workshop 7 tutorial verbetering maand

*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: Thu, 02 Dec 2010 23:39:29 +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/03/t1291333068432yg75ib50etzw.htm/, Retrieved Fri, 03 Dec 2010 00:37:48 +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/03/t1291333068432yg75ib50etzw.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:

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2 9 2 1 4 3 3 3 3 3 9 2 3 4 3 3 4 3 3 9 4 2 3 4 4 4 3 3 9 3 3 2 3 3 3 3 3 9 3 2 3 3 2 2 2 3 9 1 2 4 3 3 2 2 2 9 4 4 5 4 4 5 4 3 9 2 2 4 2 2 3 2 3 9 2 2 4 4 3 2 3 4 9 2 2 2 2 2 2 2 3 9 4 2 2 3 2 4 4 3 9 3 3 4 3 2 3 3 2 9 3 2 4 4 4 3 3 3 9 2 2 5 3 4 2 3 9 3 3 5 3 3 4 3 3 9 2 2 4 3 2 2 2 3 9 3 3 3 3 3 3 3 3 9 3 3 4 4 4 4 3 2 9 2 2 4 2 2 2 2 4 9 2 2 2 3 2 2 3 3 9 1 1 4 3 3 3 2 2 9 4 3 4 4 4 4 3 3 9 3 2 4 3 3 2 3 3 9 2 2 4 3 3 2 2 2 9 3 3 4 3 4 3 3 2 9 3 3 4 4 4 4 3 4 9 4 3 4 4 2 4 4 2 9 3 2 3 4 3 3 3 3 9 3 3 3 4 3 3 3 2 9 2 2 4 4 4 4 2 4 9 2 2 3 2 4 2 2 3 9 4 3 4 3 3 3 4 2 9 4 3 4 4 3 4 4 3 9 2 2 4 3 2 3 3 3 9 2 2 4 3 2 2 3 1 9 3 3 4 4 4 4 4 3 9 3 3 4 3 3 4 3 3 9 3 2 3 2 2 2 2 3 9 3 3 4 3 3 3 3 2 9 4 3 4 4 4 4 4 3 9 3 3 4 3 4 4 3 9 1 2 3 2 2 3 3 5 9 2 1 5 2 1 4 2 4 9 2 2 4 3 2 3 2 3 9 3 3 4 3 2 3 3 2 9 4 3 4 4 4 3 4 2 9 3 2 4 4 4 3 4 3 9 2 2 5 2 2 2 2 4 9 2 3 4 3 3 4 3 2 9 3 3 4 4 3 4 3 3 9 3 3 4 3 2 4 3 4 10 4 2 3 3 1 2 2 3 10 3 2 4 4 3 3 4 4 10 2 2 4 3 2 3 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 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 Y[t] = + 9.44285459461262 -0.474922911650721month[t] -0.151181636688754X1t[t] + 1.09640691366409X2t[t] + 0.193188674870400X3t[t] -0.418873384753806X4t[t] -0.499506180003605X5t[t] -0.0597106309863434X6t[t] -0.595998253799732X7t[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) 9.44285459461262 0.897609 10.52 0 0 month -0.474922911650721 0.067022 -7.0861 0 0 X1t -0.151181636688754 0.140581 -1.0754 0.283954 0.141977 X2t 1.09640691366409 0.153405 7.1471 0 0 X3t 0.193188674870400 0.127827 1.5113 0.132853 0.066426 X4t -0.418873384753806 0.042436 -9.8707 0 0 X5t -0.499506180003605 0.047291 -10.5624 0 0 X6t -0.0597106309863434 0.111945 -0.5334 0.594568 0.297284 X7t -0.595998253799732 0.051433 -11.588 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.832845398414658 R-squared 0.693631457660471 Adjusted R-squared 0.67695833971002 F-TEST (value) 41.6017843646172 F-TEST (DF numerator) 8 F-TEST (DF denominator) 147 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.33591350560788 Sum Squared Residuals 262.345739486433 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 2.01308138089387 -0.0130813808938687 2 3 4.14618457723569 -1.14618457723569 3 3 1.63584615056628 1.36415384943372 4 3 3.66833622179248 -0.668336221792475 5 3 3.92033304778847 -0.92033304778847 6 3 3.91637881603277 -0.916378816032772 7 2 3.55932844284918 -1.55932844284918 8 3 4.62386611311509 -1.62386611311509 9 3 2.75032554079048 0.249674459209521 10 4 4.29719939436063 -0.297199394360632 11 3 2.26454496665717 0.735455033342833 12 3 4.55421975153688 -1.55421975153688 13 2 2.03992709311178 -0.0399270931117794 14 3 2.86288142041108 0.137118579588917 15 9 8.40437001389177 0.595629986108233 16 9 9.41166402431451 -0.411664024314514 17 9 6.7110623665672 2.2889376334328 18 9 7.678276644144 1.32172335585599 19 9 8.62247709564438 0.377522904355618 20 9 7.159139566 1.84086043400000 21 9 9.7153872616963 -0.715387261696308 22 9 6.60735547869355 2.39264452130645 23 9 8.45815709692364 0.541842903076357 24 9 9.58878889336044 -0.58878889336044 25 9 7.98459414927721 1.01540585072279 26 9 6.48628013654454 2.51371986345546 27 9 7.98138987101455 1.01861012898545 28 9 7.05543267812635 1.94456732187365 29 9 7.50024929523733 1.49975070476267 30 9 7.17209531587036 