*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, 23 Nov 2010 21:18:19 +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/23/t12905470015owjiityj9125kq.htm/, Retrieved Tue, 23 Nov 2010 22:16:41 +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/23/t12905470015owjiityj9125kq.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 «

11 14 11 12 12 11 11 7 8 11 11 6 17 8 14 11 12 10 8 12 11 8 12 9 21 11 10 12 7 12 11 10 11 4 22 11 11 11 11 11 11 16 12 7 10 11 11 13 7 13 11 13 14 12 10 11 12 16 10 8 11 8 11 10 15 11 12 10 8 14 11 11 11 8 10 11 4 15 4 14 11 9 9 9 14 11 8 11 8 11 11 8 17 7 10 11 14 17 11 13 11 15 11 9 7 11 16 18 11 14 11 9 14 13 12 11 14 10 8 14 11 11 11 8 11 11 8 15 9 9 11 9 15 6 11 11 9 13 9 15 11 9 16 9 14 11 9 13 6 13 11 10 9 6 9 11 16 18 16 15 11 11 18 5 10 11 8 12 7 11 11 9 17 9 13 11 16 9 6 8 11 11 9 6 20 11 16 12 5 12 11 12 18 12 10 11 12 12 7 10 11 14 18 10 9 11 9 14 9 14 11 10 15 8 8 11 9 16 5 14 11 10 10 8 11 11 12 11 8 13 11 14 14 10 9 11 14 9 6 11 11 10 12 8 15 11 14 17 7 11 11 16 5 4 10 11 9 12 8 14 11 10 12 8 18 11 6 6 4 14 11 8 24 20 11 11 13 12 8 12 11 10 12 8 13 11 8 14 6 9 11 7 7 4 10 11 15 13 8 15 11 9 12 9 20 11 10 13 6 12 11 12 14 7 12 11 13 8 9 14 11 10 11 5 13 11 11 9 5 11 11 8 11 8 17 11 9 13 8 12 11 13 10 6 13 11 11 11 8 14 11 8 1 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 Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation Depression[t] = + 17.7769114656762 -0.329756031349403Month[t] -0.0754019001049189Doubts[t] -0.0115990201581907Expectations[t] -0.0388365785511978Criticism[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) 17.7769114656762 7.012382 2.5351 0.012221 0.00611 Month -0.329756031349403 0.625842 -0.5269 0.599007 0.299503 Doubts -0.0754019001049189 0.090844 -0.83 0.407792 0.203896 Expectations -0.0115990201581907 0.088215 -0.1315 0.895559 0.44778 Criticism -0.0388365785511978 0.108942 -0.3565 0.721953 0.360977 Multiple Linear Regression - Regression Statistics Multiple R 0.094583923349095 R-squared 0.00894611855610749 Adjusted R-squared -0.0163036618628452 F-TEST (value) 0.354304806127837 F-TEST (DF numerator) 4 F-TEST (DF denominator) 157 p-value 0.84074436535968 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.16922646287394 Sum Squared Residuals 1576.90743055793 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 12.5003403550095 -0.500340355009515 2 11 12.9282884501618 -1.92828845016178 3 14 13.1893077491045 0.81069225089553 4 12 12.8180894895823 -0.818089489582292 5 21 13.0576624711344 7.94233752886561 6 12 12.9845318280269 -0.984531828026946 7 22 13.1126405838387 8.88735941616127 8 11 12.7653826338754 -1.76538263387543 9 10 12.5321204273974 -2.53212042739743 10 13 12.8975309077638 0.102469092236164 11 10 12.5409451946398 -2.54094519463982 12 8 12.6708222115308 -4.67082221153075 13 15 13.0304249127414 1.96957508725862 14 14 12.8180894895823 1.18191051041771 15 10 12.8818923695290 -2.88189236952902 16 14 13.5186559038355 0.481344096164519 17 14 13.0170576315040 0.982942368495959 18 11 13.1080980698438 -2.10809806984378 19 10 13.0773405274458 -3.07734052744583 20 13 12.4695828126115 0.530417187388474 21 7 12.5414481905581 -5.54144819055815 22 14 12.3071799922435 1.69282000775650 23 12 12.8037162165083 -0.803716216508297 24 14 12.6672856893725 1.33271431062755 25 11 12.8818923695290 -1.88189236952902 26 9 13.0228654106598 -4.02286541065982 27 11 13.0639732462085 -2.06397324620849 28 15 12.9706615508713 2.02933844912872 29 14 12.9358644903967 1.06413550960329 30 13 13.0871712865249 -0.087171286524872 31 9 13.0581654670527 -4.05816546705272 32 15 12.1129970994875 2.88700290051249 33 10 12.9172089640753 -2.91720896407528 34 11 13.1353356282368 -2.13533562823678 35 13 12.9242654702385 0.0757345297614842 36 8 12.6057540664232 -4.6057540664232 37 20 