mini tutorial workshop 4

*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, 30 Nov 2010 17:13:46 +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/30/t12911372125dwa52b42q1yrar.htm/, Retrieved Tue, 30 Nov 2010 18:13:32 +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/30/t12911372125dwa52b42q1yrar.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:

enkel trend (geen month meer opgenomen)

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

24 14 11 12 24 26 25 11 7 8 25 23 17 6 17 8 30 25 18 12 10 8 19 23 18 8 12 9 22 19 16 10 12 7 22 29 20 10 11 4 25 25 16 11 11 11 23 21 18 16 12 7 17 22 17 11 13 7 21 25 23 13 14 12 19 24 30 12 16 10 19 18 23 8 11 10 15 22 18 12 10 8 16 15 15 11 11 8 23 22 12 4 15 4 27 28 21 9 9 9 22 20 15 8 11 8 14 12 20 8 17 7 22 24 31 14 17 11 23 20 27 15 11 9 23 21 34 16 18 11 21 20 21 9 14 13 19 21 31 14 10 8 18 23 19 11 11 8 20 28 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 24 22 9 16 9 24 23 17 9 13 6 22 23 24 10 9 6 25 29 25 16 18 16 26 24 26 11 18 5 29 18 25 8 12 7 32 25 17 9 17 9 25 21 32 16 9 6 29 26 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 22 25 12 12 7 29 23 29 14 18 10 26 30 22 9 14 9 25 23 18 10 15 8 14 17 17 9 16 5 25 23 20 10 10 8 26 23 15 12 11 8 20 25 20 14 14 10 18 24 33 14 9 6 32 24 29 10 12 8 25 23 23 14 17 7 25 21 26 16 5 4 23 24 18 9 12 8 21 24 20 10 12 8 20 28 11 6 6 4 15 16 28 8 24 20 30 20 26 13 12 8 24 29 22 10 12 8 26 27 17 8 14 6 24 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 Parental.Expectations[t] = + 5.84398572246926 + 0.0895090012114705Concern.over.Mistakes[t] -0.12590016401359Doubts.about.actions[t] + 0.665601272609036Parental.Criticism[t] + 0.118116470483094Personal.Standards[t] -0.0820356250087838Organization[t] + 0.00239657305847149t + 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) 5.84398572246926 1.892391 3.0881 0.002395 0.001197 Concern.over.Mistakes 0.0895090012114705 0.048323 1.8523 0.06592 0.03296 Doubts.about.actions -0.12590016401359 0.087456 -1.4396 0.152043 0.076022 Parental.Criticism 0.665601272609036 0.086519 7.6931 0 0 Personal.Standards 0.118116470483094 0.063446 1.8617 0.064579 0.032289 Organization -0.0820356250087838 0.063311 -1.2958 0.197025 0.098512 t 0.00239657305847149 0.004826 0.4966 0.620167 0.310084 Multiple Linear Regression - Regression Statistics Multiple R 0.639019153846926 R-squared 0.408345478983241 Adjusted R-squared 0.384990695258896 F-TEST (value) 17.4844470324754 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.44249065417534e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.70203430228648 Sum Squared Residuals 1109.75038435138 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 14.9210803410871 -3.92108034108708 2 7 13.0925046624711 -6.09250466247108 3 17 13.4348411483036 3.56515885169636 4 10 11.6361358131956 -1.63613581319559 5 12 13.4902262264019 -1.49022622640187 6 12 10.9102456737043 1.08975432629570 7 11 9.95636634526597 1.04363365473403 8 11 14.2259452167972 -3.22594521679717 9 12 10.3247194338671 1.67528056613286 10 13 11.0934668326881 1.90653316731189 11 14 14.554926132076 -0.554926132076005 12 16 14.470797082463 1.52920291753701 13 11 13.5496229211280 -2.54962292112802 14 10 11.9620371324013 -1.96203713240128 15 11 12.0743727841591 -1.07437278415910 16 15 10.0073905431218 4.99260945687818 17 9 13.5795763177156 -4.57957631771556 18 11 12.2165710111153 -1.21657101111528 19 17 11.9614155813814 5.03858441861859 20 17 15.3016742446389 1.69832575536110 21 11 13.4068964786110 -2.40689647861104 22 18 15.0869611253969 2.91303887460312 