Workshop 7 Multiple Lineair Regression 1

*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: Tue, 23 Nov 2010 11:23:19 +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/23/t12905114317cldyhux11ycpmj.htm/, Retrieved Tue, 23 Nov 2010 12:23:51 +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/23/t12905114317cldyhux11ycpmj.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 «

5,5 6 5,33 12 3,5 4 5,56 11 8,5 4 3,78 14 5 4 4,00 12 6 4,5 4,00 21 6 3,5 3,56 12 5,5 2 4,44 22 5,5 5,5 3,56 11 6 3,5 4,00 10 6,5 3,5 3,78 13 7 6 5,11 10 8 5 6,67 8 5,5 5 5,11 15 5 4 4,00 14 5,5 4 3,33 10 7,5 2 2,67 14 4,5 4,5 4,67 14 5,5 4 3,33 11 8,5 3,5 4,44 10 8,5 5,5 6,89 13 5,5 4,5 6,00 7 9 5,5 7,56 14 7 6,5 4,67 12 5 4 6,89 14 5,5 4 4,22 11 7,5 4,5 3,56 9 7,5 3 4,44 11 6,5 4,5 4,67 15 8 4,5 4,89 14 6,5 3 3,78 13 4,5 3 5,33 9 9 8 5,56 15 9 2,5 5,78 10 6 3,5 5,56 11 8,5 4,5 3,78 13 4,5 3 7,11 8 4,5 3 7,33 20 6 2,5 2,89 12 9 6 7,11 10 6 3,5 5,56 10 9 5 6,44 9 7 4,5 4,89 14 7,5 4 4,00 8 8 2,5 3,78 14 5 4 4,44 11 5,5 4 3,33 13 7 5 4,44 9 4,5 3 7,33 11 6 4 6,44 15 8,5 3,5 5,11 11 2,5 2 5,78 10 6 4 4,00 14 6 4 4,44 18 3 2 2,44 14 12 10 6,22 11 6 4 5,78 12 6 4 4,89 13 7 3 3,78 9 3,5 2 2,67 10 6,5 4 3,11 15 6 4,5 3,78 20 6,5 3 4,67 12 7 3,5 4,22 12 4 4,5 4,00 14 5,5 2,5 2,22 13 4,5 2,5 6,44 11 5,5 4 6,89 17 6,5 4 4,22 12 5 3 2,00 13 5,5 4 4,44 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 9 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Depression[t] = + 14.1670937733770 -0.00374346986010154Expect[t] -0.0356071628680679Criticism[t] -0.230056642873884Concerns[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) 14.1670937733770 1.194134 11.8639 0 0 Expect -0.00374346986010154 0.184582 -0.0203 0.983845 0.491923 Criticism -0.0356071628680679 0.233426 -0.1525 0.878958 0.439479 Concerns -0.230056642873884 0.211821 -1.0861 0.279125 0.139562 Multiple Linear Regression - Regression Statistics Multiple R 0.0996858428771909 R-squared 0.00993726727013599 Adjusted R-squared -0.0092252372343129 F-TEST (value) 0.518578731074993 F-TEST (DF numerator) 3 F-TEST (DF denominator) 155 p-value 0.67010300974329 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.15987814050084 Sum Squared Residuals 1547.64862873633 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 12.7066598054202 -0.706659805420193 2 11 12.7324480430155 -1.73244804301554 3 14 13.1232315180305 0.876768481969457 4 12 13.0857212011086 -1.08572120110864 5 21 13.0641741498145 7.9358258501855 6 12 13.2010062355471 -1.20100623554709 7 22 13.0538388690502 8.94616113094978 8 11 13.131663644741 -2.131663644741 9 10 13.0997813126826 -3.09978131268258 10 13 13.1485220391848 -0.14852203918478 11 10 12.7516570620623 -2.75165706206229 12 8 12.424632392187 -4.424632392187 13 15 12.7928794297205 2.20712057027949 14 14 13.0857212011086 0.914278798891356 15 10 13.2379874169041 -3.23798741690409 16 14 13.4535521872168 0.546447812783209 17 14 12.9156514038792 1.08434859612084 18 11 13.2379874169041 -2.23798741690409 19 10 12.9891977151678 -2.98919771516781 20 13 12.3543446143907 0.645655385609337 21 7 12.6059325989968 -5.60593259899679 22 14 12.1983349287351 1.80166507126489 23 12 12.8350784034928 -0.835078403492769 24 14 12.4208575032031 1.57914249679688 25 11 13.0332370047463 -2.03323700474634 26 9 13.1597838678889 -4.15978386788886 27 11 13.0107447664619 -2.01074476646195 28 15 12.9081644641590 2.09183553584104 29 14 12.8519367979365 1.14806320206345 30 13 13.1663256206188 -0.166325620618814 31 9 12.8172247638845 -3.8172247638845 32 15 12.5694303073127 2.43056969268729 33 10 12.7146572416548 -2.71465724165483 34 11 12.7408929497993 -1.74089294979932 35 13 13.1054279365965 -0.105427936596509 36 8 12.4077239395690 -4.40772393956898 37 20 12.3571114781367 7.64288852186327 38 