*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: Mon, 27 Dec 2010 23:09:03 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s.htm/, Retrieved Tue, 28 Dec 2010 00:08:47 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s.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 14 11 12 24 26 9 11 7 8 25 23 9 6 17 8 30 25 9 12 10 8 19 23 9 8 12 9 22 19 9 10 12 7 22 29 10 10 11 4 25 25 10 11 11 11 23 21 10 16 12 7 17 22 10 11 13 7 21 25 10 13 14 12 19 24 10 12 16 10 19 18 10 8 11 10 15 22 10 12 10 8 16 15 10 11 11 8 23 22 10 4 15 4 27 28 10 9 9 9 22 20 10 8 11 8 14 12 10 8 17 7 22 24 10 14 17 11 23 20 10 15 11 9 23 21 10 16 18 11 21 20 10 9 14 13 19 21 10 14 10 8 18 23 10 11 11 8 20 28 10 8 15 9 23 24 10 9 15 6 25 24 10 9 13 9 19 24 10 9 16 9 24 23 10 9 13 6 22 23 10 10 9 6 25 29 10 16 18 16 26 24 10 11 18 5 29 18 10 8 12 7 32 25 10 9 17 9 25 21 10 16 9 6 29 26 10 11 9 6 28 22 10 16 12 5 17 22 10 12 18 12 28 22 10 12 12 7 29 23 10 14 18 10 26 30 10 9 14 9 25 23 10 10 15 8 14 17 10 9 16 5 25 23 10 10 10 8 26 23 10 12 11 8 20 25 10 14 14 10 18 24 10 14 9 6 32 24 10 10 12 8 25 23 10 14 17 7 25 21 10 16 5 4 23 24 10 9 12 8 21 24 10 10 12 8 20 28 10 6 6 4 15 16 10 8 24 20 30 20 10 13 12 8 24 29 10 10 12 8 26 27 10 8 14 6 24 22 10 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 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 ParentalCriticism[t] = + 16.0234048905969 -1.34666003590030Month[t] + 0.150828087380878DoubtsActions[t] + 0.441218810283992ParentalExpectations[t] + 0.0296860262939057Standards[t] -0.105384926748471`Organization `[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) 16.0234048905969 9.091759 1.7624 0.079997 0.039998 Month -1.34666003590030 0.897792 -1.5 0.135683 0.067841 DoubtsActions 0.150828087380878 0.061132 2.4673 0.014718 0.007359 ParentalExpectations 0.441218810283992 0.053005 8.3241 0 0 Standards 0.0296860262939057 0.045709 0.6495 0.517016 0.258508 `Organization ` -0.105384926748471 0.048531 -2.1715 0.031435 0.015717 Multiple Linear Regression - Regression Statistics Multiple R 0.630246087960682 R-squared 0.397210131389744 Adjusted R-squared 0.377511116075683 F-TEST (value) 20.1639587084449 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 1.99840144432528e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.13581302072108 Sum Squared Residuals 697.939680700698 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 8.8409212395438 3.15907876045619 2 8 6.96940254280453 1.03059745719547 3 8 10.5651104867126 -2.56511048671264 4 8 8.26577090327395 -0.265770903273949 5 9 9.05549396019402 -0.0554939601940226 6 7 8.30330086747107 -1.30330086747107 7 4 7.02601980716237 -3.02601980716237 8 11 7.53901554894932 3.46098445105068 9 7 8.4508737116258 -1.45087371162580 10 7 7.94054140993561 -0.940541409935612 11 12 8.72942926914202 3.27057073085798 12 10 10.0933483628200 -0.0933483628199535 13 10 6.74365814970697 3.25634185029303 14 8 7.6731322024797 0.326867797520302 15 8 7.43363062220085 0.566369377799147 16 4 7.62914379635547 -3.62914379635547 17 9 6.43062065407415 2.56937934592585 18 8 7.76782139089778 0.232178609102220 19 7 9.38800334197132 -2.38800334197132 20 11 10.7441975995444 0.255802400455617 21 9 8.14232789847284 0.857672101527163 22 11 11.4277005320023 -0.42770053200232 23 13 8.44227169986392 4.55772830013608 24 8 7.1910810158415 0.808918984158504 25 8 6.71226298282831 1.28773701717169 26 9 8.53525174769724 0.464748252302757 27 6 8.74545188766593 -2.74545188766593 28 9 7.68489810933452 1.31510189066548 29 9 9.26236959840449 -0.262369598404491 30 6 7.8793411149647 -1.87934111496470 31 6 5.7220424796005 0.277957520399497 32 16 11.1545909564780 4.84540904352204 33 5 11.1218181589461 -6.12181815894612 34 