*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 07:11:14 +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/t12905825896qbs43g4nnzsm2y.htm/, Retrieved Wed, 24 Nov 2010 08:09:49 +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/t12905825896qbs43g4nnzsm2y.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 3 4 4 3 3 3 4 2 2 4 4 3 4 2 3 3 4 3 1 3 2 3 3 3 3 3 4 1 2 3 4 4 4 4 2 2 4 3 2 3 3 4 4 4 3 4 2 1 1 3 3 2 4 4 3 3 4 3 3 3 4 4 4 4 2 2 4 4 2 3 2 4 1 2 3 3 3 4 2 2 2 4 2 3 3 4 4 4 3 2 2 3 2 2 1 1 2 3 2 2 3 2 3 1 3 4 4 3 4 3 2 3 3 4 3 3 4 2 2 3 3 4 4 4 3 4 3 4 4 2 3 3 4 4 3 3 2 4 3 3 4 3 4 3 4 4 4 2 2 3 4 3 2 2 3 3 3 4 2 3 4 4 3 4 3 3 2 2 1 2 2 4 2 4 3 4 3 4 4 3 3 4 3 1 3 2 2 2 2 3 4 3 4 3 4 4 4 4 4 3 4 4 3 3 3 4 3 1 1 1 2 5 2 3 2 2 3 2 2 3 3 3 2 1 4 4 4 4 3 4 5 4 3 4 2 2 5 2 1 1 3 3 2 4 3 3 4 4 4 3 2 4 1 1 1 2 2 5 4 3 3 4 2 4 2 2 4 3 2 3 4 4 4 4 3 3 3 4 3 2 3 3 3 2 4 4 3 4 4 1 1 2 2 2 3 4 4 3 4 2 2 4 2 2 4 4 4 4 4 3 4 3 5 5 4 4 4 3 4 3 2 3 1 1 3 4 4 3 3 3 2 4 4 4 3 4 4 2 1 3 4 4 3 3 1 1 4 1 1 3 4 4 3 4 3 4 4 2 4 3 3 4 3 2 2 3 2 4 4 3 3 3 3 3 3 3 4 4 4 3 3 4 4 4 2 3 3 3 4 3 4 4 2 1 2 1 4 1 2 2 3 4 2 1 3 4 3 3 3 3 3 3 4 3 2 3 3 1 3 2 4 3 1 1 3 3 4 3 3 2 2 4 2 2 3 3 2 2 3 4 4 4 3 4 2 3 3 2 2 3 4 4 2 2 2 3 3 3 3 4 4 4 4 4 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation New[t] = + 2.94270390531953 + 0.185263472328658Popularity[t] + 0.0505286866563771Friends[t] -0.087130072775124Known[t] + 0.0597825118886497Names[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) 2.94270390531953 0.243624 12.0789 0 0 Popularity 0.185263472328658 0.095506 1.9398 0.054265 0.027133 Friends 0.0505286866563771 0.089776 0.5628 0.574386 0.287193 Known -0.087130072775124 0.075564 -1.1531 0.250708 0.125354 Names 0.0597825118886497 0.071594 0.835 0.405027 0.202514 Multiple Linear Regression - Regression Statistics Multiple R 0.247547090880362 R-squared 0.06127956220333 Adjusted R-squared 0.0364127956391799 F-TEST (value) 2.46431565781758 F-TEST (DF numerator) 4 F-TEST (DF denominator) 151 p-value 0.0475045513703866 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.70860242857057 Sum Squared Residuals 75.8197276681926 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 3.48090762684009 0.519092373159909 2 4 3.59538526050169 0.404614739498314 3 3 3.65691727393647 -0.656917273936472 4 4 3.44847267583791 0.551527324162088 5 3 3.51750901295883 -0.517509012958834 6 4 3.68251533327681 0.317484666723191 7 4 3.59121882538511 0.408781174614886 8 4 3.27246302874153 0.727536971258473 9 4 3.54069013872874 0.459309861271263 10 2 3.67326150804454 -1.67326150804454 11 2 3.54069013872874 -1.54069013872874 12 4 3.56803769961521 0.431962300384789 13 4 3.59121882538511 0.408781174614886 14 4 3.1853329559664 0.814667044033597 15 4 3.63198664662043 0.368013353379568 16 3 3.42112511495144 -0.421125114951438 17 4 3.4193756134053 0.5806243865947 18 4 3.53143631349646 0.468563686503536 19 3 3.35959310151665 -0.359593101516651 20 2 3.03667086975649 -1.03667086975649 21 2 3.26320920350925 -1.26320920350925 22 4 3.67834889816024 0.321651101839762 23 3 3.57729152484748 -0.577291524847484 24 4 3.59538526050169 0.404614739498315 25 4 3.54069013872874 0.459309861271263 26 3 3.59121882538511 -0.591218825385114 27 3 3.35542666640008 -0.355426666400079 28 2 3.48090762684009 -1.48090762684009 29 3 3.53143631349646 -0.531436313496464 30 4 3.83117741948672 