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Multiple Linear Regression - Estimated Regression Equation | USA[t] = + 135.698187089792 + 1.88117003420919Colombia[t] + 0.148421997798835t + e[t] |
Multiple Linear Regression - Regression Statistics | Multiple R | 0.775073512463964 | R-squared | 0.600738949723227 | Adjusted R-squared | 0.598502193139044 | F-TEST (value) | 268.575916562013 | F-TEST (DF numerator) | 2 | F-TEST (DF denominator) | 357 | p-value | 0 | Multiple Linear Regression - Residual Statistics | Residual Standard Deviation | 31.0592597650331 | Sum Squared Residuals | 344389.909323193 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error | 1 | 255 | 300.035129673369 | -45.0351296733693 | 2 | 280.2 | 300.183551671168 | -19.9835516711683 | 3 | 299.9 | 299.974551362467 | -0.0745513624673993 | 4 | 339.2 | 299.803174454451 | 39.3968255455494 | 5 | 374.2 | 301.211980375170 | 72.9880196248304 | 6 | 393.5 | 307.248464580043 | 86.2515354199568 | 7 | 389.2 | 307.340451476816 | 81.8595485231843 | 8 | 381.7 | 306.755217161273 | 74.944782838727 | 9 | 375.2 | 305.492761633415 | 69.7072383665851 | 10 | 369 | 304.493669910346 | 64.5063300896539 | 11 | 357.4 | 303.645071790014 | 53.7549282099859 | 12 | 352.1 | 302.683603467629 | 49.4163965323705 | 13 | 346.5 | 301.421147939771 | 45.0788520602285 | 14 | 342.9 | 301.099277429018 | 41.800722570982 | 15 | 340.3 | 300.457608012449 | 39.842391987551 | 16 | 328.3 | 299.891185397248 | 28.4088146027517 | 17 | 322.9 | 299.362386182732 | 23.5376138172681 | 18 | 314.3 | 298.871210368900 | 15.4287896311005 | 19 | 308.9 | 298.417657955751 | 10.4823420442485 | 20 | 294 | 297.945293842261 | -3.94529384226124 | 21 | 285.6 | 296.720461715087 | -11.1204617150873 | 22 | 281.2 | 294.780784974914 | -13.580784974914 | 23 | 280.3 | 293.273777342609 | -12.9737773426087 | 24 | 278.8 | 291.992510114409 | -13.1925101144086 | 25 | 274.5 | 290.805301387919 | -16.3053013879189 | 26 | 270.4 | 287.906227930299 | -17.5062279302989 | 27 | 263.4 | 270.390463306873 | -6.99046330687336 | 28 | 259.9 | 269.222066280726 | -9.32206628072575 | 29 | 258 | 271.797197622654 | -13.7971976226544 | 30 | 262.7 | 279.263371053527 | -16.5633710535270 | 31 | 284.7 | 282.891957614613 | 1.80804238538712 | 32 | 311.3 | 286.783907980488 | 24.516092019512 | 33 | 322.1 | 294.043152707598 | 28.0568472924024 | 34 | 327 | 297.01332975671 | 29.9866702432898 | 35 | 331.3 | 299.550837697955 | 31.7491623020453 | 36 | 333.3 | 301.128948921753 | 32.1710510782475 | 37 | 321.4 | 301.559546424683 | 19.8404535753172 | 38 | 327 | 299.845610088615 | 27.1543899113855 | 39 | 320 | 298.808894964862 | 21.1911050351385 | 40 | 314.7 | 304.243404758788 | 10.4565952412118 | 41 | 316.7 | 302.247292917589 | 14.4527070824114 | 42 | 314.4 | 300.138310874336 | 14.2616891256636 | 43 | 