1.82790468412964 31 9 7.28432166627242 1.71567833372759 32 9 7.86883399139395 1.13116600860605 33 9 6.96651823246102 2.03348176753898 34 9 8.85244721332457 0.147552786675434 35 9 10.5439499009276 -1.54394990092764 36 9 7.02256775935793 1.97743224064207 37 9 7.30796310022768 1.69203689977232 38 9 7.6471455241293 1.35285447587069 39 9 8.40346753403102 0.596532465968982 40 9 6.54764484770721 2.45235515229279 41 9 3.31310019267548 5.68689980732452 42 1 2.20097890491235 -1.20097890491235 43 2 2.32069329455131 -0.320693294551308 44 2 3.76513162386398 -1.76513162386398 45 3 2.85041316319599 0.149586836804005 46 4 3.83369124659728 0.166308753402724 47 3 4.24890352726165 -1.24890352726165 48 2 2.8767058272786 -0.8767058272786 49 2 2.62472845331259 -0.624728453312588 50 3 3.66142473599033 -0.661424735990331 51 3 1.71612026266977 1.28387973733023 52 4 3.54599971663640 0.454000283363596 53 3 3.40000596760518 -0.400005967605177 54 2 2.66962719006064 -0.669627190060639 55 2 1.93039381145836 0.06960618854164 56 2 2.32818232229398 -0.328182322293975 57 2 3.68577019223034 -1.68577019223034 58 3 2.85057998275980 0.149420017240196 59 1 4.17077705769191 -3.17077705769191 60 5 2.69939834607105 2.30060165392895 61 2 3.51057823783091 -1.51057823783091 62 3 3.258615157061 -0.258615157060998 63 4 3.26689680747654 0.733103192523465 64 4 3.88471970540047 0.115280294599528 65 2 2.15269724022827 -0.152697240228272 66 3 2.55649835979783 0.443501640202166 67 3 2.88739913328392 0.112600866716077 68 3 3.42203267592099 -0.422032675920988 69 3 1.60299143240696 1.39700856759304 70 1 3.60024263698929 -2.60024263698929 71 3 2.28880661173278 0.71119338826722 72 3 1.88472566918728 1.11527433081272 73 3 4.17011504627022 -1.17011504627022 74 4 3.73015678759822 0.269843212401775 75 3 2.38789295328032 0.612107046719681 76 4 2.86281586493104 1.13718413506896 77 3 2.71163422824229 0.288365771757715 78 3 2.99920505941148 0.000794940588517722 79 2 2.98113258285137 -0.98113258285137 80 1 2.29475006219414 -1.29475006219414 81 2 7.11633540462837 -5.11633540462837 82 3 3.63339249129577 -0.633392491295771 83 4 3.32565871809911 0.674341281900886 84 3 3.17663065659329 -0.176630656593286 85 4 3.9665557086469 0.0334442913531027 86 5 3.87022799132804 1.12977200867196 87 2 2.67210340849596 -0.672103408495965 88 2 3.59916760852306 -1.59916760852306 89 4 3.92165697189885 0.0783430281011534 90 4 3.21451910654197 0.785480893458035 91 3 3.26594808711277 -0.265948087112771 92 4 4.38835453719319 -0.388354537193193 93 4 4.29688353149078 -0.296883531490783 94 4 3.31623677570995 0.683763224290046 95 4 3.87022799132804 0.129772008671959 96 4 4.74384189367512 -0.743841893675125 97 2 6.54252996107965 -4.54252996107965 98 4 4.18738370691386 -0.187383706913857 99 4 3.98718474524408 0.0128152547559157 100 4 4.67008877397351 -0.670088773973514 101 4 4.23717290050444 -0.237172900504440 102 4 4.1597443835173 -0.159744383517297 103 5 5.82038917626505 -0.820389176265048 104 4 4.74258998208894 -0.742589982088943 105 4 2.8936695301464 1.10633046985360 106 4 4.66883686238733 -0.668836862387332 107 3 3.65521713541998 -0.655217135419975 108 4 4.71084390056898 -0.710843900568978 109 4 4.50575448205668 -0.505754482056675 110 4 4.49024960083001 -0.490249600830005 111 3 3.60318376824892 -0.603183768248916 112 3 4.27935733315491 -1.27935733315491 113 3 3.03176878280207 -0.0317687828020683 114 3 2.96055792994143 0.0394420700585694 115 4 3.30386140516256 0.696138594837436 116 3 2.36365719628095 0.636342803719051 117 3 2.36365719628095 0.636342803719051 118 4 3.12031434471199 0.87968565528801 119 3 3.39779691892162 -0.397796918921617 120 3 3.74216723048077 -0.74216723048077 121 3 3.53127496280567 -0.531274962805673 122 3 3.46043299370045 -0.460432993700451 123 3 2.74315487047356 0.256845129526440 