CaseStatistiek - Multipele Regressie met maandelijkse dummy’s

*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: Wed, 30 Dec 2009 10:58:49 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/30/t1262197381g1i3qtfju05so8z.htm/, Retrieved Wed, 30 Dec 2009 19:23:14 +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/2009/Dec/30/t1262197381g1i3qtfju05so8z.htm/}, year = {2009}, } @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 = {2009}, 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:

CaseStatistiek - Multipele Regressie met maandelijkse dummy’s

Dataseries X:

» Textbox « » Textfile « » CSV «

15 2.1 14.4 2.1 13.5 2.6 12.8 2.6 12.3 2.7 12.2 2.5 14.5 2.4 17.2 1.9 18 2.2 18.1 1.9 18 2 18.3 2.2 18.7 2.5 18.6 2.5 18.3 2.7 17.9 2.6 17.4 2.3 17.4 2 20.1 2.3 23.2 2.9 24.2 2.5 24.2 2.5 23.9 2.3 23.8 2.5 23.8 2.3 23.3 2.4 22.4 2.2 21.5 2.4 20.5 2.6 19.9 2.8 22 2.8 24.9 2.5 25.7 2.5 25.3 2.2 24.4 2.1 23.8 1.9 23.5 1.9 23 1.7 22.2 1.7 21.4 1.6 20.3 1.4 19.5 1.1 21.7 0.8 24.7 0.9 25.3 1 24.9 1 24.1 1.1 23.4 1.3 23.1 1.4 22.4 1.4 21.3 1.6 20.3 2 19.3 2.1 18.7 1.9 21 1.5 24 1.2 24.8 1.5 24.2 2.2 23.3 2.1 22.7 2.1 22.3 2.1 21.8 1.9 21.2 1.3 20.5 1.1 19.7 1.4 19.2 1.6 21.2 1.9 23.9 1.7 24.8 1.6 24.2 1.2 23 1.3 22.2 0.9 21.8 0.5 21.2 0.8 20.5 1 19.7 1.3 19 1.3 18.4 1.2 20.7 1.2 24.5 1 26 0.8 25.2 0.7 24.1 0.6 23.7 0.7 23.5 1 23.1 1 22.7 1.3 22.5 1.1 21.7 0.8 20.5 0.7 21.9 0.7 22.9 0.9 21.5 1.3 19 1.4 17 1.6 16.1 2.1 15.9 0.3 15.7 2.1 15.1 2.5 14.8 2.3 14.3 2.4 14.5 3 18.9 1.7 21.6 3.5 20.4 4 17.9 3.7 15.7 3.7 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y(Werkloosheid)[t] = + 22.0043815495545 -0.859314470624652`X(inflatie)`[t] -0.454235802426604M1[t] -0.664311972357226M2[t] -1.23097863902389M3[t] -1.65476403379473M4[t] -2.41986752791278M5[t] -2.63661864621485M6[t] + 0.546461332212272M7[t] + 2.40539658777127M8[t] + 2.41251531587544M9[t] + 1.39576419757337M10[t] + 0.353768738408089M11[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) 22.0043815495545 0.716941 30.692 0 0 `X(inflatie)` -0.859314470624652 0.168921 -5.0871 1e-06 0 M1 -0.454235802426604 0.879783 -0.5163 0.60621 0.303105 M2 -0.664311972357226 0.87954 -0.7553 0.450956 0.225478 M3 -1.23097863902389 0.87954 -1.3996 0.163183 0.081592 M4 -1.65476403379473 0.879537 -1.8814 0.061363 0.030681 M5 -2.41986752791278 0.87954 -2.7513 0.006479 0.003239 M6 -2.63661864621485 0.879579 -2.9976 0.003064 0.001532 M7 0.546461332212272 0.879993 0.621 0.535314 0.267657 M8 2.40539658777127 0.879624 2.7346 0.006804 0.003402 M9 2.41251531587544 0.879652 2.7426 0.006646 0.003323 M10 1.39576419757337 0.879783 1.5865 0.114201 0.0571 M11 0.353768738408089 0.892014 0.3966 0.692087 0.346043 Multiple Linear Regression - Regression Statistics Multiple R 0.597731011028019 R-squared 0.357282361544577 Adjusted R-squared 0.318911159248731 F-TEST (value) 9.31121101679044 F-TEST (DF numerator) 12 F-TEST (DF denominator) 201 p-value 3.19744231092045e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.60064391239185 Sum Squared Residuals 1359.43310057122 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 19.7455853588155 -4.74558535881555 2 14.4 19.5355091888855 -5.13550918888546 3 13.5 18.5391852869064 -5.03918528690645 4 12.8 18.1153998921356 -5.31539989213562 5 12.3 17.2643649509551 -4.9643649509551 6 12.2 17.2194767267780 -5.01947672677796 7 14.5 20.4884881522676 -5.98848815226756 