*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, 19 Nov 2009 07:03:28 -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/Nov/19/t12586394586yr2pspw9nsyzmg.htm/, Retrieved Thu, 19 Nov 2009 15:04:32 +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/Nov/19/t12586394586yr2pspw9nsyzmg.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

3.88 153.3 3.98 154.5 3.29 155.2 2.88 156.9 3.22 157 3.62 157.4 3.82 157.2 3.54 157.5 2.53 158 2.22 158.5 2.85 159 2.78 159.3 2.28 160 2.26 160.8 2.71 161.9 2.77 162.5 2.77 162.7 2.64 162.8 2.56 162.9 2.07 163 2.32 164 2.16 164.7 2.23 164.8 2.4 164.9 2.84 165 2.77 165.8 2.93 166.1 2.91 167.2 2.69 167.7 2.38 168.3 2.58 168.6 3.19 168.9 2.82 169.1 2.72 169.5 2.53 169.6 2.7 169.7 2.42 169.8 2.5 170.4 2.31 170.9 2.41 171.9 2.56 171.9 2.76 172 2.71 172 2.44 172.4 2.46 173 2.12 173.7 1.99 173.8 1.86 173.8 1.88 173.9 1.82 174.6 1.74 175 1.71 175.9 1.38 176 1.27 175.1 1.19 175.6 1.28 175.9 1.19 176.7 1.22 176.1 1.47 176.1 1.46 176.2 1.96 176.3 1.88 177.8 2.03 178.5 2.04 179.4 1.9 179.5 1.8 179.6 1.92 179.7 1.92 179.7 1.97 179.8 2.46 179.9 2.36 180.2 2.53 180.4 2.31 180.4 1.98 181.3 1.46 181.9 1.26 182.5 1.58 182.7 1.74 183.1 1.89 183.6 1.85 183.7 1.62 183.8 1.3 183.9 1.42 184.1 1.15 184.4 0.42 184.5 0.74 185.9 1.02 186.6 1.51 187.6 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[t] = -25.4133631689989 + 0.179229739292978X[t] + 0.095280873041429M1[t] + 0.0421340272055563M2[t] -0.0422355774266983M3[t] -0.132143448451306M4[t] -0.132177275468981M5[t] -0.124486492861985M6[t] -0.132564913920593M7[t] -0.139372069077023M8[t] + 0.00123723721385846M9[t] -0.0336295549066252M10[t] -0.0235177431578595M11[t] -0.0695730755602266t + 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) -25.4133631689989 7.882439 -3.224 0.001466 0.000733 X 0.179229739292978 0.051143 3.5045 0.000559 0.00028 M1 0.095280873041429 0.335873 0.2837 0.776934 0.388467 M2 0.0421340272055563 0.335719 0.1255 0.900245 0.450122 M3 -0.0422355774266983 0.336122 -0.1257 0.900125 0.450062 M4 -0.132143448451306 0.337958 -0.391 0.69619 0.348095 M5 -0.132177275468981 0.337897 -0.3912 0.696063 0.348032 M6 -0.124486492861985 0.337376 -0.369 0.712511 0.356256 M7 -0.132564913920593 0.337046 -0.3933 0.694487 0.347243 M8 -0.139372069077023 0.336799 -0.4138 0.679433 0.339716 M9 0.00123723721385846 0.340701 0.0036 0.997106 0.498553 M10 -0.0336295549066252 0.340469 -0.0988 0.921412 0.460706 M11 -0.0235177431578595 0.340263 -0.0691 0.944963 0.472481 t -0.0695730755602266 0.019631 -3.544 0.000486 0.000243 Multiple Linear Regression - Regression Statistics Multiple R 0.243310752051549 R-squared 0.0592001220638905 Adjusted R-squared 0.000960129620226513 F-TEST (value) 1.01648574424448 F-TEST (DF numerator) 13 F-TEST (DF denominator) 210 p-value 0.436507145272958 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.02046354510624 Sum Squared Residuals 218.682627847067 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.88 2.08826366209574 1.79173633790426 2 3.98 2.18061942785119 1.79938057214881 3 3.29 2.15213756516381 1.13786243483619 4 2.88 2.29734717537704 0.582652824622961 5 3.22 2.24566324672843 0.974336753271567 6 3.62 