W7 p1

*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 19:06:32 +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/t1290539131vb7v5v2t1cyw285.htm/, Retrieved Tue, 23 Nov 2010 20:05:34 +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/t1290539131vb7v5v2t1cyw285.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 «

3,50 2,20 3,00 3,43 4,33 2,67 2,75 1,40 2,00 3,57 3,83 2,78 1,50 3,40 2,00 4,29 4,17 1,89 3,00 2,00 2,00 2,71 3,83 2,00 2,00 2,40 2,25 3,14 3,17 2,00 2,50 2,40 1,75 3,14 4,83 1,78 2,50 2,20 1,00 3,57 4,17 2,22 2,75 2,20 2,75 3,29 3,50 1,78 4,00 2,40 1,75 2,43 3,67 2,00 2,75 2,60 1,75 3,00 4,17 1,89 3,25 2,80 3,00 2,71 4,00 2,56 3,00 3,20 2,50 2,71 3,00 3,33 2,00 2,20 2,50 2,14 3,67 2,56 3,00 2,00 2,00 2,29 2,50 2,00 2,75 2,20 2,00 3,29 3,67 1,67 1,00 3,00 1,00 3,86 4,67 1,33 2,25 1,80 2,25 3,14 3,33 2,33 2,00 2,20 2,00 2,00 2,00 1,67 2,00 3,40 1,75 3,14 4,00 2,22 3,50 3,40 2,75 3,29 3,33 3,44 3,75 2,20 2,25 3,29 3,50 3,00 4,00 3,60 2,75 3,00 3,33 3,78 2,25 2,80 3,25 2,71 3,50 2,33 3,50 2,00 2,00 2,57 3,83 3,44 2,75 2,20 2,00 2,86 4,67 2,11 2,00 3,00 2,25 3,29 4,00 1,78 2,25 3,00 1,50 3,57 4,00 2,22 2,25 2,60 2,25 2,71 4,00 2,33 2,25 3,20 2,25 3,43 3,83 2,44 2,25 2,60 1,50 3,14 3,83 1,89 2,50 1,80 1,50 3,57 4,83 2,67 4,00 3,60 4,00 3,71 4,00 2,78 2,75 3,60 1,25 4,14 3,00 2,89 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 Y[t] = -0.216966647663763 + 0.360374452098849X1[t] + 0.139026563992538X2[t] + 0.0835584328678894X3[t] + 0.440407549873858X4[t] -0.0776309220351274X5[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) -0.216966647663763 0.339069 -0.6399 0.523202 0.261601 X1 0.360374452098849 0.057889 6.2252 0 0 X2 0.139026563992538 0.073702 1.8863 0.061145 0.030572 X3 0.0835584328678894 0.074741 1.118 0.265333 0.132666 X4 0.440407549873858 0.074485 5.9127 0 0 X5 -0.0776309220351274 0.068675 -1.1304 0.260074 0.130037 Multiple Linear Regression - Regression Statistics Multiple R 0.638298402197689 R-squared 0.407424850248123 Adjusted R-squared 0.388059649275839 F-TEST (value) 21.0390199839005 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 5.55111512312578e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.497192288158996 Sum Squared Residuals 37.8216262249311 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.67 2.77533367772469 -0.105333677724692 2 2.78 2.41074567258854 0.36925432741146 3 1.89 2.52902965786729 -0.639029657867289 4 2 2.20550473111726 -0.205504731117258 5 2 2.16224216782134 -0.16224216782134 6 1.78 2.17178284685851 -0.391782846858507 7 2.22 2.32192036439803 -0.101920364398025 8 1.78 2.4869398387404 -0.7069398387404 9 2 2.48970703415709 -0.48970703415709 10 1.89 2.27926112424257 -0.389261124242571 11 2.56 2.47718077145792 0.0828192285420817 12 3.33 2.4785494896314 0.851450510368596 13 2.56 1.67610345234838 0.883896547651618 14 2 2.12378268647696 -0.123782686476957 15 1.67 2.41107375734351 -0.741073757343511 16 1.33 1.98148266588964 -0.651482665889637 17 2.33 2.15649889492491 0.173501105075092 18 1.67 1.70231081873076 -0.03231081873076 19 2.22 2.19505585009078 0.0249441499092237 20 3.44 2.93724981135155 0.502750188648446 21 3 2.8055350744053 0.194464925594695 22 3.78 3.01752416073607 0.762475839263932 23 2.33 2.1765113885936 0.153488611406395 24 3.44 2.32403490018434 1.11596509981566 25 2.11 2.14406758886262 -0.0340675888626247 26 1.78 2.24728557340878 -0.467285573408785 27 2.22 2.39802447574726 -0.17802447574726 28 2.33 2.02633218190964 0.303667818090356 29 2.44 2.44003881296032 -3.88129603165992e-05 30 1.89 2.16623586045046 -0.276235860450458 31 2.67 2.25685254669177 0.413147453308229 32 2.78 3.38264884446783 -0.602648844467834 33 2.89 2.96940125743846 -0.0794012574384616 34 2.78 2.67261482567188 0.107385174328116 35 1.89 2.55511938701276 -0.665119387012756 36 3.56 3.08726198928571 0.472738010714292 37 3.67 2.62637327572299 1.04362672427701 38 1.44 2.44792781772315 -1.00792781772315 39 3.56 3.09205235323611 0.467947646763895 40 2.78 2.87000854481692 -0.0900085448169176 41 3.22 2.99949304708145 0.220506952918553 42 2.44 2.44608524434564 -0.00608524434564125 43 2 1.92928563068506 0.0707143693149406 44 1.89 2.41813743707477 -0.528137437074767 45 2.22 2.46572505494169 -0.245725054941691 46 1.67 2.2729766629049 -0.6029766629049 47 2.22 2.46383811106635 -0.243838111066346 48 3.67 3.12206821395363 0.547931786046366 49 3.22 2.45967862355637 0.760321376443634 50 2.56 2.96380823570237 -0.403808235702373 51 2.89 2.58553330853655 0.304466691463455 52 2 2.10535545035758 -0.105355450357583 53 2.22 2.08177928863642 0.13822071136358 54 1.22 1.30918293503971 -0.0891829350397122 55 3.11 3.21973934661944 -0.109739346619443 56 2.89 2.59067148361304 0.299328516386964 57 2.44 2.46932296277517 -0.0293229627751708 58 1.89 2.24408669721329 -0.354086697213292 59 1.33 1.71222756666654 -0.382227566666535 60 1.56 2.33656401773723 -0.776564017737226 61 1.89 2.30242304827434 -0.412423048274343 62 2.33 2.37085040619262 -0.0408504061926172 63 2.11 2.54771983549399 -0.437719835493987 64 2 2.56477350592513 -0.564773505925133 65 1.11 1.99045399321542 -0.880453993215423 66 3.22 2.69160978764506 0.528390212354943 67 3.44 2.0491135815167 1.3908864184833 68 2.11 2.55072671706517 -0.440726717065172 69 1 2.22742461421608 -1.22742461421608 70 2.22 2.49557241029063 -0.275572410290627 71 3.11 1.95833337640515 1.15166662359485 72 2.11 2.01424716049106 0.0957528395089405 73 3.33 2.56279328559 0.767206714409996 74 3.22 3.01633327615721 0.20366672384279 75 2.89 2.38482721900129 0.505172780998712 76 2.56 2.17260746741752 0.387392532582481 77 1.44 2.52865235509974 -1.08865235509974 78 2.33 2.51379358022805 -0.183793580228048 79 2.11 2.38331018800897 -0.273310188008968 80 3.11 2.54821928047126 0.561780719528738 81 2.56 2.83762488712413 -0.277624887124132 82 2 1.53061879078525 0.469381209214753 83 2.33 2.3013416170384 0.0286583829615991 84 2.22 2.41929460838894 -0.199294608388945 85 2.56 2.21539978915521 0.344600210844785 86 2.33 2.31421726240173 0.0157827375982743 87 2.33 2.41766428634331 -0.0876642863433097 88 1.67 2.53569210125988 -0.865692101259885 89 3.11 3.01656388709069 0.093436112909305 90 2.11 1.96234261275479 0.147657387245212 91 2.89 2.36040183765006 0.529598162349939 92 1.11 1.46426234116734 -0.354262341167339 93 1.78 1.90162286667844 -0.12162286667844 94 2.44 2.35075556008975 0.0892444399102509 95 2.11 2.08051389297546 0.0294861070245435 96 3.44 3.19507696046712 0.244923039532881 97 3.44 2.79931371859859 0.640686281401414 98 3.22 2.75493567313293 0.465064326867069 99 2.11 1.93390605671242 0.176093943287585 100 2.44 2.0983127950242 0.3416872049758 101 2.56 2.48717786869275 0.0728221313072546 102 1.67 1.79448627942836 -0.124486279428358 103 2.22 2.38336392570546 -0.16336392570546 104 2 2.16607519643393 -0.16607519643393 105 2.56 2.44370669684509 0.116293303154914 106 2.78 2.33076345765631 0.449236542343687 107 2.33 1.84021453585422 0.489785464145777 108 2.67 2.16366817317931 0.506331826820692 109 2.78 2.80238079652749 -0.022380796527489 110 1.89 2.17410926717325 -0.284109267173246 