Workshop 7 (Multiple Regression)

*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: Thu, 02 Dec 2010 09:13:43 +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/02/t1291281403xys3fplft9v73nt.htm/, Retrieved Thu, 02 Dec 2010 10:16:43 +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/02/t1291281403xys3fplft9v73nt.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 «

4 2 5 2 3 1 4 2 2 4 2 3 4 4 3 4 4 2 2 1 5 2 2 4 2 2 2 3 2 3 2 2 3 2 4 2 4 5 1 2 2 3 1 3 5 1 1 1 4 1 3 4 3 3 3 3 1 3 3 2 2 4 2 2 2 4 1 2 2 4 2 4 4 4 3 2 2 2 4 3 2 2 4 2 2 3 3 3 2 4 2 2 3 3 2 2 2 1 1 4 4 1 3 3 4 3 4 5 1 1 2 4 2 3 4 2 3 1 2 2 3 2 2 2 2 2 2 3 4 2 3 2 3 2 4 4 2 4 4 3 3 2 4 1 2 3 3 4 5 4 2 3 4 4 2 4 4 4 5 1 3 2 2 4 2 2 4 2 2 3 5 2 2 2 2 1 4 4 2 3 2 4 2 4 4 2 2 2 4 2 3 4 2 2 3 3 2 4 4 3 2 3 4 2 4 4 2 2 2 2 4 1 4 1 3 3 4 2 4 4 4 4 3 4 4 5 2 1 1 2 5 3 2 4 2 3 2 5 1 4 4 2 3 1 4 4 3 5 2 2 4 4 3 2 5 2 1 4 4 2 4 4 2 1 1 2 4 5 3 2 2 5 4 2 4 4 2 2 3 4 3 4 5 2 2 2 4 3 4 4 2 1 2 3 2 3 4 2 2 2 2 1 4 5 2 1 3 3 2 2 4 2 2 1 4 1 2 5 1 2 2 3 2 4 4 2 4 4 2 4 2 4 1 2 5 4 2 4 4 2 2 2 4 2 4 3 1 2 3 3 2 1 4 1 1 2 4 2 4 4 2 2 4 3 2 2 4 2 2 2 4 1 1 2 1 1 1 2 2 4 3 5 5 3 4 3 3 5 2 2 4 4 2 2 4 2 2 2 4 2 4 4 1 2 3 4 1 3 5 1 1 2 3 1 2 3 2 3 1 1 2 2 5 2 1 1 3 2 3 4 1 1 2 3 1 2 5 1 2 1 4 2 1 4 2 3 2 2 1 3 4 1 2 1 3 4 2 5 1 2 4 5 4 3 4 2 2 4 4 1 3 4 1 4 3 4 1 3 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Yt[t] = + 1.04779067010842 -0.0580797728659307X1[t] -0.0287868899563356X2[t] + 0.139832767583328X3[t] -0.0610909867704954X4[t] + 0.291585366512453X5[t] + 0.217252184272917X6[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) 1.04779067010842 0.454059 2.3076 0.02237 0.011185 X1 -0.0580797728659307 0.077633 -0.7481 0.455539 0.227769 X2 -0.0287868899563356 0.085238 -0.3377 0.736038 0.368019 X3 0.139832767583328 0.085354 1.6383 0.103435 0.051718 X4 -0.0610909867704954 0.082531 -0.7402 0.460312 0.230156 X5 0.291585366512453 0.06371 4.5768 1e-05 5e-06 X6 0.217252184272917 0.074892 2.9009 0.004274 0.002137 Multiple Linear Regression - Regression Statistics Multiple R 0.447149626952174 R-squared 0.199942788883469 Adjusted R-squared 0.168361583181500 F-TEST (value) 6.33106888857657 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 5.77565851023198e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.86648628101019 Sum Squared Residuals 114.121368227188 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 2.04468335305416 1.95531664694584 2 2 2.94822634254786 -0.948226342547861 3 3 2.23565386832205 0.764346131677947 4 2 2.20889441202053 -0.208894412020534 5 2 2.36454961656970 -0.364549616569695 6 2 1.92411520874901 0.0758847912509917 7 1 1.9689527861459 -0.968952786145898 8 1 2.52114178647989 -1.52114178647989 9 1 2.54552007786293 -1.54552007786293 10 2 2.28631382871012 -0.286313828710122 11 2 2.09405723041192 -0.0940572304119174 12 2 2.48744030499700 -0.487440304996997 13 2 2.68535284544626 -0.685352845446256 14 2 1.74509716056511 0.254902839434894 15 1 2.40064866272022 -1.40064866272022 16 3 2.20245837979242 0.79754162020758 17 2 1.58088610159874 0.419113898401262 18 2 1.99113623479436 0.0088637652056422 19 2 2.08972365238411 -0.0897236523841077 20 2 2.55372362577259 -0.553723625772588 21 3 2.36064701094966 0.639352989050342 22 4 2.77398702395007 1.22601297604993 23 2 1.89754207463139 0.102457925368610 24 2 2.57481296077252 -0.574812960772523 25 2 1.90477556492535 0.095224435074649 26 1 2.24889606379109 -1.24889606379109 27 2 2.30998705056159 -0.309987050561589 28 2 2.44240000566706 -0.442400005667056 29 2 2.74140518465737 -0.74140518465737 30 2 1.87548268201576 0.124517317984244 31 4 2.57488798131801 1.42511201868199 32 2 2.75905597869971 -0.759055978699708 33 4 2.44799146106841 1.55200853893159 34 3 2.58230779379587 0.417692206204128 35 1 1.95731069727864 -0.95731069727864 36 4 2.92245066649609 1.07754933350391 37 3 3.04162142613252 -0.0416214261325159 38 2 1.64498830227380 