0.168822580513280 31 3 3.64591394715806 -0.645913947158063 32 3 3.42112511495144 -0.421125114951438 33 4 3.67834889816024 0.321651101839762 34 2 3.53560274861304 -1.53560274861304 35 4 3.47915812529395 0.52084187470605 36 3 3.59121882538511 -0.591218825385114 37 4 3.44847267583791 0.551527324162088 38 2 3.54485657384531 -1.54485657384531 39 3 3.53143631349646 -0.531436313496464 40 4 3.77648229771377 0.223517702286228 41 4 3.61856638627159 0.381433613728412 42 3 3.67326150804454 -0.673261508044537 43 5 3.23411214107664 1.76588785892336 44 3 3.35959310151665 -0.359593101516651 45 3 3.53560274861304 -0.535602748613036 46 4 3.71669978582512 0.283300214174878 47 4 3.91414105714527 0.0858589428547271 48 5 3.299810589628 1.700189410372 49 3 3.34442333962167 -0.344423339621670 50 4 3.54069013872874 0.459309861271263 51 4 3.57220413473178 0.427795865268217 52 2 3.03250443463992 -1.03250443463992 53 4 3.71495028427899 0.285049715721015 54 4 3.27246302874153 0.727536971258473 55 4 3.59121882538511 0.408781174614886 56 3 3.48090762684009 -0.480907626840087 57 3 3.32299171539790 -0.322991715397904 58 3 3.77648229771377 -0.776482297713772 59 2 3.12380094253162 -1.12380094253162 60 4 3.67834889816024 0.321651101839762 61 4 3.35959310151665 0.640406898483349 62 4 3.77648229771377 0.223517702286228 63 3 3.56387126449864 -0.56387126449864 64 4 3.86361237048890 0.136387629511104 65 3 3.57220413473178 -0.572204134731783 66 4 3.61856638627159 0.381433613728412 67 4 3.49016145207236 0.50983854792764 68 4 3.58613143526941 0.413868564730587 69 4 3.61856638627159 0.381433613728412 70 4 3.15114850341809 0.84885149658191 71 4 3.67834889816024 0.321651101839762 72 4 3.76547897093536 0.234521029064638 73 4 3.50825518772656 0.491744812273438 74 2 3.35542666640008 -1.35542666640008 75 3 3.56803769961521 -0.568037699615211 76 4 3.54069013872874 0.459309861271263 77 4 3.54069013872874 0.459309861271263 78 3 3.4425567391752 -0.442556739175203 79 4 3.58613143526941 0.413868564730587 80 4 3.3961944876354 0.603805512364602 81 4 3.35033927628438 0.649660723715622 82 3 3.61856638627159 -0.618566386271588 83 3 3.48090762684009 -0.480907626840087 84 3 3.5570343728368 -0.557034372836801 85 3 3.48799803571588 -0.487998035715879 86 4 3.56803769961521 0.431962300384789 87 4 3.35959310151665 0.640406898483349 88 2 3.65516777239034 -1.65516777239034 89 4 3.86361237048890 0.136387629511104 90 3 3.41012178817303 -0.410121788173028 91 4 3.64591394715806 0.354086052841937 92 3 3.38277422728655 -0.382774227286554 93 4 3.77648229771377 0.223517702286228 94 3 3.59121882538511 -0.591218825385114 95 3 3.71495028427899 -0.714950284278985 96 4 3.54485657384531 0.455143426154692 97 3 3.52167544807541 -0.521675448075406 98 4 3.35959310151665 0.640406898483349 99 2 3.57729152484748 -1.57729152484748 100 4 3.75330117194387 0.246698828056131 101 4 3.77648229771377 0.223517702286228 102 4 3.77648229771377 0.223517702286228 103 4 3.48090762684009 0.519092373159913 104 4 3.59538526050169 0.404614739498315 105 3 3.15114850341809 -0.151148503418090 106 4 3.69351866005522 0.306481339944781 107 3 3.22485831584437 -0.22485831584437 108 4 3.67834889816024 0.321651101839762 109 3 3.27246302874153 -0.272463028741527 110 2 3.299810589628 -1.29981058962800 111 3 3.50825518772656 -0.508255187726562 112 2 3.71495028427899 -1.71495028427899 113 4 3.41012178817303 0.589878211826972 114 4 3.61856638627159 