23 14 15.8199758100445 -1.81997581004447 24 10 12.4777674916039 -2.47776749160385 25 11 11.6098113580877 -0.609811358087717 26 15 13.069474603646 1.930525396354 27 15 11.5434361406758 3.45656385932416 28 13 12.9234467098743 0.0765532901256699 29 16 13.6879702615685 2.31202973843148 30 13 11.0097850697763 1.99021493022365 31 9 11.3749801486981 -2.3749801486981 32 18 17.8957920605039 0.104207939496122 33 18 12.1421476176444 5.85785238235565 34 12 13.544038263138 -1.54403826313799 35 17 13.5369924143627 3.46300758563734 36 9 12.0662067965594 -3.06620679655941 37 9 12.9976392204493 -3.99763922044934 38 12 8.61547250128739 3.38452749871261 39 18 16.7806308369954 1.21936916300456 40 12 12.8645388840027 -0.864538884002747 41 18 14.0413761651963 3.95862383480374 42 14 13.8372421818117 0.162757818188253 43 15 11.8830338881404 3.11696611185962 44 16 10.7320852314352 5.26791476856481 45 10 12.9920289324247 -2.99202893242469 46 11 11.4223100984825 -0.422310098482497 47 14 12.7974565788318 1.20254342116819 48 9 12.9546956639666 -3.95469566396656 49 12 13.6890797650787 -1.68907976507872 50 17 12.1492916522225 4.85070834777746 51 5 9.6892712670686 -4.68927126706859 52 12 12.2830691280004 -0.283069128000385 53 12 11.8923245689500 0.107675431050021 54 6 9.32418084441337 -3.32418084441337 55 24 22.6896550289955 1.31034497100449 56 12 12.4492980602770 -0.449298060277037 57 12 12.8716633115142 -0.871663311514151 58 14 11.5210578454021 2.47894215459789 59 7 9.14216034017986 -2.14216034017986 60 13 11.0182744302294 1.98172556977065 61 12 13.1530443433647 -1.15304434336469 62 13 11.4728085644371 1.52719143556287 63 14 11.3818455796194 2.61815442038062 64 8 12.828178032706 -4.828178032706 65 11 9.32125127027065 1.67874872972935 66 9 11.7415669730691 -2.74156697306911 67 11 13.7266513741233 -2.72665137412326 68 13 13.3657289960723 -0.365728996072312 69 10 9.36515809184376 0.634841908156238 70 11 12.6438553743722 -1.64385537437222 71 12 12.7299476991651 -0.729947699165077 72 9 11.8369439427810 -2.83694394278103 73 15 14.6177340222560 0.382265977744037 74 18 14.8800641483335 3.11993585166653 75 15 12.1134900297425 2.88650997025749 76 12 12.7902221279907 -0.790222127990721 77 13 9.85269945811001 3.14730054188999 78 14 13.0199242822064 0.980075717793584 79 10 11.8856399256721 -1.88563992567208 80 13 12.2987974444570 0.701202555543019 81 13 13.7281754848096 -0.728175484809557 82 11 12.0961296798454 -1.09612967984536 83 13 12.1760277134580 0.823972286541977 84 16 14.4683460594585 1.53165394054155 85 8 9.7010565910997 -1.7010565910997 86 16 11.5975615445035 4.40243845549648 87 11 11.1033545592561 -0.103354559256068 88 9 11.2973727503253 -2.29737275032527 89 16 17.7555095598081 -1.75550955980811 90 12 11.4457874619051 0.554212538094877 91 14 11.9906407849722 2.00935921502779 92 8 10.5990252105176 -2.59902521051758 93 9 9.5632762181969 -0.563276218196896 94 15 11.7309174625886 3.26908253741136 95 11 13.5607264409179 -2.56072644091785 96 21 17.2238502100413 3.77614978995873 97 14 13.2567964308858 0.743203569114158 98 18 15.7828218114244 2.21717818857561 99 12 11.7113732539281 0.28862674607195 100 13 12.6860691892339 0.313930810766054 101 15 14.5356884111199 0.464311588880138 102 12 11.0648424941588 0.93515750584118 103 19 14.4536834312106 4.54631656878938 104 15 14.0288648862901 0.971135113709867 105 11 13.0310396357798 -2.03103963577984 106 11 10.6785971868898 0.321402813110241 107 10 12.3636065048675 -2.36360650486749 108 13 14.7876214558746 -1.78762145587455 109 15 14.7777631440822 0.222236855917843 110 12 9.90926605102203 