*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, 22 Dec 2010 14:46:32 +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/22/t12930325614u4944futns6re5.htm/, Retrieved Wed, 22 Dec 2010 17:04:02 +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/22/t12930325614u4944futns6re5.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

3693 165 11.5 3436 150 11 3449 140 10.5 4341 198 10 4312 215 8.5 4425 225 10 3563 170 10 3609 160 8 3086 225 10 2372 95 15 2774 97 15.5 1835 46 20.5 2672 87 17.5 2375 95 17.5 2234 113 12.5 4615 215 14 4376 200 15 4732 193 18.5 2130 88 14.5 2228 95 14 3329 100 15.5 3288 100 15.5 4209 165 12 4096 150 13 4746 170 12 5140 175 12 2408 72 19 3282 100 15 2220 86 14 2123 90 14 2065 76 14.5 1773 65 19 1834 60 19 1955 70 20.5 2126 80 17 2226 86 16.5 4274 165 12 4135 150 13.5 4129 153 13 4633 208 11 4502 155 13.5 4422 190 12.5 2330 97 13.5 4098 130 14 4294 140 16 2933 112 14.5 2511 76 18 2395 86 16 2506 97 14.5 2164 80 15 4100 175 13 3672 150 11.5 4042 137 14.5 3777 150 12.5 4464 150 12 4363 158 13 4735 215 11 4951 225 11 3121 105 16.5 3278 100 18 3021 88 16.5 2904 95 16 4997 150 14 4499 180 12.5 2789 100 15 2401 72 19.5 2379 94 16.5 2310 85 18.5 2472 107 14 4082 145 13 4278 230 9.5 2158 75 15.5 2582 91 14 3399 150 11 2660 110 14 3664 180 11 310 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 52 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation acceleration [t] = + 18.4042054369189 + 0.00218916863715812weight[t] -0.0891828583404409horsepower[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) 18.4042054369189 0.25833 71.243 0 0 weight 0.00218916863715812 0.000163 13.4369 0 0 horsepower -0.0891828583404409 0.003574 -24.9559 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.764889185377629 R-squared 0.585055465907653 Adjusted R-squared 0.583736087420873 F-TEST (value) 443.432625110823 F-TEST (DF numerator) 2 F-TEST (DF denominator) 629 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.75526632074775 Sum Squared Residuals 1937.92374989659 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11.5 11.7736335877707 -0.273633587770679 2 11 12.548760123128 -1.54876012312801 3 10.5 13.4690478988155 -2.96904789881547 4 10 10.2491805394150 -0.249180539414952 5 8.5 8.66958605714987 -0.169586057149872 6 10 8.02513352974433 1.97486647025567 7 10 11.0431273732383 -1.04312737323828 8 8 12.0356577139520 -4.03565771395196 9 10 5.09383672458961 4.90616327541039 10 15 15.1245419019160 -0.124541901916024 11 15.5 15.8262219773727 -0.326221977372707 12 20.5 18.3189184024437 2.18108159755628 13 17.5 16.494755359787 1.00524464021301 14 17.5 15.1311094078275 2.3688905921725 15 12.5 13.2171451798603 -0.717145179860267 16 14 9.33290415420878 4.66709584579122 17 15 10.1474357250346 4.8525642749654 18 18.5 11.5510597682460 6.94894023175402 19 14.5 15.2190431001068 -0.719043100106845 20 14 14.8093016181653 -0.809301618165255 21 15.5 16.7736619959741 -1.27366199597414 22 15.5 16.6839060818507 -1.18390608185066 23 12 12.9032446045446 -0.903244604544629 24 13 13.9936114236524 -0.993611423652375 25 12 13.6329138709963 -1.63291387099633 26 12 14.0495320223344 -2.04953202233443 27 19 17.2545577146839 1.74544228531614 28 15 16.6707710700277 -1.67077107002771 29 14 15.5944339941320 -1.59443399413196 30 14 15.0253532029659 -1.02535320296586 31 14.5 16.1469414387769 -1.64694143877686 32 19 16.4887156384715 2.51128436152846 33 19 17.0681692170404 1.93183078295961 34 20.5 16.4412300387321 4.05876996126789 35 17 15.9237492922817 1.07625070771826 36 16.5 15.6075690059549 0.892430994045093 37 12 13.0455405659599 -1.04554056595991 38 