12 13.3907513491407 -1.39075134914066 39 10 12.2840568365943 -2.28405683659432 40 10 12.7408929497993 -2.74089294979932 41 9 12.4738019501879 -3.47380195018789 42 14 12.8556802677967 1.14431973220335 43 8 13.0763625264584 -5.07636252645839 44 14 13.1785139972627 0.821486002737304 45 11 12.9844962782441 -1.98449627824413 46 13 13.2379874169041 -0.237987416904095 47 9 12.9414021756559 -3.94140217565586 48 11 12.3571114781367 -1.35711147813673 49 15 12.5206395226363 2.47936047736373 50 11 12.8350597644423 -1.83505976444231 51 10 12.7567933771795 -2.75679337717952 52 14 13.0819777312485 0.918022268751458 53 18 12.9807528083840 5.01924719161597 54 14 13.5233108294482 0.476689170551759 55 11 12.3351481876995 -1.33514818769950 56 12 12.6724769069330 -0.672476906933029 57 13 12.8772273190908 0.122772680909214 58 9 13.1644538856888 -4.16445388568876 59 10 13.4685260666572 -3.4685260666572 60 15 13.2848564084762 1.71514359152375 61 20 13.1147866112468 6.88521338875324 62 12 12.9615752084611 -0.961575208461058 63 12 13.0454253813902 -1.04542538139022 64 14 13.0716610895347 0.928338910465289 65 13 13.5467610347962 -0.546761034796208 66 11 12.5796654717285 -1.57966547172852 67 17 12.4189857682731 4.58101423172693 68 12 13.0294935348862 -1.02949353488624 69 13 13.5814416497245 -0.581441649724479 70 14 12.9826245433141 1.01737545668592 71 13 12.5890555655026 0.410944434497445 72 15 13.0547840560405 1.94521594395953 73 13 12.4443077085511 0.555692291448913 74 10 12.4559983687539 -2.45599836875386 75 11 12.7024688650109 -1.70246886501094 76 19 12.8266148576585 6.17338514234147 77 13 13.3710760327766 -0.371076032776571 78 17 12.9062927292289 4.09370727077110 79 13 13.0351087396764 -0.0351087396763895 80 9 12.6049874120065 -3.60498741200654 81 11 12.7891359598604 -1.78913595986041 82 10 13.0838494661786 -3.08384946617859 83 9 12.925968045593 -3.92596804559299 84 12 12.9376587057958 -0.937658705795762 85 12 12.8875125416808 -0.887512541680836 86 13 12.9381564222369 0.0618435777631288 87 13 12.9831222597552 0.0168777402448070 88 12 13.2417308867642 -1.24173088676420 89 15 12.4569435557441 2.54305644425589 90 22 13.0491688512503 8.95083114874968 91 13 12.6687334370729 0.331266562927072 92 15 13.5345726581523 1.46542734184767 93 13 13.2422286032053 -0.242228603205305 94 15 12.9072192771687 2.0927807228313 95 10 12.9976298418783 -2.99762984187827 96 11 12.3290540932364 -1.32905409323643 97 16 12.3955669820489 3.60443301795112 98 11 12.4381947873198 -1.43819478731983 99 11 13.0491688512503 -2.04916885125032 100 10 12.8753555841607 -2.87535558416074 101 10 12.7853924900003 -2.78539249000031 102 16 13.2717228448421 2.72827715515789 103 12 12.9320435010056 -0.93204350100561 104 11 13.0407553635903 -2.04075536359032 105 16 12.7928794297205 3.20712057027949 106 19 12.7783718475974 6.22162815240256 107 11 12.9493868318172 -1.94938683181718 108 16 12.7385234984282 3.26147650157184 109 15 12.6640634192730 2.33593658072697 110 24 13.1681973555489 10.8318026444511 111 14 13.3551441862726 0.644855813727413 112 15 12.4925507186122 2.50744928138782 113 11 12.8800442410111 -1.88004424101109 114 15 12.6584482144829 2.34155178551712 115 12 13.4961672124144 -1.49616721241441 116 10 13.2347416634851 -3.2347416634851 117 14 13.0220065951660 0.977993404833966 118 13 13.1738125603390 -0.173812560339017 119 9 12.6996705821411 -3.6996705821411 120 15 13.0594540738404 1.94054592615963 121 15 12.6012125230227 2.39878747697734 122 14 13.3045317248403 0.695468275159667 123 11 12.8200731049286 -1.82007310492858 124 8 13.2829532544224 -5.28295325442242 125 11 13.0566557909705 -2.05665579097052 126 11 12.9713941337338 -1.97139413373378 127 8 13.3110734775703 -5.31107347757028 128 10 12.9826245433141 -2.98262454331408 129 11 13.0604306799544 -2.06043067995441 