7 7.37338462674195 -0.373384626741947 35 9 9.94404428847933 -0.944044288479331 36 6 7.06190988930681 -1.06190988930681 37 6 6.6996231331024 -0.699623133102397 38 5 8.4508737116258 -3.4508737116258 39 12 10.8214205130392 1.17857948696080 40 7 8.09840875088068 -1.09840875088069 41 10 10.2206252212254 -0.220625221225379 42 9 8.40961800413041 0.590381995869588 43 8 9.30742817305315 -1.30742817305315 44 5 9.2920556246984 -4.2920556246984 45 8 6.82525687666923 1.17474312333077 46 8 7.1792458504546 0.8207541495454 47 10 8.850571330229 1.14942866977101 48 6 7.06008164692371 -1.06008164692371 49 8 7.6780084709433 0.321991529056693 50 7 10.6981847253837 -3.69818472538372 51 4 5.32968834390435 -1.32968834390435 52 8 7.30305135163833 0.696948648361666 53 8 7.00265370573142 0.997346294268578 54 4 4.86821748401608 -0.868217484016083 55 20 13.1355629313044 6.8644370686956 56 8 7.46849714630121 0.531502853698792 57 8 7.28615479024333 0.713845209756673 58 6 8.3344888172041 -2.3344888172041 59 4 4.40344744475664 -0.403447444756638 60 8 9.28451591613803 -1.28451591613803 61 9 7.28672450377158 1.71327549622842 62 6 7.98415632818492 -1.98415632818492 63 7 8.30549160623679 -1.30549160623679 64 9 6.2305465389076 2.76945346109240 65 5 7.05867350289588 -2.05867350289588 66 5 5.94560179799634 -0.945601797996344 67 8 6.74069048026737 1.25930951973263 68 8 8.23854109993117 -0.238541099931174 69 6 6.85916910125758 -0.85916910125758 70 8 7.17684789454325 0.82315210545675 71 7 7.3333070914605 -0.333307091460493 72 7 6.08477984753483 0.91522015246517 73 9 8.5940540867568 0.405945913243198 74 11 11.0200897169638 -0.0200897169638392 75 6 8.64006696091746 -2.64006696091746 76 8 7.74034819297072 0.259651807029279 77 6 8.39302567207825 -2.39302567207825 78 9 8.66765926064286 0.332340739357141 79 8 6.40554541205844 1.59445458794156 80 6 8.37544029535665 -2.37544029535665 81 10 8.30099992375693 1.69900007624307 82 8 6.07983432053914 1.92016567946086 83 8 8.34815222497409 -0.348152224974092 84 10 9.03584261056905 0.964157389430953 85 5 5.91678971457353 -0.916789714573533 86 7 9.33989674124215 -2.33989674124215 87 5 7.16109076020475 -2.16109076020475 88 8 6.2659827765362 1.73401722346379 89 14 9.90929686617731 4.09070313382269 90 7 7.651290114089 -0.651290114089004 91 8 8.82088530393509 -0.820885303935087 92 6 4.87549170839104 1.12450829160896 93 5 6.26769191712096 -1.26769191712096 94 6 9.22876160315898 -3.22876160315898 95 10 6.54567776110893 3.45432223889107 96 12 11.5406251673112 0.459374832688838 97 9 9.135900657124 -0.135900657123995 98 12 10.8698313431112 1.13016865688879 99 7 7.53014805300203 -0.530148053002031 100 8 8.33296480416384 -0.332964804163844 101 10 9.15306270270441 0.846937297295586 102 6 7.25817790453418 -1.25817790453418 103 10 11.2049764113201 -1.20497641132014 104 10 8.68664954860638 1.31335045139363 105 10 7.05936231822247 2.94063768177753 106 5 8.44569321381935 -3.44569321381935 107 7 6.91842205204705 0.0815779479529461 108 10 8.63336245007076 1.36663754992924 109 11 9.72668902593402 1.27331097406598 110 6 8.1952304110247 -2.19523041102471 111 7 7.47134571394247 -0.471345713942473 112 12 8.8280404265117 3.17195957348829 113 11 6.33916461928108 4.66083538071892 114 11 10.8020068939345 0.197993106065491 115 11 5.42856498545945 5.57143501454055 116 5 7.59344207454145 -2.59344207454145 117 8 10.229254513576 -2.22925451357600 118 6 6.77828970299657 -0.778289702996566 119 9 9.4105342456886 -0.410534245688608 120 4 6.76157826914606 -2.76157826914606 121 4 5.7578134599466 -1.75781345994660 122 7 8.32904283521224 -1.32904283521224 123 11 9.58529814802869 1.41470185197131 124 6 4.36983944951113 1.63016055048887 125 7 7.03252809235574 -0.0325280923557444 126 8 9.91618650456852 -1.91618650456852 127 4 6.29947166998338 -2.29947166998338 128 8 7.04177694150087 0.958223058499127 129 9 8.12554720609025 0.874452793909746 130 8 7.65901818297979 0.340981817020209 131 11 8.76729397605663 2.23270602394337 132 8 7.47077600041422 0.52922399958578 133 5 6.71043474044521 -1.71043474044521 134 4 5.84489368127223 -1.84489368127223 135 8 7.41083423429816 0.589165765701845 136 10 11.7953141684003 -1.79531416840026 137 6 8.26853135556792 -2.26853135556792 138 9 9.35598861829815 -0.355988618298145 139 9 7.15222326425746 1.84777673574254 140 13 8.884514068192 4.11548593180800 141 9 7.84675667776327 1.15324332223673 142 10 9.52745010848113 0.472549891518867 143 20 14.8272064864292 5.17279351357077 144 5 6.00192582450364 -1.00192582450364 145 11 10.3825996586666 0.617400341333438 146 6 8.09574531078392 -2.09574531078392 147 9 10.1548141419763 -1.15481414197627 148 7 7.28337224834823 -0.283372248348227 149 9 8.13573925663856 0.864260743361444 150 10 8.42651456552542 1.57348543447458 151 9 6.91937635155906 2.08062364844094 152 8 10.2127812833222 -2.21278128332217 153 7 11.2862403955649 -4.28624039556491 154 6 9.39073604060016 -3.39073604060016 155 13 11.6450557945476 1.35494420545237 156 6 8.00105288957993 -2.00105288957993 157 8 7.70503105714045 0.294968942859549 158 10 9.47047601180467 0.529523988195328 159 16 11.7501752371107 4.24982476288931 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.838660336634167 0.322679326731665 0.161339663365833 10 0.755482639227783 0.489034721544435 0.244517360772217 11 0.872884455995811 0.254231088008377 0.127115544004189 12 0.809493174959121 0.381013650081757 0.190506825040879 13 0.860527729043807 0.278944541912386 0.139472270956193 14 0.826912778936805 0.346174442126389 0.173087221063195 15 0.757820985231337 0.484358029537325 0.242179014768663 16 0.732075055417961 0.535849889164078 0.267924944582039 17 0.707583242897783 0.584833514204435 0.292416757102217 18 0.652904217213741 0.694191565572519 0.347095782786259 19 0.589664517261401 0.820670965477197 0.410335482738598 20 0.516748600779182 0.966502798441635 0.483251399220818 21 0.442878836896695 0.88575767379339 0.557121163103305 22 0.367622075907676 0.735244151815352 0.632377924092324 23 0.642988920961456 0.714022158077089 0.357011079038544 24 0.584468611850128 0.831062776299744 0.415531388149872 25 0.524192716277863 0.951614567444274 0.475807283722137 26 0.472385892524495 0.94477178504899 0.527614107475505 27 0.467397122326794 0.934794244653588 0.532602877673206 28 0.415919016167661 0.831838032335322 0.584080983832339 29 0.358842450306076 0.717684900612152 0.641157549693924 30 0.34620224669391 0.69240449338782 0.65379775330609 31 0.288884007296493 0.577768014592985 0.711115992703507 32 0.565924206096075 0.868151587807851 0.434075793903925 33 0.792881527152358 0.414236945695284 0.207118472847642 34 0.77020885097235 0.459582298055299 0.229791149027649 35 0.729645890137307 0.540708219725385 0.270354109862693 36 0.707977812194524 0.584044375610951 0.292022187805476 37 0.659078818052058 0.681842363895884 0.340921181947942 38 0.829119560624818 0.341760878750364 0.170880439375182 39 0.829236589387132 0.341526821225736 0.170763410612868 40 0.797103654290828 0.405792691418344 0.202896345709172 41 0.756978663040018 0.486042673919965 0.243021336959982 42 0.723374285682075 0.55325142863585 0.276625714317925 43 0.705275588496476 0.589448823007048 0.294724411503524 44 0.791481581581273 0.417036836837454 0.208518418418727 45 0.765756518651034 0.468486962697932 0.234243481348966 46 0.726625123082934 0.546749753834133 0.273374876917066 47 0.689235283299234 0.621529433401531 0.310764716700766 48 0.652414778948331 0.695170442103338 0.347585221051669 49 0.60714511245038 