0.381433613728412 115 4 3.70569645904671 0.294303540953288 116 1 3.80382985860025 -2.80382985860025 117 4 3.77648229771377 0.223517702286228 118 4 3.54485657384531 0.455143426154692 119 4 3.54069013872874 0.459309861271263 120 3 3.67834889816024 -0.678348898160238 121 4 3.56803769961521 0.431962300384789 122 4 3.59121882538511 0.408781174614886 123 3 3.23411214107664 -0.234112141076643 124 4 3.49308542583158 0.50691457416842 125 4 3.71669978582512 0.283300214174878 126 4 3.68251533327681 0.317484666723191 127 4 3.71669978582512 0.283300214174878 128 4 3.54069013872874 0.459309861271263 129 3 3.41012178817303 -0.410121788173028 130 3 3.15114850341809 -0.151148503418090 131 4 3.65691727393647 0.343082726063528 132 4 3.76547897093536 0.234521029064638 133 4 3.54485657384531 0.455143426154692 134 4 3.50825518772656 0.491744812273438 135 4 3.80382985860025 0.196170141399754 136 4 3.59538526050169 0.404614739498315 137 4 3.67834889816024 0.321651101839762 138 4 3.14698206830152 0.853017931698481 139 4 3.82701098437015 0.172989015629851 140 3 3.38277422728655 -0.382774227286554 141 3 3.40595535305646 -0.405955353056456 142 4 3.62782021150386 0.372179788496139 143 4 3.53143631349646 0.468563686503536 144 2 3.27246302874153 -1.27246302874153 145 4 3.59538526050169 0.404614739498315 146 4 3.62273282138816 0.37726717861184 147 4 3.35959310151665 0.640406898483349 148 5 3.29564415451143 1.70435584548857 149 4 3.59121882538511 0.408781174614886 150 4 3.80382985860025 0.196170141399754 151 4 3.75330117194387 0.246698828056131 152 4 3.86361237048890 0.136387629511104 153 4 3.35959310151665 0.640406898483349 154 4 3.67834889816024 0.321651101839762 155 4 3.53143631349646 0.468563686503536 156 4 3.59538526050169 0.404614739498315 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.110067422146674 0.220134844293348 0.889932577853326 9 0.0799012366956454 0.159802473391291 0.920098763304355 10 0.684370004919834 0.631259990160332 0.315629995080166 11 0.935289312908133 0.129421374183735 0.0647106870918674 12 0.913175504140266 0.173648991719468 0.086824495859734 13 0.882162888976307 0.235674222047385 0.117837111023693 14 0.837637756129237 0.324724487741525 0.162362243870763 15 0.803360627136587 0.393278745726826 0.196639372863413 16 0.767925390614061 0.464149218771878 0.232074609385939 17 0.702773391702411 0.594453216595178 0.297226608297589 18 0.661794877382845 0.67641024523431 0.338205122617155 19 0.678714836888012 0.642570326223976 0.321285163111988 20 0.84059718836044 0.31880562327912 0.15940281163956 21 0.86387047912727 0.272259041745459 0.136129520872729 22 0.825496240064596 0.349007519870809 0.174503759935404 23 0.84036310833691 0.319273783326179 0.159636891663090 24 0.81601715385109 0.367965692297819 0.183982846148910 25 0.776658422820779 0.446683154358443 0.223341577179221 26 0.764424990440522 0.471150019118957 0.235575009559478 27 0.721313454534552 0.557373090930896 0.278686545465448 28 0.84774841970003 0.30450316059994 0.15225158029997 29 0.819264733201846 0.361470533596308 0.180735266798154 30 0.77977518368333 0.44044963263334 0.22022481631667 31 0.75289226076776 0.494215478464479 0.247107739232240 32 0.711652671520499 0.576694656959002 0.288347328479501 33 0.671159389449207 0.657681221101586 0.328840610550793 34 0.780651320899657 0.438697358200685 0.219348679100343 35 0.750005136737948 0.499989726524104 0.249994863262052 36 