12.9827635669478 7.0172364330522 38 12 12.6097935844998 -0.609793584499828 39 10 12.5699510141120 -2.56995101411198 40 10 12.8337280278171 -2.83372802781711 41 9 12.4968203710045 -3.49682037100453 42 14 12.9590625307131 1.04093746928691 43 8 12.9108981890012 -4.91089818900118 44 14 13.0912108046015 0.908789195398502 45 11 12.9688932897921 -1.96889328979213 46 13 12.8064904694241 0.193509530575899 47 9 12.5432164516373 -3.54321645163730 48 11 12.7565578666330 -1.75655786663304 49 15 12.9456952494757 2.05430475052425 50 11 12.6249291268163 -1.62492912681632 51 10 12.7298233041584 -2.72982330415836 52 14 13.0210971495807 0.978902850419333 53 18 12.9456952494757 5.05430475052425 54 14 13.4722432850494 0.527756714950641 55 11 12.4912718651729 -1.49127186517292 56 12 12.719489549161 -0.719489549160992 57 13 12.9456952494757 0.0543047505242517 58 9 13.1509741664716 -4.1509741664716 59 10 13.3852423647863 -3.38524236478625 60 15 12.5570867287930 2.44291327120704 61 20 12.9822605710295 7.01773942897053 62 12 13.0117693864200 -1.01176938641995 63 12 12.8105299875007 -0.810529987500727 64 14 12.7270490512426 1.27295094875744 65 13 13.0738040052875 -0.0738040052875324 66 11 13.021600145499 -2.02160014549900 67 17 13.1080980698438 3.89190193015622 68 12 13.0094981294225 -1.00949812942248 69 13 12.8203607465798 0.179639253420231 70 14 12.8818923695290 1.11810763047098 71 13 13.1353356282368 -0.135335628236784 72 15 13.0947307886064 1.90526921139356 73 13 12.9474635105549 0.0525364894451028 74 10 12.3825818923484 -2.38258189234842 75 11 13.0639732462085 -2.06397324620849 76 19 12.9456952494757 6.05430475052425 77 13 12.7101617860003 0.289838213999722 78 17 12.7328568303983 4.26714316960167 79 13 12.8180894895823 0.181910510417708 80 9 12.9363674863150 -3.93636748631503 81 11 12.5548154717955 -1.55481547179549 82 10 13.2589018700536 -3.25890187005361 83 9 12.7832924291077 -3.78329242910772 84 12 12.9724298119504 -0.972429811950427 85 12 12.8069934653424 -0.806993465342429 86 13 12.8627338472893 0.137266152710736 87 13 13.0738040052875 -0.0738040052875324 88 12 12.6788847095306 -0.678884709530645 89 15 12.5154758973260 2.48452410267404 90 22 12.9845318280269 9.01546817197305 91 13 12.6208896087397 0.379110391260309 92 15 13.4467739877355 1.5532260122645 93 13 13.021600145499 -0.0216001454989950 94 15 12.9885713461036 2.01142865389643 95 10 12.9550230126365 -2.95502301263646 96 11 12.6859577538472 -1.68595775384724 97 16 12.4312492299787 3.56875077002134 98 11 12.4945491140071 -1.49454911400706 99 11 13.0599337281319 -2.05993372813187 100 10 12.9340962293176 -2.93409622931756 101 10 12.8332250318988 -2.83322503189878 102 16 13.2495741068929 2.7504258931071 103 12 12.8622308513709 -0.862230851370937 104 11 12.9840288321086 -1.98402883210862 105 16 12.5780135121119 3.42198648788813 106 19 12.7721964048679 6.22780359513214 107 11 13.1585336685532 -2.15853366855317 108 16 12.9318249723201 3.06817502767992 109 15 12.4927808529279 2.50721914707209 110 24 12.7217608061585 11.2782391938415 111 14 13.1353356282368 0.864664371763216 112 15 12.8947566548480 2.10524334515197 113 11 13.0147863745066 -2.01478637450657 114 15 12.9857970931878 2.01420290681223 115 12 13.1771891948746 -1.17718919487459 116 10 13.201409765181 -3.20140976518099 117 14 13.1893077491045 0.81069225089553 118 13 12.9827635669478 0.0172364330522028 119 9 12.5704540100303 -3.5704540100303 120 15 13.0720357442084 1.92796425579162 121 15 13.0836347643666 1.91636523563343 122 14 12.9091299279220 1.09087007207797 123 11 12.5043798730861 -1.50437987308610 124 8 13.2437663277371 -5.24376632773712 125 11 12.2769089076105 -1.27690890761052 126 11 12.8122982485799 -1.81229824857988 127 8 13.2750434042068 -5.27504340420676 128 10 12.8818923695290 -2.88189236952902 129 11 12.8836606306082 -1.88366063060817 130 