Multiple linear regression 1

*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: Fri, 19 Nov 2010 16:51:37 +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/19/t1290185446loejfnmcrmnl8i6.htm/, Retrieved Fri, 19 Nov 2010 17:50:57 +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/19/t1290185446loejfnmcrmnl8i6.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 «

15 10 77 5 4 46 15 11 12 13 6 12 20 63 6 4 37 9 12 7 11 4 15 16 73 4 10 45 12 12 13 14 6 12 10 76 6 6 46 15 11 11 12 5 14 8 90 3 5 55 17 11 16 12 5 8 14 67 10 8 40 14 10 10 6 4 11 19 69 8 9 43 9 11 15 10 5 15 15 70 3 6 43 12 9 5 11 3 4 23 54 4 8 33 11 10 4 10 2 13 9 54 3 11 33 13 12 7 12 5 19 12 76 5 6 47 16 12 15 15 6 10 14 75 5 8 44 16 12 5 13 6 15 13 76 6 11 47 15 13 16 18 8 6 11 80 5 5 49 10 9 15 11 6 7 11 89 3 10 55 16 12 13 12 3 14 10 73 4 7 43 12 12 13 13 6 16 12 74 8 7 46 15 12 15 14 6 16 18 78 8 13 51 13 12 15 16 7 14 12 76 8 10 47 18 13 10 16 8 15 10 69 5 8 42 13 11 17 16 6 14 15 74 8 6 42 17 12 14 15 7 12 15 82 2 8 48 14 12 9 13 4 9 12 77 0 7 45 13 15 6 8 4 12 9 84 5 5 51 13 11 11 14 2 14 11 75 2 9 46 15 12 13 15 6 12 15 54 7 9 33 13 10 12 13 6 14 16 79 5 11 47 15 11 10 16 6 10 17 79 2 11 47 13 13 4 13 6 14 12 69 12 11 42 14 6 13 12 6 16 11 88 7 9 55 13 12 15 15 7 10 13 57 0 7 36 16 12 8 11 4 8 9 69 2 6 42 14 10 10 14 3 12 11 86 3 6 51 18 12 8 13 5 11 9 65 0 6 43 15 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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = -1.40033179694972 -0.076094555483637Depression[t] + 0.0719081107769395Belonging[t] + 0.0941357682157757Weighted_popularity[t] + 0.083878464867039Parental_criticism[t] -0.0399931531986932Belonging_final[t] -0.0601894895057676Happiness[t] + 0.118163788663957FindingFriends[t] + 0.230029151161890KnowingPeople[t] + 0.344271299678481Liked[t] + 0.522587758027874Celebrity[t] -0.00639854118490133t + 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) -1.40033179694972 2.56448 -0.546 0.585877 0.292939 Depression -0.076094555483637 0.063844 -1.1919 0.23527 0.117635 Belonging 0.0719081107769395 0.051482 1.3968 0.164632 0.082316 Weighted_popularity 0.0941357682157757 0.0584 1.6119 0.109169 0.054585 Parental_criticism 0.083878464867039 0.065932 1.2722 0.205353 0.102677 Belonging_final -0.0399931531986932 0.073107 -0.5471 0.585191 0.292595 Happiness -0.0601894895057676 0.085851 -0.7011 0.484374 0.242187 FindingFriends 0.118163788663957 0.093894 1.2585 0.210256 0.105128 KnowingPeople 0.230029151161890 0.064589 3.5614 5e-04 0.00025 Liked 0.344271299678481 0.094193 3.655 0.00036 0.00018 Celebrity 0.522587758027874 0.158855 3.2897 0.001261 0.00063 t -0.00639854118490133 0.003744 -1.7091 0.089591 0.044795 Multiple Linear Regression - Regression Statistics Multiple R 0.747479529845818 R-squared 0.558725647538525 Adjusted R-squared 0.525017190058829 F-TEST (value) 16.5752362852874 F-TEST (DF numerator) 11 F-TEST (DF denominator) 144 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.02389408044419 Sum Squared Residuals 589.845203835411 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 13.1041188809075 1.89588111909250 2 12 9.37957223548966 2.62042776451034 3 15 13.6692829047351 1.33071709526493 4 12 12.1780196356576 -0.17801963565763 5 14 13.6340663848125 0.365933615187533 6 8 9.12171124973133 -1.12171124973133 7 11 12.1232135702656 -1.12321357026557 8 15 8.35269535227079 6.64730464772921 9 4 6.33029989402401 -2.33029989402401 10 13 10.609066681238 2.39093331876199 11 19 14.3804043758506 4.61959562414936 12 10 11.4488108912758 -1.44881089127583 13 15 17.291412674971 -2.29141267497098 14 6 13.1906313519517 -7.19063135195172 15 7 12.1323718286991 -5.1323718286991 16 14 13.5267488143510 0.47325118564904 