WS7 - Minitutorail blog 4a multicol

*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 19:59:02 +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/t1290542271rpzxw5y8cg9uhlf.htm/, Retrieved Tue, 23 Nov 2010 20:57:54 +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/t1290542271rpzxw5y8cg9uhlf.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 «

12 6 15 4 7 2 2 2 2 9 11 6 15 3 5 4 1 2 2 9 14 13 14 5 7 7 4 3 4 9 12 8 10 3 3 3 1 2 3 9 21 7 10 6 7 7 5 4 4 9 12 9 12 5 7 2 1 2 3 9 22 5 18 6 7 7 1 2 3 9 11 8 12 6 1 2 1 3 4 9 10 9 14 5 4 1 1 2 3 9 13 11 18 5 5 2 1 2 4 9 10 8 9 3 6 6 2 3 3 9 8 11 11 5 4 1 1 2 2 9 15 12 11 7 7 1 3 3 3 9 10 8 17 5 6 1 1 1 3 9 14 7 8 5 2 2 1 3 3 9 14 9 16 3 2 2 1 1 2 9 11 12 21 5 6 2 1 3 3 9 10 20 24 6 7 1 1 2 2 9 13 7 21 5 5 7 2 3 4 9 7 8 14 2 2 1 4 4 5 9 12 8 7 5 7 2 1 3 3 9 14 16 18 4 4 4 2 3 3 9 11 10 18 6 5 2 1 1 1 9 9 6 13 3 5 1 2 2 4 9 11 8 11 5 5 1 3 1 3 9 15 9 13 4 3 5 1 3 4 9 13 9 13 5 5 2 1 3 3 9 9 11 18 2 1 1 1 2 3 9 15 12 14 2 1 3 1 2 1 9 10 8 12 5 3 1 1 3 4 9 11 7 9 2 2 2 2 2 4 9 13 8 12 2 3 5 1 2 2 9 8 9 8 2 2 2 1 2 2 9 20 4 5 5 5 6 1 1 1 9 12 8 10 5 2 4 1 2 3 9 10 8 11 1 3 1 1 3 4 9 10 8 11 5 4 3 1 1 1 9 9 6 12 2 6 6 1 2 3 9 14 8 12 6 2 7 2 3 3 9 8 4 15 1 7 4 1 2 2 9 14 7 12 4 6 1 2 1 4 9 11 14 16 3 5 5 1 1 3 9 13 10 14 2 3 3 1 3 3 9 11 9 17 5 3 2 2 3 2 9 11 8 10 3 4 2 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Depression[t] = + 7.11427357027146 + 0.0468181164894483CriticParents[t] -0.0610717012753496ExpecParents[t] + 0.586101505807562FutureWorrying[t] + 0.214964224328964SleepDepri[t] + 0.335215733141913ChangesLastYear[t] -0.0863956836856015FreqSmoking[t] + 0.284326292090269FreqHighAlc[t] + 0.192259706857739FreqBeerOrWine[t] + 0.00201094154728408Month[t] + 0.00643775319164656t + 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) 7.11427357027146 7.483087 0.9507 0.343461 0.171731 CriticParents 0.0468181164894483 0.116614 0.4015 0.688707 0.344353 ExpecParents -0.0610717012753496 0.087154 -0.7007 0.484685 0.242343 FutureWorrying 0.586101505807562 0.168914 3.4698 0.000701 0.000351 SleepDepri 0.214964224328964 0.142253 1.5111 0.133107 0.066553 ChangesLastYear 0.335215733141913 0.136964 2.4475 0.015681 0.00784 FreqSmoking -0.0863956836856015 0.276683 -0.3123 0.755332 0.377666 FreqHighAlc 0.284326292090269 0.316307 0.8989 0.370322 0.185161 FreqBeerOrWine 0.192259706857739 0.297069 0.6472 0.518617 0.259309 Month 0.00201094154728408 0.830247 0.0024 0.998071 0.499036 t 0.00643775319164656 0.009936 0.648 0.518125 0.259062 Multiple Linear Regression - Regression Statistics Multiple R 0.460266102707896 R-squared 0.211844885301915 Adjusted R-squared 0.153027339428924 F-TEST (value) 3.60172941862223 F-TEST (DF numerator) 10 F-TEST (DF denominator) 134 p-value 0.000291280874432198 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.90976371595358 Sum Squared Residuals 1134.54113427912 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 11.8036106675367 0.196389332463273 2 11 11.5508456162323 -0.550845616232324 3 14 14.9635192005732 -0.96351920057319 4 12 11.3898313870292 0.610168612970842 5 21 15.7238049273334 5.27619507266658 6 12 13.0242257831403 -1.02422578314027 7 22 14.7391410342392 7.26085896576085 8 11 12.7631853318159 -1.7631853318159 9 10 11.9412872340357 -1.94128723403571 10 13 12.5395140794335 0.460485920566535 11 10 13.3444378414633 -3.34443784146334 12 8 12.0451921235579 -4.04519212355785 13 15 14.2193383094178 0.780661690582233 14 10 