Workshop 7 - blog 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: Wed, 24 Nov 2010 13:20:43 +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/Nov/24/t12906048190vsc4rq5xo5m815.htm/, Retrieved Wed, 24 Nov 2010 14:20:22 +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/24/t12906048190vsc4rq5xo5m815.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 «

9 24 14 11 12 24 26 9 25 11 7 8 25 23 9 17 6 17 8 30 25 9 18 12 10 8 19 23 9 18 8 12 9 22 19 9 16 10 12 7 22 29 10 20 10 11 4 25 25 10 16 11 11 11 23 21 10 18 16 12 7 17 22 10 17 11 13 7 21 25 10 23 13 14 12 19 24 10 30 12 16 10 19 18 10 23 8 11 10 15 22 10 18 12 10 8 16 15 10 15 11 11 8 23 22 10 12 4 15 4 27 28 10 21 9 9 9 22 20 10 15 8 11 8 14 12 10 20 8 17 7 22 24 10 31 14 17 11 23 20 10 27 15 11 9 23 21 10 34 16 18 11 21 20 10 21 9 14 13 19 21 10 31 14 10 8 18 23 10 19 11 11 8 20 28 10 16 8 15 9 23 24 10 20 9 15 6 25 24 10 21 9 13 9 19 24 10 22 9 16 9 24 23 10 17 9 13 6 22 23 10 24 10 9 6 25 29 10 25 16 18 16 26 24 10 26 11 18 5 29 18 10 25 8 12 7 32 25 10 17 9 17 9 25 21 10 32 16 9 6 29 26 10 33 11 9 6 28 22 10 13 16 12 5 17 22 10 32 12 18 12 28 22 10 25 12 12 7 29 23 10 29 14 18 10 26 30 10 22 9 14 9 25 23 10 18 10 15 8 14 17 10 17 9 16 5 25 23 10 20 10 10 8 26 23 10 15 12 11 8 20 25 10 20 14 14 10 18 24 10 33 14 9 6 32 24 10 29 10 12 8 25 23 10 23 14 17 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 Expectations[t] = -10.7203715104562 + 1.67214624631751Month[t] + 0.0839950133200945Concern[t] -0.12716234602162Doubts[t] + 0.675005667880218Criticisim[t] + 0.122931469316262Standards[t] -0.0806109913942159Organization[t] + 0.000183508410492625t + 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) -10.7203715104562 11.994434 -0.8938 0.372863 0.186431 Month 1.67214624631751 1.19575 1.3984 0.164041 0.08202 Concern 0.0839950133200945 0.048333 1.7379 0.084276 0.042138 Doubts -0.12716234602162 0.087187 -1.4585 0.146781 0.073391 Criticisim 0.675005667880218 0.08651 7.8026 0 0 Standards 0.122931469316262 0.063341 1.9408 0.054147 0.027074 Organization -0.0806109913942159 0.063121 -1.2771 0.203534 0.101767 t 0.000183508410492625 0.005064 0.0362 0.971142 0.485571 Multiple Linear Regression - Regression Statistics Multiple R 0.644910701893747 R-squared 0.415909813417085 Adjusted R-squared 0.388832784899996 F-TEST (value) 15.3602457948662 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 4.32986979603811e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.69358099715557 Sum Squared Residuals 1095.56216682387 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 13.5192731920947 -2.51927319209472 2 7 11.6496805238682 -4.6496805238682 3 17 12.0671510196189 4.93284898038108 4 10 10.1973312855293 -0.197331285529335 5 12 12.0724082194322 -0.0724082194321785 6 12 9.49415575945664 2.50584424054336 7 11 10.16868693735 0.831313062649986 8 11 14.5073487485644 -3.50734874856437 9 12 10.5214880746943 1.4785119253057 10 13 11.3233812029752 1.6766187970248 11 14 14.7829864914258 -0.782986491425795 12 16 14.6319520517034 1.36804794829657 13 11 13.7386500081178 -2.73865000811783 14 10 12.1474061391567 -2.14740613915671 15 11 12.3190102990829 -1.31901029908286 16 15 10.2653824470633 4.73461755293671 17 9 13.79096826922 -4.79096826922004 18 11 12.400774552475 -1.400774552475 19 17 12.1620473174053 4.83795268259475 20 17 15.4686000026211 1.53139999737894 21 11 13.5750187845749 -2.5750187845749 22 18 15.2207644287266 