0.78570977509924 0.39285488754962 50 0.672229510082408 0.655540979835184 0.327770489917592 51 0.678918679773628 0.642162640452744 0.321081320226372 52 0.636047465388116 0.727905069223768 0.363952534611884 53 0.59340354800088 0.81319290399824 0.40659645199912 54 0.565567717995443 0.868864564009115 0.434432282004557 55 0.940005193721248 0.119989612557504 0.0599948062787521 56 0.924889634975787 0.150220730048426 0.0751103650242132 57 0.908809497526439 0.182381004947122 0.091190502473561 58 0.91006007479179 0.179879850416421 0.0899399252082107 59 0.889555172628284 0.220889654743432 0.110444827371716 60 0.877391582106027 0.245216835787947 0.122608417893973 61 0.868104156429424 0.263791687141152 0.131895843570576 62 0.863140674429674 0.273718651140653 0.136859325570326 63 0.846682696757365 0.306634606485271 0.153317303242635 64 0.863500618133283 0.272998763733434 0.136499381866717 65 0.861290621260115 0.27741875747977 0.138709378739885 66 0.840095530109311 0.319808939781377 0.159904469890689 67 0.820282379816496 0.359435240367008 0.179717620183504 68 0.789311084007848 0.421377831984304 0.210688915992152 69 0.760697635885933 0.478604728228134 0.239302364114067 70 0.728230393935207 0.543539212129586 0.271769606064793 71 0.688801366502435 0.622397266995131 0.311198633497565 72 0.653459989325123 0.693080021349753 0.346540010674877 73 0.611427129806118 0.777145740387764 0.388572870193882 74 0.565766916032882 0.868466167934236 0.434233083967118 75 0.590020058412148 0.819959883175703 0.409979941587852 76 0.544463854718121 0.911072290563757 0.455536145281879 77 0.556934710068578 0.886130579862843 0.443065289931422 78 0.511249969936869 0.977500060126261 0.488750030063131 79 0.486476188990789 0.972952377981577 0.513523811009211 80 0.497384534987735 0.99476906997547 0.502615465012265 81 0.476461968417484 0.952923936834968 0.523538031582516 82 0.463708826004922 0.927417652009844 0.536291173995078 83 0.418860649520733 0.837721299041465 0.581139350479267 84 0.382566175414923 0.765132350829847 0.617433824585077 85 0.348467274054649 0.696934548109297 0.651532725945351 86 0.356501585089814 0.713003170179628 0.643498414910186 87 0.36085832498307 0.72171664996614 0.63914167501693 88 0.340972531362385 0.68194506272477 0.659027468637615 89 0.453417929316626 0.906835858633251 0.546582070683374 90 0.410839666822008 0.821679333644015 0.589160333177992 91 0.372006840075324 0.744013680150648 0.627993159924676 92 0.338713815028698 0.677427630057396 0.661286184971302 93 0.309993232463082 0.619986464926164 0.690006767536918 94 0.362091956250047 0.724183912500095 0.637908043749953 95 0.42923944513204 0.85847889026408 0.57076055486796 96 0.385480204064634 0.770960408129268 0.614519795935366 97 0.340658328262293 0.681316656524586 0.659341671737707 98 0.309314223345479 0.618628446690958 0.690685776654521 99 0.269881740413003 0.539763480826007 0.730118259586997 100 0.231925027644654 0.463850055289309 0.768074972355346 101 0.201591045346707 0.403182090693413 0.798408954653293 102 0.178958652271175 0.357917304542349 0.821041347728826 103 0.158482858435882 0.316965716871764 0.841517141564118 104 0.139585463528294 0.279170927056589 0.860414536471706 105 0.171041463122252 0.342082926244504 0.828958536877748 106 0.218911912064528 0.437823824129057 0.781088087935472 107 0.185010778274116 0.370021556548231 0.814989221725884 108 0.165287930581554 0.330575861163108 0.834712069418446 109 0.146107543496278 0.292215086992557 0.853892456503722 110 0.141777780787293 0.283555561574585 0.858222219212707 111 0.116112433298432 0.232224866596864 0.883887566701568 112 0.155957901488322 0.311915802976644 0.844042098511678 113 0.286130847646506 0.572261695293013 0.713869152353494 114 0.248102017369415 