17 16 14.3203940197277 1.67960598027230 18 16 15.7798749483539 0.220125051646122 19 14 15.1842230800641 -1.18422308006412 20 15 15.2061068182984 -0.206106818298382 21 14 14.6590612639979 -0.659061263997852 22 12 11.365027849543 0.634972150456999 23 9 9.07843878284137 -0.0784387828413666 24 12 11.5645865588674 0.435413441132648 25 14 13.9043636743032 0.0956363256968038 26 12 12.0395860686947 -0.0395860686946777 27 14 13.7449173963345 0.255082603665467 28 10 11.3237347453513 -1.32373474535133 29 14 12.9587063725915 1.04129362740849 30 16 16.0209419101327 -0.0209419101327301 31 10 8.83074442797802 1.16925557202198 32 8 10.7103914354383 -2.71039143543826 33 12 11.7448545892799 0.255145410720076 34 11 10.8912398290721 0.108760170927926 35 8 10.3166168319753 -2.31661683197533 36 13 12.1237887246381 0.876211275361948 37 11 10.0155668966914 0.98443310330859 38 12 9.78578488571004 2.21421511428996 39 16 15.2696303658561 0.730369634143928 40 16 12.9784721070763 3.02152789292375 41 13 13.8822688592405 -0.882268859240485 42 14 15.2715261726568 -1.27152617265677 43 5 5.55350869007313 -0.553508690073128 44 14 13.3175077245915 0.682492275408454 45 13 9.03216589577066 3.96783410422934 46 16 15.4830206203974 0.516979379602634 47 14 14.6731379723986 -0.673137972398646 48 15 14.2082259830187 0.791774016981327 49 15 13.3012294874653 1.69877051253468 50 11 12.1583384993798 -1.15833849937977 51 15 13.6027018993587 1.3972981006413 52 16 12.6145287868068 3.38547121319315 53 13 13.3125508280339 -0.312550828033874 54 11 13.6932708599582 -2.69327085995817 55 12 13.8771452843589 -1.87714528435892 56 12 11.5368928032068 0.463107196793213 57 10 13.3738483993187 -3.37384839931873 58 8 9.03838872227876 -1.03838872227876 59 9 9.60405812870067 -0.604058128700668 60 12 12.0926494029421 -0.0926494029421035 61 14 13.9481472148274 0.0518527851726437 62 12 13.0528342079952 -1.05283420799521 63 11 11.0075014050402 -0.00750140504018929 64 14 13.9094005521977 0.0905994478022505 65 7 11.5459981683963 -4.54599816839630 66 16 14.0447539727401 1.95524602725989 67 16 15.5371528714492 0.462847128550839 68 11 12.2647601803260 -1.26476018032602 69 16 15.3546121445055 0.645387855494538 70 13 14.4183599616621 -1.41835996166212 71 11 10.8207328878061 0.17926711219393 72 13 12.8031760504 0.19682394960001 73 14 14.3362199694722 -0.336219969472208 74 15 13.4861689395864 1.51383106041364 75 10 9.35965940722294 0.640340592777062 76 15 14.7244744198531 0.275525580146891 77 11 12.9958102339005 -1.99581023390055 78 11 11.4024329141157 -0.402432914115743 79 6 8.49918198128773 -2.49918198128773 80 11 9.63233741840193 1.36766258159807 81 12 11.5566437019636 0.443356298036368 82 13 13.2091406540391 -0.209140654039053 83 12 12.3210617317896 -0.321061731789568 84 8 10.6490833407533 -2.64908334075331 85 9 10.7349212539284 -1.73492125392839 86 10 11.6467410654182 -1.64674106541819 87 16 13.1158790701389 2.88412092986111 88 15 12.7652299159938 2.23477008400617 89 14 13.5696071875676 0.430392812432445 90 12 13.6433703651392 -1.64337036513920 91 12 10.2682747618807 1.73172523811934 92 10 8.82033206271318 1.17966793728682 93 12 11.4263746133836 0.573625386616377 94 8 9.3413456607946 -1.34134566079460 95 16 14.0520765069226 1.94792349307736 96 11 7.75087376463123 3.24912623536877 97 12 11.4922744805770 0.507725519422968 98 9 10.2998349775947 -1.29983497759473 99 14 11.3107199255873 2.68928007441269 100 15 14.4417914627296 0.558208537270431 101 8 10.7050914338505 -2.70509143385053 102 12 12.2985131903579 -0.298513190357948 103 10 10.4127573387016 -0.412757338701639 104 16 14.7838902026429 1.21610979735713 105 17 14.2719966698276 2.72800333017243 106 8 10.0794170593795 -2.07941705937948 107 9 10.5838716669164 -1.58387166691636 108 8 11.3755467072374 -3.37554670723741 109 11 12.3744237176035 -1.37442371760347 110 16 15.2759600290629 0.724039970937076 111 13 13.4306727557511 -0.430672755751130 112 5 7.71119025790909 -2.71119025790909 113 15 12.7846787100066 2.21532128999339 114 15 13.940839216779 1.05916078322099 115 12 11.3972919071503 0.60270809284972 116 12 11.3956027799066 0.60439722009336 117 16 15.7234388724739 0.276561127526108 118 12 12.4369449584 -0.436944958399993 119 10 11.6255542363726 -1.62555423637263 120 12 10.5660991565575 1.43390084344252 121 4 6.22293211352812 -2.22293211352812 122 11 12.9176944639492 -1.91769446394925 123 16 14.6788101160740 1.32118988392603 124 7 8.79712611731686 -1.79712611731686 125 9 10.7125218131455 -1.71252181314545 126 14 10.8281029013784 3.17189709862156 127 11 9.64537312488019 1.35462687511981 128 10 10.7811590578546 -0.781159057854605 129 6 8.4773317134976 -2.47733171349761 130 14 12.8023524491645 1.19764755083547 131 11 10.8201744273176 0.179825572682416 132 11 9.11860432423373 1.88139567576627 133 9 13.8648278690724 -4.86482786907245 134 16 11.372357927454 4.62764207254599 135 7 8.44596341492404 -1.44596341492404 136 8 8.78090798916263 -0.780907989162627 137 10 9.90724711312378 0.0927528868762226 138 14 11.9107259183342 2.08927408166581 139 9 9.55187003377597 -0.551870033775968 140 13 12.2440385058042 0.755961494195762 141 13 9.5840268701916 3.41597312980839 142 12 11.6521364140392 0.347863585960838 143 11 12.5351681163983 -1.53516811639827 144 10 14.9020014400070 -4.90200144000698 145 12 11.9172044351705 0.0827955648294793 146 14 13.2419318675388 0.758068132461205 147 11 13.3186321462926 -2.3186321462926 148 13 10.9918777612751 2.00812223872485 149 14 13.5428872367616 0.457112763238448 150 13 12.5641894932098 0.435810506790199 151 16 16.0433459968011 -0.0433459968011405 152 13 12.1290136015778 0.87098639842222 153 12 11.1692656051966 0.83073439480335 154 9 9.09291427494277 -0.0929142749427714 155 14 11.2577678270325 2.74223217296746 156 15 14.5279979189494 0.472002081050603 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.933649257395563 0.132701485208874 0.066350742604437 16 0.999930621874146 0.000138756251707923 6.93781258539613e-05 17 0.99982533042272 0.000349339154560413 0.000174669577280207 18 0.999578824249336 0.000842351501327179 0.000421175750663589 19 0.99944246296334 0.00111507407331862 0.000557537036659311 20 0.998941708262373 0.00211658347525386 0.00105829173762693 21 0.999034755321167 0.00193048935766501 0.000965244678832506 22 0.999567250471365 0.000865499057270978 0.000432749528635489 23 0.999157827831607 0.00168434433678615 0.000842172168393073 24 0.998445326001666 0.00310934799666861 0.00155467399833431 25 0.997235517460621 0.00552896507875728 0.00276448253937864 26 0.995267882314468 0.00946423537106505 0.00473211768553253 27 0.995942688768337 0.00811462246332684 0.00405731123166342 28 0.993516932421401 0.0129661351571970 0.00648306757859852 29 0.996582457718479 0.00683508456304207 0.00341754228152104 30 0.995217176268008 0.0095656474639834 0.0047828237319917 31 0.992921336992382 0.0141573260152365 0.00707866300761823 32 0.996284334548904 0.00743133090219159 0.00371566545109579 33 0.994330861757432 0.0113382764851356 0.00566913824256779 34 0.992277437072564 0.0154451258548714 0.00772256292743568 35 0.991279356100053 0.0174412877998932 0.00872064389994661 36 0.987757815396007 0.0244843692079857 0.0122421846039929 37 0.984893642637731 0.0302127147245372 0.0151063573622686 38 0.986023059249697 0.0279538815006067 0.0139769407503034 39 0.985261760143423 0.0294764797131537 0.0147382398565768 40 0.989836355867045 0.0203272882659101 0.0101636441329550 41 0.98602298353575 