13 12.6556866692143 0.344313330785737 131 11 12.7421845935590 -1.74218459355904 132 20 13.0210971495807 6.97890285041933 133 10 13.1492059053925 -3.14920590539245 134 15 13.2866424243649 1.71335757563505 135 12 12.9456952494757 -0.945695249475748 136 14 12.5490242307931 1.45097576920693 137 23 12.7971627062634 10.2028372937366 138 14 12.7444558505565 1.25554414944348 139 16 13.0576624711344 2.94233752886561 140 11 12.525306656405 -1.52530665640500 141 12 12.6400481309794 -0.640048130979447 142 10 12.6824212316889 -2.68242123168894 143 14 12.0388604645434 1.96113953545659 144 12 12.7431905853957 -0.743190585395701 145 12 12.5449847127164 -0.544984712716445 146 11 12.5825560261068 -1.58255602610682 147 12 12.9242654702385 -0.924265470238516 148 13 13.0715327482901 -0.0715327482900557 149 11 12.9822605710295 -1.98226057102947 150 19 12.9956278522668 6.00437214773319 151 12 13.1446633913975 -1.14466339139750 152 17 12.4468877682135 4.55311223178653 153 9 12.8047387464983 -3.80473874649831 154 12 13.0755722663667 -1.07557226636668 155 19 12.5833182953493 6.41668170465069 156 18 13.0871712865249 4.91282871347513 157 15 12.6556866692143 2.34431333078574 158 14 12.6070193315840 1.39298066841598 159 11 12.1013980793293 -1.10139807932932 160 11 12.6443303842269 -1.64433038422688 161 12 11.0818054166538 0.91819458334616 162 8 12.5909729167308 -4.59097291673082 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.976770988220887 0.0464580235582252 0.0232290117791126 9 0.955293077112068 0.089413845775865 0.0447069228879325 10 0.921349051033638 0.157301897932723 0.0786509489663615 11 0.872449880478084 0.255100239043831 0.127550119521916 12 0.848956174722854 0.302087650554293 0.151043825277146 13 0.78201086777703 0.43597826444594 0.21798913222297 14 0.705117695733052 0.589764608533897 0.294882304266948 15 0.725140560144084 0.549718879711832 0.274859439855916 16 0.781608431366398 0.436783137267204 0.218391568633602 17 0.718369037656008 0.563261924687983 0.281630962343992 18 0.730645831966459 0.538708336067082 0.269354168033541 19 0.706914339399765 0.586171321200471 0.293085660600235 20 0.733827334639986 0.532345330720029 0.266172665360014 21 0.770425043650554 0.459149912698892 0.229574956349446 22 0.81490065021618 0.37019869956764 0.18509934978382 23 0.76461263376061 0.470774732478779 0.235387366239390 24 0.726265271780742 0.547469456438516 0.273734728219258 25 0.687254845539151 0.625490308921698 0.312745154460849 26 0.71345897238627 0.573082055227459 0.286541027613730 27 0.683035076464792 0.633929847070416 0.316964923535208 28 0.651398748413857 0.697202503172286 0.348601251586143 29 0.603609977924788 0.792780044150423 0.396390022075212 30 0.543482255096405 0.91303548980719 0.456517744903595 31 0.59356427784426 0.812871444311479 0.406435722155739 32 0.627509218607025 0.74498156278595 0.372490781392975 33 0.600018389264995 0.79996322147001 0.399981610735005 34 0.565141767659792 0.869716464680415 0.434858232340208 35 0.507418476576463 0.985163046847073 0.492581523423537 36 0.509396534510799 0.981206930978402 0.490603465489201 37 0.740911675294623 0.518176649410755 0.259088324705377 38 0.698771325540865 0.602457348918271 0.301228674459136 39 0.669990647651349 0.660018704697303 0.330009352348651 40 0.647355297321819 0.705289405356363 0.352644702678181 41 0.629619514674016 0.740760970651967 0.370380485325984 42 0.584238064906738 0.831523870186524 0.415761935093262 43 0.633889198936292 0.732221602127416 0.366110801063708 44 0.594885249711311 0.810229500577379 0.405114750288689 45 0.562412340563319 0.875175318873361 0.437587659436681 46 0.513125338226196 0.973749323547609 0.486874661773804 47 0.503161472798558 0.993677054402885 0.496838527201442 48 0.460650685227359 0.921301370454719 0.539349314772641 49 0.435364793375615 0.87072958675123 0.564635206624385 