13.5 14.0789890005015 -0.578989000501541 39 13 13.7983054136573 -0.79830541365727 40 11 9.99658919806071 1.00341080193929 41 13.5 14.4364995986364 -0.936499598636367 42 12.5 11.1399660657483 1.36003393425171 43 13.5 14.8542311024745 -1.35423110247450 44 14 15.7816469277355 -1.78164692773551 45 16 15.3188953972141 0.681104602785909 46 14.5 14.8365569155742 -0.336556915574235 47 18 17.1233106509494 0.87668934905062 48 16 15.9775385056346 0.0224614943653709 49 14.5 15.2395247826143 -0.739524782614331 50 15 16.0069377004937 -1.00693770049375 51 13 11.772796639690 1.22720336031001 52 11.5 13.0654039214973 -1.56540392149733 53 14.5 15.0347734756716 -0.534773475671568 54 12.5 13.2952666283989 -0.795266628398935 55 12 14.7992254821266 -2.79922548212656 56 13 13.8646565830501 -0.864656583050066 57 11 9.59560439066776 1.40439560933224 58 11 9.1766362328895 1.82336376711050 59 16.5 15.8724006277430 0.627599372256953 60 18 16.6620143954791 1.33798560452092 61 16.5 17.1695923558147 -0.66959235581473 62 16 16.2891796168841 -0.289179616884144 63 14 15.9660523657318 -1.96605236573184 64 12.5 12.2003606342139 0.299639365786130 65 15 15.5915109319088 -0.591510931908756 66 19.5 17.2392335342238 2.26076646577625 67 16.5 15.2290489407166 1.27095105928343 68 18.5 15.8806420298166 2.61935797018337 69 14 14.2732644655465 -0.273264465546546 70 13 14.4088773544344 -1.40887735443437 71 9.5 7.25741144837988 2.24258855162012 72 15.5 16.439716980373 -0.939716980373004 73 14 15.940998749081 -1.94099874908099 74 11 12.4677608835532 -1.46776088355316 75 14 14.4172795943109 -0.41727959431095 76 11 10.3724048221868 0.627595177813159 77 16.5 16.7226350070415 -0.222635007041452 78 16 15.8366978192705 0.163302180729535 79 16.5 16.6352290993581 -0.135229099358129 80 21 16.6266332626125 4.3733667373875 81 17 17.7631662199696 -0.763166219969612 82 18 16.5451515096286 1.45484849037136 83 14 14.9839525957289 -0.983952595728899 84 14.5 15.3136801118587 -0.813680111858721 85 16 16.0719694083965 -0.0719694083964852 86 15.5 14.3460675742348 1.15393242576517 87 15.5 16.7262919628507 -1.22629196285070 88 14.5 16.4830303518281 -1.98303035182813 89 19 17.3489558583797 1.65104414162033 90 14.5 16.3674744153468 -1.86747441534679 91 14 16.6323638204429 -2.63236382044292 92 15 15.2023089157826 -0.202308915782643 93 16 16.8072912024255 -0.807291202425548 94 16 17.0772803262611 -1.07728032626107 95 19.5 18.8964341925524 0.603565807447553 96 11.5 13.462158717298 -1.96215871729800 97 14 15.1925997265370 -1.19259972653697 98 13.5 15.4001007457790 -1.90010074577896 99 21 17.1471728848471 3.85282711515287 100 19 16.7596900360701 2.24030996392986 101 19 18.2178371862204 0.782162813779552 102 13.5 15.6454031997567 -2.14540319975665 103 12 13.8370921221561 -1.83709212215606 104 17 16.7792442281225 0.220755771877467 105 16 15.8651570115535 0.134842988446479 106 13.5 15.7577846938378 -2.25778469383776 107 16.5 16.9387443751500 -0.438744375150046 108 14.5 16.2859473911759 -1.78594739117591 109 15 15.8294542030809 -0.829454203080939 110 17 17.0294855630366 -0.0294855630366109 111 13.5 13.9954461576175 -0.495446157617485 112 17.5 17.6070716485743 -0.107071648574306 113 16.9 16.0403482858342 0.859651714165836 114 14.9 15.8299242043690 -0.92992420436897 115 15.3 15.8225775336844 -0.522577533684434 116 13 15.1459510748786 -2.1459510748786 117 13.9 16.3757485764864 -2.47574857648641 118 12.8 14.0757567747933 -1.27575677479331 119 14.5 16.3802877515637 -1.88028775156373 120 17.6 17.7741698464634 -0.174169846463392 121 22.2 18.2216549798327 3.9783450201673 122 22.1 17.7905948673026 4.30940513269743 123 17.7 