11.8890449362461 -1.8890449362461 15 14 12.442321304433 1.55767869556696 16 14 10.1207063777474 3.87929362225262 17 11 12.7552121739999 -1.75521217399988 18 10 12.9422437533277 -2.94224375332767 19 13 14.1009755624887 -1.10097556248867 20 7 10.471036383413 -3.47103638341297 21 12 13.6636587629925 -1.66365876299254 22 14 12.7258943378747 1.27410566212531 23 11 12.3013828475795 -1.3013828475795 24 9 11.1070961196034 -2.10709611960338 25 11 11.9385348373061 -0.938534837306142 26 15 13.1281839409482 1.87181605905182 27 13 12.9527447423218 0.0472552576781619 28 9 9.5097567821449 -0.50975678214491 29 15 10.0932115094958 4.90678849050425 30 10 12.4134271117406 -2.41342711174058 31 11 10.5474868678832 0.452513132116783 32 13 11.3400153274631 1.65998467253691 33 8 10.4169465784909 -2.41694657849088 34 20 13.6399829770906 6.36001702290945 35 12 12.8818562563983 -0.881856256398277 36 10 10.1687193089356 -0.168719308935558 37 10 12.2595270712165 -2.25952707121649 38 9 12.4573737266206 -3.45737372662062 39 14 14.5751431802521 -0.575143180252132 40 8 10.9595694415788 -2.9595694415788 41 14 11.8411671796724 2.15883282032757 42 11 12.3649781224478 -1.36497812244781 43 13 11.1884779756636 1.81152202433642 44 11 12.1093159022772 -1.10931590227716 45 11 11.817854051164 -0.81785405116399 46 10 12.1460502681753 -2.14605026817532 47 14 10.6098120005329 3.39018799946709 48 18 13.7219336641805 4.27806633581946 49 14 12.4857298554586 1.51427014454136 50 11 12.9662549813077 -1.96625498130772 51 12 11.4241398370063 0.575860162993728 52 13 13.0811240404095 -0.0811240404094553 53 9 13.6873941433871 -4.68739414338714 54 10 12.2383282348886 -2.23832823488863 55 15 13.4831526599615 1.51684734003852 56 20 14.108927054757 5.89107294524297 57 12 11.6716728367125 0.328327163287499 58 12 11.9836341976523 0.0163658023476846 59 14 11.3360290363818 2.66397096361824 60 13 14.9334498006976 -1.93344980069765 61 11 14.3350803358606 -3.33508033586061 62 17 13.177850756168 3.82214924383195 63 12 12.2093348402978 -0.209334840297785 64 13 12.8277784887814 0.172221511218607 65 14 13.7962544782571 0.203745521742893 66 13 10.7293720042401 2.27062799575992 67 15 13.7963061293053 1.20369387069474 68 13 11.9119366957431 1.0880633042569 69 10 13.5687290267362 -3.56872902673615 70 11 11.2740290370396 -0.274029037039564 71 13 12.7322278454552 0.267772154544794 72 17 14.1405875078338 2.85941249216623 73 13 12.8679211337016 0.13207886629842 74 9 12.0559796182532 -3.05597961825323 75 11 12.3405120902909 -1.34051209029094 76 10 10.2977621453233 -0.297762145323322 77 9 10.3067320766891 -1.30673207668907 78 12 11.2847818028269 0.71521819717314 79 12 12.4356251708188 -0.435625170818834 80 13 12.3644571038532 0.63554289614679 81 13 12.4242190216587 0.575780978341261 82 22 14.5127421626098 7.48725783739022 83 13 11.921241989622 1.07875801037795 84 15 13.7397553889324 1.26024461106757 85 13 14.1020870449101 -1.10208704491012 86 15 11.5952583591029 3.40474164089706 87 10 11.6879387993883 -1.68793879938832 88 11 10.8755490820834 0.124450917916564 89 16 14.1842235180053 1.81577648199473 90 11 12.0431181019344 -1.04311810193439 91 11 12.4260672197303 -1.42606721973026 92 10 12.7077254873256 -2.70772548732559 93 10 14.5624853048147 -4.56248530481474 94 16 14.2260127790261 1.77398722097385 95 12 13.3895944532429 -1.3895944532429 96 11 13.9190171801555 -2.91901718015545 97 16 14.4214751161114 1.57852488388861 98 19 14.9907964038188 4.00920359618118 99 11 14.8962880701177 -3.89628807011766 