130 13 12.3177608454086 0.68223915459144 131 11 12.8219448398586 -1.82194483985863 132 20 13.1832026541131 6.81679734588695 133 10 13.1878726719129 -3.18787267191295 134 15 13.2600321846393 1.73996781536066 135 12 12.9278397805230 -0.92783978052304 136 14 12.6218958646246 1.37810413537545 137 23 13.1175848941166 9.8824151058834 138 14 13.0623024148845 0.937697585115542 139 16 13.1147866112468 2.88521338875324 140 11 12.7882094119206 -1.78820941192062 141 12 12.4555381181314 -0.455538118131391 142 10 12.4265041271171 -2.42650412711705 143 14 12.5398985998573 1.46010140014274 144 12 12.9906091994754 -0.990609199475396 145 12 12.8650703615707 -0.865070361570685 146 11 12.5581184204344 -1.55811842043438 147 12 12.3899517772587 -0.389951777258731 148 13 13.0004281247481 -0.000428124748118182 149 11 13.1653990726790 -2.16539907267902 150 19 12.8378766863626 6.16212331363738 151 12 12.9648209618801 -0.96482096188005 152 17 12.5637650443483 4.43623495565168 153 9 12.0614842039521 -3.06148420395208 154 12 12.9090910120988 -0.909091012098752 155 19 12.8767610217735 6.12323897822654 156 18 13.1663256206188 4.83367437938119 157 15 12.5731237189986 2.42687628100143 158 14 12.8360049514326 1.16399504856743 159 11 12.2615832373604 -1.26158323736039 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.979153320591476 0.0416933588170488 0.0208466794085244 8 0.955073871594818 0.0898522568103642 0.0449261284051821 9 0.972604516765093 0.0547909664698138 0.0273954832349069 10 0.95577303438501 0.088453931229981 0.0442269656149905 11 0.934300151067005 0.131399697865991 0.0656998489329954 12 0.931673862778714 0.136652274442572 0.068326137221286 13 0.924381999410865 0.151236001178271 0.0756180005891354 14 0.887234595972923 0.225530808054153 0.112765404027077 15 0.900753780201612 0.198492439596775 0.0992462197983876 16 0.873536240047257 0.252927519905487 0.126463759952743 17 0.829865207146101 0.340269585707797 0.170134792853898 18 0.80375664409993 0.392486711800141 0.196243355900071 19 0.783691861967779 0.432616276064443 0.216308138032221 20 0.754869772747396 0.490260454505208 0.245130227252604 21 0.846237593381558 0.307524813236885 0.153762406618442 22 0.838372096291887 0.323255807416227 0.161627903708113 23 0.80225496271169 0.39549007457662 0.19774503728831 24 0.756327627365949 0.487344745268102 0.243672372634051 25 0.721813350655717 0.556373298688566 0.278186649344283 26 0.721650368707474 0.556699262585052 0.278349631292526 27 0.694492217985778 0.611015564028444 0.305507782014222 28 0.67473222282821 0.65053555434358 0.32526777717179 29 0.63416271375647 0.731674572487061 0.365837286243530 30 0.575808469007133 0.848383061985735 0.424191530992867 31 0.62874100139156 0.74251799721688 0.37125899860844 32 0.640170683186908 0.719658633626183 0.359829316813092 33 0.622228326057523 0.755543347884953 0.377771673942477 34 0.576460813783471 0.847078372433057 0.423539186216528 35 0.519799738085183 0.960400523829634 0.480200261914817 36 0.535177439693196 0.929645120613608 0.464822560306804 37 0.789400259228532 0.421199481542936 0.210599740771468 38 0.752204002763523 0.495591994472955 0.247795997236477 39 0.724917169608227 0.550165660783545 0.275082830391773 40 0.707714961522894 0.584570076954212 0.292285038477106 41 0.700795834981328 0.598408330037344 0.299204165018672 42 0.665029701703648 0.669940596592705 0.334970298296352 43 0.712299826072661 0.575400347854678 0.287700173927339 44 0.675998345619904 0.648003308760193 0.324001654380096 45 0.642645120133346 0.714709759733307 0.357354879866654 46 0.594264480672837 0.811471038654326 0.405735519327163 47 0.602843914886612 0.794312170226777 0.397156085113388 48 0.562193721075974 0.875612557848052 0.437806278924026 49 0.54889659516285 0.902206809674301 0.451103404837151 50 0.509949681797777 