111 1.44 1.6183983445312 -0.178398344531196 112 3.11 2.02066627494903 1.08933372505097 113 2.33 2.23590268779756 0.094097312202441 114 2.78 3.12631220427894 -0.346312204278936 115 1 2.3017840483425 -1.3017840483425 116 1.78 1.98039832548046 -0.200398325480461 117 2.11 2.35477711850275 -0.244777118502746 118 1.89 2.16312412988436 -0.273124129884356 119 2.78 2.72178611907598 0.0582138809240194 120 2.22 1.73076297281317 0.489237027186827 121 3.22 2.40126524422861 0.818734755771389 122 1.56 2.11686989106866 -0.556869891068656 123 2.44 2.98956893444633 -0.549568934446332 124 1.67 1.73179643037957 -0.0617964303795683 125 2.11 2.82335888800903 -0.713358888009026 126 2.22 2.43776649714552 -0.217766497145517 127 1.67 1.93774983585031 -0.267749835850306 128 2.22 2.42149440578267 -0.201494405782667 129 2 2.24633109292469 -0.246331092924691 130 3.67 2.8275103063471 0.842489693652895 131 2.44 2.64302298233732 -0.203022982337319 132 1.78 1.83148155096471 -0.0514815509647076 133 1.89 2.11698129809999 -0.226981298099985 134 1.78 1.67210947636967 0.107890523630329 135 2.33 1.89595695971783 0.434043040282172 136 2.89 3.06825918596047 -0.178259185960469 137 2 2.3482452143226 -0.348245214322604 138 2 2.56639579777148 -0.566395797771483 139 1.89 2.03615144554984 -0.146151445549843 140 2.44 2.74828138357633 -0.308281383576326 141 3.33 2.75065901456468 0.579340985435324 142 3.33 3.02851425538898 0.301485744611022 143 2.67 3.32104261600875 -0.651042616008752 144 2.33 2.4442217398624 -0.114221739862402 145 2.33 2.8207616848349 -0.490761684834899 146 3.22 3.04517670518964 0.174823294810365 147 3.44 2.58073759128435 0.859262408715652 148 2.22 2.10867324710564 0.111326752894362 149 1.78 1.57686979259688 0.203130207403119 150 2.44 2.10300734014503 0.336992659854974 151 2.22 2.25656008440865 -0.0365600844086538 152 3.11 3.03660723917036 0.0733927608296406 153 4.22 2.95253182494365 1.26746817505635 154 2.44 2.14673051412749 0.29326948587251 155 2.22 2.85382118408923 -0.633821184089225 156 1.89 2.00247881827629 -0.112478818276291 157 3.11 2.7173934491284 0.392606550871604 158 2.44 2.67820031853983 -0.238200318539832 159 3.44 2.89874521119134 0.541254788808662 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.213914533504365 0.42782906700873 0.786085466495635 10 0.103674339229257 0.207348678458515 0.896325660770743 11 0.23040843780071 0.46081687560142 0.76959156219929 12 0.652406760115806 0.695186479768388 0.347593239884194 13 0.666813009586893 0.666373980826214 0.333186990413107 14 0.641707144109755 0.716585711780489 0.358292855890244 15 0.645932871197808 0.708134257604385 0.354067128802192 16 0.581013347277822 0.837973305444357 0.418986652722178 17 0.495952354345927 0.991904708691854 0.504047645654073 18 0.4651119891909 0.9302239783818 0.5348880108091 19 0.401169778327927 0.802339556655854 0.598830221672073 20 0.435009261113867 0.870018522227733 0.564990738886133 21 0.394813697998086 0.789627395996173 0.605186302001914 22 0.400009069203689 0.800018138407378 0.599990930796311 23 0.338659943227518 0.677319886455036 0.661340056772482 24 0.600113845928922 0.799772308142156 0.399886154071078 25 0.530211989085808 0.939576021828384 0.469788010914192 26 0.499958693214714 0.999917386429427 0.500041306785286 27 0.438206384653251 0.876412769306502 0.561793615346749 28 0.391236757217297 0.782473514434595 0.608763242782703 29 0.331086324099912 0.662172648199825 0.668913675900088 30 0.279169872896638 0.558339745793275 0.720830127103362 31 0.340635398513716 0.681270797027432 0.659364601486284 