2.77923557127344 23 14 16.0426865918609 -2.04268659186087 24 10 12.5878267118584 -2.58782671185842 25 11 11.8043650801541 -0.804365080154082 26 15 13.300294628075 1.69970537192498 27 15 11.7301417787361 3.26985822126386 28 13 13.1017484882098 -0.10174848820981 29 16 13.8811953479159 2.11880465208408 30 13 11.1905238474528 1.80947615254724 31 9 11.5366385626658 -2.53663856266579 32 18 18.1338861133562 -0.13388611335617 33 18 12.2812743748265 5.71872562517346 34 12 13.7334787119315 -1.73347871193151 35 17 13.7464747838831 3.2535252161169 36 9 12.180100986597 -3.18010098659698 37 9 13.0996037346963 -4.09960373469627 38 12 8.75682341623767 3.24317658376233 39 18 16.9388473994568 1.06115260054315 40 12 13.0183579531476 -1.01835795314763 41 18 14.1921424787276 3.80785752127238 42 14 14.0065124265686 -0.00651242656858649 43 15 11.9999676536833 3.00003234631672 44 16 10.8868817052682 5.11311829473177 45 10 13.1598363805743 -3.1598363805743 46 11 11.5869093316551 -0.586909331655076 47 14 12.9375026031449 1.06249739685507 48 9 13.0506391836234 -4.05063918362344 49 12 13.7935940647809 -1.79359406478086 50 17 12.2673744240925 4.73262557590748 51 5 9.75250536396423 -4.75250536396423 52 12 12.4250249208537 -0.425024920853655 53 12 12.0206606749896 -0.0206606749895912 54 6 9.42619032623413 -3.42619032623413 55 24 22.9215831292935 1.07841687070647 56 12 12.5548091279476 -0.554809127947605 57 12 13.0075845425635 -1.00758454256354 58 14 11.6492983589949 2.35070164100508 59 7 9.2771289240683 -2.2771289240683 60 13 11.1119065046674 1.88809349533261 61 12 13.3058705676628 -1.30587056766278 62 13 11.5704657710856 1.42953422891441 63 14 11.500896263116 2.49910373688399 64 8 12.9623777135221 -4.96237771352209 65 11 9.43801912672872 1.56198087327128 66 9 11.817846234235 -2.81784623423502 67 11 13.7698065355102 -2.76980653551015 68 13 13.4913778588218 -0.491377858821848 69 10 9.48705479407752 0.512945205922478 70 11 12.7531082927103 -1.7531082927103 71 12 12.7589089054675 -0.758908905467533 72 9 11.9182954258976 -2.9182954258976 73 15 14.6881912583045 0.311808741695511 74 18 14.9415241099432 3.0584758900568 75 15 12.1623092709661 2.83769072903386 76 12 12.8411433481507 -0.841143348150716 77 13 9.94320350725274 3.05679649274726 78 14 13.0982312786184 0.901768721381636 79 10 11.9752956048536 -1.97529560485363 80 13 12.3187251217982 0.681274878201805 81 13 13.8144142400931 -0.814414240093145 82 11 12.1590693511798 -1.15906935117982 83 13 12.2165707276303 0.783429272369743 84 16 14.5677867756767 1.43221322432329 85 8 9.70253111843646 -1.70253111843646 86 16 11.630987417531 4.36901258246903 87 11 11.1459107521002 -0.145910752100214 88 9 11.3866424352244 -2.38664243522445 89 16 17.8391226331453 -1.83912263314527 90 12 11.4639323367882 0.536067663211767 91 14 11.9766042480505 2.02339575194953 92 8 10.6731802604061 -2.67318026040613 93 9 9.57410215748894 -0.574102157488939 94 15 11.7369140804858 3.26308591951421 95 11 13.6250891574027 -2.62508915740272 96 21 17.2889189692663 3.71108103073375 97 14 13.2294762268217 0.77052377317829 98 18 15.7906177158744 2.20938228412561 99 12 11.7156777278205 0.284322272179452 100 13 12.6769115808384 0.323088419161647 101 15 14.5645368021223 0.435463197877748 102 12 11.0824986932509 0.917501306749067 103 19 14.4743416740269 4.52565832597313 104 15 14.0729630227698 0.92703697723024 105 11 13.0429391125752 -2.04293911257523 106 11 10.5958437797951 0.404156220204941 