100 15 12.7676318314541 2.2323681685459 101 24 16.5720384528752 7.4279615471248 102 14 11.6955904986755 2.30440950132447 103 15 13.6529041812879 1.34709581871206 104 11 14.9181760885708 -3.91817608857076 105 15 13.5622175456571 1.43778245434289 106 12 12.9353799338188 -0.935379933818797 107 10 10.847922758518 -0.847922758518026 108 14 13.9973467009923 0.00265329900766953 109 9 12.9090591348176 -3.90905913481764 110 15 10.720384787291 4.27961521270903 111 15 9.7988526496398 5.20114735036021 112 14 13.1670225466734 0.832977453326589 113 11 14.2205581250718 -3.22055812507182 114 8 14.4199190525284 -6.41991905252838 115 11 14.3118270389759 -3.31182703897588 116 8 11.8963767425822 -3.8963767425822 117 10 11.3258760802794 -1.32587608027941 118 11 13.7111430389992 -2.71114303899924 119 13 14.1597103656976 -1.1597103656976 120 11 13.8536302177452 -2.85363021774524 121 20 12.774475453894 7.22552454610595 122 10 12.2969266458795 -2.29692664587946 123 12 11.070090923955 0.929909076044998 124 14 12.6760573573323 1.3239426426677 125 23 14.1249388859686 8.8750611140314 126 14 13.138499305452 0.861500694547955 127 16 15.3457418790671 0.65425812093294 128 11 13.5615720081091 -2.56157200810915 129 12 14.3746587974792 -2.37465879747916 130 10 13.7928820084057 -3.79288200840569 131 14 13.9163293194792 0.083670680520829 132 12 9.9953446817404 2.00465531825959 133 12 13.8348264611174 -1.83482646111738 134 11 10.3670685047542 0.632931495245838 135 12 12.5528936335421 -0.552893633542136 136 13 15.9196808217229 -2.91968082172285 137 17 16.4624508260438 0.537549173956198 138 11 12.6660009479622 -1.6660009479622 139 12 13.8578614879676 -1.85786148796757 140 19 15.2845874539023 3.71541254609766 141 15 14.1067073208563 0.893292679143717 142 14 13.6464936282831 0.353506371716863 143 11 13.8720868687904 -2.8720868687904 144 9 10.7770318219383 -1.77703182193828 145 18 12.012959816005 5.98704018399503 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 14 0.68311727933409 0.63376544133182 0.31688272066591 15 0.647686378735782 0.704627242528435 0.352313621264218 16 0.7409553327876 0.518089334424801 0.2590446672124 17 0.634796713357325 0.73040657328535 0.365203286642675 18 0.540273870019096 0.919452259961808 0.459726129980904 19 0.665029473373891 0.669941053252218 0.334970526626109 20 0.587883290908774 0.824233418182453 0.412116709091226 21 0.507231657701736 0.985536684596528 0.492768342298264 22 0.531075105726838 0.937849788546324 0.468924894273162 23 0.580527192154862 0.838945615690275 0.419472807845138 24 0.500070827400118 0.999858345199765 0.499929172599882 25 0.426433828477759 0.852867656955518 0.573566171522241 26 0.386764964616073 0.773529929232145 0.613235035383927 27 0.325203467854637 0.650406935709275 0.674796532145363 28 0.277154874816906 0.554309749633813 0.722845125183094 29 0.331169249183927 0.662338498367855 0.668830750816073 30 0.284178128457894 0.568356256915787 0.715821871542106 31 0.232617076062244 0.465234152124487 0.767382923937756 32 0.189450845007783 0.378901690015567 0.810549154992217 33 0.184922901762141 0.369845803524281 0.81507709823786 34 0.20071539448522 0.40143078897044 0.79928460551478 35 0.207448760992178 0.414897521984357 0.792551239007822 36 0.203788039361156 0.407576078722312 0.796211960638844 37 0.255580022349218 0.511160044698436 0.744419977650782 38 0.301645471233817 0.603290942467633 0.698354528766183 39 0.305573361138401 0.611146722276802 0.694426638861599 40 0.277441614818607 0.554883229637214 