2.09073394897797 111 12 11.0205836554597 0.979416344540333 112 16 15.7559093666238 0.244090633376166 113 9 15.5029829815267 -6.50298298152667 114 18 17.534703773785 0.465296226215003 115 8 15.0299439185223 -7.02994391852227 116 13 10.3865281475061 2.6134718524939 117 17 14.1988780020735 2.80112199792652 118 9 11.0607927299636 -2.06079272996361 119 15 13.2244194544224 1.77558054557755 120 8 9.66830879116794 -1.66830879116794 121 7 11.2734798663308 -4.27347986633081 122 12 11.3592107547492 0.640789245250814 123 14 15.0612088247332 -1.06120882473319 124 6 10.7816409078796 -4.78164090787956 125 8 10.1787563197468 -2.17875631974678 126 17 12.4696688337318 4.53033116626818 127 10 9.77589664781187 0.224103352188126 128 11 12.5827045162717 -1.58270451627169 129 14 12.8432351120806 1.15676488791943 130 11 13.6916827520720 -2.69168275207195 131 13 15.4220010557674 -2.42200105576743 132 12 11.9513014928660 0.0486985071339539 133 11 10.4630404176466 0.536959582353384 134 9 9.49175140350905 -0.491751403509054 135 12 12.1160648040677 -0.116064804067656 136 20 14.7827087662005 5.2172912337995 137 12 10.7438841957670 1.25611580423302 138 13 13.6794670666938 -0.679467066693821 139 12 13.1935634194986 -1.19356341949856 140 12 16.5328463645447 -4.53284636454473 141 9 14.6631617883371 -5.66316178833711 142 15 15.6353737848601 -0.635373784860085 143 24 21.5444244849536 2.45557551504643 144 7 10.0198760511055 -3.01987605110552 145 17 14.6679847788291 2.33201522117085 146 11 11.9891411384082 -0.98914113840824 147 17 15.2226058638896 1.77739413611038 148 11 12.3546993714627 -1.35469937146269 149 12 12.6052306846408 -0.605230684640806 150 14 14.5430980313602 -0.543098031360177 151 11 14.3714030662813 -3.37140306628126 152 16 12.8908647093164 3.10913529068361 153 21 13.9326550693200 7.06734493067997 154 14 12.3025475987315 1.69745240126850 155 20 16.4676321019483 3.53236789805169 156 13 11.1214751137120 1.87852488628796 157 11 13.1546479026359 -2.15464790263593 158 15 14.0049314867086 0.995068513291381 159 19 18.0023051118859 0.997694888114127 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.568556767294595 0.86288646541081 0.431443232705405 11 0.588147825866375 0.82370434826725 0.411852174133625 12 0.614663340459394 0.770673319081211 0.385336659540606 13 0.612210156559909 0.775579686880182 0.387789843440091 14 0.573587636677876 0.852824726644248 0.426412363322124 15 0.636041220959063 0.727917558081873 0.363958779040937 16 0.559367019067781 0.881265961864438 0.440632980932219 17 0.713207109308357 0.573585781383287 0.286792890691643 18 0.636306592547314 0.727386814905371 0.363693407452686 19 0.662630794959175 0.67473841008165 0.337369205040825 20 0.614202456423977 0.771595087152046 0.385797543576023 21 0.653369627537255 0.69326074492549 0.346630372462745 22 0.658742183833347 0.682515632333307 0.341257816166653 23 0.610682044363425 0.778635911273151 0.389317955636575 24 0.719199909854557 0.561600180290887 0.280800090145443 25 0.706122317304841 0.587755365390317 0.293877682695159 26 0.647881531902798 0.704236936194405 0.352118468097202 27 0.597742245050239 0.804515509899522 0.402257754949761 28 0.540240502378914 0.919518995242171 0.459759497621086 29 0.480592185020466 0.961184370040931 0.519407814979534 30 0.426223133200142 0.852446266400285 0.573776866799858 31 0.592880374993129 0.814239250013741 0.407119625006871 32 0.53831330632137 0.92337338735726 0.46168669367863 33 0.560853041383025 0.87829391723395 0.439146958616975 34 0.665848609414127 0.668302781171746 0.334151390585873 35 0.644493508581396 0.711012982837209 