*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, 20 Dec 2010 17:00:25 +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/20/t1292867445hx46p4l8vbmknp6.htm/, Retrieved Mon, 20 Dec 2010 18:50:56 +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/20/t1292867445hx46p4l8vbmknp6.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 «

9,4 0,5 5,1 -1,0 2504,7 9,4 0,8 5,0 3,0 2661,4 9,5 1,0 5,0 2,0 2880,4 9,5 1,3 5,1 3,0 3064,4 9,4 1,3 5,0 5,0 3141,1 9,4 1,2 4,9 5,0 3327,7 9,3 1,2 4,8 3,0 3565,0 9,4 1,0 4,5 2,0 3403,1 9,4 0,8 4,3 1,0 3149,9 9,2 0,7 4,3 -4,0 3006,8 9,1 0,6 4,2 1,0 3230,7 9,1 0,7 4,0 1,0 3361,1 9,1 1,0 3,8 6,0 3484,7 9,0 1,0 4,1 3,0 3411,1 9,0 1,3 4,2 2,0 3288,2 8,9 1,1 4,0 2,0 3280,4 8,8 0,8 4,3 2,0 3174,0 8,7 0,7 4,7 -8,0 3165,3 8,5 0,7 5,0 0,0 3092,7 8,3 0,9 5,1 -2,0 3053,1 8,1 1,3 5,4 3,0 3182,0 7,9 1,4 5,4 5,0 2999,9 7,8 1,6 5,4 8,0 3249,6 7,6 2,1 5,5 8,0 3210,5 7,4 0,3 5,8 9,0 3030,3 7,2 2,1 5,7 11,0 2803,5 7,0 2,5 5,5 13,0 2767,6 7,0 2,3 5,6 12,0 2882,6 6,8 2,4 5,6 13,0 2863,4 6,8 3,0 5,5 15,0 2897,1 6,7 1,7 5,5 13,0 3012,6 6,8 3,5 5,7 16,0 3143,0 6,7 4,0 5,6 10,0 3032,9 6,7 3,7 5,6 14,0 3045,8 6,7 3,7 5,4 14,0 3110,5 6,5 3,0 5,2 15,0 3013,2 6,3 2,7 5,1 13,0 2987,1 6,3 2,5 5,1 8,0 2995,6 6,3 2,2 5,0 7,0 2833,2 6,5 2,9 5,3 3,0 2849,0 6,6 3,1 5,4 3,0 2794,8 6,5 3,0 5,3 4,0 2845,3 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation werkloosheid[t] = + 12.8816810957190 -0.149333856903572hicp[t] -0.948425862863806rente[t] -0.0146403830228089consumer[t] + 0.000113042993792547bel20[t] -0.0119659263556134t + 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) 12.8816810957190 0.470978 27.3509 0 0 hicp -0.149333856903572 0.036618 -4.0782 7.4e-05 3.7e-05 rente -0.948425862863806 0.0816 -11.6229 0 0 consumer -0.0146403830228089 0.007864 -1.8618 0.064614 0.032307 bel20 0.000113042993792547 7.1e-05 1.6002 0.111693 0.055847 t -0.0119659263556134 0.001441 -8.3043 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.786066260077825 R-squared 0.617900165232739 Adjusted R-squared 0.604991387031142 F-TEST (value) 47.866665270948 F-TEST (DF numerator) 5 F-TEST (DF denominator) 148 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.504543978966511 Sum Squared Residuals 37.6755647532812 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.4 8.25585550988127 1.14414449011873 2 9.4 8.253084317777 1.14691568222300 3 9.5 8.25064841870404 1.24935158129596 4 9.5 8.105199276826 1.394800723174 5 9.4 8.16746556833504 1.23253443166496 6 9.4 8.28636943659785 1.11363056340215 7 9.3 8.42535196500121 0.874648034998794 8 9.4 8.72411929121325 0.675880708786756 9 9.4 8.91772320580564 0.482276794194357 10 9.2 8.97771612784272 0.222283872157282 11 9.1 9.02763458465995 0.0723654153400512 12 9.1 9.20516125157729 -0.105161251577288 13 9.1 9.27885053964208 -0.178850539642079 14 9 9.01795803915262 -0.0179580391526186 15 9 8.86709676852526 0.132903231474743 16 8.9 9.07380105077154 -0.173801050771537 17 8.8 8.81007974808833 -0.0100797480883266 18 8.7 8.57909721845964 0.120902781540358 19 8.5 8.15727354771308 0.342726452286924 20 8.3 8.0454025271818 0.254597472818199 21 8.1 7.63054462599143 0.469455374008568 22 7.9 7.55377941873022 