0.730749162328106 0.538501675343787 0.269250837671894 37 0.750675191613602 0.498649616772796 0.249324808386398 38 0.868356717548298 0.263286564903403 0.131643282451702 39 0.849434822180131 0.301130355639738 0.150565177819869 40 0.818862352729707 0.362275294540587 0.181137647270293 41 0.798180702166528 0.403638595666943 0.201819297833472 42 0.779198459812053 0.441603080375894 0.220801540187947 43 0.91212842370368 0.175743152592639 0.0878715762963194 44 0.895024351429624 0.209951297140752 0.104975648570376 45 0.881833816986995 0.236332366026010 0.118166183013005 46 0.869031934977104 0.261936130045792 0.130968065022896 47 0.840087587111252 0.319824825777495 0.159912412888748 48 0.949290537678596 0.101418924642808 0.0507094623214039 49 0.945640388059008 0.108719223881984 0.054359611940992 50 0.936608548754392 0.126782902491215 0.0633914512456076 51 0.927353377746986 0.145293244506028 0.0726466222530141 52 0.9442453815366 0.111509236926801 0.0557546184634006 53 0.932620055216403 0.134759889567193 0.0673799447835967 54 0.933211620169676 0.133576759660648 0.0667883798303242 55 0.922768564858327 0.154462870283347 0.0772314351416733 56 0.912989432590656 0.174021134818687 0.0870105674093437 57 0.897815891795913 0.204368216408173 0.102184108204087 58 0.900565446531648 0.198869106936703 0.0994345534683515 59 0.93044118471139 0.139117630577220 0.0695588152886102 60 0.917209473064178 0.165581053871643 0.0827905269358216 61 0.913391746431267 0.173216507137467 0.0866082535687335 62 0.89515833902465 0.209683321950699 0.104841660975349 63 0.88751938598287 0.224961228034260 0.112480614017130 64 0.864488612539806 0.271022774920388 0.135511387460194 65 0.855345526138497 0.289308947723007 0.144654473861503 66 0.836187840595447 0.327624318809106 0.163812159404553 67 0.819883943125419 0.360232113749163 0.180116056874581 68 0.803473128780772 0.393053742438456 0.196526871219228 69 0.779181865556877 0.441636268886245 0.220818134443123 70 0.791568597491059 0.416862805017882 0.208431402508941 71 0.76421188423909 0.47157623152182 0.23578811576091 72 0.736722799500135 0.52655440099973 0.263277200499865 73 0.716112718592203 0.567774562815594 0.283887281407797 74 0.816556549675882 0.366886900648237 0.183443450324118 75 0.806986834357273 0.386026331285454 0.193013165642727 76 0.786254188618423 0.427491622763155 0.213745811381577 77 0.764180788385532 0.471638423228936 0.235819211614468 78 0.74093794178934 0.518124116421321 0.259062058210660 79 0.71524588099307 0.56950823801386 0.28475411900693 80 0.71346848436288 0.573063031274241 0.286531515637121 81 0.701840431196502 0.596319137606996 0.298159568803498 82 0.696500947725774 0.606998104548452 0.303499052274226 83 0.686594290300823 0.626811419398353 0.313405709699177 84 0.667299126034075 0.665401747931849 0.332700873965925 85 0.649608555323119 0.700782889353762 0.350391444676881 86 0.620381478826637 0.759237042346725 0.379618521173363 87 0.61228751293628 0.77542497412744 0.38771248706372 88 0.782452751209485 0.435094497581030 0.217547248790515 89 0.748220379185291 0.503559241629418 0.251779620814709 90 0.727431742720123 0.545136514559755 0.272568257279877 91 0.693856048870889 0.612287902258222 0.306143951129111 92 0.668646395856595 0.66270720828681 0.331353604143405 93 0.627738304215607 0.744523391568786 0.372261695784393 94 0.626286904447698 0.747426191104604 0.373713095552302 95 0.613733056178541 0.772533887642918 