50 0.394296166865963 0.788592333731926 0.605703833134037 51 0.369491223660537 0.738982447321073 0.630508776339463 52 0.327419560491526 0.654839120983052 0.672580439508474 53 0.408090577668770 0.816181155337539 0.59190942233123 54 0.363708811598372 0.727417623196744 0.636291188401628 55 0.327666264985817 0.655332529971633 0.672333735014183 56 0.286744340282279 0.573488680564557 0.713255659717722 57 0.246545675811799 0.493091351623598 0.753454324188201 58 0.275367194129763 0.550734388259525 0.724632805870237 59 0.292272254026137 0.584544508052274 0.707727745973863 60 0.296850030939347 0.593700061878693 0.703149969060654 61 0.475650502547741 0.951301005095483 0.524349497452259 62 0.432023982315315 0.86404796463063 0.567976017684685 63 0.389146494594576 0.778292989189152 0.610853505405424 64 0.352170601468972 0.704341202937943 0.647829398531028 65 0.309789005257880 0.619578010515761 0.69021099474212 66 0.284283386572342 0.568566773144684 0.715716613427658 67 0.300393772024354 0.600787544048707 0.699606227975646 68 0.264716951448125 0.529433902896249 0.735283048551875 69 0.230108551584919 0.460217103169839 0.76989144841508 70 0.200630877037723 0.401261754075445 0.799369122962277 71 0.169595877521659 0.339191755043318 0.830404122478341 72 0.149822051811550 0.299644103623099 0.85017794818845 73 0.124336838981039 0.248673677962079 0.87566316101896 74 0.113100287776415 0.22620057555283 0.886899712223585 75 0.100010806536154 0.200021613072308 0.899989193463846 76 0.168425948913347 0.336851897826695 0.831574051086653 77 0.146161793028501 0.292323586057003 0.853838206971499 78 0.174330253970235 0.348660507940469 0.825669746029765 79 0.146285624937846 0.292571249875692 0.853714375062154 80 0.160423236002786 0.320846472005572 0.839576763997214 81 0.140300422270837 0.280600844541674 0.859699577729163 82 0.148492228813978 0.296984457627955 0.851507771186022 83 0.160583123692093 0.321166247384185 0.839416876307908 84 0.136576579555783 0.273153159111565 0.863423420444217 85 0.115656114423968 0.231312228847936 0.884343885576032 86 0.0970761509555898 0.194152301911180 0.90292384904441 87 0.079165074998258 0.158330149996516 0.920834925001742 88 0.0646338418809012 0.129267683761802 0.935366158119099 89 0.0593853701869556 0.118770740373911 0.940614629813044 90 0.228110652841201 0.456221305682403 0.771889347158799 91 0.198615786164720 0.397231572329441 0.80138421383528 92 0.178572927786235 0.35714585557247 0.821427072213765 93 0.150083365228500 0.300166730456999 0.8499166347715 94 0.135146431805903 0.270292863611806 0.864853568194097 95 0.132706370384651 0.265412740769302 0.867293629615349 96 0.116941980582646 0.233883961165291 0.883058019417354 97 0.122828964550517 0.245657929101035 0.877171035449483 98 0.107905257297777 0.215810514595555 0.892094742702223 99 0.0961666096975174 0.192333219395035 0.903833390302483 100 0.094367681892392 0.188735363784784 0.905632318107608 101 0.0917962512931593 0.183592502586319 0.90820374870684 102 0.0863142614127654 0.172628522825531 0.913685738587235 103 0.0718447338313027 0.143689467662605 0.928155266168697 104 0.0629282570954887 0.125856514190977 0.937071742904511 105 0.0636608065221548 0.127321613044310 0.936339193477845 106 0.109336932165075 0.218673864330151 0.890663067834925 107 0.0971492970533296 0.194298594106659 0.90285070294667 108 0.0943275205296247 0.188655041059249 0.905672479470375 109 0.084618088404315 0.16923617680863 0.915381911595685 110 0.480520408905404 0.961040817810808 0.519479591094596 111 0.434653849585668 0.869307699171336 0.565346150414332 112 0.403557623485607 0.807115246971213 0.596442376514393 113 0.369364414638213 0.738728829276427 0.630635585361787 114 0.336328883617693 0.672657767235386 0.663671116382307 115 0.29486861488299 0.58973722976598 0.70513138511701 116 0.296387803281836 0.592775606563673 