0.34622058126978 23 7.8 7.49625240747547 0.303747592524535 24 7.6 7.3103569853244 0.289643014675603 25 7.4 7.24765351203185 0.152346487968155 26 7.2 7.00681031249842 0.193189687501585 27 7 7.09145700643136 -0.0914570064313644 28 7 7.04215559247904 -0.0421555924790369 29 6.8 6.99844547192944 -0.198445471929441 30 6.8 6.96625060056326 -0.166250600563256 31 6.7 7.19075592001094 -0.490755920010942 32 6.8 6.69112353597826 0.10887646402174 33 6.7 6.77472953197754 -0.074729531977535 34 6.7 6.75046048522168 -0.0504604852216817 35 6.7 6.93549361313721 -0.235493613137206 36 6.5 7.19210709286803 -0.692107092868031 37 6.3 7.3461142537775 -1.04611425377750 38 6.3 7.43817787936389 -1.13817787936389 39 6.3 7.56213689719662 -1.26213689719662 40 6.5 7.22145712354252 -0.721457123542525 41 6.6 7.07865490925626 -0.47865490925626 42 6.5 7.1675332430411 -0.6675332430411 43 6.3 7.3829983573063 -1.08299835730630 44 6.3 7.56670454333842 -1.26670454333842 45 6.5 7.67032147240518 -1.17032147240518 46 7 8.18834622509164 -1.18834622509164 47 7.1 8.0622361221325 -0.9622361221325 48 7.3 7.58706401954116 -0.28706401954116 49 7.3 7.39226201477597 -0.0922620147759719 50 7.4 7.36884260870619 0.0311573912938133 51 7.4 7.05655550193194 0.343444498068062 52 7.3 7.31170466664977 -0.0117046666497718 53 7.4 7.31357469982842 0.0864253001715847 54 7.5 7.56794084842575 -0.0679408484257549 55 7.7 7.68720565924836 0.0127943407516353 56 7.7 7.85416503068909 -0.154165030689087 57 7.7 8.12479423420912 -0.424794234209124 58 7.7 7.89404546246819 -0.194045462468187 59 7.7 8.03290314067242 -0.332903140672421 60 7.8 8.32889193037574 -0.528891930375738 61 8 8.53069105580773 -0.530691055807734 62 8.1 8.59194622749124 -0.491946227491236 63 8.1 8.43380024299724 -0.333800242997243 64 8.2 8.37161222393298 -0.171612223932986 65 8.2 8.80804050134144 -0.608040501341446 66 8.2 8.63184507717409 -0.43184507717409 67 8.1 8.39532505235666 -0.295325052356665 68 8.1 8.33458893540488 -0.234588935404875 69 8.2 8.31831859160917 -0.118318591609173 70 8.3 8.2161262717235 0.083873728276508 71 8.3 7.92389117788145 0.376108822118551 72 8.4 8.11904205995177 0.280957940048230 73 8.5 8.12532984974472 0.374670150255284 74 8.5 8.31379766643891 0.186202333561089 75 8.4 8.3573958146064 0.0426041853935949 76 8 7.97826617278344 0.0217338272165596 77 7.9 7.78883432315929 0.111165676840711 78 8.1 7.7540726621365 0.345927337863499 79 8.5 7.8798426890085 0.620157310991504 80 8.8 8.04883279166187 0.751167208338128 81 8.8 8.08344139116951 0.716558608830489 82 8.6 8.19789207917441 0.402107920825588 83 8.3 8.36559914181523 -0.0655991418152265 84 8.3 8.50171936133706 -0.201719361337056 85 8.3 8.6713443229883 -0.371344322988296 86 8.4 8.39212926140775 0.0078707385922525 87 8.4 8.29374992421863 0.106250075781372 88 8.5 8.57660472548431 -0.0766047254843145 89 8.6 8.8505431618887 -0.250543161888706 90 8.6 8.87775582683457 -0.277755826834576 91 8.6 8.77822728299282 -0.178227282992822 92 8.6 8.92223498071363 -0.322234980713634 93 8.6 8.86129286574961 -0.261292865749611 94 8.5 8.69333524099364 -0.193335240993644 95 8.4 8.59399977935765 -0.193999779357649 96 8.4 8.65320876282357 -0.253208762823565 97 8.4 8.4125299611313 -0.0125299611313071 