0.386266943821459 96 0.5904429346509 0.8191141306982 0.4095570653491 97 0.562254893327149 0.875490213345701 0.437745106672851 98 0.553524507806981 0.892950984386037 0.446475492193019 99 0.719168058351071 0.561663883297858 0.280831941648929 100 0.680262405213606 0.639475189572788 0.319737594786394 101 0.638056217641328 0.723887564717344 0.361943782358672 102 0.593615643948824 0.812768712102352 0.406384356051176 103 0.560210636220262 0.879578727559476 0.439789363779738 104 0.526496558357452 0.947006883285096 0.473503441642548 105 0.477883345033489 0.955766690066978 0.522116654966511 106 0.433944770863013 0.867889541726025 0.566055229136987 107 0.395148229834862 0.790296459669723 0.604851770165138 108 0.354207343482538 0.708414686965075 0.645792656517462 109 0.324388081106625 0.64877616221325 0.675611918893375 110 0.484132160246792 0.968264320493584 0.515867839753208 111 0.489212877763361 0.978425755526722 0.510787122236639 112 0.715847164375938 0.568305671248123 0.284152835624062 113 0.691476278063712 0.617047443872575 0.308523721936288 114 0.652209701041188 0.695580597917623 0.347790298958812 115 0.611637443734608 0.776725112530784 0.388362556265392 116 0.998812492191953 0.00237501561609453 0.00118750780804726 117 0.998148427554467 0.00370314489106532 0.00185157244553266 118 0.997187080765923 0.00562583846815396 0.00281291923407698 119 0.995744183731565 0.00851163253687024 0.00425581626843512 120 0.997542483385526 0.00491503322894708 0.00245751661447354 121 0.99621665443561 0.00756669112877881 0.00378334556438941 122 0.994198020597923 0.0116039588041545 0.00580197940207724 123 0.99268974708467 0.0146205058306607 0.00731025291533033 124 0.98997168317269 0.0200566336546183 0.0100283168273091 125 0.98491482855799 0.0301703428840192 0.0150851714420096 126 0.978098692090386 0.0438026158192273 0.0219013079096137 127 0.968231221712965 0.0635375565740699 0.0317687782870350 128 0.954798132654633 0.0904037346907345 0.0452018673453672 129 0.952573594227903 0.094852811544194 0.047426405772097 130 0.943831522226333 0.112336955547334 0.0561684777736671 131 0.920941157633583 0.158117684732835 0.0790588423664175 132 0.890430997140396 0.219138005719209 0.109569002859604 133 0.854373763550198 0.291252472899604 0.145626236449802 134 0.81198347173201 0.376033056535981 0.188016528267991 135 0.755497399817756 0.489005200364488 0.244502600182244 136 0.692269707089683 0.615460585820634 0.307730292910317 137 0.618983590165047 0.762032819669906 0.381016409834953 138 0.600023653080147 0.799952693839705 0.399976346919853 139 0.521219579628738 0.957560840742523 0.478780420371262 140 0.503045959925915 0.99390808014817 0.496954040074085 141 0.612660138258753 0.774679723482494 0.387339861741247 142 0.517213119128132 0.965573761743735 0.482786880871868 143 0.418983553607387 0.837967107214775 0.581016446392613 144 0.994687631700698 0.0106247365986042 0.00531236829930212 145 0.985249614623504 0.029500770752991 0.0147503853764955 146 0.971534389344233 0.0569312213115334 0.0284656106557667 147 0.935481603909209 0.129036792181582 0.064518396090791 148 1 3.89377133056926e-45 1.94688566528463e-45 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.049645390070922 NOK 5% type I error level 14 0.099290780141844 NOK 10% type I error level 18 0.127659574468085 NOK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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