0.0279540329285006 0.0139770164642503 42 0.98077854240216 0.0384429151956809 0.0192214575978405 43 0.973489036583066 0.0530219268338682 0.0265109634169341 44 0.96769041426965 0.064619171460701 0.0323095857303505 45 0.991292554964444 0.0174148900711116 0.00870744503555578 46 0.988013678177197 0.0239726436456056 0.0119863218228028 47 0.983986894232742 0.0320262115345167 0.0160131057672583 48 0.979021719539053 0.0419565609218936 0.0209782804609468 49 0.976520832207837 0.0469583355843252 0.0234791677921626 50 0.972010259031866 0.0559794819362689 0.0279897409681344 51 0.969431950633464 0.0611360987330716 0.0305680493665358 52 0.982138988658216 0.0357220226835678 0.0178610113417839 53 0.976067376203782 0.0478652475924353 0.0239326237962177 54 0.976737935371232 0.046524129257535 0.0232620646287675 55 0.973376010621936 0.053247978756128 0.026623989378064 56 0.966385646299197 0.0672287074016055 0.0336143537008028 57 0.975072812968049 0.0498543740639027 0.0249271870319513 58 0.968604685384795 0.0627906292304099 0.0313953146152050 59 0.958784031714412 0.0824319365711752 0.0412159682855876 60 0.946744710982143 0.106510578035714 0.0532552890178569 61 0.93284309119605 0.134313817607899 0.0671569088039494 62 0.919899115767245 0.160201768465510 0.0801008842327551 63 0.900251949790252 0.199496100419497 0.0997480502097483 64 0.884622774641366 0.230754450717268 0.115377225358634 65 0.936158227263073 0.127683545473854 0.0638417727369268 66 0.941302434161088 0.117395131677823 0.0586975658389117 67 0.928161402578554 0.143677194842892 0.0718385974214462 68 0.915566004464006 0.168867991071989 0.0844339955359943 69 0.898446226792583 0.203107546414835 0.101553773207417 70 0.885460236405788 0.229079527188424 0.114539763594212 71 0.862778079944178 0.274443840111644 0.137221920055822 72 0.83686833746627 0.326263325067459 0.163131662533729 73 0.820712211572717 0.358575576854567 0.179287788427283 74 0.815138334240323 0.369723331519353 0.184861665759677 75 0.79024755103446 0.41950489793108 0.20975244896554 76 0.756152108081876 0.487695783836248 0.243847891918124 77 0.74665857493936 0.506682850121282 0.253341425060641 78 0.705733685052797 0.588532629894405 0.294266314947203 79 0.711337750520457 0.577324498959087 0.288662249479543 80 0.697204070710098 0.605591858579805 0.302795929289902 81 0.661898688272877 0.676202623454246 0.338101311727123 82 0.619964852095304 0.760070295809392 0.380035147904696 83 0.57265445659414 0.85469108681172 0.42734554340586 84 0.581423658877749 0.837152682244502 0.418576341122251 85 0.563090203733514 0.873819592532972 0.436909796266486 86 0.539508849729024 0.920982300541952 0.460491150270976 87 0.59179092784014 0.81641814431972 0.40820907215986 88 0.62074372516261 0.758512549674781 0.379256274837390 89 0.58586147562107 0.82827704875786 0.41413852437893 90 0.569916826068621 0.860166347862758 0.430083173931379 91 0.558209635856616 0.883580728286768 0.441790364143384 92 0.526465841611335 0.94706831677733 0.473534158388665 93 0.482947475442566 0.965894950885132 0.517052524557434 94 0.465465526368109 0.930931052736217 0.534534473631892 95 0.479307314937569 0.958614629875137 0.520692685062431 96 0.619056654163523 0.761886691672954 0.380943345836477 97 0.573905600368762 0.852188799262475 0.426094399631238 98 0.537911331018487 0.924177337963026 0.462088668981513 99 0.604984796249609 0.790030407500782 0.395015203750391 100 0.57059121340375 0.8588175731925 0.42940878659625 101 0.590821822007804 0.818356355984392 0.409178177992196 102 0.544423758730519 0.911152482538961 0.455576241269481 103 0.494212308851229 0.988424617702457 0.505787691148771 104 0.500220397650356 0.999559204699287 0.499779602349644 105 0.551934366440812 0.896131267118377 0.448065633559188 106 