124 3 3.46006410994504 -0.460064109945035 125 4 3.05635205115495 0.943647948845047 126 3 1.18295638327763 1.81704361672237 127 4 3.65325278481544 0.346747215184564 128 3 4.27845485329416 -1.27845485329416 129 4 6.35633489063803 -2.35633489063803 130 1 1.48994020298125 -0.489940202981251 131 4 3.46006410994504 0.539935890054964 132 3 3.26724431883005 -0.267244318830050 133 4 2.46370298006517 1.53629701993483 134 4 2.41028478078870 1.58971521921130 135 4 4.36365123249414 -0.363651232494137 136 3 3.03176878280207 -0.0317687828020683 137 3 4.46536890166213 -1.46536890166213 138 3 2.32627070442541 0.673729295574589 139 4 3.64085008308039 0.359149916919610 140 3 5.03176281901526 -2.03176281901526 141 3 2.51483883296970 0.485161167030297 142 3 3.39779691892162 -0.397796918921617 143 4 3.30925135701170 0.690748642988304 144 2 3.27186486515616 -1.27186486515616 145 3 3.18295041949082 -0.182950419490822 146 3 4.82549109766627 -1.82549109766627 147 3 2.67549772760101 0.324502272398989 148 3 2.83395956160556 0.166040438394438 149 3 2.90084729895509 0.0991527010449129 150 4 2.05733969114774 1.94266030885226 151 3 2.49025556461682 0.509744435383182 152 4 4.80846784960512 -0.808467849605116 153 3 3.15746467127719 -0.157464671277189 154 4 2.55684587115135 1.44315412884865 155 3 5.36768466059506 -2.36768466059506 156 3 2.77997402099768 0.220025979002319 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.0533434299160143 0.106686859832029 0.946656570083986 13 0.0174393669981379 0.0348787339962757 0.982560633001862 14 0.0248581711976915 0.0497163423953829 0.975141828802308 15 0.00872714204048026 0.0174542840809605 0.99127285795952 16 0.00556378137494784 0.0111275627498957 0.994436218625052 17 0.00626221242530834 0.0125244248506167 0.993737787574692 18 0.00277556308030608 0.00555112616061216 0.997224436919694 19 0.00122879675797283 0.00245759351594566 0.998771203242027 20 0.000464089824637281 0.000928179649274563 0.999535910175363 21 0.00204152125563125 0.0040830425112625 0.997958478744369 22 0.0103638980219250 0.0207277960438499 0.989636101978075 23 0.00863567239098022 0.0172713447819604 0.99136432760902 24 0.00610923502906098 0.0122184700581220 0.993890764970939 25 0.0033820739906698 0.0067641479813396 0.99661792600933 26 0.00305738991361626 0.00611477982723251 0.996942610086384 27 0.00238412181344104 0.00476824362688208 0.997615878186559 28 0.00205504502186214 0.00411009004372428 0.997944954978138 29 0.00117677098300274 0.00235354196600548 0.998823229016997 30 0.000822364393924212 0.00164472878784842 0.999177635606076 31 0.000549279215354025 0.00109855843070805 0.999450720784646 32 0.000508798498370451 0.00101759699674090 0.99949120150163 33 0.000613739609654513 0.00122747921930903 0.999386260390346 34 0.000582967874704328 0.00116593574940866 0.999417032125296 35 0.000764225292638797 0.00152845058527759 0.999235774707361 36 0.000790462486340808 0.00158092497268162 0.99920953751366 37 0.000862193955874583 0.00172438791174917 0.999137806044125 38 0.00136913588264356 0.00273827176528712 0.998630864117356 39 0.00307587698433512 0.00615175396867024 0.996924123015665 40 0.0326589731464425 0.065317946292885 0.967341026853557 41 0.400868166301473 0.801736332602946 0.599131833698527 42 0.999753808634828 0.000492382730344592 0.000246191365172296 43 0.99998315170967 3.36965806609238e-05 1.68482903304619e-05 44 0.9999960991938 7.80161240151947e-06 3.90080620075973e-06 45 0.999994805592554 1.03888148924719e-05 5.19440744623593e-06 46 0.999993507266213 1.29854675744658e-05 6.4927337872329e-06 47 0.999995986904238 8.02619152315625e-06 4.01309576157812e-06 48 0.999992900482803 1.41990343938368e-05 7.09951719691839e-06 49 0.999993020461136 1.39590777280158e-05 6.97953886400791e-06 50 0.999988645151132 2.2709697736734e-05 