2.25547284949240 1.36452715050760 7 3.82 2.14197540501496 1.67802459498504 8 3.54 2.1193640960862 1.42063590391380 9 2.53 2.28001519646334 0.249984803536656 10 2.22 2.26519019842912 -0.0451901984291231 11 2.85 2.29534380426415 0.554656195735849 12 2.78 2.30305739364968 0.47694260635032 13 2.28 2.45422600863596 -0.174226008635964 14 2.26 2.47488987867425 -0.214889878674251 15 2.71 2.51809991170404 0.191900088295957 16 2.77 2.46615680869499 0.303843191305007 17 2.77 2.43239585397568 0.337604146024316 18 2.64 2.38843653495176 0.251563465048243 19 2.56 2.32870801226222 0.231291987737782 20 2.07 2.27025075547486 -0.200250755474859 21 2.32 2.52051672549849 -0.200516725498491 22 2.16 2.54153767532286 -0.381537675322863 23 2.23 2.49999938544070 -0.269999385440704 24 2.4 2.47186702696763 -0.0718670269676341 25 2.84 2.51549779837813 0.324502201621867 26 2.77 2.53616166841642 0.233838331583582 27 2.93 2.43598791001183 0.494012089988174 28 2.91 2.47365967664927 0.436340323350734 29 2.69 2.49366764371785 0.196332356282147 30 2.38 2.53932319434041 -0.159323194340413 31 2.58 2.51544061950947 0.0645593804905305 32 3.19 2.49282931058071 0.697170689419292 33 2.82 2.59971148916996 0.220288510830043 34 2.72 2.56696351720644 0.153036482793562 35 2.53 2.52542522732427 0.00457477267572591 36 2.7 2.49729286885120 0.202707131148797 37 2.42 2.54092364026171 -0.120923640261707 38 2.5 2.52574156244139 -0.0257415624413933 39 2.31 2.4614137518954 -0.151413751895402 40 2.41 2.48116254460354 -0.071162544603544 41 2.56 2.41155564202564 0.148444357974358 42 2.76 2.36759632300171 0.392403676998291 43 2.71 2.28994482638287 0.420055173617126 44 2.44 2.28525649138341 0.15474350861659 45 2.46 2.46383056568985 -0.0038305656898506 46 2.12 2.48485151551422 -0.364851515514222 47 1.99 2.44331322563206 -0.453313225632063 48 1.86 2.39725789322970 -0.537257893229696 49 1.88 2.44088866464019 -0.560888664640195 50 1.82 2.44362956074918 -0.623629560749178 51 1.74 2.36137877627389 -0.621378776273889 52 1.71 2.36320459505274 -0.653204595052735 53 1.38 2.31152066640413 -0.93152066640413 54 1.27 2.08833160808722 -0.818331608087219 55 1.19 2.10029498111487 -0.910294981114872 56 1.28 2.07768367218611 -0.797683672186112 57 1.19 2.29210369435115 -1.10210369435115 58 1.22 2.08012598309465 -0.86012598309465 59 1.47 2.02066471928319 -0.550664719283189 60 1.46 1.99253236081012 -0.532532360810118 61 1.96 2.03616313222062 -0.0761631322206229 62 1.88 2.18228781976399 -0.30228781976399 63 2.03 2.15380595707659 -0.123805957076591 64 2.04 2.15563177585544 -0.115631775855437 65 1.9 2.10394784720683 -0.203947847206832 66 1.8 2.0599885281829 -0.259988528182898 67 1.92 2.00026000549336 -0.0802600054933604 68 1.92 1.92387977477670 -0.00387977477670409 69 1.97 2.01283897943666 -0.0428389794366607 70 2.46 1.92632208568525 0.533677914314753 71 2.36 1.92062974366168 0.439370256338324 72 2.53 1.91042035911791 0.619579640882092 73 2.31 1.93612815659911 0.37387184340089 74 1.98 1.97471500056669 0.00528499943330803 75 1.46 1.92831016395000 -0.468310163949996 76 1.26 1.87636706094095 -0.616367060940947 77 1.58 1.84260610622164 -0.262606106221639 78 1.74 1.8524157089856 -0.112415708985600 