32 0.400734364523601 0.801468729047203 0.599265635476399 33 0.357466852591406 0.714933705182812 0.642533147408594 34 0.368888955661906 0.737777911323812 0.631111044338094 35 0.383166828367579 0.766333656735158 0.616833171632421 36 0.374960486994901 0.749920973989802 0.625039513005099 37 0.555846272861847 0.888307454276306 0.444153727138153 38 0.761225769445785 0.47754846110843 0.238774230554215 39 0.75816710415581 0.48366579168838 0.24183289584419 40 0.71645993342239 0.567080133155221 0.28354006657761 41 0.691674408127364 0.616651183745272 0.308325591872636 42 0.642449688217542 0.715100623564917 0.357550311782458 43 0.59400650507189 0.81198698985622 0.40599349492811 44 0.580411555337072 0.839176889325856 0.419588444662928 45 0.546217164137437 0.907565671725126 0.453782835862563 46 0.567801386790791 0.864397226418419 0.432198613209209 47 0.527004721977711 0.945990556044577 0.472995278022289 48 0.518098066250446 0.96380386749911 0.481901933749554 49 0.582287685374829 0.835424629250342 0.417712314625171 50 0.560658852357121 0.878682295285758 0.439341147642879 51 0.525244088579245 0.94951182284151 0.474755911420755 52 0.475927593756266 0.951855187512532 0.524072406243734 53 0.437525139155515 0.87505027831103 0.562474860844485 54 0.390688518579317 0.781377037158635 0.609311481420683 55 0.347979786712239 0.695959573424478 0.652020213287761 56 0.320809086790988 0.641618173581976 0.679190913209012 57 0.277701480864341 0.555402961728682 0.722298519135659 58 0.253853814070854 0.507707628141709 0.746146185929146 59 0.234246442377129 0.468492884754257 0.765753557622871 60 0.292391587801294 0.584783175602588 0.707608412198706 61 0.280581578759664 0.561163157519327 0.719418421240337 62 0.243157332006569 0.486314664013138 0.756842667993431 63 0.230670207601977 0.461340415203953 0.769329792398023 64 0.265075174520626 0.530150349041253 0.734924825479374 65 0.3416973519365 0.683394703873001 0.6583026480635 66 0.344015714228578 0.688031428457157 0.655984285771422 67 0.676060056971544 0.647879886056912 0.323939943028456 68 0.669284550546907 0.661430898906186 0.330715449453093 69 0.845153476896679 0.309693046206643 0.154846523103321 70 0.82558688510356 0.34882622979288 0.17441311489644 71 0.930938168018634 0.138123663962732 0.0690618319813658 72 0.914700518228473 0.170598963543053 0.0852994817715266 73 0.937471372301013 0.125057255397974 0.062528627698987 74 0.925504607849663 0.148990784300674 0.074495392150337 75 0.927475137402538 0.145049725194924 0.072524862597462 76 0.92135979714713 0.15728040570574 0.07864020285287 77 0.970618219539936 0.0587635609201277 0.0293817804600638 78 0.96339098074384 0.07321803851232 0.03660901925616 79 0.95615491023777 0.0876901795244605 0.0438450897622303 80 0.958809779857824 0.0823804402843522 0.0411902201421761 81 0.951104465668324 0.097791068663353 0.0488955343316765 82 0.95079758933412 0.0984048213317613 0.0492024106658806 83 0.938135175180862 0.123729649638276 0.0618648248191382 84 0.92554708941661 0.14890582116678 0.07445291058339 85 0.91750226940211 0.16499546119578 0.0824977305978902 86 0.902438409340973 0.195123181318053 0.0975615906590265 87 0.8817937473565 0.236412505287001 0.118206252643501 88 0.925132401160953 0.149735197678094 0.0748675988390469 89 0.90941944406885 0.181161111862299 0.0905805559311496 90 0.890345237614264 0.219309524771472 0.109654762385736 91 0.892252183606677 0.215495632786646 0.107747816393323 92 0.881727629569269 0.236544740861463 0.118272370430731 93 0.860680619778083 0.278638760443834 0.139319380221917 