1.1354848868367e-05 51 0.999984473258057 3.10534838870089e-05 1.55267419435045e-05 52 0.999993619551984 1.27608960323095e-05 6.38044801615475e-06 53 0.999991488109207 1.70237815854708e-05 8.5118907927354e-06 54 0.999989629610223 2.07407795542818e-05 1.03703897771409e-05 55 0.999989439851155 2.11202976903845e-05 1.05601488451922e-05 56 0.999985864393079 2.82712138424194e-05 1.41356069212097e-05 57 0.999982432179225 3.51356415501308e-05 1.75678207750654e-05 58 0.999971621503453 5.67569930943644e-05 2.83784965471822e-05 59 0.99998952984947 2.09403010613926e-05 1.04701505306963e-05 60 0.999998449187676 3.10162464780139e-06 1.55081232390069e-06 61 0.999998446489243 3.10702151421813e-06 1.55351075710907e-06 62 0.999997619103905 4.76179219081849e-06 2.38089609540924e-06 63 0.999998512325386 2.97534922826259e-06 1.48767461413130e-06 64 0.99999835608567 3.28782865935373e-06 1.64391432967686e-06 65 0.999997859832694 4.28033461108889e-06 2.14016730554445e-06 66 0.99999618633585 7.62732829980064e-06 3.81366414990032e-06 67 0.999996570574322 6.8588513560866e-06 3.4294256780433e-06 68 0.999995015523695 9.9689526109255e-06 4.98447630546275e-06 69 0.99999195355494 1.60928901209039e-05 8.04644506045194e-06 70 0.999996432633568 7.13473286499744e-06 3.56736643249872e-06 71 0.999994149590905 1.1700818188996e-05 5.850409094498e-06 72 0.999990138724358 1.97225512838829e-05 9.86127564194144e-06 73 0.999985657698884 2.86846022310108e-05 1.43423011155054e-05 74 0.999991726721876 1.65465562483211e-05 8.27327812416055e-06 75 0.999988814385036 2.23712299277285e-05 1.11856149638642e-05 76 0.999995607429226 8.78514154753947e-06 4.39257077376973e-06 77 0.999993359064332 1.32818713351153e-05 6.64093566755764e-06 78 0.999995008106854 9.9837862921105e-06 4.99189314605525e-06 79 0.999996449281408 7.1014371835832e-06 3.5507185917916e-06 80 0.999998195707556 3.60858488824148e-06 1.80429244412074e-06 81 0.999999860651436 2.78697127330956e-07 1.39348563665478e-07 82 0.999999998941967 2.11606596973921e-09 1.05803298486961e-09 83 0.999999999301808 1.39638399402073e-09 6.98191997010366e-10 84 0.999999999493753 1.01249390819751e-09 5.06246954098756e-10 85 0.999999999056151 1.88769707608614e-09 9.43848538043069e-10 86 0.999999999543497 9.1300640282551e-10 4.56503201412755e-10 87 0.999999999874085 2.51829922612369e-10 1.25914961306184e-10 88 0.999999999994942 1.01153259957115e-11 5.05766299785576e-12 89 0.999999999990631 1.8737570422458e-11 9.368785211229e-12 90 0.999999999979936 4.0128189918622e-11 2.0064094959311e-11 91 0.999999999986554 2.6891733364626e-11 1.3445866682313e-11 92 0.999999999966082 6.783644897242e-11 3.391822448621e-11 93 0.99999999992545 1.49101845592559e-10 7.45509227962793e-11 94 0.999999999818579 3.62842767286198e-10 1.81421383643099e-10 95 0.999999999588215 8.23570539624442e-10 4.11785269812221e-10 96 0.999999999331623 1.33675322488615e-09 6.68376612443075e-10 97 0.999999999999168 1.66334659404346e-12 8.31673297021728e-13 98 0.999999999997787 4.4265896809772e-12 2.2132948404886e-12 99 0.999999999994571 1.08570659679548e-11 5.42853298397742e-12 100 0.999999999985275 2.94505112022479e-11 1.47252556011239e-11 101 0.999999999964649 7.070242064539e-11 3.5351210322695e-11 102 0.999999999908915 1.82170985746861e-10 9.10854928734304e-11 103 0.99999999984293 3.14139099820627e-10 1.57069549910313e-10 104 0.999999999762926 4.74147656508791e-10 2.37073828254395e-10 105 0.999999999808116 3.83767621414964e-10 1.91883810707482e-10 106 0.999999999552617 8.94765236496539e-10 4.47382618248269e-10 107 0.999999999476518 1.04696378805167e-09 5.23481894025837e-10 108 0.999999999078911 1.84217760803723e-09 9.21088804018616e-10 109 0.999999997848846 4.30230815310365e-09 2.15115407655182e-09 110 0.9999999997312 5.37600013387153e-10 2.68800006693576e-10 