79 1.89 1.86437908201325 0.0256209179867456 80 1.85 1.80592182522589 0.0440781747741052 81 1.62 1.89488102988585 -0.274881029885851 82 1.3 1.80836413613444 -0.508364136134438 83 1.42 1.78474882018157 -0.364748820181570 84 1.15 1.7924624095671 -0.642462409567099 85 0.42 1.83609318097760 -1.41609318097760 86 0.74 1.96429489459167 -1.22429489459167 87 1.02 1.93581303190427 -0.91581303190427 88 1.51 1.95556182461241 -0.445561824612412 89 1.86 1.92180086989311 -0.0618008698931087 90 1.59 1.87784155086918 -0.287841550869175 91 1.03 1.81811302817964 -0.788113028179637 92 0.44 1.79550171925088 -1.35550171925088 93 0.82 1.88446092391083 -1.06446092391083 94 0.86 1.79794403015941 -0.937944030159414 95 0.58 1.73848276634795 -1.15848276634795 96 0.59 1.71035040787488 -1.12035040787488 97 0.95 1.73605820535609 -0.786058205356085 98 0.98 1.75672207539437 -0.77672207539437 99 1.23 1.71031723877767 -0.480317238777674 100 1.17 1.89137279684950 -0.721372796849498 101 0.84 1.92930373784738 -1.08930373784738 102 0.74 1.95703631454064 -1.21703631454064 103 0.65 1.96899968756829 -1.31899968756829 104 0.91 1.96431135256883 -1.05431135256883 105 1.19 2.08911650508738 -0.899116505087375 106 1.3 2.11013745491175 -0.810137454911752 107 1.53 2.05067619110029 -0.520676191100291 108 1.94 2.00462085869792 -0.0646208586979243 109 1.79 2.03032865617913 -0.240328656179127 110 1.95 2.01514657835881 -0.065146578358813 111 2.26 1.95081876781282 0.309181232187179 112 2.04 1.82718376908658 0.212816230913421 113 2.16 1.75757686650868 0.402423133491323 114 2.75 1.69569457355545 1.05430542644455 115 2.79 1.61804307693661 1.17195692306339 116 2.88 1.68504663765434 1.19495336234566 117 3.36 1.88154368589008 1.47845631410992 118 2.97 1.83087273999726 1.13912726000274 119 3.1 1.80725742404439 1.29274257595561 120 2.49 1.81497101342992 0.675028986570077 121 2.2 1.85860178484042 0.341398215159578 122 2.25 1.89718862880800 0.352811371191996 123 2.09 1.83286081826201 0.257139181737988 124 2.79 1.90637853275805 0.88362146724195 125 3.14 1.99807839554382 1.14192160445618 126 2.93 2.06165692009568 0.86834307990432 127 2.65 2.09154326705263 0.558456732947368 128 2.67 2.01516303633597 0.654836963664025 129 2.26 2.17581413671312 0.0841858632868812 130 2.35 2.08929724296171 0.260702757038295 131 2.13 2.06568192700884 0.0643180729911573 132 2.18 2.05547254246507 0.124527457534931 133 2.9 2.13494926173417 0.765050738265833 134 2.63 2.06599826212596 0.564001737874042 135 2.67 2.01959342550926 0.650406574490738 136 1.81 2.00349627035881 -0.193496270358812 137 1.33 2.0055812634981 -0.675581263498101 138 0.88 1.97954491840346 -1.09954491840346 139 1.28 2.02735423928972 -0.747354239289718 140 1.26 1.98681995643166 -0.726819956431655 141 1.26 2.1474710568088 -0.887471056808798 142 1.29 2.06095416305738 -0.770954163057385 143 1.1 2.07318479496312 -0.973184794963116 144 1.37 2.04505243649005 -0.675052436490045 145 1.21 2.17829807754703 -0.968298077547034 146 1.74 2.07350113008024 -0.333501130080236 147 1.76 1.93748142381705 -0.177481423817052 148 1.48 1.79592345116151 -0.315923451161514 149 1.04 1.86970034001800 -0.829700340017996 150 1.62 1.91535589064055 -0.295355890640551 