107 10 12.3347421333432 -2.33474213334316 108 13 14.7689187914377 -1.76891879143766 109 15 14.7774197105239 0.222580289476144 110 12 9.87009448775867 2.12990551224133 111 12 11.0105682003709 0.9894317996291 112 16 15.7343761682779 0.265623831722135 113 9 15.5316216970419 -6.53162169704191 114 18 17.5890267414159 0.410973258584075 115 8 15.1511976184637 -7.15119761846366 116 13 10.370924774866 2.62907522513404 117 17 14.2002708101278 2.79972918987216 118 9 11.0289289224772 -2.02892892247722 119 15 13.1874104846857 1.8125895153143 120 8 9.55441530664951 -1.55441530664951 121 7 11.1831641135043 -4.18316411350431 122 12 11.325722150273 0.674277849727017 123 14 15.0580201790477 -1.05802017904769 124 6 10.7598610359995 -4.75986103599955 125 8 10.1221506439949 -2.12215064399493 126 17 12.4328808692213 4.56711913077873 127 10 9.73687415549733 0.263125844502671 128 11 12.5602093198084 -1.5602093198084 129 14 12.8257764075318 1.17422359246825 130 11 13.5974984017525 -2.59749840175249 131 13 15.3986548064744 -2.39865480647444 132 12 11.8988911946542 0.101108805345784 133 11 10.4155180409869 0.5844819590131 134 9 9.41103884182004 -0.411038841820042 135 12 12.0310324576761 -0.0310324576761144 136 20 14.7296410149395 5.27035898506052 137 12 10.658543442843 1.34145655715705 138 13 13.6210461793078 -0.621046179307752 139 12 13.1591631531483 -1.15916315314826 140 12 16.4919630614362 -4.49196306143619 141 9 14.5404641195754 -5.54046411957543 142 15 15.5626788726532 -0.562678872653223 143 24 21.5385044301026 2.46149556989742 144 7 9.90590165480888 -2.90590165480888 145 17 14.6175287839649 2.38247121603512 146 11 11.8636609159468 -0.863660915946791 147 17 15.104179895128 1.89582010487197 148 11 12.2580700525978 -1.25807005259778 149 12 12.484315620769 -0.484315620768967 150 14 14.455674976405 -0.455674976404969 151 11 14.3163919694258 -3.31639196942581 152 16 12.7619838809013 3.2380161190987 153 21 13.7745259743509 7.22547402564915 154 14 12.1511804543419 1.84881954565809 155 20 16.4238583346581 3.57614166534192 156 13 11.0060734820145 1.99392651798552 157 11 13.017226114997 -2.01722611499701 158 15 13.9059722694249 1.0940277305751 159 19 17.8772225031398 1.12277749686019 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.658658755878906 0.682682488242187 0.341341244121094 12 0.549077615906845 0.90184476818631 0.450922384093155 13 0.426496573831552 0.852993147663103 0.573503426168448 14 0.600633939899325 0.79873212020135 0.399366060100675 15 0.719708485652366 0.560583028695268 0.280291514347634 16 0.643828713086307 0.712342573827386 0.356171286913693 17 0.740556580542859 0.518886838914283 0.259443419457141 18 0.66513258731971 0.66973482536058 0.33486741268029 19 0.720181930300299 0.559636139399402 0.279818069699701 20 0.678518795061071 0.642962409877858 0.321481204938929 21 0.701783173009988 0.596433653980025 0.298216826990012 22 0.711944119455768 0.576111761088463 0.288055880544232 23 0.662829922088142 0.674340155823716 0.337170077911858 24 0.741815806783423 0.516368386433153 0.258184193216577 25 0.711903524902944 0.576192950194112 0.288096475097056 26 0.656727735110542 0.686544529778916 0.343272264889458 27 0.608182452574199 0.783635094851603 0.391817547425801 28 0.544032782507238 0.911934434985523 0.455967217492762 29 0.485776457449606 0.971552914899212 0.514223542550394 30 0.425027305782438 0.850054611564876 0.574972694217562 31 0.575914618266744 0.848170763466513 0.424085381733256 