98 8.5 8.4317199991916 0.068280000808406 99 8.5 8.28060598723625 0.219394012763753 100 8.6 8.0020374951633 0.597962504836698 101 8.6 7.97881430485858 0.621185695141424 102 8.4 7.83213148563034 0.56786851436966 103 8.2 7.94480668493518 0.255193315064816 104 8 8.15562532594515 -0.155625325945151 105 8 8.31042156336818 -0.310421563368183 106 8 8.19395473017033 -0.193954730170333 107 8 8.25360115157232 -0.253601151572321 108 7.9 8.08423574460699 -0.184235744606989 109 7.9 7.85713108533064 0.0428689146693596 110 7.8 7.99727180354744 -0.197271803547436 111 7.8 7.90328499705487 -0.103284997054866 112 8 7.77904130879004 0.220958691209962 113 7.8 7.56916319647094 0.230836803529059 114 7.4 7.46844901652104 -0.068449016521039 115 7.2 7.57398212306118 -0.373982123061181 116 7 7.55086057475528 -0.550860574755279 117 7 7.51965391843545 -0.51965391843545 118 7.2 7.48410217305958 -0.284102173059577 119 7.2 7.52762362636597 -0.327623626365966 120 7.2 7.23884421839426 -0.0388442183942559 121 7 7.54502555755802 -0.545025557558023 122 6.9 7.46024428671025 -0.560244286710246 123 6.8 7.13385829874828 -0.333858298748282 124 6.8 7.15112095173139 -0.351120951731389 125 6.8 6.7281872465094 0.0718127534905994 126 6.9 6.32290077124951 0.577099228750486 127 7.2 6.55647629963698 0.643523700363021 128 7.2 6.7812095273709 0.418790472629092 129 7.2 6.71545470770509 0.484545292294909 130 7.1 6.83872417661005 0.261275823389953 131 7.2 6.16974769278821 1.03025230721179 132 7.3 7.20764708465829 0.0923529153417114 133 7.5 7.31173777515272 0.188262224847284 134 7.6 7.5672140662278 0.0327859337722017 135 7.7 8.0179821548806 -0.3179821548806 136 7.7 7.9837663304829 -0.283766330482903 137 7.7 7.79895883304842 -0.0989588330484179 138 7.8 8.07897261870466 -0.278972618704662 139 8 8.35124255307575 -0.351242553075754 140 8.1 8.22210642838432 -0.122106428384317 141 8.1 8.27188580386928 -0.171885803869278 142 8 8.26752858011221 -0.267528580112215 143 8.1 8.08664752588517 0.0133524741148251 144 8.2 8.1071302967503 0.0928697032496925 145 8.3 7.92986005502561 0.370139944974391 146 8.4 8.00625935141206 0.393740648587936 147 8.4 8.00666356289828 0.393336437101725 148 8.4 7.89503154416106 0.504968455838942 149 8.5 8.25221052380467 0.247789476195335 150 8.5 7.86962852508947 0.630371474910534 151 8.6 7.96744805677735 0.632551943222654 152 8.6 8.39055563142263 0.209444368577366 153 8.5 7.9330080474054 0.566991952594606 154 8.5 7.6800998120174 0.819900187982593 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.00259179499539543 0.00518358999079085 0.997408205004605 10 0.00125427746230030 0.00250855492460060 0.9987457225377 11 0.000180110544067547 0.000360221088135094 0.999819889455932 12 8.31308663298562e-05 0.000166261732659712 0.99991686913367 13 4.15361081653174e-05 8.30722163306349e-05 0.999958463891835 14 7.07031090149108e-06 1.41406218029822e-05 0.999992929689099 15 1.17189380928912e-06 2.34378761857823e-06 0.99999882810619 16 1.85219213973971e-07 3.70438427947942e-07 0.999999814780786 17 1.04347295726033e-07 2.08694591452066e-07 0.999999895652704 18 1.92031223119275e-08 3.84062446238551e-08 0.999999980796878 19 3.7125008034218e-09 7.4250016068436e-09 0.9999999962875 20 