8 17.2 22.7770806431389 -5.57708064313887 9 18 22.5264050300556 -4.52640503005565 10 18.1 21.7674482529410 -3.66744825294097 11 18 20.6395213467132 -2.63952134671324 12 18.3 20.1138897141802 -1.81388971418021 13 18.7 19.4018595705662 -0.701859570566215 14 18.6 19.1917834006356 -0.591783400635587 15 18.3 18.453253839844 -0.153253839843991 16 17.9 18.1153998921356 -0.215399892135621 17 17.4 17.6080907392050 -0.208090739204965 18 17.4 17.6491339620903 -0.249133962090290 19 20.1 20.57441959933 -0.474419599330017 20 23.2 21.9177661725142 1.28223382748578 21 24.2 22.2686106888683 1.93138931113175 22 24.2 21.2518595705662 2.94814042943382 23 23.9 20.3817270055258 3.51827299447416 24 23.8 19.8560953729928 3.94390462700719 25 23.8 19.5737224646911 4.22627753530886 26 23.3 19.2777148476981 4.02228515230195 27 22.4 18.8829110751563 3.51708892484368 28 21.5 18.2872627862605 3.21273721373945 29 20.5 17.3502963980176 3.14970360198243 30 19.9 16.9616823855906 2.93831761440943 31 22 20.1447623640177 1.85523763598231 32 24.9 22.2614919607641 2.63850803923592 33 25.7 22.2686106888683 3.43138931113175 34 25.3 21.5096539117536 3.79034608824642 35 24.4 20.5535898996508 3.84641010034923 36 23.8 20.3716840553676 3.42831594463240 37 23.5 19.917448252941 3.582551747059 38 23 19.8792349771353 3.12076502286469 39 22.2 19.3125683104686 2.88743168953136 40 21.4 18.9747143627603 2.42528563723973 41 20.3 18.3814737627672 1.91852623723285 42 19.5 18.4225169856525 1.07748301434753 43 21.7 21.863391305267 -0.163391305266996 44 24.7 23.6363951137635 1.06360488623647 45 25.3 23.5575823948052 1.74241760519477 46 24.9 22.5408312765032 2.35916872349684 47 24.1 21.4129043702754 2.68709562972459 48 23.4 20.8872727377424 2.5127272622576 49 23.1 20.3471054882533 2.75289451174667 50 22.4 20.1370293183227 2.26297068167729 51 21.3 19.3984997575311 1.90150024246889 52 20.3 18.6309885745104 1.66901142548959 53 19.3 17.7799536333299 1.52004636667011 54 18.7 17.7350654091528 0.964934590847246 55 21 21.2618711758297 -0.261871175829739 56 24 23.3786007725761 0.621399227423869 57 24.8 23.1279251594929 1.67207484050710 58 24.2 21.5096539117536 2.69034608824642 59 23.3 20.5535898996508 2.74641010034924 60 22.7 20.1998211612427 2.50017883875732 61 22.3 19.7455853588161 2.55441464118393 62 21.8 19.7073720830104 2.09262791698962 63 21.2 19.6562940987185 1.54370590128150 64 20.5 19.4043715980726 1.09562840192740 65 19.7 18.3814737627672 1.31852623723285 66 19.2 17.9928597503401 1.20714024965985 67 21.2 20.9181453875799 0.281854612420120 68 23.9 22.9489435372638 0.951056462736195 69 24.8 23.0419937124304 1.75800628756956 70 24.2 22.3689683823782 1.83103161762177 71 23 21.2410414761505 1.75895852384951 72 22.2 21.2309985259923 0.969001474007742 73 21.8 21.1204885118155 0.679511488184485 74 21.2 20.6526180006975 0.547381999302503 75 20.5 19.9140884399059 0.585911560094101 76 19.7 19.2325087039477 0.467491296052333 77 19 18.4674052098296 0.532594790170386 78 18.4 18.33658553859 0.0634144614099895 79 20.7 21.5196655170171 -0.819665517017136 80 24.5 23.5504636667011 0.94953633329894 81 26 23.7294452889302 2.27055471106984 82 25.2 22.7986256176906 2.40137438230944 83 24.1 21.8425616055877 2.25743839441226 84 23.7 21.4028614201172 2.29713857988281 85 23.5 20.6908312765032 2.80916872349681 86 23.1 20.4807551065726 2.61924489342744 87 22.7 19.6562940987185 3.04370590128150 88 22.5 