111 0.999999999427645 1.14471035885304e-09 5.72355179426518e-10 112 0.999999998686935 2.62613036374892e-09 1.31306518187446e-09 113 0.999999997237937 5.52412592831873e-09 2.76206296415936e-09 114 0.999999994094088 1.18118235505390e-08 5.90591177526948e-09 115 0.999999987578242 2.48435154251054e-08 1.24217577125527e-08 116 0.99999997517482 4.96503611386481e-08 2.48251805693241e-08 117 0.999999952767767 9.44644669506648e-08 4.72322334753324e-08 118 0.99999994179043 1.16419141759578e-07 5.82095708797889e-08 119 0.99999987442466 2.5115068053868e-07 1.2557534026934e-07 120 0.999999694114435 6.11771130662753e-07 3.05885565331376e-07 121 0.999999531916808 9.36166383230297e-07 4.68083191615148e-07 122 0.999998895460615 2.20907877075577e-06 1.10453938537788e-06 123 0.999997565108253 4.86978349488229e-06 2.43489174744114e-06 124 0.999995929383145 8.141233710448e-06 4.070616855224e-06 125 0.999990535683338 1.89286333234370e-05 9.46431666171852e-06 126 0.999984619382894 3.07612342119976e-05 1.53806171059988e-05 127 0.999968524950732 6.29500985360561e-05 3.14750492680280e-05 128 0.99993888665044 0.000122226699118716 6.1113349559358e-05 129 0.999895645324198 0.000208709351605083 0.000104354675802541 130 0.999953066955706 9.3866088587614e-05 4.6933044293807e-05 131 0.999920931048432 0.000158137903136749 7.90689515683743e-05 132 0.999817316287287 0.00036536742542599 0.000182683712712995 133 0.999721044929532 0.000557910140935694 0.000278955070467847 134 0.999719368840776 0.000561262318448683 0.000280631159224341 135 0.999732828894965 0.000534342210070815 0.000267171105035408 136 0.999408266283413 0.00118346743317365 0.000591733716586824 137 0.998973195512265 0.00205360897546997 0.00102680448773499 138 0.998692865103773 0.00261426979245457 0.00130713489622729 139 0.997592313380887 0.00481537323822632 0.00240768661911316 140 0.994214146504698 0.0115717069906050 0.00578585349530252 141 0.98750111520878 0.0249977695824388 0.0124988847912194 142 0.968316519242613 0.0633669615147736 0.0316834807573868 143 0.924468236426122 0.151063527147755 0.0755317635738777 144 0.880028360813349 0.239943278373303 0.119971639186651 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 117 0.8796992481203 NOK 5% type I error level 127 0.954887218045113 NOK 10% type I error level 129 0.969924812030075 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/10b3cb1291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/10b3cb1291333157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/142fh1291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/142fh1291333157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/242fh1291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/242fh1291333157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/3wbe21291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/3wbe21291333157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/4wbe21291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/4wbe21291333157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/5wbe21291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/5wbe21291333157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/67kvn1291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/67kvn1291333157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/7icvq1291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/7icvq1291333157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/8icvq1291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/8icvq1291333157.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/9icvq1291333157.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333068432yg75ib50etzw/9icvq1291333157.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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