4.90645696640869e-09 9.81291393281737e-09 0.999999995093543 21 7.84580934563705e-09 1.56916186912741e-08 0.99999999215419 22 8.0569879272158e-09 1.61139758544316e-08 0.999999991943012 23 6.2279099989468e-09 1.24558199978936e-08 0.99999999377209 24 1.28803882005952e-08 2.57607764011905e-08 0.999999987119612 25 4.38280521773852e-09 8.76561043547704e-09 0.999999995617195 26 2.00302508341381e-09 4.00605016682761e-09 0.999999997996975 27 1.33321340297769e-09 2.66642680595537e-09 0.999999998666787 28 4.37214752488268e-10 8.74429504976536e-10 0.999999999562785 29 2.48037724981095e-10 4.96075449962191e-10 0.999999999751962 30 6.03997072977186e-11 1.20799414595437e-10 0.9999999999396 31 4.99261524333757e-11 9.98523048667513e-11 0.999999999950074 32 2.56860893033364e-11 5.13721786066727e-11 0.999999999974314 33 8.22904525693566e-12 1.64580905138713e-11 0.999999999991771 34 4.63633693678049e-12 9.27267387356099e-12 0.999999999995364 35 1.95960901718554e-12 3.91921803437108e-12 0.99999999999804 36 5.9409644705727e-13 1.18819289411454e-12 0.999999999999406 37 9.99020094216675e-13 1.99804018843335e-12 0.999999999999 38 3.7210637987867e-12 7.4421275975734e-12 0.99999999999628 39 3.98282207141061e-12 7.96564414282121e-12 0.999999999996017 40 3.45162259591303e-12 6.90324519182606e-12 0.999999999996548 41 3.34716916541256e-11 6.69433833082512e-11 0.999999999966528 42 7.66185483482766e-11 1.53237096696553e-10 0.999999999923382 43 1.13121301235413e-10 2.26242602470825e-10 0.999999999886879 44 3.02700665323924e-10 6.05401330647848e-10 0.9999999996973 45 2.17731656021549e-09 4.35463312043099e-09 0.999999997822683 46 5.33584091738647e-09 1.06716818347729e-08 0.99999999466416 47 5.35694425197961e-09 1.07138885039592e-08 0.999999994643056 48 0.000262419290370888 0.000524838580741776 0.99973758070963 49 0.0871925668426005 0.174385133685201 0.9128074331574 50 0.63014355569403 0.739712888611939 0.369856444305969 51 0.947515572412018 0.104968855175965 0.0524844275879824 52 0.98068634963918 0.0386273007216395 0.0193136503608198 53 0.992532616844438 0.0149347663111239 0.00746738315556194 54 0.995193233776472 0.00961353244705536 0.00480676622352768 55 0.997344926182 0.00531014763600163 0.00265507381800081 56 0.997807829878628 0.00438434024274387 0.00219217012137193 57 0.99801310140541 0.00397379718917929 0.00198689859458964 58 0.997982285757783 0.00403542848443343 0.00201771424221671 59 0.997931165187256 0.00413766962548719 0.00206883481274359 60 0.998085424757115 0.00382915048576918 0.00191457524288459 61 0.998194592774977 0.00361081445004523 0.00180540722502261 62 0.99818597377645 0.0036280524470992 0.0018140262235496 63 0.99769030475265 0.00461939049470079 0.00230969524735039 64 0.997684359871484 0.00463128025703131 0.00231564012851566 65 0.998212291047693 0.00357541790461366 0.00178770895230683 66 0.998641279300694 0.00271744139861096 0.00135872069930548 67 0.998664428703312 0.00267114259337593 0.00133557129668797 68 0.998959715550364 0.00208056889927169 0.00104028444963585 69 0.999488975424921 0.00102204915015741 0.000511024575078705 70 0.999647330433334 0.000705339133331364 0.000352669566665682 71 0.99988879252524 0.000222414949518807 0.000111207474759403 72 