*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, 16 Nov 2010 08:42:30 +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/16/t1289897053zkqmmlh8l9u333i.htm/, Retrieved Tue, 16 Nov 2010 09:44:16 +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/16/t1289897053zkqmmlh8l9u333i.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 «

18 15 15 0 17 3 21 2 22 3 24 12 17 3 25 0 16 12 18 15 21 0 19 10 18 20 20 20 25 2 28 3 19 16 20 4 25 2 20 4 21 0 21 0 23 15 19 9 23 1 20 15 19 5 17 4 19 15 21 4 18 12 18 2 24 4 22 2 20 4 17 8 25 30 24 6 18 6 21 7 13 4 21 17 21 5 16 0 18 3 19 4 22 15 18 0 18 8 20 10 19 4 18 0 20 6 20 11 23 10 17 0 17 0 18 0 22 0 16 0 18 0 14 0 13 7 21 4 25 12 16 6 17 12 22 10 24 9 18 0 18 16 18 2 19 0 15 0 25 1 22 10 15 14 21 12 16 12 23 12 20 5 19 0 20 4 18 3 18 0 20 3 20 0 16 12 18 12 18 15 16 0 23 8 14 6 21 14 13 5 27 10 20 16 22 4 21 0 19 8 22 12 12 6 28 4 21 20 18 0 21 13 19 0 23 0 21 0 21 0 22 10 18 6 15 16 23 6 24 0 18 4 15 9 19 17 17 12 14 3 16 8 22 3 15 0 23 10 24 3 24 0 20 8 9 0 23 4 18 13 20 12 25 16 17 20 21 20 26 14 20 12 21 15 15 9 20 4 20 8 16 0 19 13 22 0 17 21 25 0 19 1 17 16 21 12 12 2

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 9 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Perf[t] = + 19.2989199323664 + 0.0380163102865228`Sport `[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) 19.2989199323664 0.41199 46.8431 0 0 `Sport ` 0.0380163102865228 0.043996 0.8641 0.388944 0.194472 Multiple Linear Regression - Regression Statistics Multiple R 0.0710889771773798 R-squared 0.00505364267612603 Adjusted R-squared -0.00171469989070294 F-TEST (value) 0.746658820269144 F-TEST (DF numerator) 1 F-TEST (DF denominator) 147 p-value 0.388943910291832 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.36064818342967 Sum Squared Residuals 1660.21156328 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 18 19.8691645866642 -1.86916458666418 2 15 19.2989199323664 -4.29891993236637 3 17 19.4129688632259 -2.41296886322594 4 21 19.3749525529394 1.62504744706058 5 22 19.4129688632259 2.58703113677406 6 24 19.7551156558046 4.24488434419535 7 17 19.4129688632259 -2.41296886322594 8 25 19.2989199323664 5.70108006763363 9 16 19.7551156558046 -3.75511565580464 10 18 19.8691645866642 -1.86916458666421 11 21 19.2989199323664 1.70108006763363 12 19 19.6790830352316 -0.6790830352316 13 18 20.0592461380968 -2.05924613809683 14 20 20.0592461380968 -0.0592461380968274 15 25 19.3749525529394 5.62504744706058 16 28 19.4129688632259 8.58703113677406 17 19 19.9071808969507 -0.907180896950736 18 20 19.4509851735125 0.549014826487537 19 25 19.3749525529394 5.62504744706058 20 20 19.4509851735125 0.549014826487537 21 21 19.2989199323664 1.70108006763363 22 21 19.2989199323664 1.70108006763363 23 23 19.8691645866642 3.13083541333579 24 19 19.6410667249451 -0.641066724945077 25 23 19.3369362426529 3.66306375734711 26 20 19.8691645866642 0.130835413335786 27 19 19.489001483799 -0.489001483798986 28 17 19.4509851735125 -2.45098517351246 29 19 19.8691645866642 -0.869164586664213 30 21 19.4509851735125 1.54901482648754 31 18 19.7551156558046 -1.75511565580465 32 18 19.3749525529394 -1.37495255293942 33 24 19.4509851735125 4.54901482648754 34 22 19.3749525529394 2.62504744706058 35 20 19.4509851735125 