PAPER BAEYENS (Multiple Linear Regression2)

*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, 21 Dec 2010 12:37:56 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935255bwz6pye1fjz9ows.htm/, Retrieved Tue, 21 Dec 2010 13:40:55 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935255bwz6pye1fjz9ows.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 «

13 14 5 12 18 3 15 11 0 12 12 7 10 16 4 12 18 1 15 14 6 9 14 3 12 15 12 11 15 0 11 17 5 11 19 6 15 10 6 7 16 6 11 18 2 11 14 1 10 14 5 14 17 7 10 14 3 6 16 3 11 18 3 15 11 7 11 14 8 12 12 6 14 17 3 15 9 5 9 16 5 13 14 10 13 15 2 16 11 6 13 16 4 12 13 6 14 17 8 11 15 4 9 14 5 16 16 10 12 9 6 10 15 7 13 17 4 16 13 10 14 15 4 15 16 3 5 16 3 8 12 3 11 12 3 16 11 7 17 15 15 9 15 0 9 17 0 13 13 4 10 16 5 6 14 5 12 11 2 8 12 3 14 12 0 12 15 9 11 16 2 16 15 7 8 12 7 15 12 0 7 8 0 16 13 10 14 11 2 16 14 1 9 15 8 14 10 6 11 11 11 13 12 3 15 15 8 5 15 6 15 14 9 13 16 9 11 15 8 11 15 8 12 13 7 12 12 6 12 17 5 12 13 4 14 15 6 6 13 3 7 15 2 14 16 12 14 15 8 10 16 5 13 15 9 12 14 6 9 15 5 12 14 2 16 13 4 10 7 7 14 17 5 10 13 6 16 15 7 15 14 8 12 13 6 10 16 0 8 12 1 8 14 5 11 17 5 13 15 5 16 17 7 16 12 7 14 16 1 11 11 3 4 15 4 14 9 8 9 16 6 14 15 6 8 10 2 8 10 2 11 15 3 12 11 3 11 13 0 14 14 2 15 18 8 16 16 8 1 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 33 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation HS[t] = + 15.3521568601490 -0.0793757965371474IEP[t] + 0.00940023589763553WP[t] -0.00515599648553805t + 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) 15.3521568601490 0.841111 18.2522 0 0 IEP -0.0793757965371474 0.06701 -1.1845 0.238048 0.119024 WP 0.00940023589763553 0.063034 0.1491 0.881649 0.440824 t -0.00515599648553805 0.004168 -1.2371 0.217945 0.108973 Multiple Linear Regression - Regression Statistics Multiple R 0.144154143804449 R-squared 0.0207804171759936 Adjusted R-squared 0.00145371488341473 F-TEST (value) 1.07521794775991 F-TEST (DF numerator) 3 F-TEST (DF denominator) 152 p-value 0.361465610277966 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.33699119495458 Sum Squared Residuals 830.152232484875 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 14.3621166881687 -0.362116688168747 2 18 14.4175360164251 3.58246398357491 3 11 14.1460519226352 -3.1460519226352 4 12 14.4448249670446 -2.44482496704455 5 16 14.5702198559404 1.42978014405960 6 18 14.3781115586877 3.62188844131234 7 14 14.1818293520789 -0.181829352078861 8 14 14.6247274271233 -0.624727427123301 9 15 14.4660461641050 0.53395383589496 10 15 14.4274631333850 0.572536866614977 11 17 14.4693083163877 2.53069168361234 12 19 14.4735525557998 4.52644744420024 13 10 14.1508933731656 -4.15089337316563 14 16 14.7807437489773 1.21925625102273 15 18 14.4204836227526 3.57951637724740 16 14 14.4059273903694 -0.405927390369430 17 14 14.5177481340116 -0.517748134011582 18 17 14.2138894231727 2.78611057682727 19 14 14.4886356692452 -0.488635669245235 20 16 14.8009828589083 1.19901714109171 21 18 14.398947879737 3.60105212026299 22 11 14.1138896406934 -3.11388964069343 23 14 14.4356370662541 -0.435637066254113 24 12 14.3323048014362 -2.33230480143616 25 17 14.1401965041834 2.85980349581658 26 9 14.074465182956 -5.074465182956 27 16 14.5455639656933 1.45443603430665 28 14 14.2699059625474 -0.269905962547399 29 15 14.1895480788808 0.810451921119223 30 11 13.9838656363743 -2.98386563637434 31 16 14.1980365577050 1.80196344229503 32 13 14.2910568295519 -1.29105682955185 33 17 14.1459497117873 2.85405028821271 34 15 14.3413201613227 0.658679838677348 35 14 14.5043159938090 -0.504315993809045 36 16 13.9905306010517 2.00946939894835 37 9 14.2652768471242 -5.26527684712416 38 15 14.4282726796106 0.571727320389446 39 17 14.1567885858207 2.84321141417933 40 13 13.9699066151095 -0.9699066151095 41 15 14.0671007963124 0.932899203687556 42 16 13.9731687673921 2.02683123260788 43 16 14.7617707362781 1.23822926372194 44 12 14.5184873501811 -2.51848735018108 45 12 14.2752039640841 -2.2752039640841 46 11 13.9107699285034 -2.91076992850336 47 15 13.9014400226618 1.09855997733824 48 15 14.3902868600089 0.609713139991128 49 17 14.3851308635233 2.61486913647667 50 13 14.1000726244797 -1.10007262447975 51 16 14.3424442535033 1.65755574649671 52 14 14.6547914431663 -0.65479144316634 53 11 14.145179959765 -3.14517995976501 54 12 14.4669273853257 -2.4669273853257 55 12 13.9573159019244 -1.95731590192437 56 15 14.1955136215918 0.804486378408154 57 16 14.20393177036 1.79606822963999 58 15 13.8488979706769 1.15110202932309 59 12 14.4787483464885 -2.47874834648855 60 12 13.8521601229595 -1.85216012295953 61 8 14.4820104987712 -6.48201049877117 62 13 13.8564746924277 -0.856474692427663 63 11 13.9348684018353 -2.93486840183534 64 14 13.7615605763779 0.238439423622133 65 15 14.3778368069358 0.62216319306419 66 10 13.9570013559693 -3.95700135596926 67 11 14.2369739285833 -3.23697392858335 68 12 13.9978644518424 -1.99786445184243 69 15 13.8809580417708 1.11904195822923 70 15 14.6507595388614 0.349240461138562 71 14 13.8800462846973 0.119953715302668 72 16 14.0336418812861 1.96635811871391 73 15 14.1778372419772 0.82216275802279 74 15 14.1726812454917 0.827318754508328 75 13 14.0787492165714 -1.07874921657135 76 12 14.0641929841882 -2.06419298418818 77 17 14.049636751805 2.95036324819500 78 13 14.0350805194218 -1.03508051942183 79 15 13.8899734016573 1.11002659834273 80 13 14.491623069776 -1.49162306977600 81 15 14.3976910408557 0.602308959144317 82 16 13.9309068275865 2.06909317241353 83 15 13.8881498875104 1.11185011248961 84 16 14.1722963694805 1.82770363051947 85 15 13.9666139269741 1.03338607302591 86 14 14.0126330193328 -0.0126330193327973 87 15 14.2362041765611 0.763795823438934 88 14 13.9647200827712 0.0352799172288209 89 13 13.6608613719323 -0.660861371932323 90 7 14.1601608623626 -7.16016086236258 91 17 13.8187012079332 3.18129879206682 92 13 14.1404486334939 -1.14044863349386 93 15 13.6684380936831 1.33156190631692 94 14 13.7520581296323 0.247941870367678 95 13 13.9662290509630 -0.966229050962955 96 16 14.0634232321659 1.9365767678341 97 12 14.2264190646523 -2.22641906465229 98 14 14.2588640117573 -0.258864011757295 99 17 14.0155806256603 2.98441937433969 100 15 13.8516730361005 1.14832696389952 101 17 13.6271901217988 3.37280987820123 102 12 13.6220341253132 -1.62203412531323 103 16 13.7192283065162 2.28077169348382 104 11 13.9710001714374 -2.97100017143735 105 15 14.5308749866095 0.469125013390517 106 9 13.769561968343 -4.76956196834301 107 16 14.1424844827479 1.85751551725206 108 15 13.7404495035767 1.25955049642333 109 10 14.1739473427235 -4.17394734272347 110 10 14.1687913462379 -4.16879134623793 111 15 13.9349081960386 1.06509180396141 112 11 13.8503764030159 -2.8503764030159 113 13 13.8963954953746 -0.896395495374604 114 14 13.6719125810729 0.328087418927105 115 18 13.6437822034360 4.35621779656398 116 16 13.5592504104133 2.44074958958666 117 14 13.4788925267467 0.521107473253285 118 14 13.9176166924351 0.0823833075649084 119 14 13.7119342499287 0.288065750071346 120 14 13.6785775457502 0.321422454249791 121 12 13.8321731423390 -1.83217314233897 122 14 13.6400648450862 0.359935154913774 123 15 14.1675650432094 0.832434956790614 124 15 13.7467295922428 1.25327040775716 125 15 13.5128464420435 1.48715355795651 126 13 13.7499917445255 -0.749991744525462 127 17 13.4931342131748 3.50686578682522 128 17 13.7396797515544 3.26032024844561 129 19 13.8609007310942 5.13909926890583 130 15 14.3643741308805 0.63562586911951 131 13 13.5383118785161 -0.53831187851608 132 9 13.5279295554890 -4.52792955548897 133 15 13.8914518339963 1.10854816600374 134 15 13.7045698632851 1.29543013671491 135 15 13.5030613301347 1.49693866986528 136 16 13.7172322514654 2.28276774853465 137 11 13.5909256054961 -2.59092560549606 138 14 14.1131994770777 -0.113199477077649 139 11 13.1743343939416 -2.17433439394161 140 15 13.7624099168067 1.23759008319335 141 13 13.7008525049353 -0.700852504935298 142 15 13.6163207119126 1.38367928808739 143 16 13.4242124146599 2.57578758534013 144 14 14.0686893529107 -0.0686893529107224 145 15 13.6896287548908 1.31037124510922 146 16 13.8244238796843 2.17557612031573 147 16 13.9874197121707 2.01258028782934 148 11 13.8893137738943 -2.88931377389428 149 12 13.4590780870301 -1.45907808703009 150 9 13.3087446427240 -4.30874464272396 151 16 13.5981174512357 2.40188254876432 152 13 13.3736345369340 -0.373634536933968 153 16 13.8489072290274 2.15109277097262 154 12 13.4844731934466 -1.48447319344664 155 9 13.5357186123469 -4.53571861234692 156 13 13.6423130294475 -0.642313029447498 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.809870267167501 0.380259465664998 0.190129732832499 8 0.848984784426246 0.302030431147507 0.151015215573754 9 0.780210527163785 0.43957894567243 0.219789472836215 10 0.680684763665777 0.638630472668446 0.319315236334223 11 0.624085873083039 0.751828253833922 0.375914126916961 12 0.667568993733082 0.664862012533836 0.332431006266918 13 0.76054675816044 0.478906483679119 0.239453241839560 14 0.741230454727901 0.517539090544197 0.258769545272099 15 0.74394063387829 0.512118732243421 0.256059366121711 16 0.708168423789966 0.583663152420067 0.291831576210034 17 0.66696042597753 0.66607914804494 0.33303957402247 18 0.725896976539965 0.548206046920069 0.274103023460035 19 0.697280306599609 0.605439386800781 0.302719693400391 20 0.647655008406818 0.704689983186363 0.352344991593182 21 0.67408275465848 0.65183449068304 0.32591724534152 22 0.691169920780616 0.617660158438768 0.308830079219384 23 0.633566512814624 0.732866974370752 0.366433487185376 24 0.620077025704588 0.759845948590825 0.379922974295412 25 0.68051131595747 0.638977368085059 0.319488684042530 26 0.78204362676287 0.43591274647426 0.21795637323713 27 0.74078367353738 0.518432652925241 0.259216326462620 28 0.694047272733228 0.611905454533544 0.305952727266772 29 0.650706696257869 0.698586607484262 0.349293303742131 30 0.617299577402828 0.765400845194344 0.382700422597172 31 0.611914527563888 0.776170944872224 0.388085472436112 32 0.565526140798074 0.868947718403853 0.434473859201926 33 0.654751780571809 0.690496438856383 