0.999949832584713 0.000100334830574375 5.01674152871874e-05 73 0.999976982982848 4.60340343031472e-05 2.30170171515736e-05 74 0.999980556865729 3.88862685411357e-05 1.94431342705678e-05 75 0.999977102251428 4.57954971432442e-05 2.28977485716221e-05 76 0.999980296727273 3.94065454542001e-05 1.97032727271000e-05 77 0.999988214630474 2.35707390524654e-05 1.17853695262327e-05 78 0.999992644944831 1.47101103372869e-05 7.35505516864346e-06 79 0.999996580603226 6.8387935468657e-06 3.41939677343285e-06 80 0.999998611340168 2.77731966346435e-06 1.38865983173217e-06 81 0.999999335038913 1.32992217474706e-06 6.64961087373528e-07 82 0.99999952272082 9.54558357970348e-07 4.77279178985174e-07 83 0.999999147709151 1.70458169722680e-06 8.52290848613398e-07 84 0.999998567190049 2.86561990252088e-06 1.43280995126044e-06 85 0.999998220082933 3.55983413465125e-06 1.77991706732563e-06 86 0.999996990210287 6.01957942632581e-06 3.00978971316291e-06 87 0.999995425809954 9.14838009153298e-06 4.57419004576649e-06 88 0.999992386069201 1.52278615969034e-05 7.61393079845172e-06 89 0.999986824152573 2.63516948536068e-05 1.31758474268034e-05 90 0.999978211131097 4.35777378057213e-05 2.17888689028606e-05 91 0.999963075888437 7.38482231264949e-05 3.69241115632474e-05 92 0.999942631023613 0.000114737952774709 5.73689763873543e-05 93 0.999904737165765 0.0001905256684696 9.52628342348e-05 94 0.999849241468782 0.000301517062436205 0.000150758531218103 95 0.99976008203726 0.000479835925481662 0.000239917962740831 96 0.999693594245354 0.000612811509292256 0.000306405754646128 97 0.999558453825388 0.00088309234922443 0.000441546174612215 98 0.999307972313591 0.00138405537281752 0.00069202768640876 99 0.999140942885446 0.00171811422910719 0.000859057114553594 100 0.999576923575504 0.000846152848992909 0.000423076424496454 101 0.999899947966479 0.000200104067042929 0.000100052033521465 102 0.999951062660374 9.787467925159e-05 4.8937339625795e-05 103 0.99996049585946 7.90082810817747e-05 3.95041405408874e-05 104 0.999947085815727 0.000105828368545664 5.29141842728322e-05 105 0.99993552118385 0.000128957632299553 6.44788161497765e-05 106 0.99992565275027 0.000148694499459545 7.43472497297726e-05 107 0.99991414163394 0.00017171673211856 8.585836605928e-05 108 0.999942407441448 0.000115185117104779 5.75925585523896e-05 109 0.99997567762622 4.86447475598347e-05 2.43223737799173e-05 110 0.999984151880246 3.16962395080822e-05 1.58481197540411e-05 111 0.99999561477579 8.77044842192828e-06 4.38522421096414e-06 112 0.999999975371503 4.92569948629919e-08 2.46284974314959e-08 113 0.999999999972871 5.42577139579907e-11 2.71288569789953e-11 114 0.99999999999892 2.16152244610829e-12 1.08076122305415e-12 115 0.999999999999418 1.1644085087537e-12 5.8220425437685e-13 116 0.999999999998756 2.48850019908797e-12 1.24425009954399e-12 117 0.999999999996545 6.91103139035736e-12 3.45551569517868e-12 118 0.9999999999983 3.40153275783666e-12 1.70076637891833e-12 119 0.999999999999376 1.24709834114218e-12 6.23549170571092e-13 120 0.999999999999996 8.17259066743203e-15 4.08629533371602e-15 121 0.999999999999995 1.07871844894429e-14 5.39359224472144e-15 122 0.99999999999998 4.13752972085881e-14 