0.722558385181393 41 0.319837211644628 0.639674423289255 0.680162788355372 42 0.281535374704289 0.563070749408577 0.718464625295711 43 0.290217977579703 0.580435955159406 0.709782022420297 44 0.245849794437236 0.491699588874471 0.754150205562764 45 0.208525645188416 0.417051290376832 0.791474354811584 46 0.183736905039568 0.367473810079136 0.816263094960432 47 0.191979390294511 0.383958780589022 0.808020609705489 48 0.294752491271766 0.589504982543532 0.705247508728234 49 0.267701144436493 0.535402288872985 0.732298855563507 50 0.242730424789298 0.485460849578596 0.757269575210702 51 0.204605126569084 0.409210253138169 0.795394873430916 52 0.168367770366836 0.336735540733672 0.831632229633164 53 0.256232966366131 0.512465932732263 0.743767033633869 54 0.254446303410919 0.508892606821838 0.745553696589081 55 0.234464772540683 0.468929545081367 0.765535227459317 56 0.308570819657855 0.61714163931571 0.691429180342145 57 0.267586177885504 0.535172355771009 0.732413822114496 58 0.238143157213732 0.476286314427463 0.761856842786268 59 0.208484884434669 0.416969768869338 0.791515115565331 60 0.235632560556164 0.471265121112328 0.764367439443836 61 0.200360908754896 0.400721817509791 0.799639091245104 62 0.321340378871703 0.642680757743407 0.678659621128297 63 0.276060001343578 0.552120002687157 0.723939998656422 64 0.236345620373494 0.472691240746987 0.763654379626507 65 0.200080852312932 0.400161704625863 0.799919147687068 66 0.184187140601981 0.368374281203962 0.815812859398019 67 0.155354826723128 0.310709653446256 0.844645173276872 68 0.129767947084091 0.259535894168182 0.870232052915909 69 0.143052226386343 0.286104452772686 0.856947773613657 70 0.116302478818932 0.232604957637863 0.883697521181068 71 0.0931960382013929 0.186392076402786 0.906803961798607 72 0.0949980970831094 0.189996194166219 0.90500190291689 73 0.0754600702384655 0.150920140476931 0.924539929761535 74 0.0764878859488304 0.152975771897661 0.92351211405117 75 0.0632141909268903 0.126428381853781 0.93678580907311 76 0.0505123221330846 0.101024644266169 0.949487677866915 77 0.044523998661522 0.089047997323044 0.955476001338478 78 0.034048952045869 0.068097904091738 0.965951047954131 79 0.0259938309901171 0.0519876619802341 0.974006169009883 80 0.0196339248593474 0.0392678497186948 0.980366075140653 81 0.014834895930607 0.029669791861214 0.985165104069393 82 0.0678801129076602 0.13576022581532 0.93211988709234 83 0.053063519393785 0.10612703878757 0.946936480606215 84 0.0412752733541987 0.0825505467083975 0.9587247266458 85 0.0335754238296065 0.0671508476592129 0.966424576170394 86 0.0336083453875839 0.0672166907751677 0.966391654612416 87 0.0287996406657452 0.0575992813314905 0.971200359334255 88 0.0212736009483744 0.0425472018967487 0.978726399051626 89 0.018459770724648 0.0369195414492959 0.981540229275352 90 0.0143952061086949 0.0287904122173898 0.985604793891305 91 0.0116400034142736 0.0232800068285472 0.988359996585726 92 0.0115221304854555 0.0230442609709109 0.988477869514545 93 0.0178228629237879 0.0356457258475758 0.982177137076212 94 0.0137558923703684 0.0275117847407368 0.986244107629632 95 0.0108631939703725 0.0217263879407449 0.989136806029628 96 0.0116979041531237 0.0233958083062475 0.988302095846876 97 0.00981309941302263 0.0196261988260453 0.990186900586977 98 0.0146681249326634 0.0293362498653269 0.985331875067337 99 0.0174887926787057 0.0349775853574113 0.982511207321294 100 0.0138727648062623 0.0277455296125247 