671983174527 85 0.164712234413298 0.329424468826595 0.835287765586702 86 0.165987531164426 0.331975062328851 0.834012468835574 87 0.173430639889546 0.346861279779092 0.826569360110454 88 0.162531117017903 0.325062234035805 0.837468882982097 89 0.154260555976373 0.308521111952746 0.845739444023627 90 0.159509018828885 0.319018037657769 0.840490981171115 91 0.22444076751975 0.4488815350395 0.77555923248025 92 0.19328339243042 0.38656678486084 0.80671660756958 93 0.174548983987257 0.349097967974513 0.825451016012743 94 0.148320651811033 0.296641303622066 0.851679348188967 95 0.135191003260830 0.270382006521660 0.86480899673917 96 0.141112182585688 0.282224365171375 0.858887817414312 97 0.165420870115283 0.330841740230566 0.834579129884717 98 0.160773967750728 0.321547935501456 0.839226032249272 99 0.153455019896338 0.306910039792675 0.846544980103663 100 0.148015403589884 0.296030807179769 0.851984596410116 101 0.121828068381285 0.243656136762569 0.878171931618715 102 0.101817176876280 0.203634353752560 0.89818282312372 103 0.082125042147522 0.164250084295044 0.917874957852478 104 0.0666162031903619 0.133232406380724 0.933383796809638 105 0.0707244022049659 0.141448804409932 0.929275597795034 106 0.0581562997272135 0.116312599454427 0.941843700272786 107 0.0512635623975983 0.102527124795197 0.948736437602402 108 0.0447647003418493 0.0895294006836986 0.95523529965815 109 0.0342928127154953 0.0685856254309906 0.965707187284505 110 0.0335539414370995 0.0671078828741989 0.9664460585629 111 0.0419047638821792 0.0838095277643584 0.95809523611782 112 0.169006385173003 0.338012770346006 0.830993614826997 113 0.153004924261723 0.306009848523447 0.846995075738276 114 0.573449854700273 0.853100290599454 0.426550145299727 115 0.861369408820611 0.277261182358777 0.138630591179389 116 0.829520692637699 0.340958614724603 0.170479307362301 117 0.882164680698267 0.235670638603467 0.117835319301733 118 0.858376033908855 0.283247932182290 0.141623966091145 119 0.83037306545795 0.339253869084099 0.169626934542049 120 0.863328698144713 0.273342603710575 0.136671301855287 121 0.83993124707909 0.320137505841818 0.160068752920909 122 0.800976223658472 0.398047552683057 0.199023776341528 123 0.832395605479453 0.335208789041094 0.167604394520547 124 0.791485957280983 0.417028085438033 0.208514042719017 125 0.751514164047219 0.496971671905562 0.248485835952781 126 0.703118310799959 0.593763378400082 0.296881689200041 127 0.667557583770967 0.664884832458066 0.332442416229033 128 0.627070266196097 0.745859467607805 0.372929733803903 129 0.568452642062959 0.863094715874082 0.431547357937041 130 0.506014462953606 0.987971074092789 0.493985537046394 131 0.504620066418134 0.990759867163732 0.495379933581866 132 0.501189229958031 0.997621540083938 0.498810770041969 133 0.45301077639033 0.90602155278066 0.54698922360967 134 0.403268059694927 0.806536119389854 0.596731940305073 135 0.547757074836976 0.904485850326049 0.452242925163024 136 0.513733694848921 0.972532610302158 0.486266305151079 137 0.438794496783966 0.877588993567932 0.561205503216034 138 0.45280697684006 0.90561395368012 0.54719302315994 139 0.378081348329738 0.756162696659476 0.621918651670262 140 0.341975051085856 0.683950102171711 0.658024948914144 141 0.297949356448869 0.595898712897739 0.70205064355113 142 0.346174481670879 0.692348963341759 0.65382551832912 143 0.505558773304085 0.98888245339183 0.494441226695915 144 0.424751349731996 0.849502699463993 0.575248650268004 145 0.365044588405198 0.730089176810396 0.634955411594802 146 0.323918023796309 0.647836047592618 0.676081976203691 147 0.276621033235619 0.553242066471239 0.72337896676438 148 0.176320393283949 0.352640786567899 0.82367960671605 149 0.312420858802892 0.624841717605784 0.687579141197108 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 4 0.0285714285714286 OK

Charts produced by software:

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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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Software written by Ed van Stee & Patrick Wessa

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