0.549014826487537 36 17 19.6030504146586 -2.60305041465855 37 25 20.4394092409621 4.56059075903794 38 24 19.5270177940855 4.47298220591449 39 18 19.5270177940855 -1.52701779408551 40 21 19.565034104372 1.43496589562797 41 13 19.4509851735125 -6.45098517351246 42 21 19.9451972072373 1.05480279276274 43 21 19.489001483799 1.51099851620101 44 16 19.2989199323664 -3.29891993236637 45 18 19.4129688632259 -1.41296886322594 46 19 19.4509851735125 -0.450985173512463 47 22 19.8691645866642 2.13083541333579 48 18 19.2989199323664 -1.29891993236637 49 18 19.6030504146586 -1.60305041465855 50 20 19.6790830352316 0.3209169647684 51 19 19.4509851735125 -0.450985173512463 52 18 19.2989199323664 -1.29891993236637 53 20 19.5270177940855 0.472982205914491 54 20 19.7170993455181 0.282900654481878 55 23 19.6790830352316 3.3209169647684 56 17 19.2989199323664 -2.29891993236637 57 17 19.2989199323664 -2.29891993236637 58 18 19.2989199323664 -1.29891993236637 59 22 19.2989199323664 2.70108006763363 60 16 19.2989199323664 -3.29891993236637 61 18 19.2989199323664 -1.29891993236637 62 14 19.2989199323664 -5.29891993236637 63 13 19.565034104372 -6.56503410437203 64 21 19.4509851735125 1.54901482648754 65 25 19.7551156558046 5.24488434419535 66 16 19.5270177940855 -3.52701779408551 67 17 19.7551156558046 -2.75511565580464 68 22 19.6790830352316 2.3209169647684 69 24 19.6410667249451 4.35893327505492 70 18 19.2989199323664 -1.29891993236637 71 18 19.9071808969507 -1.90718089695074 72 18 19.3749525529394 -1.37495255293942 73 19 19.2989199323664 -0.298919932366372 74 15 19.2989199323664 -4.29891993236637 75 25 19.3369362426529 5.6630637573471 76 22 19.6790830352316 2.3209169647684 77 15 19.8311482763777 -4.83114827637769 78 21 19.7551156558046 1.24488434419535 79 16 19.7551156558046 -3.75511565580464 80 23 19.7551156558046 3.24488434419536 81 20 19.489001483799 0.510998516201014 82 19 19.2989199323664 -0.298919932366372 83 20 19.4509851735125 0.549014826487537 84 18 19.4129688632259 -1.41296886322594 85 18 19.2989199323664 -1.29891993236637 86 20 19.4129688632259 0.58703113677406 87 20 19.2989199323664 0.701080067633628 88 16 19.7551156558046 -3.75511565580464 89 18 19.7551156558046 -1.75511565580465 90 18 19.8691645866642 -1.86916458666421 91 16 19.2989199323664 -3.29891993236637 92 23 19.6030504146586 3.39694958534145 93 14 19.5270177940855 -5.52701779408551 94 21 19.8311482763777 1.16885172362231 95 13 19.489001483799 -6.48900148379899 96 27 19.6790830352316 7.3209169647684 97 20 19.9071808969507 0.0928191030492637 98 22 19.4509851735125 2.54901482648754 99 21 19.2989199323664 1.70108006763363 100 19 19.6030504146586 -0.603050414658554 101 22 19.7551156558046 2.24488434419536 102 12 19.5270177940855 -7.52701779408551 103 28 19.4509851735125 8.54901482648754 104 21 20.0592461380968 0.940753861903173 105 18 19.2989199323664 -1.29891993236637 106 21 19.7931319660912 1.20686803390883 107 19 19.2989199323664 -0.298919932366372 108 23 19.2989199323664 3.70108006763363 109 21 19.2989199323664 1.70108006763363 110 21 19.2989199323664 1.70108006763363 111 22 19.6790830352316 2.3209169647684 112 18 19.5270177940855 -1.52701779408551 113 15 19.9071808969507 -4.90718089695074 114 23 19.5270177940855 3.47298220591449 115 24 19.2989199323664 4.70108006763363 