321.3 | 298.894667046820 | 22.4053329531796 | 44 | 318.2 | 297.387659414515 | 20.8123405854848 | 45 | 307.2 | 295.843028381526 | 11.3569716184743 | 46 | 301.3 | 293.903351641352 | 7.39664835864767 | 47 | 287.5 | 291.926051500495 | -4.42605150049479 | 48 | 277.7 | 297.322937893737 | -19.6229378937373 | 49 | 274.4 | 296.643645076484 | -22.2436450764841 | 50 | 258.8 | 294.929708740416 | -36.1297087404158 | 51 | 253.3 | 293.535571310163 | -40.2355713101631 | 52 | 251 | 292.329550883331 | -41.3295508833313 | 53 | 248.4 | 291.010660254447 | -42.6106602544470 | 54 | 249.5 | 289.353159019405 | -39.853159019405 | 55 | 246.1 | 287.714469484705 | -41.6144694847051 | 56 | 244.5 | 285.962909747953 | -41.4629097479526 | 57 | 243.6 | 284.267785112226 | -40.6677851122265 | 58 | 244 | 291.545841539678 | -47.5458415396781 | 59 | 240.8 | 296.265506720605 | -55.4655067206053 | 60 | 249.8 | 294.927804391379 | -45.1278043913789 | 61 | 248 | 292.894069149495 | -44.8940691494950 | 62 | 259.4 | 291.217756214111 | -31.817756214111 | 63 | 260.5 | 297.686909526853 | -37.1869095268527 | 64 | 260.8 | 297.722461322599 | -36.922461322599 | 65 | 261.3 | 295.895654784478 | -34.5956547844782 | 66 | 259.5 | 293.937166343963 | -34.4371663439627 | 67 | 256.6 | 292.392535310973 | -35.7925353109732 | 68 | 257.9 | 290.4528585708 | -32.5528585707999 | 69 | 256.5 | 288.851792436784 | -32.3517924367842 | 70 | 254.2 | 300.21198783847 | -46.0119878384698 | 71 | 253.3 | 297.237667579481 | -43.9376675794814 | 72 | 253.8 | 294.376217522546 | -40.5762175225455 | 73 | 255.5 | 292.173176977583 | -36.6731769775828 | 74 | 257.1 | 289.951324732278 | -32.8513247322781 | 75 | 257.3 | 287.353238480131 | -30.0532384801315 | 76 | 253.2 | 290.680837835744 | -37.4808378357439 | 77 | 252.8 | 290.170850321570 | -37.3708503215695 | 78 | 252 | 287.704445971818 | -35.7044459718176 | 79 | 250.7 | 285.294476723092 | -34.5944767230919 | 80 | 252.2 | 282.621143669577 | -30.4211436695769 | 81 | 250 | 287.660607756320 | -37.6606077563197 | 82 | 251 | 288.787238171907 | -37.7872381719073 | 83 | 253.4 | 288.239627257049 | -34.8396272570487 | 84 | 251.2 | 285.641541004902 | -34.4415410049021 | 85 | 255.6 | 285.169176891412 | -29.5691768914119 | 86 | 261.1 | 282.627525740292 | -21.5275257402916 | 87 | 258.9 | 281.007647905934 | -22.1076479059338 | 88 | 259.9 | 281.099634802706 | -21.1996348027064 | 89 | 261.2 | 280.608458988874 | -19.4084589888741 | 90 | 264.7 | 279.534120464437 | -14.8341204644369 | 91 | 267.1 | 276.691482107843 | -9.59148210784312 | 92 | 266.4 | 279.642847456614 | -13.2428474566137 | 93 | 267.7 | 280.807101272885 | -13.1071012728855 | 94 | 268.6 | 278.284261822107 | -9.68426182210724 | 95 | 267.5 | 277.002994593907 | -9.50299459390712 | 96 | 268.5 | 278.599917518047 | -10.0999175180470 | 97 | 268.5 | 276.039454666585 | -7.53945466658463 | 98 | 270.5 | 272.914640804859 | -2.41464080485945 | 99 | 270.9 | 275.753135951577 | -4.85313595157747 | 100 | 270.1 | 269.900625540249 | 0.199374459751070 | 101 | 269.3 | 264.800583142604 | 4.49941685739588 | 102 | 269.8 | 268.109370797874 | 1.69062920212559 | 103 | 270.1 | 264.457829326571 | 5.64217067342935 | 104 | 264.9 | 261.445885666898 | 3.45411433310191 | 105 | 263.7 | 265.018037126958 | -1.31803712695765 | 106 | 264.8 | 261.648671160785 | 3.15132883921473 | 107 | 263.7 | 267.96733087079 | -4.26733087079028 | 108 | 255.9 | 268.078129467905 | -12.1781294679049 | 109 | 276.2 | 278.742291956933 | -2.54229195693315 | 110 | 360.1 | 296.987569683824 | 63.1124303161756 | 111 | 380.5 | 324.751567783814 | 55.7484322161858 | 112 | 373.7 | 327.552439529848 | 46.1475604701519 | 113 | 369.8 | 329.582031561856 | 40.2179684381439 | 114 | 366.6 | 327.774036724077 | 38.8259632759227 | 115 | 359.3 | 324.912586667141 | 34.3874133328585 | 116 | 345.8 | 322.145195111916 | 23.654804888084 | 117 | 326.2 | 318.907511048138 | 7.29248895186166 | 118 | 324.5 | 316.836152405570 | 7.66384759442967 | 119 | 328.1 | 318.959802939289 | 9.14019706071121 | 120 | 327.5 | 315.740930575853 | 11.7590694241468 | 121 | 324.4 | 312.898292219259 | 11.5017077807406 | 122 | 316.5 | 310.375452768481 | 6.12454723151881 | 123 | 310.9 | 307.64568461394 | 3.25431538606003 | 124 | 301.5 | 305.066410062135 | -3.56641006213545 | 125 | 291.7 | 302.487135510331 | -10.7871355103310 | 126 | 290.4 | 300.208848164 | -9.80884816399996 | 127 | 287.4 | 297.892937416985 | -10.4929374169847 | 128 | 277.7 | 295.859202175101 | -18.1592021751009 | 129 | 281.6 | 294.051207337322 | -12.4512073373221 | 130 | 288 | 297.002572686093 | -9.00257268609269 | 131 | 276 | 300.254925240337 | -24.2549252403367 | 132 | 272.9 | 298.540988904268 | -25.6409889042685 | 133 | 283 | 298.915151306172 | -15.9151513061724 | 134 | 283.3 | 302.675419769653 | -19.3754197696529 | 135 | 276.8 | 299.625852709296 | -22.8258527092960 | 136 | 284.5 | 301.316834135146 | -16.8168341351464 | 137 | 282.7 | 300.223683910367 | -17.5236839103672 | 138 | 281.2 | 297.249363651379 | -16.0493636513788 | 139 | 287.4 | 294.613653998548 | -7.21365399854804 | 140 | 283.1 | 292.053191147086 | -8.95319114708557 | 141 | 284 | 289.417481494255 | -5.41748149425484 | 142 | 285.5 | 292.14310643892 | -6.64310643892025 | 143 | 289.2 | 300.436994684845 | -11.2369946848449 | 144 | 292.5 | 297.895343533725 | -5.39534353372459 | 145 | 296.4 | 298.175447433918 | -1.77544743391811 | 146 | 305.2 | 292.623924228063 | 12.5760757719369 | 147 | 303.9 | 291.098104895416 | 12.8018951045843 | 148 | 311.5 | 303.398885314206 | 8.10111468579407 | 149 | 316.3 | 300.368129954191 | 15.9318700458088 | 150 | 316.7 | 302.059111380042 | 14.6408886199584 | 151 | 322.5 | 