0.980100636404446 0.490050318202223 51 0.499203190288746 0.998406380577492 0.500796809711254 52 0.459129149585906 0.918258299171811 0.540870850414095 53 0.549358975763393 0.901282048473213 0.450641024236607 54 0.501647474690565 0.99670505061887 0.498352525309435 55 0.459219165759487 0.918438331518973 0.540780834240513 56 0.412473693611207 0.824947387222415 0.587526306388793 57 0.366912370561911 0.733824741123823 0.633087629438089 58 0.390711297419381 0.781422594838762 0.609288702580619 59 0.394812741041222 0.789625482082445 0.605187258958778 60 0.370162204903771 0.740324409807542 0.629837795096229 61 0.558193253717077 0.883613492565847 0.441806746282923 62 0.51471428440557 0.970571431188861 0.485285715594431 63 0.472067263427144 0.944134526854287 0.527932736572856 64 0.429296685680719 0.858593371361438 0.570703314319281 65 0.385480723668148 0.770961447336296 0.614519276331852 66 0.3499453644487 0.6998907288974 0.6500546355513 67 0.406722375236096 0.813444750472192 0.593277624763904 68 0.366357499557753 0.732714999115506 0.633642500442247 69 0.325725958813916 0.651451917627831 0.674274041186084 70 0.289772699305552 0.579545398611103 0.710227300694448 71 0.25256244242408 0.50512488484816 0.74743755757592 72 0.230301533143322 0.460603066286644 0.769698466856678 73 0.198668786661973 0.397337573323946 0.801331213338027 74 0.183577241080461 0.367154482160922 0.816422758919539 75 0.162562442225519 0.325124884451038 0.837437557774481 76 0.259860274322569 0.519720548645138 0.740139725677431 77 0.226298704345742 0.452597408691485 0.773701295654258 78 0.252413361337772 0.504826722675544 0.747586638662228 79 0.216900930092459 0.433801860184919 0.78309906990754 80 0.225837716387888 0.451675432775775 0.774162283612112 81 0.202320648204036 0.404641296408072 0.797679351795964 82 0.201226414852491 0.402452829704981 0.79877358514751 83 0.219984940448215 0.43996988089643 0.780015059551785 84 0.191512111615067 0.383024223230134 0.808487888384933 85 0.163965369516436 0.327930739032872 0.836034630483564 86 0.139782553145113 0.279565106290226 0.860217446854887 87 0.116469192644836 0.232938385289673 0.883530807355164 88 0.0987178686133083 0.197435737226617 0.901282131386692 89 0.0934151787299262 0.186830357459852 0.906584821270074 90 0.296735443641746 0.593470887283492 0.703264556358254 91 0.258701148363892 0.517402296727784 0.741298851636108 92 0.228258091082351 0.456516182164703 0.771741908917649 93 0.19519004504489 0.39038009008978 0.80480995495511 94 0.176661022966976 0.353322045933953 0.823338977033024 95 0.172487292397801 0.344974584795602 0.827512707602199 96 0.151322981228490 0.302645962456979 0.84867701877151 97 0.158710026538032 0.317420053076064 0.841289973461968 98 0.137825606498786 0.275651212997573 0.862174393501214 99 0.125034629078452 0.250069258156903 0.874965370921548 100 0.122742015830017 0.245484031660034 0.877257984169983 101 0.119564379914554 0.239128759829108 0.880435620085446 102 0.110089341525213 0.220178683050426 0.889910658474787 103 0.0954409757084338 0.190881951416868 0.904559024291566 104 0.0873274202551513 0.174654840510303 0.912672579744849 105 0.0881359762606834 0.176271952521367 0.911864023739317 106 0.149030927930302 0.298061855860604 0.850969072069698 107 0.131822499812597 0.263644999625194 0.868177500187403 108 0.132214131611816 0.264428263223632 0.867785868388184 109 0.119234040118229 0.238468080236458 0.880765959881771 110 0.513945638599574 0.972108722800852 0.486054361400426 111 0.464284692129966 0.928569384259931 0.535715307870035 112 0.443781527929871 0.887563055859742 0.556218472070129 113 0.404513811682943 0.809027623365886 0.595486188317057 114 0.37487339855524 0.74974679711048 0.62512660144476 115 0.336030818747368 0.672061637494735 0.663969181252632 116 0.353550815203963 0.707101630407927 