0.554892150976265 0.890215698047471 0.445107849023735 107 0.511942038192078 0.976115923615844 0.488057961807922 108 0.60972456271276 0.78055087457448 0.39027543728724 109 0.593066740902704 0.813866518194592 0.406933259097296 110 0.550577261245747 0.898845477508505 0.449422738754253 111 0.494826599668513 0.989653199337027 0.505173400331487 112 0.616809343277845 0.76638131344431 0.383190656722155 113 0.626154390803578 0.747691218392843 0.373845609196422 114 0.615235488097312 0.769529023805377 0.384764511902688 115 0.559987629609119 0.880024740781762 0.440012370390881 116 0.521138877655042 0.957722244689916 0.478861122344958 117 0.477016181848517 0.954032363697034 0.522983818151483 118 0.463883416582805 0.92776683316561 0.536116583417195 119 0.49473937214882 0.98947874429764 0.50526062785118 120 0.44153085835672 0.88306171671344 0.558469141643279 121 0.413482952204301 0.826965904408603 0.586517047795699 122 0.368587832917053 0.737175665834107 0.631412167082947 123 0.426064031980692 0.852128063961384 0.573935968019308 124 0.387390103702172 0.774780207404344 0.612609896297828 125 0.415133168427088 0.830266336854177 0.584866831572912 126 0.444862550468138 0.889725100936275 0.555137449531862 127 0.432032123037265 0.86406424607453 0.567967876962735 128 0.361613594633677 0.723227189267353 0.638386405366323 129 0.598066118848158 0.803867762303684 0.401933881151842 130 0.738468831650333 0.523062336699334 0.261531168349667 131 0.741820011049845 0.516359977900309 0.258179988950155 132 0.789267218156797 0.421465563686407 0.210732781843203 133 0.762622726087927 0.474754547824146 0.237377273912073 134 0.808958022446945 0.382083955106110 0.191041977553055 135 0.732637529174614 0.534724941650772 0.267362470825386 136 0.668174881262813 0.663650237474374 0.331825118737187 137 0.758245179336002 0.483509641327995 0.241754820663998 138 0.704237223954689 0.591525552090623 0.295762776045311 139 0.646950914700121 0.706098170599757 0.353049085299879 140 0.503093950827842 0.993812098344316 0.496906049172158 141 0.40212766654133 0.80425533308266 0.59787233345867 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.118110236220472 NOK 5% type I error level 36 0.283464566929134 NOK 10% type I error level 44 0.346456692913386 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/102q961290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/102q961290185485.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/1dpcc1290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/1dpcc1290185485.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/2dpcc1290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/2dpcc1290185485.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/3dpcc1290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/3dpcc1290185485.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/4ogcx1290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/4ogcx1290185485.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/5ogcx1290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/5ogcx1290185485.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/6ogcx1290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/6ogcx1290185485.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/7rha31290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/7rha31290185485.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/8rha31290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/8rha31290185485.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/9rha31290185485.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290185446loejfnmcrmnl8i6/9rha31290185485.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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