151 1.49 1.89147331580961 -0.401473315809607 152 1.79 1.86886200688085 -0.0788620068808458 153 1.8 1.97574418547009 -0.175744185470093 154 1.58 1.90715026564798 -0.327150265647982 155 1.86 1.93730387148301 -0.0773038714830098 156 1.74 1.98086340872713 -0.240863408727131 157 1.59 2.06034012799622 -0.470340127996224 158 1.26 1.99138912838802 -0.73138912838802 159 1.13 1.89121536998343 -0.761215369983435 160 1.92 1.82134929304509 0.0986507069549115 161 2.61 1.78758833832578 0.82241166167422 162 2.26 1.88701281073623 0.372987189263769 163 2.41 1.89897618376388 0.511023816236115 164 2.26 1.91221082269372 0.347789177306283 165 2.03 2.03701597521226 -0.00701597521226226 166 2.86 1.98634502931945 0.873654970680553 167 2.55 1.99857566122518 0.551424338774821 168 2.27 1.98836627668140 0.281633723318596 169 2.26 2.10368894380910 0.156311056190903 170 2.57 2.03473794420089 0.535262055799107 171 3.07 1.95248715972560 1.11751284027440 172 2.76 1.99015892636304 0.769841073636957 173 2.51 2.01016689343163 0.499833106568371 174 2.87 1.96620757440770 0.903792425592304 175 3.14 2.03193986922324 1.10806013077676 176 3.11 1.99140558636518 1.11859441363482 177 3.16 2.09828776495443 1.06171223504557 178 2.47 2.04761681906162 0.422383180938384 179 2.57 2.05984745096735 0.510152549032653 180 2.89 2.04963806642357 0.840361933576427 181 2.63 2.12911478569267 0.500885214307329 182 2.38 2.11393270787236 0.266067292127643 183 1.69 2.15714274090215 -0.46714274090215 184 1.96 2.06935369003451 -0.109353690034508 185 2.19 2.0714386831738 0.118561316826202 186 1.87 2.08124828593776 -0.211248285937759 187 1.6 2.03944273717752 -0.439442737177518 188 1.63 2.05267737610735 -0.422677376107351 189 1.22 2.1774825286259 -0.957482528625901 190 1.21 2.16265753059168 -0.95265753059168 191 1.49 2.15696518856811 -0.666965188568109 192 1.64 2.16467877795364 -0.524678777953637 193 1.66 2.20830954936414 -0.548309549364137 194 1.77 2.13935854975593 -0.369358549755932 195 1.82 2.02126181742205 -0.201261817422045 196 1.78 1.87970384476651 -0.0997038447665063 197 1.28 1.84594289004720 -0.565942890047203 198 1.29 1.83782951888186 -0.547829518881863 199 1.37 1.81394694405092 -0.443946944050924 200 1.12 1.75548968726356 -0.635489687263563 201 1.51 1.86237186585281 -0.352371865852812 202 2.24 1.86546984174789 0.374530158252107 203 2.94 1.84185452579503 1.09814547420497 204 3.09 1.92126001089774 1.16873998910226 205 3.46 1.98281375623754 1.47718624376246 206 3.64 2.05724654806372 1.58275345193628 207 4.39 2.27968632038649 2.11031367961351 208 4.15 2.28151213916533 1.86848786083467 209 5.21 2.37321200195111 2.83678799804889 210 5.8 2.34717565685648 3.45282434314352 211 5.91 2.34121605595483 3.56878394404517 212 5.39 2.39029664274326 2.99970335725674 213 5.46 2.586793690979 2.873206309021 214 4.72 2.51819977115688 2.20180022884312 215 3.14 2.62004527270910 0.519954727290896 216 2.63 2.60983588816533 0.0201641118346695 217 2.32 2.68931260743443 -0.369312607434429 218 1.93 2.60243863389692 -0.672438633896922 219 0.62 2.52018784942163 -1.90018784942163 220 0.6 2.41447582462469 -1.81447582462469 221 -0.37 2.48825271348117 -2.85825271348117 222 -1.1 2.55183123803303 -3.65183123803303 223 -1.68 2.52794866320208 -4.20794866320208 224 -0.78 2.57702924999051 -3.35702924999051 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.105569161514926 0.211138323029852 0.894430838485074 18 0.0583122061066794 0.116624412213359 0.94168779389332 19 0.0294025140167272 0.0588050280334544 0.970597485983273 20 0.0184872859798937 0.0369745719597874 0.981512714020106 21 0.0140919760320525 0.028183952064105 0.985908023967948 22 0.0123489036387007 0.0246978072774015 0.9876510963613 23 0.00534121735590218 0.0106824347118044 0.994658782644098 24 0.00245558333124941 0.00491116666249883 0.99754441666875 25 0.00192252297970522 0.00384504595941045 0.998077477020295 26 0.000896997011073061 0.00179399402214612 0.999103002988927 27 0.000375637692556752 0.000751275385113503 0.999624362307443 28 0.000157071603458844 0.000314143206917688 0.999842928396541 29 5.85799754359013e-05 0.000117159950871803 0.999941420024564 30 2.27264862028407e-05 4.54529724056813e-05 0.999977273513797 31 8.44764101096282e-06 1.68952820219256e-05 0.99999155235899 32 3.52649078479996e-05 7.05298156959992e-05 0.999964735092152 33 3.38566903511268e-05 6.77133807022536e-05 0.99996614330965 34 2.79890554237129e-05 5.59781108474258e-05 0.999972010944576 35 1.1448409369302e-05 2.2896818738604e-05 0.99998855159063 36 4.64761704384565e-06 9.2952340876913e-06 0.999995352382956 37 2.71666113619686e-06 5.43332227239371e-06 0.999997283338864 38 1.66632083897859e-06 3.33264167795719e-06 0.99999833367916 39 1.32958304833509e-06 2.65916609667017e-06 0.999998670416952 40 6.65412812802654e-07 1.33082562560531e-06 0.999999334587187 41 3.09328146785560e-07 6.18656293571119e-07 0.999999690671853 42 1.30548614817264e-07 2.61097229634527e-07 0.999999869451385 43 6.06131650654585e-08 1.21226330130917e-07 0.999999939386835 44 3.09919078898864e-08 6.19838157797728e-08 0.999999969008092 45 1.19737900412192e-08 2.39475800824385e-08 0.99999998802621 46 4.41998024589396e-09 8.83996049178792e-09 0.99999999558002 47 2.09520721737462e-09 4.19041443474924e-09 0.999999997904793 48 1.50044632037613e-09 3.00089264075227e-09 0.999999998499554 49 1.09958605447830e-09 2.19917210895661e-09 0.999999998900414 50 8.95715942187337e-10 1.79143188437467e-09 0.999999999104284 51 6.9246695786768e-10 1.38493391573536e-09 0.999999999307533 52 4.42573908266205e-10 8.8514781653241e-10 0.999999999557426 53 6.50414549481049e-10 1.30082909896210e-09 0.999999999349585 54 1.02781036956121e-09 2.05562073912242e-09 0.99999999897219 55 1.40015266211776e-09 2.80030532423553e-09 0.999999998599847 56 9.2537831103017e-10 1.85075662206034e-09 0.999999999074622 57 4.53294894538617e-10 9.06589789077234e-10 0.999999999546705 58 1.83054463894812e-10 3.66108927789624e-10 0.999999999816946 59 7.71256933508241e-11 1.54251386701648e-10 0.999999999922874 60 3.06808424460704e-11 6.13616848921409e-11 0.999999999969319 61 1.94788377984282e-11 3.89576755968565e-11 0.999999999980521 62 9.15826709799255e-12 1.83165341959851e-11 0.999999999990842 63 5.80364021499214e-12 1.16072804299843e-11 0.999999999994196 64 3.97694921272862e-12 7.95389842545724e-12 0.999999999996023 65 2.03388368837039e-12 4.06776737674078e-12 