0.345248219428191 34 0.602744046697484 0.794511906605032 0.397255953302516 35 0.571156707782338 0.857686584435325 0.428843292217662 36 0.617376901630072 0.765246196739855 0.382623098369928 37 0.793923944514443 0.412152110971114 0.206076055485557 38 0.75513480636426 0.48973038727148 0.24486519363574 39 0.786495251523864 0.427009496952272 0.213504748476136 40 0.746741973184772 0.506516053630456 0.253258026815228 41 0.714549573825646 0.570900852348707 0.285450426174354 42 0.711671258119667 0.576657483760665 0.288328741880333 43 0.681294407660693 0.637411184678615 0.318705592339307 44 0.717058391589608 0.565883216820784 0.282941608410392 45 0.712026377039114 0.575947245921772 0.287973622960886 46 0.702435330287932 0.595129339424136 0.297564669712068 47 0.696907190601176 0.606185618797649 0.303092809398824 48 0.656591656110296 0.686816687779409 0.343408343889704 49 0.66996059103548 0.660078817929039 0.330039408964520 50 0.627884163574886 0.744231672850229 0.372115836425114 51 0.608269948811934 0.783460102376132 0.391730051188066 52 0.574062560075513 0.851874879848974 0.425937439924487 53 0.592126499285949 0.815747001428102 0.407873500714051 54 0.589990482768619 0.820019034462762 0.410009517231381 55 0.553551077690621 0.892897844618758 0.446448922309379 56 0.521386714601391 0.957226570797218 0.478613285398609 57 0.521043998780578 0.957912002438844 0.478956001219422 58 0.50662687472427 0.986746250551459 0.493373125275729 59 0.50300413506035 0.9939917298793 0.49699586493965 60 0.46566203643333 0.93132407286666 0.53433796356667 61 0.717198749650465 0.565602500699069 0.282801250349535 62 0.677717111972953 0.644565776054093 0.322282888027047 63 0.674845827960264 0.650308344079472 0.325154172039736 64 0.646958398934346 0.706083202131307 0.353041601065654 65 0.61363563817857 0.77272872364286 0.38636436182143 66 0.662069686076539 0.675860627846923 0.337930313923461 67 0.676784371632255 0.64643125673549 0.323215628367745 68 0.656653549258558 0.686692901482883 0.343346450741442 69 0.646001180319513 0.707997639360973 0.353998819680486 70 0.608263295301662 0.783473409396676 0.391736704698338 71 0.573356948953358 0.853286102093283 0.426643051046642 72 0.581030283015215 0.83793943396957 0.418969716984785 73 0.549650975586452 0.900698048827097 0.450349024413548 74 0.517069915021591 0.965860169956818 0.482930084978409 75 0.476853293460108 0.953706586920217 0.523146706539892 76 0.457915929205863 0.915831858411726 0.542084070794137 77 0.50962012270936 0.98075975458128 0.49037987729064 78 0.470783365406948 0.941566730813895 0.529216634593052 79 0.445697707902484 0.891395415804968 0.554302292097516 80 0.412827197354205 0.82565439470841 0.587172802645795 81 0.375918019633526 0.751836039267051 0.624081980366475 82 0.374888918062311 0.749777836124622 0.625111081937689 83 0.347321999930701 0.694643999861402 0.652678000069299 84 0.338719860580934 0.677439721161868 0.661280139419066 85 0.309470983791357 0.618941967582713 0.690529016208643 86 0.270169833683183 0.540339667366367 0.729830166316817 87 0.239805807925057 0.479611615850114 0.760194192074943 88 0.206642398609794 0.413284797219588 0.793357601390206 89 0.177438194181193 0.354876388362386 0.822561805818807 90 0.495613824111425 0.99122764822285 0.504386175888575 91 0.542218569224457 0.915562861551087 0.457781430775543 92 0.505337593492501 0.989324813014997 0.494662406507499 93 0.476247041297218 