32 0.522826409357754 0.954347181284491 0.477173590642246 33 0.557004732242412 0.885990535515177 0.442995267757588 34 0.66611027688441 0.66777944623118 0.33388972311559 35 0.650933286115643 0.698133427768714 0.349066713884357 36 0.723149012962529 0.553701974074942 0.276850987037471 37 0.790401305293445 0.41919738941311 0.209598694706555 38 0.773424492096641 0.453151015806718 0.226575507903359 39 0.745188304225058 0.509623391549883 0.254811695774942 40 0.721889334488805 0.556221331022391 0.278110665511195 41 0.759242861915379 0.481514276169243 0.240757138084621 42 0.72068663705195 0.5586267258961 0.27931336294805 43 0.704844032721676 0.590311934556649 0.295155967278324 44 0.745313388331734 0.509373223336532 0.254686611668266 45 0.815137653257031 0.369724693485938 0.184862346742969 46 0.799907313962098 0.400185372075805 0.200092686037902 47 0.76294395914919 0.474112081701619 0.237056040850809 48 0.807655080676167 0.384689838647667 0.192344919323833 49 0.786233239606965 0.427533520786069 0.213766760393035 50 0.838143284513206 0.323713430973588 0.161856715486794 51 0.901029137790675 0.197941724418649 0.0989708622093247 52 0.88276743280981 0.234465134380379 0.11723256719019 53 0.856787047443088 0.286425905113824 0.143212952556912 54 0.886058772715988 0.227882454568024 0.113941227284012 55 0.863818088945584 0.272363822108833 0.136181911054416 56 0.835732468889129 0.328535062221742 0.164267531110871 57 0.810039609022595 0.37992078195481 0.189960390977405 58 0.798814225945212 0.402371548109576 0.201185774054788 59 0.800769674169296 0.398460651661408 0.199230325830704 60 0.781482531916463 0.437034936167074 0.218517468083537 61 0.757295038747982 0.485409922504035 0.242704961252018 62 0.732025074684961 0.535949850630077 0.267974925315039 63 0.726416259247262 0.547167481505476 0.273583740752738 64 0.817295547842604 0.365408904314791 0.182704452157396 65 0.79870174603864 0.40259650792272 0.20129825396136 66 0.791547195804891 0.416905608390218 0.208452804195109 67 0.787340785094952 0.425318429810096 0.212659214905048 68 0.75304661347896 0.49390677304208 0.24695338652104 69 0.722922988455694 0.554154023088612 0.277077011544306 70 0.69362426869603 0.61275146260794 0.30637573130397 71 0.665862429166732 0.668275141666537 0.334137570833268 72 0.662385060307592 0.675229879384816 0.337614939692408 73 0.631658294028041 0.736683411943918 0.368341705971959 74 0.664097487567307 0.671805024865386 0.335902512432693 75 0.676549025637078 0.646901948725844 0.323450974362922 76 0.637435624976722 0.725128750046556 0.362564375023278 77 0.670265017340882 0.659469965318235 0.329734982659118 78 0.633927271976122 0.732145456047756 0.366072728023878 79 0.607492515582031 0.785014968835938 0.392507484417969 80 0.56755006476515 0.8648998704697 0.43244993523485 81 0.522631470429064 0.954737059141871 0.477368529570936 82 0.485103598344401 0.970207196688801 0.514896401655599 83 0.444270865126832 0.888541730253664 0.555729134873168 84 0.412751308969673 0.825502617939346 0.587248691030327 85 0.382311261131586 0.764622522263171 0.617688738868414 86 0.466719673764492 0.933439347528983 0.533280326235508 87 0.421808482783923 0.843616965567847 0.578191517216077 88 0.40288484341274 0.80576968682548 0.59711515658726 89 0.378627190220381 0.757254380440761 0.62137280977962 90 0.336512912412601 0.673025824825203 0.663487087587399 91 0.321173682424268 0.642347364848536 0.678826317575732 92 0.314734579116251 