116 18 19.4509851735125 -1.45098517351246 117 15 19.6410667249451 -4.64106672494508 118 19 19.9451972072373 -0.94519720723726 119 17 19.7551156558046 -2.75511565580464 120 14 19.4129688632259 -5.41296886322594 121 16 19.6030504146586 -3.60305041465855 122 22 19.4129688632259 2.58703113677406 123 15 19.2989199323664 -4.29891993236637 124 23 19.6790830352316 3.3209169647684 125 24 19.4129688632259 4.58703113677406 126 24 19.2989199323664 4.70108006763363 127 20 19.6030504146586 0.396949585341446 128 9 19.2989199323664 -10.2989199323664 129 23 19.4509851735125 3.54901482648754 130 18 19.7931319660912 -1.79313196609117 131 20 19.7551156558046 0.244884344195355 132 25 19.9071808969507 5.09281910304926 133 17 20.0592461380968 -3.05924613809683 134 21 20.0592461380968 0.940753861903173 135 26 19.8311482763777 6.16885172362231 136 20 19.7551156558046 0.244884344195355 137 21 19.8691645866642 1.13083541333579 138 15 19.6410667249451 -4.64106672494508 139 20 19.4509851735125 0.549014826487537 140 20 19.6030504146586 0.396949585341446 141 16 19.2989199323664 -3.29891993236637 142 19 19.7931319660912 -0.793131966091168 143 22 19.2989199323664 2.70108006763363 144 17 20.0972624483834 -3.09726244838335 145 25 19.2989199323664 5.70108006763363 146 19 19.3369362426529 -0.336936242652895 147 17 19.9071808969507 -2.90718089695074 148 21 19.7551156558046 1.24488434419535 149 12 19.3749525529394 -7.37495255293942 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.590260185206526 0.819479629586949 0.409739814793474 6 0.65184806096759 0.69630387806482 0.34815193903241 7 0.550327600018094 0.899344799963813 0.449672399981906 8 0.765996147797529 0.468007704404943 0.234003852202471 9 0.764717993780674 0.470564012438651 0.235282006219326 10 0.682091064475396 0.635817871049208 0.317908935524604 11 0.597617372563207 0.804765254873585 0.402382627436792 12 0.50130525279526 0.99738949440948 0.49869474720474 13 0.410596895564458 0.821193791128916 0.589403104435542 14 0.34361690414518 0.68723380829036 0.65638309585482 15 0.452966564533974 0.905933129067949 0.547033435466026 16 0.746054286954419 0.507891426091163 0.253945713045581 17 0.68061427164183 0.63877145671634 0.31938572835817 18 0.613028136805587 0.773943726388826 0.386971863194413 19 0.644901101498239 0.710197797003523 0.355098898501761 20 0.580933060460789 0.838133879078421 0.419066939539211 21 0.515698659765644 0.968602680468711 0.484301340234356 22 0.451038686197894 0.902077372395788 0.548961313802106 23 0.46252033405257 0.92504066810514 0.53747966594743 24 0.404891447054457 0.809782894108913 0.595108552945543 25 0.36896992979497 0.737939859589941 0.63103007020503 26 0.310214511827951 0.620429023655902 0.689785488172049 27 0.27018583418361 0.54037166836722 0.72981416581639 28 0.284973753334437 0.569947506668875 0.715026246665563 29 0.23541134352849 0.47082268705698 0.76458865647151 30 0.192713842783397 0.385427685566795 0.807286157216603 31 0.164366694220954 0.328733388441907 0.835633305779046 32 0.154349008893138 0.308698017786275 0.845650991106862 33 0.165810882256699 0.331621764513398 0.834189117743301 34 0.139424089251765 0.27884817850353 0.860575910748235 35 0.111119971573102 0.222239943146204 0.888880028426898 36 0.109665306202712 0.219330612405423 0.890334693797288 37 0.20015428188087 