0.999999999997966 66 8.74671210972071e-13 1.74934242194414e-12 0.999999999999125 67 4.09047105278113e-13 8.18094210556227e-13 0.99999999999959 68 2.04529359709146e-13 4.09058719418291e-13 0.999999999999795 69 1.6300845607625e-13 3.260169121525e-13 0.999999999999837 70 9.06840849910715e-13 1.81368169982143e-12 0.999999999999093 71 1.43575146826882e-12 2.87150293653763e-12 0.999999999998564 72 2.86025089291462e-12 5.72050178582923e-12 0.99999999999714 73 2.02028555369731e-12 4.04057110739463e-12 0.99999999999798 74 8.98465435341542e-13 1.79693087068308e-12 0.999999999999102 75 4.08004635386087e-13 8.16009270772174e-13 0.999999999999592 76 2.23052207106661e-13 4.46104414213321e-13 0.999999999999777 77 8.86418511474694e-14 1.77283702294939e-13 0.999999999999911 78 3.58091840827335e-14 7.16183681654671e-14 0.999999999999964 79 1.58688494174678e-14 3.17376988349356e-14 0.999999999999984 80 6.91703500979581e-15 1.38340700195916e-14 0.999999999999993 81 2.7036105022098e-15 5.4072210044196e-15 0.999999999999997 82 1.04795676226988e-15 2.09591352453975e-15 0.999999999999999 83 3.92244174883461e-16 7.84488349766922e-16 1 84 1.89663061228806e-16 3.79326122457612e-16 1 85 8.64932013690124e-16 1.72986402738025e-15 1 86 8.20501202783818e-16 1.64100240556764e-15 1 87 3.71957175675032e-16 7.43914351350065e-16 1 88 1.56721488441748e-16 3.13442976883497e-16 1 89 1.06497629006968e-16 2.12995258013937e-16 1 90 4.53575303915952e-17 9.07150607831905e-17 1 91 2.10432033356265e-17 4.2086406671253e-17 1 92 3.21357703021077e-17 6.42715406042154e-17 1 93 1.64207347390141e-17 3.28414694780283e-17 1 94 7.49490765405992e-18 1.49898153081198e-17 1 95 5.76392312817392e-18 1.15278462563478e-17 1 96 4.32495854429692e-18 8.64991708859383e-18 1 97 1.9095245127049e-18 3.8190490254098e-18 1 98 8.27711203092661e-19 1.65542240618532e-18 1 99 3.54871195198804e-19 7.09742390397608e-19 1 100 1.47819861262597e-19 2.95639722525193e-19 1 101 6.564851408498e-20 1.3129702816996e-19 1 102 3.17933675240047e-20 6.35867350480094e-20 1 103 1.68533087448815e-20 3.3706617489763e-20 1 104 7.49855194606341e-21 1.49971038921268e-20 1 105 5.47402683644425e-21 1.09480536728885e-20 1 106 5.76531840203866e-21 1.15306368040773e-20 1 107 7.9775186200676e-21 1.59550372401352e-20 1 108 3.32336665762621e-20 6.64673331525243e-20 1 109 5.62777153427498e-20 1.12555430685500e-19 1 110 1.29737272154566e-19 2.59474544309132e-19 1 111 7.54369234855256e-19 1.50873846971051e-18 1 112 1.67435343832858e-18 3.34870687665716e-18 1 113 4.34583498138839e-18 8.69166996277678e-18 1 114 8.61213357610963e-17 1.72242671522193e-16 1 115 1.22820020556069e-15 2.45640041112138e-15 0.999999999999999 116 1.91386527010659e-14 3.82773054021318e-14 0.99999999999998 117 1.15777325290436e-12 2.31554650580871e-12 0.999999999998842 118 1.03481182033721e-11 2.06962364067442e-11 0.999999999989652 119 7.90332009277555e-11 1.58066401855511e-10 0.999999999920967 120 1.15437078057088e-10 2.30874156114175e-10 0.999999999884563 121 9.8991249595998e-11 1.97982499191996e-10 0.999999999901009 122 8.52955733418688e-11 1.70591146683738e-10 0.999999999914704 123 6.05131734654685e-11 1.21026346930937e-10 