17.4785742971391 0.221425702860943 124 16.2 16.5736107019117 -0.373610701911699 125 17.8 16.9218493530228 0.87815064697716 126 17 16.5178509410326 0.482149058967356 127 16.4 16.4331494744615 -0.0331494744615312 128 15.7 16.2034350932420 -0.503435093241956 129 13.2 13.6521011162557 -0.452101116255709 130 16.7 16.0648866300100 0.635113369990039 131 12.1 11.9398495663921 0.160150433607945 132 15 15.2825164784635 -0.282516478463457 133 14 13.2471049183815 0.752895081618544 134 14.8 15.9872351827593 -1.18723518275932 135 18.6 17.2268324159868 1.37316758401316 136 16.8 16.4193383523605 0.380661647639471 137 12.5 13.9666652897284 -1.46666528972843 138 13.7 14.5358491353895 -0.835849135389537 139 16.9 16.5379078934391 0.362092106560883 140 17.7 17.4326017557587 0.267398244241264 141 11.1 11.5895825844468 -0.489582584446756 142 11.4 12.3610068928075 -0.961006892807467 143 14.5 14.6060055862736 -0.106005586273606 144 14.5 15.6949296424512 -1.19492964245121 145 18.2 16.6739580245489 1.52604197545108 146 15.8 16.4980906399902 -0.698090639990229 147 15.9 15.5445531167654 0.355446883234647 148 16.4 16.7744536728682 -0.374453672868178 149 14.5 15.9159778914962 -1.41597789149619 150 12.8 14.2859294760815 -1.48592947608146 151 21.5 18.4689279813366 3.03107201866345 152 14.4 16.4586403333344 -2.05864033333437 153 18.6 16.6929844320053 1.90701556799471 154 13.2 14.0951501290427 -0.895150129042703 155 12.8 13.8231201622521 -1.02312016225205 156 18.2 16.8386609448108 1.36133905518917 157 15.8 17.3145474871552 -1.51454748715520 158 17.2 16.9947680283271 0.205231971672888 159 17.2 17.4049795115567 -0.204979511556734 160 16.7 17.5444101940568 -0.844410194056802 161 18.7 16.5188814859827 2.18111851401725 162 13.2 12.9705935598215 0.229406440178519 163 13.4 11.2307197657558 2.16928023424418 164 13.7 14.8504133088623 -1.15041330886225 165 16.5 17.0574294828446 -0.557429482844616 166 14.7 14.7885560433598 -0.0885560433597586 167 14.5 16.5973371222484 -2.09733712224839 168 17.6 17.0737389370678 0.526261062932197 169 15.9 15.4137182710109 0.486281728989084 170 13.6 14.1303376650402 -0.530337665040234 171 15.8 14.0079503303494 1.7920496696506 172 14.9 16.4286680826922 -1.52866808269220 173 16.6 17.0136461101015 -0.413646110101452 174 18.2 17.3692767030842 0.830723296915848 175 17.3 16.8828112643470 0.417188735652984 176 16.6 15.9496976403216 0.650302359678368 177 15.4 15.2168414193487 0.183158580651286 178 13.2 14.7551329458984 -1.55513294589837 179 15.2 14.7490354412749 0.450964558725071 180 14.3 14.6151292076153 -0.31512920761526 181 15 15.1483010813188 -0.14830108131876 182 14 16.2863721212769 -2.28637212127693 183 15.2 16.9309277031775 -1.73092770317748 184 15 17.1146570308958 -2.11465703089576 185 24.8 19.0556704472819 5.74432955271805 186 22.2 17.8647049253599 4.33529507464006 187 14.9 16.8681179229779 -1.96811792297794 188 19.2 17.0294402918496 2.17055970815041 189 16 16.2228284474913 -0.222828447491348 190 11.3 13.8290693411935 -2.52906934119347 191 13.2 15.9732632228553 -2.77326322285532 192 14.7 16.3198857611123 -1.61988576111235 193 15.5 16.8024428638632 -1.3024428638632 194 16.4 17.0272511232124 -0.627251123212436 195 18.1 16.8390278916039 1.26097210839615 196 20.1 16.951821603665 3.148178396335 197 15.8 16.2378434644664 -0.437843464466425 198 15.5 16.3125843616148 -0.812584361614831 199 15 15.5278189324411 -0.52781893244115 200 15.2 16.6739580245489 -1.47395802454892 201 14.4 15.1696774952153 -0.76967749521529 202 19.2 17.2264654691938 1.97353453080618 203 19.9 18.8870014077258 1.01299859227424 204 13.8 16.4789159068518 -2.67891590685183 205 15.3 16.9138843553682 -1.61388435536824 206 15.1 16.0290354958554 -0.92903549585535 207 15.7 16.3638752428455 -0.663875242845533 208 16.4 16.6813046952335 -0.281304695233461 209 12.6 14.5595755557262 -1.95957555572623 210 12.9 16.1340125359439 -3.23401253594393 211 16.4 16.8011936978021 -0.401193697802108 212 16.1 16.9061707378907 -0.806170737890684 213 19.4 16.9309277031775 2.46907229682252 214 17.3 17.3626639259857 -0.0626639259856584 215 14.9 17.6346938927763 -2.73469389277631 216 16.2 17.0841695077785 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15.9369873585997 -4.3369873585997 240 18.6 17.1053273005641 1.49467269943592 241 18 15.7817172231645 2.21828277683553 242 17 17.3766358858897 -0.376635885889661 243 17 17.0735906113858 -0.0735906113857769 244 16 16.9061707378907 -0.906170737890685 245 19 16.4887156384715 2.51128436152846 246 18 17.6070716485743 0.392928351425694 247 17 17.6070716485743 -0.607071648574306 248 14 16.4586403333344 -2.45864033333437 249 16 16.993737483377 -0.99373748337701 250 12 16.0674552575611 -4.06745525756111 251 19 17.2268324159868 1.77316758401315 252 19 17.0681692170404 1.93183078295961 253 21 18.3189184024437 2.68108159755628 254 21 16.6266332626125 4.3733667373875 255 15 16.9138843553682 -1.91388435536824 256 14 16.4789159068518 -2.47891590685183 257 20 18.1214232238115 1.87857677618855 258 16 16.8011936978021 -0.801193697802106 259 14 15.4618347098414 -1.46183470984138 260 14 16.2863721212769 -2.28637212127693 261 14 16.4018250032633 -2.40182500326326 262 14 16.4018250032633 -2.40182500326326 263 15 15.6949296424512 -0.694929642451212 264 17 16.4193383523605 0.580661647639470 265 21 18.5706727957169 2.4293272042831 266 19 16.6978327705676 2.30216722943236 267 21 16.4412300387321 4.55876996126789 268 16 16.7262919628507 -0.726291962850698 269 15 16.730670300125 -1.73067030012501 270 16 16.730670300125 -0.730670300125014 271 19 17.3615178144196 1.63848218558043 272 18 16.6524332849704 1.34756671502964 273 15 16.9309277031775 -1.93092770317748 274 19 16.9309277031775 2.06907229682252 275 15 16.1392278212993 -1.1392278212993 276 22 18.4689279813366 3.53107201866345 277 16 16.7744536728682 -0.774453672868176 278 19 18.1121965479748 0.88780345202521 279 16 16.6852708145277 -0.685270814527736 280 15 16.4286680826922 -1.42866808269220 281 17 16.5178509410326 0.482149058967356 282 16 16.7963453592398 -0.796345359239758 283 16 16.8072912024255 -0.807291202425548 284 19 17.3489558583797 1.65104414162033 285 16 17.0272511232124 -1.02725112321243 286 19 17.0294402918496 1.97055970815041 287 18 16.7728375600141 1.22716243998594 288 22 18.2216549798327 3.77834502016730 289 16 17.0841695077785 -1.08416950777855 290 19 16.8166209327572 2.18337906724278 291 17 17.3626639259857 -0.362663925985659 292 17 17.2756702362824 -0.275670236282376 293 15 16.1469414387769 -1.14694143877686 294 18 16.9495871638408 1.05041283615917 295 19 16.6929844320053 2.30701556799471 296 20 16.7017411065539 3.29825889344607 297 16 15.5445531167654 0.455446883234646 298 22 18.6878448450524 3.31215515494763 299 17 15.1533680409921 1.84663195900790 300 16 16.3302585485151 -0.330258548515098 301 18 17.2264654691938 0.773534530806177 302 19 17.2264654691938 1.77353453080618 303 16 16.8024428638632 -0.8024428638632 304 14 15.0253532029659 -1.02535320296586 305 14 15.027542371603 -1.02754237160301 306 15 16.3674744153468 -1.36747441534679 307 15 17.4376687154321 -2.43766871543208 308 17 16.813388707049 0.186611292951009 309 17 15.9237492922817 1.07625070771826 310 15 16.9135174085752 -1.91351740857522 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14.4812807572636 -2.48128075726359 525 16 16.2999646222669 -0.299964622266933 526 19 17.381104765538 1.61889523446199 527 20 19.2648906338731 0.735109366126937 528 19 16.7787164435265 2.22128355647349 529 10 11.0431273732383 -1.04312737323828 530 13 13.8231201622521 -0.823120162252053 531 21 19.2720311955676 1.72796880443242 532 15 15.1483010813188 -0.14830108131876 533 8 12.0356577139520 -4.03565771395196 534 17 16.9494715972248 0.0505284027751579 535 19 16.5188814859827 2.48111851401725 536 18 17.4326017557587 0.567398244241265 537 18 16.5451515096286 1.45484849037136 538 16 16.5736107019117 -0.573610701911698 539 18 17.4785742971391 0.521425702860944 540 11 10.3724048221868 0.627595177813159 541 12 13.0654039214973 -1.06540392149733 542 12 13.0654039214973 -1.06540392149733 543 12 11.7736335877710 0.226366412228961 544 13 15.0542698844160 -2.05426988441597 545 19 17.1946584845866 1.80534151541345 546 19 16.7596900360701 2.24030996392986 547 13 14.0951501290427 -1.09515012904270 548 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-2.34976980123110 572 19 17.4821156863323 1.51788431366768 573 14 13.9520172195464 0.0479827804536292 574 14 14.8504133088623 -0.850413308862254 575 13 14.4088773544344 -1.40887735443437 576 13 13.9936114236524 -0.993611423652375 577 14 15.7816469277355 -1.78164692773551 578 13 11.772796639690 1.22720336031001 579 13 13.7983054136573 -0.79830541365727 580 14 14.0789890005015 -0.0789890005015414 581 14 14.5358491353895 -0.535849135389537 582 14 14.9839525957289 -0.983952595728899 583 14 13.8530346295862 0.146965370413777 584 11 12.3610068928075 -1.36100689280747 585 13 14.1993932755452 -1.19939327554524 586 12 12.9032446045446 -0.903244604544629 587 13 15.1459510748786 -2.1459510748786 588 13 14.0757567747933 -1.07575677479331 589 11 11.5895825844468 -0.589582584446755 590 15 14.3022842014917 0.69771579850833 591 16 14.3460675742348 1.65393242576517 592 12 13.0455405659599 -1.04554056595991 593 10 7.25741144837988 2.74258855162012 594 16 15.3188953972141 0.681104602785909 595 15 16.2129131492557 -1.21291314925566 596 9 8.66958605714987 0.330413942850128 597 12 10.9276167079439 1.07238329205605 598 15 14.6060055862736 0.393994413726394 599 10 10.2491805394150 -0.249180539414952 600 9 8.31561684820831 0.684383151791692 601 15 14.1256376521599 0.874362347840086 602 13 13.8646565830501 -0.864656583050066 603 15 10.1474357250346 4.8525642749654 604 12 11.9398495663921 0.060150433607945 605 14 9.26874215345314 4.73125784654686 606 12 12.3967097012800 -0.396709701280049 607 13 11.1399660657483 1.86003393425171 608 10 8.02513352974433 1.97486647025567 609 14 15.1925997265370 -1.19259972653697 610 14 13.8898835496249 0.110116450375110 611 14 14.7839013016665 -0.783901301666456 612 12 12.5696540236155 -0.569654023615541 613 12 14.7992254821266 -2.79922548212656 614 15 14.8736572157899 0.126342784210061 615 13 12.2003606342139 0.79963936578613 616 14 14.4364995986364 -0.436499598636367 617 14 9.33290415420878 4.66709584579122 618 11 9.99658919806071 1.00341080193929 619 16 16.0719694083965 -0.0719694083964852 620 13 13.4315103563778 -0.431510356377788 621 14 15.4001007457790 -1.40010074577896 622 12 13.462158717298 -1.46215871729800 623 15 15.3136801118587 -0.313680111858721 624 19 11.5510597682460 7.44894023175402 625 11 9.59560439066776 1.40439560933224 626 12 13.6329138709963 -1.63291387099633 627 13 14.2507294279630 -1.25072942796296 628 11 9.1766362328895 1.82336376711050 629 12 11.5867625767186 0.413237423281437 630 12 13.1986215327580 -1.19862153275797 631 14 15.9660523657318 -1.96605236573184 632 12 14.0495320223344 -2.04953202233443 