0.355506491418604 36 0.729833087248922 0.540333825502157 0.270166912751078 37 0.806185451501761 0.387629096996478 0.193814548498239 38 0.781399238785626 0.437201522428749 0.218600761214374 39 0.750293813080566 0.499412373838868 0.249706186919434 40 0.731965954860188 0.536068090279623 0.268034045139812 41 0.76226264937811 0.47547470124378 0.23773735062189 42 0.729115824186943 0.541768351626114 0.270884175813057 43 0.702968437898305 0.594063124203391 0.297031562101695 44 0.740426565303621 0.519146869392757 0.259573434696379 45 0.818445949020775 0.363108101958450 0.181554050979225 46 0.809539772309609 0.380920455380782 0.190460227690391 47 0.773356333219843 0.453287333560313 0.226643666780157 48 0.822857048523623 0.354285902952754 0.177142951476377 49 0.807959128754009 0.384081742491983 0.192040871245991 50 0.849576586753071 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0.817574928552754 0.364850142894492 0.182425071447246 69 0.79298140062721 0.41403719874558 0.20701859937279 70 0.770514688511034 0.458970622977932 0.229485311488966 71 0.742735543949464 0.514528912101073 0.257264456050536 72 0.745320455335979 0.509359089328043 0.254679544664021 73 0.714116696373574 0.571766607252852 0.285883303626426 74 0.729383682877141 0.541232634245718 0.270616317122859 75 0.733185732199788 0.533628535600424 0.266814267800212 76 0.698375928037295 0.603248143925409 0.301624071962705 77 0.725776286100431 0.548447427799138 0.274223713899569 78 0.690931599256775 0.61813680148645 0.309068400743225 79 0.667829763166658 0.664340473666684 0.332170236833342 80 0.626839025081021 0.746321949837958 0.373160974918979 81 0.58446084972528 0.831078300549439 0.415539150274719 82 0.54876856517263 0.902462869654739 0.451231434827369 83 0.505686899907911 0.988626200184177 0.494313100092089 84 0.472679302499521 0.945358604999041 0.52732069750048 85 0.443813207663266 0.887626415326532 0.556186792336734 86 0.520592747951703 0.958814504096595 0.479407252048297 87 0.476495743360037 0.952991486720073 0.523504256639963 88 0.458358152714902 0.916716305429804 0.541641847285098 89 0.436092261081063 0.872184522162125 0.563907738918937 90 0.391271320149089 0.782542640298178 0.608728679850911 91 0.369496303264734 0.738992606529469 0.630503696735266 92 0.364789811603488 0.729579623206977 0.635210188396512 93 0.322731081818244 0.645462163636489 0.677268918181756 94 0.342920096827973 0.685840193655947 0.657079903172027 95 0.337970099657111 0.675940199314223 0.662029900342889 96 0.371436689043011 0.742873378086023 0.628563310956989 97 0.330263135189319 0.660526270378638 0.669736864810681 98 0.308464802882551 0.616929605765101 0.69153519711745 99 0.268220292980001 0.536440585960002 0.731779707019999 100 0.230310653365581 0.460621306731162 0.769689346634419 101 0.197378545170942 0.394757090341883 0.802621454829058 102 0.173447637374175 0.346895274748349 0.826552362625825 103 0.248271257083183 0.496542514166367 0.751728742916817 104 0.225234675478418 0.450469350956837 0.774765324521582 105 0.203011813139750 0.406023626279499 0.79698818686025 106 0.175904967064540 0.351809934129081 0.82409503293546 107 0.165124511622290 0.330249023244580 0.83487548837771 108 0.147355265503062 0.294710531006124 0.852644734496938 109 0.122009125339945 0.244018250679891 0.877990874660055 110 0.123551452413675 0.247102904827351 0.876448547586325 111 0.110793200219102 0.221586400438203 0.889206799780898 112 0.089195257429356 0.178390514858712 0.910804742570644 113 0.211616619562739 0.423233239125479 0.78838338043726 114 0.187270463442716 0.374540926885432 0.812729536557284 