0.999999999939487 124 1.12011198651809e-10 2.24022397303618e-10 0.999999999887989 125 3.4844639607776e-10 6.9689279215552e-10 0.999999999651554 126 5.79856088169844e-10 1.15971217633969e-09 0.999999999420144 127 5.80597418529365e-10 1.16119483705873e-09 0.999999999419403 128 6.15396830002977e-10 1.23079366000595e-09 0.999999999384603 129 3.86802678010283e-10 7.73605356020565e-10 0.999999999613197 130 2.73892944694178e-10 5.47785889388356e-10 0.999999999726107 131 1.58457997720567e-10 3.16915995441134e-10 0.999999999841542 132 9.32529492271335e-11 1.86505898454267e-10 0.999999999906747 133 1.05320783396260e-10 2.10641566792521e-10 0.999999999894679 134 8.79011687102461e-11 1.75802337420492e-10 0.999999999912099 135 7.9849320328525e-11 1.5969864065705e-10 0.99999999992015 136 4.13566461597519e-11 8.27132923195039e-11 0.999999999958643 137 2.43237537234584e-11 4.86475074469168e-11 0.999999999975676 138 2.11854265504617e-11 4.23708531009234e-11 0.999999999978815 139 1.27111846628271e-11 2.54223693256541e-11 0.999999999987289 140 7.35736066219996e-12 1.47147213243999e-11 0.999999999992643 141 4.57653813975035e-12 9.1530762795007e-12 0.999999999995423 142 2.68570021000332e-12 5.37140042000663e-12 0.999999999997314 143 1.85912374984060e-12 3.71824749968121e-12 0.99999999999814 144 1.02876961776939e-12 2.05753923553878e-12 0.999999999998971 145 6.85955555623753e-13 1.37191111124751e-12 0.999999999999314 146 3.29798457299554e-13 6.59596914599107e-13 0.99999999999967 147 1.55437306353259e-13 3.10874612706519e-13 0.999999999999845 148 7.56711091522304e-14 1.51342218304461e-13 0.999999999999924 149 4.99946304889092e-14 9.99892609778184e-14 0.99999999999995 150 2.35382980071706e-14 4.70765960143413e-14 0.999999999999976 151 1.12642514907938e-14 2.25285029815877e-14 0.999999999999989 152 5.22321100614032e-15 1.04464220122806e-14 0.999999999999995 153 2.84827008446185e-15 5.6965401689237e-15 0.999999999999997 154 1.67220448921215e-15 3.34440897842429e-15 0.999999999999998 155 8.80613367648499e-16 1.76122673529700e-15 1 156 4.5397890548242e-16 9.0795781096484e-16 1 157 2.43719737426711e-16 4.87439474853422e-16 1 158 1.71635745751694e-16 3.43271491503389e-16 1 159 1.25849240836846e-16 2.51698481673692e-16 1 160 6.3297963575885e-17 1.26595927151770e-16 1 161 5.72267608762334e-17 1.14453521752467e-16 1 162 3.06660738576770e-17 6.13321477153539e-17 1 163 1.78498621153908e-17 3.56997242307817e-17 1 164 8.93874038715898e-18 1.78774807743180e-17 1 165 5.37496917779563e-18 1.07499383555913e-17 1 166 5.73710680388486e-18 1.14742136077697e-17 1 167 3.66881974775862e-18 7.33763949551724e-18 1 168 1.92721223264974e-18 3.85442446529948e-18 1 169 9.173480123934e-19 1.83469602478680e-18 1 170 5.0799312621858e-19 1.01598625243716e-18 1 171 5.49666840435996e-19 1.09933368087199e-18 1 172 3.36860987149096e-19 6.73721974298193e-19 1 173 1.51562482778953e-19 3.03124965557907e-19 1 174 1.03699673771848e-19 2.07399347543696e-19 1 175 1.00573774369087e-19 2.01147548738174e-19 1 176 9.88556134672596e-20 1.97711226934519e-19 1 177 8.06198328374075e-20 1.61239665674815e-19 1 178 3.36460386354377e-20 6.72920772708754e-20 1 179 1.36669474994476e-20 