2.06876486042940e-14 123 0.999999999999895 2.09135049988995e-13 1.04567524994497e-13 124 0.999999999999823 3.52928343045464e-13 1.76464171522732e-13 125 0.999999999999963 7.41089789122334e-14 3.70544894561167e-14 126 0.999999999999987 2.68938125772153e-14 1.34469062886076e-14 127 0.999999999999967 6.5061801250305e-14 3.25309006251525e-14 128 0.99999999999983 3.40553117939959e-13 1.70276558969979e-13 129 0.999999999999413 1.17436212431948e-12 5.8718106215974e-13 130 0.999999999997313 5.37456057696809e-12 2.68728028848404e-12 131 0.999999999990996 1.80079081017913e-11 9.00395405089566e-12 132 0.999999999979525 4.09496960923173e-11 2.04748480461586e-11 133 0.999999999879636 2.40727846275965e-10 1.20363923137983e-10 134 0.999999999270794 1.45841208157028e-09 7.2920604078514e-10 135 0.99999999538933 9.22133885116278e-09 4.61066942558139e-09 136 0.999999974718736 5.05625275504592e-08 2.52812637752296e-08 137 0.9999999233371 1.53325800586287e-07 7.66629002931435e-08 138 0.999999964728747 7.0542505930822e-08 3.5271252965411e-08 139 0.99999986048215 2.79035701362843e-07 1.39517850681421e-07 140 0.999998895768323 2.20846335458023e-06 1.10423167729011e-06 141 0.99999552181079 8.95637841953813e-06 4.47818920976906e-06 142 0.9999765453025 4.69093950011839e-05 2.34546975005920e-05 143 0.999885167410537 0.000229665178925959 0.000114832589462979 144 0.999872755737044 0.000254488525912464 0.000127244262956232 145 0.999295746517123 0.00140850696575407 0.000704253482877036 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 132 0.963503649635037 NOK 5% type I error level 134 0.978102189781022 NOK 10% type I error level 134 0.978102189781022 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/10z92e1292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/10z92e1292864413.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/1s8n21292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/1s8n21292864413.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/2s8n21292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/2s8n21292864413.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/33hnn1292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/33hnn1292864413.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/43hnn1292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/43hnn1292864413.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/53hnn1292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/53hnn1292864413.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/6w84q1292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/6w84q1292864413.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/770lt1292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/770lt1292864413.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/870lt1292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/870lt1292864413.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/970lt1292864413.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292867445hx46p4l8vbmknp6/970lt1292864413.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') }

Copyright

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

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by