0.49620403473883 0.751897982630585 115 0.593853576475726 0.812292847048547 0.406146423524274 116 0.590831988988102 0.818336022023795 0.409168011011898 117 0.599834664948913 0.800330670102175 0.400165335051087 118 0.550593704439669 0.898812591120662 0.449406295560331 119 0.49642168830235 0.9928433766047 0.50357831169765 120 0.582027939694749 0.835944120610503 0.417972060305251 121 0.550291634172907 0.899416731654185 0.449708365827093 122 0.547966236574179 0.904067526851643 0.452033763425821 123 0.508060687744051 0.983878624511899 0.491939312255949 124 0.52768559945417 0.94462880109166 0.47231440054583 125 0.468468019297094 0.936936038594188 0.531531980702906 126 0.453220183536115 0.90644036707223 0.546779816463885 127 0.429228502784117 0.858457005568234 0.570771497215883 128 0.411370383172973 0.822740766345947 0.588629616827027 129 0.385322649388436 0.770645298776872 0.614677350611564 130 0.343051148638562 0.686102297277125 0.656948851361438 131 0.340517097041328 0.681034194082657 0.659482902958672 132 0.286380651697515 0.572761303395029 0.713619348302485 133 0.239619196427524 0.479238392855047 0.760380803572476 134 0.204602210843068 0.409204421686135 0.795397789156932 135 0.164617589650523 0.329235179301046 0.835382410349477 136 0.152030053794104 0.304060107588207 0.847969946205896 137 0.163100196449602 0.326200392899205 0.836899803550398 138 0.147351756940228 0.294703513880456 0.852648243059772 139 0.182073900425255 0.364147800850511 0.817926099574745 140 0.231895279034719 0.463790558069439 0.76810472096528 141 0.176992280601213 0.353984561202426 0.823007719398787 142 0.140774895620776 0.281549791241552 0.859225104379224 143 0.212972168907178 0.425944337814356 0.787027831092822 144 0.161709529022066 0.323419058044131 0.838290470977934 145 0.116398567880763 0.232797135761526 0.883601432119237 146 0.0850317124533807 0.170063424906761 0.91496828754662 147 0.0513979929105728 0.102795985821146 0.948602007089427 148 0.0279705012082839 0.0559410024165678 0.972029498791716 149 0.0159589872335166 0.0319179744670332 0.984041012766483 150 0.00844095093437735 0.0168819018687547 0.991559049065623 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 2 0.0140845070422535 OK 10% type I error level 3 0.0211267605633803 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/10ovso1293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/10ovso1293491331.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/1s3uf1293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/1s3uf1293491331.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/2s3uf1293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/2s3uf1293491331.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/3s3uf1293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/3s3uf1293491331.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/42uc01293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/42uc01293491331.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/52uc01293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/52uc01293491331.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/62uc01293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/62uc01293491331.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/7v3b31293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/7v3b31293491331.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/8ovso1293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/8ovso1293491331.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/9ovso1293491331.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t12934913271vg79phyhb77w3s/9ovso1293491331.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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