0.703612196718164 117 0.254722761436881 0.509445522873762 0.745277238563119 118 0.215179381524537 0.430358763049075 0.784820618475463 119 0.231060374687298 0.462120749374596 0.768939625312702 120 0.208780068801704 0.417560137603409 0.791219931198295 121 0.191896732365759 0.383793464731517 0.808103267634241 122 0.161373639038150 0.322747278076301 0.83862636096185 123 0.138118955622399 0.276237911244798 0.8618810443776 124 0.168465882604135 0.336931765208271 0.831534117395865 125 0.140087171431936 0.280174342863873 0.859912828568064 126 0.125930429231052 0.251860858462104 0.874069570768948 127 0.181572714352459 0.363145428704919 0.81842728564754 128 0.177535086272963 0.355070172545926 0.822464913727037 129 0.161401869805216 0.322803739610433 0.838598130194784 130 0.128391256138091 0.256782512276182 0.871608743861909 131 0.110898374283408 0.221796748566816 0.889101625716592 132 0.211630112025059 0.423260224050118 0.788369887974941 133 0.222321116233167 0.444642232466335 0.777678883766832 134 0.184026558205649 0.368053116411297 0.815973441794351 135 0.151797512217429 0.303595024434858 0.848202487782571 136 0.119275638223107 0.238551276446213 0.880724361776893 137 0.552433175460755 0.89513364907849 0.447566824539245 138 0.491455035815526 0.982910071631052 0.508544964184474 139 0.47395059660319 0.94790119320638 0.52604940339681 140 0.415526812656727 0.831053625313453 0.584473187343273 141 0.345342143249260 0.690684286498519 0.65465785675074 142 0.336255870693663 0.672511741387326 0.663744129306337 143 0.272611200770282 0.545222401540564 0.727388799229718 144 0.210978612539719 0.421957225079437 0.789021387460281 145 0.165421142391952 0.330842284783904 0.834578857608048 146 0.131365233420338 0.262730466840677 0.868634766579662 147 0.0997836406114375 0.199567281222875 0.900216359388562 148 0.0660570040492695 0.132114008098539 0.93394299595073 149 0.0513307484232234 0.102661496846447 0.948669251576777 150 0.0946533088131093 0.189306617626219 0.90534669118689 151 0.0580634924902724 0.116126984980545 0.941936507509728 152 0.053559517674136 0.107119035348272 0.946440482325864 153 0.166327916022567 0.332655832045134 0.833672083977433 154 0.21078976115501 0.42157952231002 0.78921023884499 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 1 0.00680272108843537 OK 10% type I error level 2 0.0136054421768707 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/10d0191290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/10d0191290547088.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/16hmf1290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/16hmf1290547088.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/2zq301290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/2zq301290547088.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/3zq301290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/3zq301290547088.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/4zq301290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/4zq301290547088.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/5zq301290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/5zq301290547088.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/6rz2l1290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/6rz2l1290547088.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/7k91o1290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/7k91o1290547088.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/8k91o1290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/8k91o1290547088.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/9k91o1290547088.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905470015owjiityj9125kq/9k91o1290547088.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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