19.4043715980726 3.0956284019274 89 21.7 18.8970624451419 2.80293755485806 90 20.5 18.7662427739023 1.73375722609766 91 21.9 21.9493227523295 -0.0493227523294619 92 22.9 23.6363951137635 -0.736395113763527 93 21.5 23.2997880536178 -1.79978805361783 94 19 22.1971054882533 -3.1971054882533 95 17 20.9832471349631 -3.98324713496309 96 16.1 20.1998211612427 -4.09982116124267 97 15.9 21.2923514059404 -5.39235140594045 98 15.7 19.5355091888854 -3.83550918888545 99 15.1 18.6251167339689 -3.52511673396892 100 14.8 18.373194233323 -3.57319423332301 101 14.3 17.5221592921425 -3.2221592921425 102 14.5 16.7898194914656 -2.28981949146564 103 18.9 21.0900082817048 -2.19000828170481 104 21.6 21.4021774901394 0.19782250986057 105 20.4 20.9796389829313 -0.579638982931277 106 17.9 20.2206822058166 -2.3206822058166 107 15.7 19.1786867466513 -3.47868674665132 108 14.5 19.4264381376805 -4.92643813768049 109 14 19.2299966764413 -5.22999667644128 110 13.9 19.1917834006356 -5.29178340063559 111 14.4 18.8829110751563 -4.48291107515632 112 15.8 17.8576055509482 -2.05760555094822 113 15.6 16.9206391627052 -1.32063916270524 114 14.7 16.7898194914656 -2.08981949146564 115 16.7 20.1447623640177 -3.44476236401769 116 17.9 22.2614919607641 -4.36149196076408 117 18.7 22.7841993712430 -4.08419937124304 118 20.1 21.767448252941 -1.66744825294097 119 19.5 20.8113842408382 -1.31138424083816 120 19.4 20.2857526083051 -0.885752608305142 121 18.6 19.3159281235037 -0.715928123503746 122 17.8 19.1917834006356 -1.39178340063559 123 17.1 18.6251167339689 -1.52511673396892 124 16.5 18.9747143627603 -2.47471436276027 125 15.5 18.3814737627671 -2.88147376276715 126 14.9 18.6803113268399 -3.78031132683987 127 18.6 21.6055969640796 -3.0055969640796 128 19.1 23.2926693255137 -4.19266932551366 129 18.8 23.3857195006803 -4.5857195006803 130 18.2 22.2830369353158 -4.08303693531577 131 18 21.4129043702754 -3.41290437027542 132 19 20.8872727377424 -1.88727273774240 133 20.7 20.5189683823783 0.18103161762174 134 21.2 19.9651664241978 1.23483357580222 135 20.7 19.3125683104686 1.38743168953136 136 19.6 19.0606458098227 0.539354190177265 137 18.6 18.8111309980795 -0.211130998079474 138 18.7 18.0787911974026 0.621208802597385 139 23.8 21.3478026228922 2.45219737710780 140 24.9 23.0348749843263 1.86512501567373 141 24.8 22.9560622653680 1.84393773463203 142 23.8 22.1971054882533 1.6028945117467 143 22.3 20.8113842408382 1.48861575916184 144 21.7 20.5435469494925 1.15645305050746 145 20.7 20.3471054882533 0.352894511746670 146 19.7 20.3088922124476 -0.608892212447636 147 18.4 19.9140884399059 -1.5140884399059 148 17.4 18.8887829156978 -1.48878291569781 149 17 17.5221592921425 -0.522159292142498 150 18 17.6491339620903 0.350866037909712 151 23.8 20.7462824934549 3.05371750654505 152 25.5 22.6911491960764 2.80885080392359 153 25.6 22.8701308183055 2.72986918169449 154 23.7 21.0799966764413 2.62000332355875 155 22 20.3817270055258 1.61827299447416 156 21.3 20.3716840553676 0.928315944632394 157 20.7 19.8315168058785 0.868483194121461 158 20.4 19.3636462947605 1.03635370523948 159 20.3 18.3673223927815 1.93267760721847 160 20.4 18.2872627862605 2.11273721373945 161 19.8 17.6080907392050 2.19190926079504 162 19.5 17.0476138326530 2.45238616734697 163 23.1 20.2306938110802 2.86930618891984 164 23.5 21.9177661725142 1.58223382748578 165 23.5 21.8389534535559 1.66104654644407 166 22.9 