0.646449184796037 117 0.308529645815714 0.617059291631428 0.691470354184286 118 0.2636858992733 0.5273717985466 0.7363141007267 119 0.284232631824177 0.568465263648354 0.715767368175823 120 0.257200670454049 0.514401340908099 0.74279932954595 121 0.266469771622559 0.532939543245118 0.733530228377441 122 0.224237866370253 0.448475732740505 0.775762133629748 123 0.199148261757036 0.398296523514073 0.800851738242964 124 0.259214635223307 0.518429270446614 0.740785364776693 125 0.231830293701845 0.46366058740369 0.768169706298155 126 0.229669525525086 0.459339051050172 0.770330474474914 127 0.3949141474747 0.7898282949494 0.6050858525253 128 0.414719750091026 0.829439500182053 0.585280249908974 129 0.441836852312032 0.883673704624064 0.558163147687968 130 0.424197131064682 0.848394262129363 0.575802868935318 131 0.396567425188674 0.793134850377348 0.603432574811326 132 0.493362780369842 0.986725560739684 0.506637219630158 133 0.617002958462268 0.765994083075464 0.382997041537732 134 0.560569890109839 0.878860219780322 0.439430109890161 135 0.526627991097605 0.94674401780479 0.473372008902395 136 0.462461062023742 0.924922124047485 0.537538937976258 137 0.820861708631857 0.358276582736286 0.179138291368143 138 0.771327640737168 0.457344718525664 0.228672359262832 139 0.723809253008328 0.552381493983344 0.276190746991672 140 0.685026645711085 0.62994670857783 0.314973354288915 141 0.62635664425124 0.747286711497519 0.373643355748760 142 0.574235185251457 0.851529629497086 0.425764814748543 143 0.504097422359712 0.991805155280576 0.495902577640288 144 0.421607010505872 0.843214021011744 0.578392989494128 145 0.418346788735205 0.83669357747041 0.581653211264795 146 0.32998145457549 0.65996290915098 0.67001854542451 147 0.246873320493041 0.493746640986083 0.753126679506959 148 0.182263474150936 0.364526948301872 0.817736525849064 149 0.32483265509225 0.6496653101845 0.67516734490775 150 0.371920875764899 0.743841751529798 0.628079124235101 151 0.40033500905172 0.80067001810344 0.59966499094828 152 0.475808539758062 0.951617079516124 0.524191460241938 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 1 0.00684931506849315 OK 10% type I error level 4 0.0273972602739726 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/10xkxl1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/10xkxl1290511386.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/18jis1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/18jis1290511386.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/28jis1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/28jis1290511386.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/38jis1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/38jis1290511386.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/48jis1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/48jis1290511386.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/5jshc1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/5jshc1290511386.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/6jshc1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/6jshc1290511386.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/7u1zf1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/7u1zf1290511386.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/8u1zf1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/8u1zf1290511386.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/95agi1290511386.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905114317cldyhux11ycpmj/95agi1290511386.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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') }

Copyright

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

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by