0.986127235193738 101 0.0666106280974114 0.133221256194823 0.933389371902589 102 0.0592133116474592 0.118426623294918 0.94078668835254 103 0.0489544601322428 0.0979089202644855 0.951045539867757 104 0.0505349790749298 0.10106995814986 0.94946502092507 105 0.0418267813081927 0.0836535626163855 0.958173218691807 106 0.0311854609731846 0.0623709219463693 0.968814539026815 107 0.0249451903822615 0.049890380764523 0.975054809617738 108 0.0180741559493218 0.0361483118986436 0.981925844050678 109 0.0165843631165886 0.0331687262331772 0.983415636883411 110 0.0249433465863773 0.0498866931727546 0.975056653413623 111 0.0363572563311682 0.0727145126623363 0.963642743668832 112 0.0292781223673607 0.0585562447347214 0.97072187763264 113 0.025629219026761 0.051258438053522 0.97437078097324 114 0.0449844914344846 0.0899689828689693 0.955015508565515 115 0.0414144488805389 0.0828288977610778 0.95858555111946 116 0.061972417775428 0.123944835550856 0.938027582224572 117 0.0468773178743193 0.0937546357486385 0.95312268212568 118 0.0406098757203631 0.0812197514407262 0.959390124279637 119 0.0306168802889339 0.0612337605778678 0.969383119711066 120 0.0677928614399973 0.135585722879995 0.932207138560003 121 0.145109878244906 0.290219756489813 0.854890121755094 122 0.3668839223259 0.7337678446518 0.6331160776741 123 0.310387192039348 0.620774384078696 0.689612807960652 124 0.238216274538241 0.476432549076483 0.761783725461759 125 0.488251399902644 0.976502799805288 0.511748600097356 126 0.914016258993131 0.171967482013737 0.0859837410068685 127 0.866177864039285 0.267644271921431 0.133822135960715 128 0.797356913213175 0.405286173573649 0.202643086786825 129 0.74574545013031 0.508509099739379 0.25425454986969 130 0.679843124891131 0.640313750217738 0.320156875108869 131 0.610445671813246 0.779108656373508 0.389554328186754 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 19 0.161016949152542 NOK 10% type I error level 37 0.313559322033898 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/10qvc51290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/10qvc51290542328.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/1u3ww1290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/1u3ww1290542328.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/2u3ww1290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/2u3ww1290542328.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/3u3ww1290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/3u3ww1290542328.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/4u3ww1290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/4u3ww1290542328.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/54ceh1290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/54ceh1290542328.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/64ceh1290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/64ceh1290542328.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/7f3d21290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/7f3d21290542328.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/8f3d21290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/8f3d21290542328.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/9qvc51290542328.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290542271rpzxw5y8cg9uhlf/9qvc51290542328.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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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