115 0.389818205601655 0.77963641120331 0.610181794398345 116 0.397996944335834 0.795993888671668 0.602003055664166 117 0.453940434167192 0.907880868334384 0.546059565832808 118 0.412379434236482 0.824758868472964 0.587620565763518 119 0.396180124988937 0.792360249977874 0.603819875011063 120 0.363018384034183 0.726036768068367 0.636981615965817 121 0.37569736230763 0.75139472461526 0.62430263769237 122 0.372553683036160 0.745107366072321 0.62744631696384 123 0.322188985054299 0.644377970108599 0.6778110149457 124 0.408299521892262 0.816599043784523 0.591700478107738 125 0.360054946542827 0.720109893085654 0.639945053457173 126 0.500649696250315 0.99870060749937 0.499350303749685 127 0.453862973847097 0.907725947694194 0.546137026152903 128 0.405168177058571 0.810336354117142 0.594831822941429 129 0.354331142110283 0.708662284220567 0.645668857889717 130 0.351469676685576 0.702939353371152 0.648530323314424 131 0.320023500588473 0.640047001176945 0.679976499411527 132 0.263655267620465 0.52731053524093 0.736344732379535 133 0.214507621791096 0.429015243582191 0.785492378208904 134 0.168379515643071 0.336759031286141 0.83162048435693 135 0.128657214543669 0.257314429087339 0.87134278545633 136 0.255848933549163 0.511697867098326 0.744151066450837 137 0.310553056223090 0.621106112446181 0.68944694377691 138 0.313088134764783 0.626176269529565 0.686911865235217 139 0.247349786324218 0.494699572648436 0.752650213675782 140 0.248429579937389 0.496859159874778 0.751570420062611 141 0.414436434159839 0.828872868319677 0.585563565840161 142 0.368294778516482 0.736589557032964 0.631705221483518 143 0.297153187303325 0.59430637460665 0.702846812696675 144 0.248899479930882 0.497798959861764 0.751100520069118 145 0.275883551627299 0.551767103254599 0.7241164483727 146 0.207166140004366 0.414332280008732 0.792833859995634 147 0.134962110971092 0.269924221942183 0.865037889028908 148 0.0856555256560498 0.171311051312100 0.91434447434395 149 0.0429394703903827 0.0858789407807654 0.957060529609617 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 1 0.00714285714285714 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/10x8sr1291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/10x8sr1291137214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/18odx1291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/18odx1291137214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/28odx1291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/28odx1291137214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/31yci1291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/31yci1291137214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/41yci1291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/41yci1291137214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/51yci1291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/51yci1291137214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/6t7u31291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/6t7u31291137214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/7mgt61291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/7mgt61291137214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/8mgt61291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/8mgt61291137214.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/9mgt61291137214.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911372125dwa52b42q1yrar/9mgt61291137214.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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