0.355011697726202 39 4 3.15545026718935 0.844549732810647 40 2 2.60157241707404 -0.601572417074042 41 3 2.28120016060525 0.718799839394746 42 3 2.15382585305917 0.846174146940832 43 2 1.93356245488169 0.0664375451183134 44 1 2.41662432961528 -1.41662432961528 45 2 2.13456122978100 -0.134561229780997 46 1 2.04027475448087 -1.04027475448087 47 2 2.33647144149967 -0.336471441499671 48 4 3.16106992824748 0.838930071752519 49 2 2.30998705056159 -0.309987050561589 50 2 2.27327435517413 -0.273274355174133 51 2 2.40548458834655 -0.405484588346548 52 2 2.67590559931358 -0.675905599313578 53 2 2.42614659629345 -0.42614659629345 54 1 1.73696863320093 -0.736968633200934 55 2 2.86658464946888 -0.866584649468876 56 3 2.92245066649609 0.0775493335039101 57 2 2.42614659629345 -0.42614659629345 58 2 2.46173964949071 -0.461739649490714 59 1 2.04328596838543 -1.04328596838543 60 1 1.45050058014809 -0.450500580148088 61 2 1.94961314232224 0.0503868576777594 62 2 2.07207285834177 -0.0720728583417701 63 1 1.96594157224133 -0.965941572241334 64 2 1.98863101384305 0.0113689861569474 65 1 1.71939650505882 -0.719396505058822 66 4 3.05794985605161 0.942050143948391 67 4 2.95123755645243 1.04876244354757 68 1 2.39763744881565 -1.39763744881565 69 1 1.75170060187298 -0.751700601872982 70 3 2.71773196280590 0.282268037194097 71 4 1.82251657725469 2.17748342274531 72 2 2.06906164443721 -0.0690616444372054 73 4 2.71261829470103 1.28738170529897 74 4 2.49536611042812 1.50463388957188 75 3 2.92546188040065 0.0745381195993453 76 4 2.42614659629345 1.57385340370655 77 2 1.71939650505882 0.280603494941178 78 2 2.20378074391567 -0.203780743915665 79 2 1.90477556492535 0.095224435074649 80 2 2.95424877035699 -0.95424877035699 81 2 1.76634018201075 0.233659817989246 82 2 1.96234934483802 0.0376506551619778 83 2 1.73263870052786 0.267361299472137 84 1 2.08081503494288 -1.08081503494288 85 3 2.49607117995969 0.50392882004031 86 3 1.73564991443243 1.26435008556757 87 2 2.28631382871012 -0.286313828710122 88 4 2.02703255901183 1.97296744098817 89 4 3.17282331875315 0.827176681246849 90 2 1.99465344165218 0.00534655834781807 91 2 2.45865341504066 -0.458653415040662 92 1 2.02703255901183 -1.02703255901183 93 1 1.88059635012062 -0.880596350120624 94 1 2.62293949455252 -1.62293949455252 95 2 2.49235489652355 -0.492354896523553 96 2 3.18102686666281 -1.18102686666281 97 3 3.13282166698259 -0.132821666982592 98 4 3.02997933726526 0.970020662734741 99 2 2.15382585305917 -0.153825853059168 100 2 1.99465344165218 0.00534655834781807 101 4 2.44981981814492 1.55018018185508 102 2 2.07207285834177 -0.0720728583417701 103 3 2.22955641996744 0.770443580032564 104 2 2.50047977853299 -0.500479778532987 105 2 2.33927993347118 -0.339279933471184 106 4 2.47622554318277 1.52377445681723 107 2 2.73398537217951 -0.733985372179509 108 3 2.32888154282695 0.671118457173055 109 2 2.29365862064250 -0.293658620642496 110 2 1.82302257020795 0.176977429792047 111 2 1.47285143787631 0.52714856212369 112 4 2.33647144149967 1.66352855850033 113 3 2.02050413824944 0.97949586175056 114 1 3.19216296257681 -2.19216296257681 115 1 2.16854045374243 -1.16854045374243 116 1 2.2119056259251 -1.2119056259251 117 2 2.07597546396181 -0.0759754639618074 118 2 2.2002598917031 -0.200259891703102 119 3 2.75765859403098 0.242341405969024 120 1 2.46677829705010 -1.46677829705010 121 3 1.99773967610223 1.00226032389777 122 1 1.67076397832557 -0.67076397832557 123 2 2.31943429669427 -0.319434296694267 124 1 1.67126997127883 -0.671269971278829 125 2 1.79071847339379 0.209281526606207 126 2 1.90426957197209 0.0957304280279084 127 3 2.23124526974876 0.768754730251244 128 2 2.36806682342752 -0.368066823427520 129 2 2.22823405584419 -0.228234055844191 130 4 2.89014656968193 1.10985343031807 131 2 2.84452525685324 -0.844525256853242 132 3 1.64197708836923 1.35802291163077 133 2 1.87856891646581 0.121431083534192 134 1 1.72240771896339 -0.722407718963387 135 2 2.57481296077252 -0.574812960772523 136 3 2.30998705056159 0.690012949438411 137 1 2.38943390090599 -1.38943390090599 138 2 1.74005851300572 0.259941486994276 139 2 2.35173839350843 -0.351738393508427 140 3 2.13537760095098 0.864622399049017 141 3 2.72745695141712 0.27254304858288 142 3 3.28898286448501 -0.288982864485013 143 4 3.0545439508322 0.945456049167802 144 4 2.20448581344724 1.79551418655276 145 2 2.04410233955542 -0.04410233955542 146 3 2.65965218993997 0.340347810060027 147 3 2.47118689562339 0.528813104376608 148 2 2.49997378557973 -0.499973785579727 149 1 1.57296029616762 -0.572960296167617 150 2 2.15514821718241 -0.155148217182413 151 2 2.69145029380087 -0.691450293800873 152 4 2.89315778358649 1.10684221641351 153 4 3.60291908872569 0.397080911274312 154 2 1.7932236943451 0.206776305654901 155 3 2.44169493613548 0.558305063864516 156 2 2.15081463915460 -0.150814639154603 157 4 2.51673318790659 1.48326681209341 158 2 2.58965258572825 -0.589652585728246 159 4 2.64492386662266 1.35507613337734 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.700904353137251 0.598191293725498 0.299095646862749 11 0.548350795765601 0.903298408468797 0.451649204234399 12 0.667445216461547 0.665109567076905 0.332554783538453 13 0.688269018828925 0.623461962342151 0.311730981171075 14 0.585004296314544 0.829991407370911 0.414995703685456 15 0.594330712308339 0.811338575383322 0.405669287691661 16 0.66370282946078 0.67259434107844 0.33629717053922 17 0.576746172409873 0.846507655180253 0.423253827590127 18 0.487244031173466 0.974488062346931 0.512755968826534 19 0.398345465161099 0.796690930322198 0.601654534838901 20 0.346589093351314 0.693178186702628 0.653410906648686 21 0.395543028554495 0.79108605710899 0.604456971445505 22 0.669866825308829 0.660266349382342 0.330133174691171 23 0.61373906568817 0.772521868623659 0.386260934311830 24 0.549929681138955 0.90014063772209 0.450070318861045 25 0.476960381831964 0.953920763663929 0.523039618168036 26 0.56570907024076 0.86858185951848 0.43429092975924 27 0.5030889767728 0.9938220464544 0.4969110232272 28 0.438700434274991 0.877400868549983 0.561299565725009 29 0.385658676637406 0.771317353274812 0.614341323362594 30 0.324213713924165 0.64842742784833 0.675786286075835 31 0.443566249546796 0.887132499093591 0.556433750453204 32 0.393298773982683 0.786597547965367 0.606701226017317 33 0.534859419251352 0.930281161497296 0.465140580748648 34 0.480035185873147 0.960070371746293 0.519964814126853 35 0.543774131214557 0.912451737570886 0.456225868785443 36 0.621550300027261 0.756899399945477 0.378449699972739 37 0.564776482669887 0.870447034660227 0.435223517330113 38 0.513854975886206 0.972290048227588 0.486145024113794 39 0.552240168114169 0.895519663771662 0.447759831885831 40 0.523258797318652 0.953482405362695 0.476741202681348 41 0.49527895475044 0.99055790950088 0.50472104524956 42 0.481909062676729 0.963818125353459 0.518090937323271 43 0.428559670900642 0.857119341801283 0.571440329099358 44 0.516374714643145 0.96725057071371 0.483625285356855 45 0.471561401221563 0.943122802443126 0.528438598778437 46 0.50370356102363 0.99259287795274 0.49629643897637 47 0.460559211136162 0.921118422272324 0.539440788863838 48 0.462195543510216 0.924391087020432 0.537804456489784 49 0.419980363937573 0.839960727875146 0.580019636062427 50 0.376786596214604 0.753573192429208 0.623213403785396 51 0.349075484956314 0.698150969912628 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104 0.433382017380138 0.866764034760276 0.566617982619862 105 0.390957364085224 0.781914728170449 0.609042635914776 106 0.489795424361867 0.979590848723734 0.510204575638133 107 0.480893360444426 0.961786720888851 0.519106639555574 108 0.467082574176083 0.934165148352166 0.532917425823917 109 0.420600749068694 0.841201498137389 0.579399250931306 110 0.373125817822229 0.746251635644458 0.626874182177771 111 0.337616840037471 