21.5096539117536 1.39034608824642 167 21.9 20.3817270055258 1.51827299447416 168 21.5 19.5983010318054 1.90169896819458 169 20.5 19.1440652293788 1.35593477062118 170 20.2 18.9339890594482 1.26601094055181 171 19.4 18.8829110751563 0.517088924843682 172 19.2 18.1153998921356 1.08460010786438 173 18.8 17.1784335038926 1.62156649610736 174 18.8 17.2194767267780 1.58052327322204 175 22.6 20.4884881522676 2.11151184773245 176 23.3 22.4333548548890 0.866645145110988 177 23 22.7841993712430 0.215800628756956 178 21.4 21.9393111470659 -0.539311147065905 179 19.9 20.6395213467132 -0.739521346713232 180 18.8 20.1998211612427 -1.39982116124267 181 18.6 20.0893111470659 -1.48931114706593 182 18.4 19.7933035300728 -1.39330353007285 183 18.6 19.2266368634062 -0.626636863406177 184 19.9 18.8028514686353 1.09714853136466 185 19.2 18.4674052098296 0.732594790170385 186 18.4 18.2506540915275 0.149345908472455 187 21.1 21.4337340699547 -0.333734069954668 188 20.5 23.3786007725761 -2.87860077257613 189 19.1 23.2138566065554 -4.11385660655537 190 18.1 21.5096539117536 -3.40965391175358 191 17 19.8661383231510 -2.86613832315104 192 17.1 19.3405066906180 -2.24050669061802 193 17.4 18.5425450999416 -1.14254509994156 194 16.8 18.2465374829485 -1.44653748294847 195 15.3 16.9924192397821 -1.69241923978208 196 14.3 16.8264281861986 -2.52642818619864 197 13.4 15.2020102214559 -1.80201022145594 198 15.3 14.3837389737166 0.916261026283388 199 22.1 17.4808875050813 4.61911249491873 200 23.7 19.7694799959526 3.9305200040474 201 22.2 19.6906672769943 2.5093327230057 202 19.5 19.2754362881295 0.224563711870515 203 16.6 19.6083439819636 -3.00834398196365 204 17.3 19.6842324788679 -2.38423247886788 205 19.8 19.7455853588161 0.0544146411839275 206 21.2 19.7073720830104 1.49262791698962 207 21.5 20.2578142281558 1.24218577184424 208 20.6 19.7480973863225 0.851902613677544 209 19.1 19.7563769157666 -0.65637691576659 210 19.6 20.2270773739642 -0.627077373964241 211 23.5 24.0116774818286 -0.511677481828623 212 24 25.0112982667630 -1.01129826676297 213 23.2 25.2762113360545 -2.07621133605453 214 21.2 24.17352877069 -2.97352877069 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.670780947236252 0.658438105527496 0.329219052763748 17 0.925119635734492 0.149760728531016 0.074880364265508 18 0.948514333546752 0.102971332906496 0.051485666453248 19 0.961966080955408 0.076067838089183 0.0380339190445915 20 0.97007453451443 0.0598509309711417 0.0299254654855708 21 0.976455333869618 0.0470893322607644 0.0235446661303822 22 0.973407599860457 0.0531848002790858 0.0265924001395429 23 0.975343578297574 0.0493128434048529 0.0246564217024264 24 0.975085864102994 0.0498282717940109 0.0249141358970055 25 0.992694724862413 0.0146105502751748 0.00730527513758739 26 0.997026825537488 0.00594634892502461 0.00297317446251231 27 0.999647299083781 0.00070540183243718 0.00035270091621859 28 0.999882244995411 0.000235510009177725 0.000117755004588863 29 0.999923716113012 0.000152567773976914 7.62838869884571e-05 30 0.999903838313903 0.000192323372194532 9.6161686097266e-05 31 0.999864416872355 0.000271166255291145 0.000135583127645573 32 0.99987233927817 0.000255321443660258 0.000127660721830129 33 0.999879128491621 0.000241743016757411 0.000120871508378705 34 0.999900490915118 0.000199018169764679 9.95090848823397e-05 35 0.99991187426705 0.000176251465899266 8.81257329496329e-05 