301.210513259710 | 21.2894867402904 | 152 | 317.1 | 298.537180206195 | 18.5628197938054 | 153 | 309.8 | 295.769788650969 | 14.0302113490308 | 154 | 303.8 | 295.222177736111 | 8.57782226388937 | 155 | 290.3 | 296.329996451356 | -6.02999645135613 | 156 | 293.7 | 293.412111293394 | 0.287888706605987 | 157 | 291.7 | 290.268485731327 | 1.43151426867324 | 158 | 296.5 | 287.030801667549 | 9.46919833245096 | 159 | 289.1 | 290.903940333082 | -1.80394033308204 | 160 | 288.5 | 295.190936406141 | -6.69093640614113 | 161 | 293.8 | 292.160181046126 | 1.63981895387358 | 162 | 297.7 | 289.279919288848 | 8.42008071115153 | 163 | 305.4 | 286.625397935676 | 18.7746020643244 | 164 | 302.7 | 283.952064882161 | 18.7479351178393 | 165 | 302.5 | 295.933046395135 | 6.5669536048647 | 166 | 303 | 294.538908964883 | 8.46109103511739 | 167 | 294.5 | 292.034881214447 | 2.46511878555351 | 168 | 294.1 | 289.380359861274 | 4.71964013872641 | 169 | 294.5 | 287.120884215285 | 7.37911578471533 | 170 | 297.1 | 285.105960673743 | 11.9940393262571 | 171 | 289.4 | 287.587033513961 | 1.8129664860388 | 172 | 292.4 | 294.620537836966 | -2.22053783696568 | 173 | 287.9 | 292.586802595082 | -4.68680259508185 | 174 | 286.6 | 290.553067353198 | -3.95306735319799 | 175 | 280.5 | 288.613390613025 | -8.11339061302464 | 176 | 272.4 | 286.560843670799 | -14.1608436707987 | 177 | 269.2 | 283.887510617284 | -14.6875106172838 | 178 | 270.6 | 287.365603575633 | -16.7656035756328 | 179 | 267.3 | 286.366511852564 | -19.0665118525641 | 180 | 262.5 | 284.125847906917 | -21.6258479069173 | 181 | 266.8 | 284.274269904716 | -17.4742699047161 | 182 | 268.8 | 277.349492573888 | -8.54949257388833 | 183 | 263.1 | 273.998938308058 | -10.8989383080581 | 184 | 261.2 | 272.905788083279 | -11.7057880832789 | 185 | 266 | 271.831449558842 | -5.83144955884172 | 186 | 262.5 | 270.738299334062 | -8.23829933406247 | 187 | 265.2 | 263.738275201866 | 1.46172479813362 | 188 | 261.3 | 257.584777585064 | 3.7152224149356 | 189 | 253.7 | 256.679744363706 | -2.97974436370610 | 190 | 249.2 | 255.774711142348 | -6.5747111423478 | 191 | 239.1 | 254.907301321674 | -15.8073013216737 | 192 | 236.4 | 254.002268100315 | -17.6022681003153 | 193 | 235.2 | 253.210105081010 | -18.0101050810096 | 194 | 245.2 | 252.455565462388 | -7.255565462388 | 195 | 246.2 | 251.719837544109 | -5.51983754410852 | 196 | 247.7 | 256.778113331193 | -9.07811333119335 | 197 | 251.4 | 257.547321440281 | -6.1473214402812 | 198 | 253.3 | 256.378924414134 | -3.07892441413360 | 199 | 254.8 | 255.586761394828 | -0.786761394827835 | 200 | 250 | 267.605366308487 | -17.6053663084867 | 201 | 249.3 | 266.719144787470 | -17.4191447874705 | 202 | 241.5 | 265.832923266454 | -24.3329232664543 | 203 | 243.3 | 265.454617654675 | -22.1546176546745 | 204 | 248 | 264.116915325448 | -16.1169153254481 | 205 | 253 | 263.381187407169 | -10.3811874071686 | 206 | 252.9 | 276.415624139300 | -23.5156241393004 | 207 | 251.5 | 313.52903730931 | -62.0290373093099 | 208 | 251.6 | 311.476490367084 | -59.876490367084 | 209 | 253.5 | 310.044729536147 | -56.5447295361471 | 210 | 259.8 | 311.999074766787 | -52.1990747667868 | 211 | 334.1 | 309.739599120798 | 24.3604008792022 | 212 | 448 | 346.758953789097 | 101.241046210903 | 213 | 445.8 | 373.619990272666 | 72.1800097273338 | 214 | 445 | 378.678266059751 | 66.3217339402489 | 215 | 448.2 | 378.318772148313 | 69.8812278516865 | 216 | 438.2 | 370.792020406539 | 67.4079795934612 | 217 | 439.8 | 367.234537436945 | 72.5654625630545 | 218 | 423.4 | 365.689906403956 | 57.7100935960439 | 219 | 410.8 | 361.9254947306 | 48.8745052694002 | 220 | 408.4 | 360.606604101715 | 47.7933958982845 | 221 | 406.7 | 366.454971303168 | 40.2450286968319 | 222 | 405.9 | 360.24503858534 | 45.6549614146601 | 223 | 402.7 | 356.706367316089 | 45.9936326839113 | 224 | 405.1 | 349.969706988682 | 55.1302930113181 | 225 | 399.6 | 347.352809036193 | 52.2471909638068 | 226 | 386.5 | 341.387428422812 | 45.1125715771878 | 227 | 381.4 | 341.761590824716 | 39.6384091752839 | 228 | 375.2 | 341.740707519436 | 33.4592924805639 | 229 | 357.7 | 330.018946601375 | 27.6810533986251 | 230 | 359 | 335.058410688118 | 23.9415893118823 | 231 | 355 | 334.360306170522 | 20.6396938294777 | 232 | 352.7 | 328.978088267746 | 23.7219117322538 | 233 | 344.4 | 330.537387791202 | 13.8626122087981 | 234 | 343.8 | 328.503652549318 | 15.2963474506819 | 235 | 338 | 333.731233639482 | 4.26876636051827 | 236 | 339 | 363.583330477444 | -24.5833304774437 | 237 | 333.3 | 367.362410641266 | -34.0624106412663 | 238 | 334.4 | 372.270192825614 | -37.8701928256144 | 239 | 328.3 | 372.493861624782 | -44.1938616247816 | 240 | 330.7 | 358.044404157117 | -27.3444041571171 | 241 | 330 | 349.14439829037 | -19.1443982903697 | 242 | 331.6 | 385.016239237801 | -53.4162392378011 | 243 | 351.2 | 467.729214037042 | -116.529214037042 | 244 | 389.4 | 449.159994194459 | -59.7599941944589 | 245 | 410.9 | 495.415893730725 | -84.515893730725 | 246 | 442.8 | 495.677185930576 | -52.8771859305764 | 247 | 462.8 | 422.008495786007 | 40.7915042139935 | 248 | 466.9 | 409.571890254946 | 57.3281097450542 | 249 | 461.7 | 400.615449287172 | 61.0845507128278 | 250 | 439.2 | 389.984766988952 | 49.2152330110477 | 251 | 430.3 | 380.783773916731 | 49.5162260832686 | 252 | 416.1 | 394.796419066652 | 21.303580933348 | 253 | 402.5 | 394.530983656925 | 7.96901634307517 | 254 | 397.3 | 407.885219294872 | -10.5852192948722 | 255 | 403.3 | 379.703220577481 | 23.5967794225194 | 256 | 395.9 | 383.012008232751 | 12.8879917672491 | 257 | 387.8 | 361.545786537486 | 26.2542134625139 | 258 | 378.6 | 358.740771581576 | 19.8592284184236 | 259 | 377.1 | 360.751551913242 | 16.3484480867576 | 260 | 370.4 | 358.586134768964 | 11.8138652310360 | 261 | 362 | 342.895105078721 | 19.1048949212786 | 262 | 350.3 | 339.958408220417 | 10.3415917795829 | 263 | 348.2 | 350.321583503972 | -2.12158350397189 | 264 | 344.6 | 352.501669138717 | -7.90166913871662 | 265 | 343.5 | 350.35506369478 | -6.85506369478026 | 266 | 342.8 | 345.029280893030 | -2.22928089303034 | 267 | 347.6 | 347.378671830854 | 0.221328169146103 | 268 | 346.6 | 344.742962178023 | 1.85703782197686 | 269 | 349.5 | 341.825077020061 | 7.674922979939 | 270 | 342.1 | 342.086369219912 | 0.0136307800876353 | 271 | 342 | 331.004206113482 | 10.9957938865177 | 272 | 342.8 | 326.355644524048 | 16.4443554759523 | 273 | 339.3 | 318.603152378168 | 20.6968476218321 | 274 | 348.2 | 318.695139274941 | 29.5048607250595 | 275 | 333.7 | 335.473104375149 | -1.77310437514863 | 276 | 334.7 | 358.628235891326 | -23.9282358913259 | 277 | 354 | 341.37583507269 | 12.6241649273103 | 278 | 367.7 | 331.949101596364 | 35.7508984036363 | 279 | 363.3 | 334.147998931451 | 29.1520010685494 | 280 | 358.4 | 326.451941886597 | 31.9480581134029 | 281 | 353.1 | 324.437018345055 | 28.6629816549447 | 282 | 343.1 | 314.445933858467 | 28.6540661415334 | 283 | 344.6 | 313.992381445319 | 30.6076185546815 | 284 | 344.4 | 306.634935006623 | 37.7650649933773 | 285 | 333.9 | 305.203174175686 | 28.6968258243142 | 286 | 331.7 | 307.496130012483 | 24.2038699875169 | 287 | 324.3 | 310.108884755096 | 14.1911152449041 | 288 | 321.2 | 307.397928300897 | 13.8020716991032 | 289 | 322.4 | 301.432547687516 | 20.9674523124842 | 290 | 321.7 | 289.654351668428 | 32.0456483315717 | 291 | 320.5 | 290.197819373411 | 30.3021806265889 | 292 | 312.8 | 296.365985480679 | 16.4340145193207 | 293 | 309.7 | 303.869782312236 | 5.83021768776385 | 294 | 315.6 | 283.964931745365 | 31.6350682546351 | 295 | 309.7 | 283.379697429822 | 26.3203025701778 | 296 | 304.6 | 284.694444848831 | 19.9055551511693 | 297 | 302.5 | 286.535919877418 | 15.9640801225821 | 298 | 301.5 | 275.660685474751 | 25.8393145252492 | 299 | 298.8 | 281.433805874835 | 17.3661941251649 | 300 | 291.3 | 279.832739740819 | 11.4672602591806 | 301 | 293.6 | 283.988053911484 | 9.61194608851618 | 302 | 294.6 | 281.371155958995 | 13.2288440410049 | 303 | 285.9 | 291.245227033656 | -5.34522703365556 | 304 | 297.6 | 297.168841036477 | 0.431158963523426 | 305 | 301.1 | 286.143113031073 | 14.9568869689272 | 306 | 293.8 | 281.41930464027 | 12.3806953597302 | 307 | 297.7 | 268.568841701683 | 29.1311582983169 | 308 | 292.9 | 265.255910836537 | 27.6440891634629 | 309 | 292.1 | 275.619086120092 | 16.4809138799082 | 310 | 287.2 | 275.767508117891 | 11.4324918821093 | 311 | 288.2 | 282.236661430632 | 5.9633385693676 | 312 | 283.8 | 268.972341084520 | 14.8276589154804 | 313 | 299.9 | 