0.40030856376174 0.79984571811913 38 0.215127224670129 0.430254449340259 0.78487277532987 39 0.195750862966799 0.391501725933598 0.804249137033201 40 0.162665233764147 0.325330467528294 0.837334766235853 41 0.322584273949821 0.645168547899641 0.677415726050179 42 0.279948048440255 0.55989609688051 0.720051951559745 43 0.241165239217453 0.482330478434906 0.758834760782547 44 0.262770679895494 0.525541359790989 0.737229320104506 45 0.235979201684364 0.471958403368728 0.764020798315636 46 0.200909507744901 0.401819015489801 0.7990904922551 47 0.178056633848766 0.356113267697532 0.821943366151234 48 0.155996164719829 0.311992329439659 0.84400383528017 49 0.136840265767589 0.273680531535179 0.86315973423241 50 0.110853891979101 0.221707783958201 0.8891461080209 51 0.0900594617704655 0.180118923540931 0.909940538229534 52 0.076067317337069 0.152134634674138 0.923932682662931 53 0.0597193211810432 0.119438642362086 0.940280678818957 54 0.0462218169243002 0.0924436338486005 0.9537781830757 55 0.0451626550815649 0.0903253101631298 0.954837344918435 56 0.0413241605771379 0.0826483211542758 0.958675839422862 57 0.0373590895853185 0.0747181791706371 0.962640910414681 58 0.0301087473623743 0.0602174947247486 0.969891252637626 59 0.0269340748656444 0.0538681497312888 0.973065925134356 60 0.0281365371554907 0.0562730743109814 0.97186346284451 61 0.0223445790823518 0.0446891581647037 0.977655420917648 62 0.0360574673992816 0.0721149347985632 0.963942532600718 63 0.0772078987340543 0.154415797468109 0.922792101265946 64 0.0642708544664525 0.128541708932905 0.935729145533547 65 0.0876702234612797 0.175340446922559 0.91232977653872 66 0.0910533053847074 0.182106610769415 0.908946694615293 67 0.0862786101654347 0.172557220330869 0.913721389834565 68 0.0764112539407481 0.152822507881496 0.923588746059252 69 0.0880051721553457 0.176010344310691 0.911994827844654 70 0.0729083543542121 0.145816708708424 0.927091645645788 71 0.0635119200098591 0.127023840019718 0.936488079990141 72 0.0521444381095224 0.104288876219045 0.947855561890478 73 0.0407317695952468 0.0814635391904936 0.959268230404753 74 0.047883553948943 0.095767107897886 0.952116446051057 75 0.0741427367054375 0.148285473410875 0.925857263294563 76 0.0655271606569692 0.131054321313938 0.934472839343031 77 0.0843487343441313 0.168697468688263 0.915651265655869 78 0.0695754277451849 0.13915085549037 0.930424572254815 79 0.0737496750964304 0.147499350192861 0.92625032490357 80 0.0723195494788116 0.144639098957623 0.927680450521188 81 0.0577131086476518 0.115426217295304 0.942286891352348 82 0.0453538490336229 0.0907076980672457 0.954646150966377 83 0.0353884567445423 0.0707769134890847 0.964611543255458 84 0.0284102725633942 0.0568205451267883 0.971589727436606 85 0.022439635823733 0.0448792716474661 0.977560364176267 86 0.0169636991587062 0.0339273983174124 0.983036300841294 87 0.0127224685491631 0.0254449370983261 0.987277531450837 88 0.013653232464912 0.027306464929824 0.986346767535088 89 0.0108886191291813 0.0217772382583625 0.989111380870819 90 0.0087140681549197 0.0174281363098394 0.99128593184508 91 0.00855908254793839 0.0171181650958768 0.991440917452062 92 0.00850371252396118 0.0170074250479224 0.991496287476039 93 0.0141603710390444 0.0283207420780887 0.985839628960956 