36 0.999939618855308 0.000120762289383923 6.03811446919614e-05 37 0.99997357172323 5.28565535380958e-05 2.64282767690479e-05 38 0.999987857843286 2.4284313427405e-05 1.21421567137025e-05 39 0.999992490698985 1.50186020310527e-05 7.50930101552635e-06 40 0.99999326351742 1.34729651613177e-05 6.73648258065883e-06 41 0.999991455316487 1.70893670266910e-05 8.54468351334549e-06 42 0.999986283994768 2.74320104647483e-05 1.37160052323741e-05 43 0.999976512518819 4.69749623622928e-05 2.34874811811464e-05 44 0.999961369343521 7.72613129582194e-05 3.86306564791097e-05 45 0.999940177480236 0.000119645039528207 5.98225197641037e-05 46 0.999915019330576 0.000169961338847936 8.49806694239678e-05 47 0.999887154580994 0.000225690838011042 0.000112845419005521 48 0.999848996594662 0.000302006810676449 0.000151003405338224 49 0.999814287073712 0.000371425852576814 0.000185712926288407 50 0.999753045084295 0.000493909831410321 0.000246954915705161 51 0.999656393677233 0.000687212645533518 0.000343606322766759 52 0.999526396021156 0.000947207957688438 0.000473603978844219 53 0.99934823927432 0.00130352145135878 0.00065176072567939 54 0.999066010368358 0.00186797926328446 0.000933989631642232 55 0.998631290387197 0.00273741922560593 0.00136870961280296 56 0.998016218015332 0.00396756396933610 0.00198378198466805 57 0.997342423655131 0.00531515268973773 0.00265757634486886 58 0.997002328822266 0.00599534235546787 0.00299767117773393 59 0.996637609856918 0.00672478028616472 0.00336239014308236 60 0.9960877470752 0.00782450584960228 0.00391225292480114 61 0.995615527701244 0.0087689445975115 0.00438447229875575 62 0.994718092579832 0.0105638148403353 0.00528190742016766 63 0.993160712274282 0.013678575451435 0.0068392877257175 64 0.990970921160006 0.0180581576799874 0.00902907883999369 65 0.988306386881555 0.0233872262368909 0.0116936131184454 66 0.985022414332848 0.0299551713343045 0.0149775856671522 67 0.980847545922717 0.0383049081545667 0.0191524540772834 68 0.975677725741778 0.0486445485164444 0.0243222742582222 69 0.970874540408861 0.058250919182277 0.0291254595911385 70 0.966258142967193 0.0674837140656143 0.0337418570328071 71 0.961957886334037 0.0760842273319261 0.0380421136659631 72 0.957887880833981 0.0842242383320381 0.0421121191660191 73 0.951392125799835 0.097215748400331 0.0486078742001655 74 0.94199451532337 0.116010969353261 0.0580054846766303 75 0.930227485039135 0.139545029921731 0.0697725149608653 76 0.91551387266665 0.168972254666699 0.0844861273333494 77 0.89864627801241 0.202707443975180 0.101353721987590 78 0.878789474644062 0.242421050711876 0.121210525355938 79 0.85820858177914 0.283582836441721 0.141791418220861 80 0.835358666554344 0.329282666891311 0.164641333445656 81 0.825099498687042 0.349801002625917 0.174900501312958 82 0.820127862137614 0.359744275724771 0.179872137862386 83 0.819161945720413 0.361676108559173 0.180838054279587 84 0.819076370934197 0.361847258131605 0.180923629065803 85 0.824546359753374 0.350907280493253 0.175453640246626 86 0.826446431328153 0.347107137343694 0.173553568671847 87 0.837719529714892 0.324560940570216 0.162280470285108 88 0.849420639643854 0.301158720712293 0.150579360356147 89 0.854747742329642 0.290504515340716 0.145252257670358 90 0.84228195290038 0.315436094199239 0.157718047099619 91 0.815795274266113 0.368409451467774 0.184204725733887 92 0.793166922330757 0.413666155338486 