0.629469158232502 0.685265420883749 93 0.274080995793447 0.548161991586895 0.725919004206553 94 0.297823390123759 0.595646780247517 0.702176609876241 95 0.291831663318195 0.58366332663639 0.708168336681805 96 0.326583400802839 0.653166801605679 0.67341659919716 97 0.289227727693072 0.578455455386145 0.710772272306928 98 0.27128658697595 0.5425731739519 0.72871341302405 99 0.233328652811451 0.466657305622903 0.766671347188549 100 0.198073902104615 0.39614780420923 0.801926097895385 101 0.167810368990086 0.335620737980172 0.832189631009914 102 0.146197881287439 0.292395762574877 0.853802118712561 103 0.216464074295397 0.432928148590794 0.783535925704603 104 0.194927415148686 0.389854830297373 0.805072584851314 105 0.173766983701549 0.347533967403098 0.826233016298451 106 0.148452760188124 0.296905520376249 0.851547239811876 107 0.13685550430267 0.273711008605339 0.86314449569733 108 0.119793628753219 0.239587257506437 0.880206371246781 109 0.097725869595077 0.195451739190154 0.902274130404923 110 0.0995994073492811 0.199198814698562 0.900400592650719 111 0.0886083264839568 0.177216652967914 0.911391673516043 112 0.0704858265364107 0.140971653072821 0.929514173463589 113 0.174663918501696 0.349327837003393 0.825336081498304 114 0.152660829653794 0.305321659307587 0.847339170346206 115 0.339187216528738 0.678374433057475 0.660812783471262 116 0.347780138189278 0.695560276378556 0.652219861810722 117 0.402226803129021 0.804453606258041 0.597773196870979 118 0.359885559914151 0.719771119828302 0.640114440085849 119 0.34497281465085 0.689945629301699 0.65502718534915 120 0.310960690746572 0.621921381493144 0.689039309253428 121 0.319248108048598 0.638496216097197 0.680751891951402 122 0.315659136660352 0.631318273320703 0.684340863339648 123 0.267862945806517 0.535725891613034 0.732137054193483 124 0.345943743987018 0.691887487974037 0.654056256012982 125 0.298875639940614 0.597751279881227 0.701124360059386 126 0.434739448262936 0.869478896525872 0.565260551737064 127 0.388359949790297 0.776719899580595 0.611640050209703 128 0.340568150799983 0.681136301599967 0.659431849200017 129 0.292761795038938 0.585523590077876 0.707238204961062 130 0.287914641706011 0.575829283412023 0.712085358293989 131 0.257674391617799 0.515348783235597 0.742325608382201 132 0.206904290513505 0.413808581027011 0.793095709486495 133 0.16407175218226 0.32814350436452 0.83592824781774 134 0.124910385058355 0.249820770116711 0.875089614941645 135 0.0924821877990713 0.184964375598143 0.907517812200929 136 0.197604779774703 0.395209559549406 0.802395220225297 137 0.243717814552236 0.487435629104472 0.756282185447764 138 0.24363190349426 0.48726380698852 0.75636809650574 139 0.185162248200208 0.370324496400416 0.814837751799792 140 0.183360259232114 0.366720518464227 0.816639740767886 141 0.322974332218596 0.645948664437191 0.677025667781404 142 0.27802788071927 0.556055761438541 0.72197211928073 143 0.213818188112 0.427636376224 0.786181811888 144 0.170295437401175 0.34059087480235 0.829704562598825 145 0.187068179596723 0.374136359193445 0.812931820403277 146 0.129528681764359 0.259057363528718 0.870471318235641 147 0.0754584987823203 0.150916997564641 0.92454150121768 148 0.0413569204578931 0.0827138409157862 0.958643079542107 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 0.0072463768115942 OK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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