94 0.010757141192416 0.021514282384832 0.989242858807584 95 0.023679888044048 0.047359776088096 0.976320111955952 96 0.0593901776370262 0.118780355274052 0.940609822362974 97 0.0464144042658301 0.0928288085316603 0.95358559573417 98 0.0409681877728945 0.081936375545789 0.959031812227106 99 0.033220979378673 0.066441958757346 0.966779020621327 100 0.0252957629476183 0.0505915258952365 0.974704237052382 101 0.0214969341701795 0.042993868340359 0.97850306582982 102 0.0591703436034845 0.118340687206969 0.940829656396516 103 0.174887810942722 0.349775621885443 0.825112189057278 104 0.14809689464305 0.2961937892861 0.85190310535695 105 0.124833675988709 0.249667351977417 0.875166324011291 106 0.104195921047811 0.208391842095623 0.895804078952189 107 0.0830968305216342 0.166193661043268 0.916903169478366 108 0.084348345320636 0.168696690641272 0.915651654679364 109 0.0698810896657802 0.13976217933156 0.93011891033422 110 0.0575778405649838 0.115155681129968 0.942422159435016 111 0.0506251724967783 0.101250344993557 0.949374827503222 112 0.0398848244163586 0.0797696488327173 0.960115175583641 113 0.0492027941281099 0.0984055882562198 0.95079720587189 114 0.0499315981440894 0.0998631962881788 0.95006840185591 115 0.0661222967229797 0.132244593445959 0.93387770327702 116 0.0515325077255818 0.103065015451164 0.948467492274418 117 0.0595598226053504 0.119119645210701 0.94044017739465 118 0.04543313373955 0.0908662674791 0.95456686626045 119 0.0395509349103746 0.0791018698207493 0.960449065089625 120 0.0547471964193716 0.109494392838743 0.945252803580628 121 0.0545404440849071 0.109080888169814 0.945459555915093 122 0.0474345108800423 0.0948690217600846 0.952565489119958 123 0.0529794975712117 0.105958995142423 0.947020502428788 124 0.0498434585811195 0.099686917162239 0.95015654141888 125 0.061231651211612 0.122463302423224 0.938768348788388 126 0.0848189655005478 0.169637931001096 0.915181034499452 127 0.0633759328568055 0.126751865713611 0.936624067143195 128 0.347806091841439 0.695612183682878 0.652193908158561 129 0.349004917260878 0.698009834521755 0.650995082739122 130 0.299640786135952 0.599281572271905 0.700359213864048 131 0.239561011096779 0.479122022193558 0.760438988903221 132 0.321957119244175 0.64391423848835 0.678042880755825 133 0.291709031672218 0.583418063344436 0.708290968327782 134 0.234876578905688 0.469753157811376 0.765123421094312 135 0.452017947530171 0.904035895060342 0.547982052469829 136 0.378765302292335 0.75753060458467 0.621234697707665 137 0.347066034549873 0.694132069099745 0.652933965450127 138 0.355353924161403 0.710707848322806 0.644646075838597 139 0.2716789870747 0.543357974149401 0.7283210129253 140 0.200656192883116 0.401312385766233 0.799343807116884 141 0.194859749798902 0.389719499597805 0.805140250201098 142 0.12505527864359 0.250110557287181 0.87494472135641 143 0.0858483044446017 0.171696608889203 0.914151695555398 144 0.0436422486770012 0.0872844973540023 0.956357751322999 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 13 0.0928571428571429 NOK 10% type I error level 38 0.271428571428571 NOK

Charts produced by software:

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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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