0.952494082594436 0.523752958702782 94 0.430684342637112 0.861368685274224 0.569315657362888 95 0.392157087801342 0.784314175602684 0.607842912198658 96 0.380392440430662 0.760784880861323 0.619607559569338 97 0.376922252977092 0.753844505954185 0.623077747022908 98 0.334296169906600 0.668592339813199 0.6657038300934 99 0.359808507911819 0.719617015823638 0.640191492088181 100 0.326523167384091 0.653046334768181 0.673476832615909 101 0.379010281274303 0.758020562548606 0.620989718725697 102 0.349813782693322 0.699627565386645 0.650186217306678 103 0.348690195241721 0.697380390483442 0.651309804758279 104 0.371869380129339 0.743738760258678 0.628130619870661 105 0.327678990248280 0.655357980496559 0.67232100975172 106 0.476364934847424 0.952729869694848 0.523635065152576 107 0.452003801976278 0.904007603952556 0.547996198023722 108 0.414320178849467 0.828640357698933 0.585679821150533 109 0.54819958199991 0.90360083600018 0.45180041800009 110 0.727755270866175 0.544489458267649 0.272244729133825 111 0.689282083002583 0.621435833994834 0.310717916997417 112 0.771695415689217 0.456609168621567 0.228304584310783 113 0.785269936407076 0.429460127185848 0.214730063592924 114 0.759061365367445 0.481877269265109 0.240938634632555 115 0.82755883044305 0.344882339113899 0.172441169556950 116 0.824750981907069 0.350498036185863 0.175249018092931 117 0.790430061219874 0.419139877560252 0.209569938780126 118 0.76078188318887 0.47843623362226 0.23921811681113 119 0.714927545251137 0.570144909497726 0.285072454748863 120 0.667177244348793 0.665645511302414 0.332822755651207 121 0.702396674493954 0.595206651012092 0.297603325506046 122 0.662865397937924 0.674269204124153 0.337134602062077 123 0.619588968053565 0.760822063892871 0.380411031946435 124 0.565138117453699 0.869723765092602 0.434861882546301 125 0.517303496739745 0.96539300652051 0.482696503260255 126 0.540806079656859 0.918387840686281 0.459193920343141 127 0.59583448966964 0.808331020660719 0.404165510330359 128 0.577523274669484 0.844953450661032 0.422476725330516 129 0.745373606181415 0.509252787637169 0.254626393818584 130 0.752478715582101 0.495042568835798 0.247521284417899 131 0.734123448367203 0.531753103265595 0.265876551632797 132 0.878965486914118 0.242069026171764 0.121034513085882 133 0.849918655763159 0.300162688473683 0.150081344236841 134 0.821247148502187 0.357505702995625 0.178752851497812 135 0.792842941216601 0.414314117566797 0.207157058783398 136 0.757063945639703 0.485872108720593 0.242936054360297 137 0.758092451164835 0.483815097670329 0.241907548835165 138 0.798916316859807 0.402167366280385 0.201083683140193 139 0.751909158796395 0.49618168240721 0.248090841203605 140 0.702948537492822 0.594102925014355 0.297051462507177 141 0.696978973813918 0.606042052372163 0.303021026186082 142 0.61026488533957 0.77947022932086 0.38973511466043 143 0.570645803784314 0.858708392431372 0.429354196215686 144 0.480321738953281 0.960643477906561 0.519678261046719 145 0.391938699562139 0.783877399124279 0.60806130043786 146 0.308075130423595 0.61615026084719 0.691924869576405 147 0.217923897251358 0.435847794502716 0.782076102748642 148 0.441093570026151 0.882187140052303 0.558906429973849 149 0.374851615098879 0.749703230197758 0.625148384901121 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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