0.206833077669243 93 0.790708282554362 0.418583434891276 0.209291717445638 94 0.829155713792549 0.341688572414903 0.170844286207451 95 0.88078662602296 0.238426747954082 0.119213373977041 96 0.91707553339219 0.16584893321562 0.08292446660781 97 0.965709548240314 0.0685809035193729 0.0342904517596865 98 0.97440490338204 0.051190193235918 0.025595096617959 99 0.979131146336142 0.0417377073277156 0.0208688536638578 100 0.98330950170015 0.0333809965997007 0.0166904982998503 101 0.985321403499388 0.0293571930012238 0.0146785965006119 102 0.984152452832554 0.0316950943348911 0.0158475471674456 103 0.983554201465571 0.0328915970688571 0.0164457985344285 104 0.979340387190532 0.0413192256189355 0.0206596128094677 105 0.973784339172747 0.0524313216545059 0.0262156608272530 106 0.971350580056835 0.0572988398863295 0.0286494199431647 107 0.974048728821476 0.0519025423570488 0.0259512711785244 108 0.985240745507532 0.0295185089849363 0.0147592544924682 109 0.993262416038679 0.0134751679226422 0.00673758396132109 110 0.997435215102009 0.00512956979598238 0.00256478489799119 111 0.998716948629157 0.00256610274168601 0.00128305137084300 112 0.998535632431823 0.00292873513635358 0.00146436756817679 113 0.998119522872233 0.00376095425553447 0.00188047712776724 114 0.997997791009294 0.00400441798141232 0.00200220899070616 115 0.998999399567671 0.00200120086465781 0.00100060043232891 116 0.999590109506774 0.000819780986451642 0.000409890493225821 117 0.999794237930224 0.000411524139551406 0.000205762069775703 118 0.999735649959789 0.000528700080422759 0.000264350040211379 119 0.999639891850693 0.000720216298614591 0.000360108149307296 120 0.999485539502288 0.00102892099542401 0.000514460497712005 121 0.99928222210863 0.00143555578274176 0.000717777891370882 122 0.999097131587959 0.00180573682408286 0.00090286841204143 123 0.998898957312574 0.00220208537485113 0.00110104268742556 124 0.998937179339501 0.00212564132099745 0.00106282066049873 125 0.999107755431797 0.00178448913640566 0.000892244568202828 126 0.999560803275857 0.0008783934482869 0.00043919672414345 127 0.999801133049286 0.000397733901427627 0.000198866950713813 128 0.999944013732896 0.000111972534208244 5.59862671041218e-05 129 0.999987072029643 2.58559407141902e-05 1.29279703570951e-05 130 0.999994930979472 1.01380410549322e-05 5.06902052746612e-06 131 0.999996479340989 7.0413180221202e-06 3.5206590110601e-06 132 0.999995272593777 9.4548124452998e-06 4.7274062226499e-06 133 0.999992198602644 1.56027947123428e-05 7.80139735617141e-06 134 0.999988955624169 2.20887516627836e-05 1.10443758313918e-05 135 0.999985031935416 2.99361291681931e-05 1.49680645840966e-05 136 0.999975952130845 4.80957383097843e-05 2.40478691548921e-05 137 0.99996126584595 7.74683081017599e-05 3.87341540508800e-05 138 0.999937981789803 0.000124036420394537 6.20182101972684e-05 139 0.999919376999748 0.000161246000504187 8.06230002520935e-05 140 0.999891348724493 0.000217302551014073 0.000108651275507036 141 0.9998685599771 0.000262880045798238 0.000131440022899119 142 0.99985584063387 0.000288318732260937 0.000144159366130468 143 0.999848896964843 0.000302206070313117 0.000151103035156559 144 0.999822579697356 0.000354840605287746 0.000177420302643873 145 0.99973245711047 0.000535085779060187 0.000267542889530093 146 0.99959192109982 0.000816157800360451 0.000408078900180226 147 0.999462806913507 