94 0.834244650492111 0.331510699015778 0.165755349507889 95 0.80260689869766 0.39478620260468 0.19739310130234 96 0.774138451139077 0.451723097721847 0.225861548860923 97 0.792542146728634 0.414915706542731 0.207457853271366 98 0.787254318354797 0.425491363290406 0.212745681645203 99 0.753472559030936 0.493054881938128 0.246527440969064 100 0.729696231361559 0.540607537276882 0.270303768638441 101 0.68855320386068 0.622893592278641 0.31144679613932 102 0.650582825690919 0.698834348618162 0.349417174309081 103 0.612912206288403 0.774175587423195 0.387087793711597 104 0.571141982573687 0.857716034852626 0.428858017426313 105 0.525841817775981 0.948316364448037 0.474158182224019 106 0.506455371766822 0.987089256466357 0.493544628233179 107 0.502845304274143 0.994309391451715 0.497154695725857 108 0.515722713733246 0.968554572533509 0.484277286266754 109 0.465612427071962 0.931224854143924 0.534387572928038 110 0.44215144117773 0.88430288235546 0.55784855882227 111 0.402862059065549 0.805724118131098 0.597137940934451 112 0.627016416835166 0.745967166329669 0.372983583164835 113 0.618705079529067 0.762589840941866 0.381294920470933 114 0.59019976732862 0.819600465342761 0.40980023267138 115 0.790856394365981 0.418287211268037 0.209143605634019 116 0.768862942412738 0.462274115174523 0.231137057587262 117 0.758178538392075 0.483642923215849 0.241821461607924 118 0.73164739270579 0.536705214588419 0.26835260729421 119 0.68424321436467 0.631513571270661 0.31575678563533 120 0.69262613619288 0.614747727614241 0.307373863807121 121 0.744060439103157 0.511879121793687 0.255939560896843 122 0.748484082697425 0.50303183460515 0.251515917302575 123 0.754800397920494 0.490399204159012 0.245199602079506 124 0.705646412197117 0.588707175605765 0.294353587802883 125 0.748694891327312 0.502610217345377 0.251305108672688 126 0.722183754724737 0.555632490550526 0.277816245275263 127 0.711373217355495 0.57725356528901 0.288626782644505 128 0.677955171177694 0.644089657644612 0.322044828822306 129 0.652646037319432 0.694707925361136 0.347353962680568 130 0.725038745898242 0.549922508203517 0.274961254101758 131 0.672175381238835 0.655649237522329 0.327824618761165 132 0.611605960384688 0.776788079230624 0.388394039615312 133 0.611274215461097 0.777451569077806 0.388725784538903 134 0.552056016063216 0.895887967873568 0.447943983936784 135 0.510957869753659 0.978084260492681 0.489042130246341 136 0.482805571494661 0.965611142989322 0.517194428505339 137 0.488165618959138 0.976331237918277 0.511834381040862 138 0.531794875235959 0.936410249528082 0.468205124764041 139 0.46421279106608 0.92842558213216 0.53578720893392 140 0.3900803480841 0.7801606961682 0.6099196519159 141 0.501502200891913 0.996995598216175 0.498497799108087 142 0.448832931405856 0.897665862811713 0.551167068594144 143 0.37835813076096 0.75671626152192 0.62164186923904 144 0.298580028253468 0.597160056506937 0.701419971746532 145 0.356986235371026 0.713972470742053 0.643013764628974 146 0.264382584575563 0.528765169151126 0.735617415424437 147 0.341586892893946 0.683173785787893 0.658413107106054 148 0.235739310940021 0.471478621880043 0.764260689059979 149 0.146765436085882 0.293530872171764 0.853234563914118 150 0.0921983424101697 0.184396684820339 0.90780165758983 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 6 0.0422535211267606 OK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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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