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.170858810313012 0.341717620626024 0.829141189686988 7 0.0824803239825906 0.164960647965181 0.91751967601741 8 0.267842564214982 0.535685128429965 0.732157435785018 9 0.175572131175136 0.351144262350272 0.824427868824864 10 0.326972089483816 0.653944178967631 0.673027910516184 11 0.399771662273971 0.799543324547943 0.600228337726029 12 0.612274341928245 0.77545131614351 0.387725658071755 13 0.623478851024512 0.753042297950976 0.376521148975488 14 0.590207164356103 0.819585671287794 0.409792835643897 15 0.712182383122536 0.575635233754929 0.287817616877464 16 0.967830929461745 0.0643381410765104 0.0321690705382552 17 0.994513862210046 0.0109722755799071 0.00548613778995355 18 0.99990082113853 0.000198357722941293 9.91788614706467e-05 19 0.99982560556581 0.000348788868380286 0.000174394434190143 20 0.999707772606672 0.000584454786655948 0.000292227393327974 21 0.999575768036123 0.00084846392775407 0.000424231963877035 22 0.999355041670986 0.00128991665802825 0.000644958329014127 23 0.999214716110532 0.00157056777893490 0.000785283889467448 24 0.998930384378593 0.00213923124281427 0.00106961562140714 25 0.99877931225892 0.00244137548215896 0.00122068774107948 26 0.998542960857011 0.0029140782859776 0.0014570391429888 27 0.998831835334675 0.00233632933064895 0.00116816466532447 28 0.998352067754483 0.00329586449103333 0.00164793224551667 29 0.997988246521646 0.00402350695670873 0.00201175347835436 30 0.997286891015759 0.00542621796848241 0.00271310898424120 31 0.996521007595509 0.00695798480898293 0.00347899240449146 32 0.99772224830537 0.00455550338925879 0.00227775169462939 33 0.997976855426696 0.00404628914660706 0.00202314457330353 34 0.999379121893198 0.00124175621360334 0.00062087810680167 35 0.999132393565249 0.00173521286950192 0.000867606434750962 36 0.998762427023899 0.00247514595220244 0.00123757297610122 37 0.99834615192995 0.00330769614009962 0.00165384807004981 38 0.997642146602906 0.00471570679418894 0.00235785339709447 39 0.996744990056623 0.00651001988675361 0.00325500994337680 40 0.995560071091651 0.0088798578166972 0.0044399289083486 41 0.993947611563472 0.0121047768730550 0.00605238843652752 42 0.992415950324254 0.0151680993514917 0.00758404967574584 43 0.992164994749926 0.0156700105001486 0.00783500525007429 44 0.990202341047093 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0.272201828918002 0.544403657836004 0.727798171081998 612 0.256725840001773 0.513451680003546 0.743274159998227 613 0.318139894625033 0.636279789250067 0.681860105374967 614 0.257953458715955 0.515906917431911 0.742046541284045 615 0.214598562211465 0.42919712442293 0.785401437788535 616 0.172303842142665 0.344607684285330 0.827696157857335 617 0.161242653411964 0.322485306823928 0.838757346588036 618 0.151369473440229 0.302738946880458 0.84863052655977 619 0.122503399838262 0.245006799676524 0.877496600161738 620 0.09089053554533 0.18178107109066 0.90910946445467 621 0.0618937294609168 0.123787458921834 0.938106270539083 622 0.0767322346018966 0.153464469203793 0.923267765398103 623 0.0471858602167346 0.0943717204334691 0.952814139783265 624 0.994182987824638 0.0116340243507233 0.00581701217536163 625 0.979173794194894 0.0416524116102122 0.0208262058051061 626 0.97883696474537 0.0423260705092594 0.0211630352546297 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 25 0.0402576489533011 NOK 5% type I error level 82 0.132045088566828 NOK 10% type I error level 114 0.183574879227053 NOK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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