0.00107438617298532 0.000537193086492661 148 0.999335259872234 0.00132948025553292 0.000664740127766462 149 0.999042462074085 0.00191507585182953 0.000957537925914763 150 0.998582463048032 0.00283507390393596 0.00141753695196798 151 0.998421999644966 0.00315600071006836 0.00157800035503418 152 0.998473612263954 0.00305277547209167 0.00152638773604583 153 0.998833603363887 0.00233279327222648 0.00116639663611324 154 0.999209820783226 0.00158035843354855 0.000790179216774277 155 0.999322882597916 0.00135423480416724 0.000677117402083619 156 0.999240045117758 0.00151990976448318 0.000759954882241588 157 0.99895951125192 0.00208097749616125 0.00104048874808063 158 0.99854310923144 0.00291378153712013 0.00145689076856006 159 0.998304332083545 0.00339133583291022 0.00169566791645511 160 0.998062252234336 0.00387549553132831 0.00193774776566416 161 0.997918628772 0.00416274245599918 0.00208137122799959 162 0.997585806096443 0.00482838780711477 0.00241419390355738 163 0.997020949633918 0.00595810073216333 0.00297905036608166 164 0.99592314825729 0.00815370348541904 0.00407685174270952 165 0.995433683988874 0.00913263202225132 0.00456631601112566 166 0.995957900580964 0.00808419883807207 0.00404209941903604 167 0.99753875068038 0.00492249863923957 0.00246124931961979 168 0.998641083545402 0.00271783290919534 0.00135891645459767 169 0.998426654186136 0.00314669162772819 0.00157334581386410 170 0.997907678047696 0.00418464390460838 0.00209232195230419 171 0.99680790833543 0.00638418332914126 0.00319209166457063 172 0.99539296540195 0.00921406919610076 0.00460703459805038 173 0.994480520641205 0.0110389587175909 0.00551947935879544 174 0.992369933514406 0.0152601329711888 0.00763006648559439 175 0.988948391824314 0.0221032163513721 0.0110516081756860 176 0.98370278460781 0.0325944307843787 0.0162972153921894 177 0.978236881974556 0.0435262360508877 0.0217631180254439 178 0.972095039646192 0.0558099207076169 0.0279049603538084 179 0.970176003023279 0.0596479939534428 0.0298239969767214 180 0.959300618348032 0.081398763303936 0.040699381651968 181 0.94213978196269 0.115720436074618 0.057860218037309 182 0.921863540562192 0.156272918875617 0.0781364594378084 183 0.890797412617674 0.218405174764653 0.109202587382326 184 0.87309783995 0.253804320099999 0.126902160049999 185 0.857980811536534 0.284038376926933 0.142019188463466 186 0.808586749148021 0.382826501703958 0.191413250851979 187 0.777506820061393 0.444986359877214 0.222493179938607 188 0.825381123203564 0.349237753592872 0.174618876796436 189 0.88186300854708 0.236273982905841 0.118136991452921 190 0.86370643123604 0.272587137527920 0.136293568763960 191 0.805260309280232 0.389479381439536 0.194739690719768 192 0.728259390953646 0.543481218092708 0.271740609046354 193 0.65475544355566 0.690489112888678 0.345244556444339 194 0.653967648255355 0.69206470348929 0.346032351744645 195 0.726037804247524 0.547924391504952 0.273962195752476 196 0.869831926596633 0.260336146806733 0.130168073403367 197 0.956272360282436 0.0874552794351283 0.0437276397175642 198 0.993983257639536 0.0120334847209288 0.00601674236046441 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 99 0.540983606557377 NOK 5% type I error level 124 0.6775956284153 NOK 10% type I error level 141 0.770491803278688 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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