0.675233680074941 0.66238315996253 112 0.403152179080101 0.806304358160202 0.596847820919899 113 0.420981651008435 0.841963302016871 0.579018348991565 114 0.745491473368884 0.509017053262232 0.254508526631116 115 0.850539899779238 0.298920200441524 0.149460100220762 116 0.871406280353181 0.257187439293638 0.128593719646819 117 0.839307220261477 0.321385559477047 0.160692779738523 118 0.828087258813845 0.34382548237231 0.171912741186155 119 0.79399735412459 0.412005291750819 0.206002645875409 120 0.857594479821773 0.284811040356454 0.142405520178227 121 0.899187669433472 0.201624661133057 0.100812330566529 122 0.879466361075454 0.241067277849093 0.120533638924546 123 0.846770103291865 0.306459793416269 0.153229896708135 124 0.845276084500333 0.309447830999333 0.154723915499667 125 0.812700360685052 0.374599278629896 0.187299639314948 126 0.767786842693416 0.464426314613167 0.232213157306584 127 0.771572166544629 0.456855666910742 0.228427833455371 128 0.732678572162316 0.534642855675368 0.267321427837684 129 0.687443777390876 0.625112445218248 0.312556222609124 130 0.654356379107007 0.691287241785987 0.345643620892993 131 0.688222636096606 0.623554727806789 0.311777363903394 132 0.772589920763949 0.454820158472102 0.227410079236051 133 0.718705809592374 0.562588380815251 0.281294190407626 134 0.681991904371887 0.636016191256225 0.318008095628113 135 0.72200618420021 0.55598763159958 0.27799381579979 136 0.695885606557144 0.608228786885712 0.304114393442856 137 0.831329044727345 0.337341910545309 0.168670955272655 138 0.77459856569307 0.450802868613861 0.225401434306930 139 0.709727986404954 0.580544027190093 0.290272013595046 140 0.926166352368753 0.147667295262494 0.073833647631247 141 0.911574832342628 0.176850335314745 0.0884251676573723 142 0.904570826855883 0.190858346288234 0.095429173144117 143 0.96971113538641 0.0605777292271805 0.0302888646135902 144 0.989255806471385 0.0214883870572300 0.0107441935286150 145 0.97844685165793 0.0431062966841401 0.0215531483420700 146 0.952890043832138 0.0942199123357246 0.0471099561678623 147 0.957094496860412 0.0858110062791766 0.0429055031395883 148 0.922152775304786 0.155694449390428 0.0778472246952139 149 0.978178742314237 0.0436425153715268 0.0218212576857634 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 3 0.0214285714285714 OK 10% type I error level 6 0.0428571428571429 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/1030ym1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/1030ym1291281211.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/1wh1a1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/1wh1a1291281211.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/27q0v1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/27q0v1291281211.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/37q0v1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/37q0v1291281211.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/47q0v1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/47q0v1291281211.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/57q0v1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/57q0v1291281211.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/60zzy1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/60zzy1291281211.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/7trhj1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/7trhj1291281211.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/8trhj1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/8trhj1291281211.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/9trhj1291281211.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291281403xys3fplft9v73nt/9trhj1291281211.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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Software written by Ed van Stee & Patrick Wessa

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