2.73338949988952e-20 1 180 7.21257540233168e-21 1.44251508046634e-20 1 181 2.71214626866744e-21 5.42429253733489e-21 1 182 9.07824035514116e-22 1.81564807102823e-21 1 183 3.92826012831211e-22 7.85652025662422e-22 1 184 1.28890602551098e-22 2.57781205102195e-22 1 185 3.93173388011845e-23 7.86346776023689e-23 1 186 1.27381881558634e-23 2.54763763117268e-23 1 187 4.73428924244326e-24 9.46857848488651e-24 1 188 1.74050712048236e-24 3.48101424096473e-24 1 189 5.43234818385883e-24 1.08646963677177e-23 1 190 4.37040665714175e-23 8.74081331428349e-23 1 191 2.30210142941914e-22 4.60420285883828e-22 1 192 2.18953563241501e-21 4.37907126483001e-21 1 193 1.89572250623896e-19 3.79144501247791e-19 1 194 1.88521690660393e-16 3.77043381320785e-16 1 195 1.9219719249649e-14 3.8439438499298e-14 0.99999999999998 196 1.01045020935834e-12 2.02090041871667e-12 0.99999999999899 197 3.76972645864679e-11 7.53945291729358e-11 0.999999999962303 198 2.55865874322735e-09 5.1173174864547e-09 0.999999997441341 199 4.37581582106050e-07 8.75163164212101e-07 0.999999562418418 200 6.91675890738798e-05 0.000138335178147760 0.999930832410926 201 0.00163494721577925 0.00326989443155850 0.99836505278422 202 0.0387324739248021 0.0774649478496042 0.961267526075198 203 0.0251525576387745 0.0503051152775491 0.974847442361225 204 0.0165833504720129 0.0331667009440257 0.983416649527987 205 0.0100563256875120 0.0201126513750241 0.989943674312488 206 0.0115368993754433 0.0230737987508865 0.988463100624557 207 0.227386881722105 0.454773763444211 0.772613118277895 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 178 0.931937172774869 NOK 5% type I error level 185 0.968586387434555 NOK 10% type I error level 188 0.984293193717278 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/10duqh1258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/10duqh1258639400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/1zqkz1258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/1zqkz1258639400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/2jpb61258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/2jpb61258639400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/3bjn91258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/3bjn91258639400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/4l8331258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/4l8331258639400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/5mpxv1258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/5mpxv1258639400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/6gtyu1258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/6gtyu1258639400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/7h0n31258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/7h0n31258639400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/8jzu91258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/8jzu91258639400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/9gj9a1258639400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586394586yr2pspw9nsyzmg/9gj9a1258639400.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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