277.059300626681 | 22.8406993733187 | 314 | 292.4 | 274.611707977271 | 17.7882920227285 | 315 | 293.3 | 268.702762464917 | 24.5972375350833 | 316 | 300.8 | 273.742226551659 | 27.0577734483406 | 317 | 293.7 | 276.731215301114 | 16.9687846988859 | 318 | 293.1 | 270.427224081575 | 22.6727759184246 | 319 | 294.4 | 278.062702815527 | 16.3372971844731 | 320 | 292.1 | 272.699296613093 | 19.4007033869073 | 321 | 291.9 | 273.73186852697 | 18.1681314730301 | 322 | 282.5 | 271.604074783376 | 10.8959252166244 | 323 | 277.9 | 273.313867909568 | 4.58613209043188 | 324 | 287.5 | 276.265233258339 | 11.2347667416614 | 325 | 289.2 | 288.415520074392 | 0.784479925607875 | 326 | 285.6 | 289.090669681769 | -3.4906696817695 | 327 | 293.2 | 293.753899761670 | -0.553899761670429 | 328 | 290.8 | 290.083546590025 | 0.716453409975422 | 329 | 283.1 | 293.204217241874 | -10.1042172418739 | 330 | 275 | 303.548580825087 | -28.5485808250866 | 331 | 287.8 | 287.838739434502 | -0.0387394345019337 | 332 | 287.8 | 289.830708065826 | -2.03070806582579 | 333 | 287.4 | 302.771086296247 | -15.3710862962472 | 334 | 284 | 300.756162754705 | -16.7561627547054 | 335 | 277.8 | 316.348990733362 | -38.5489907333617 | 336 | 277.6 | 334.613080160595 | -57.0130801605951 | 337 | 304.9 | 336.210003084735 | -31.3100030847350 | 338 | 294 | 362.092831150516 | -68.0928311505156 | 339 | 300.9 | 388.483575125533 | -87.5835751255327 | 340 | 324 | 374.617280368473 | -50.6172803684731 | 341 | 332.9 | 369.347932667749 | -36.4479326677494 | 342 | 341.6 | 356.610339931215 | -15.0103399312153 | 343 | 333.4 | 338.304483893422 | -4.90448389342193 | 344 | 348.2 | 338.340035689168 | 9.8599643108318 | 345 | 344.7 | 329.534088324131 | 15.1659116758687 | 346 | 344.7 | 348.061541556154 | -3.36154155615394 | 347 | 329.3 | 355.283162882579 | -25.9831628825793 | 348 | 323.5 | 355.563266782773 | -32.0632667827728 | 349 | 323.2 | 384.512402004314 | -61.3124020043144 | 350 | 317.4 | 366.959013980205 | -49.5590139802047 | 351 | 330.1 | 355.726357271038 | -25.6263572710379 | 352 | 329.2 | 358.075748208862 | -28.8757482088615 | 353 | 334.9 | 351.696510187954 | -16.7965101879545 | 354 | 315.8 | 338.695553646631 | -22.8955536466310 | 355 | 315.4 | 341.176626486849 | -25.7766264868493 | 356 | 319.6 | 352.856620794350 | -33.2566207943504 | 357 | 317.3 | 346.025901965233 | -28.7259019652332 | 358 | 313.8 | 343.503062514455 | -29.7030625144549 | 359 | 315.8 | 366.564135528922 | -50.7641355289218 | 360 | 311.3 | 381.348060392868 | -70.0480603928681 |
Goldfeld-Quandt test for Heteroskedasticity | p-values | Alternative Hypothesis | breakpoint index | greater | 2-sided | less | 6 | 0.0169054038264475 | 0.0338108076528951 | 0.983094596173552 | 7 | 0.0629708161866201 | 0.125941632373240 | 0.93702918381338 | 8 | 0.2468436518234 | 0.4936873036468 | 0.7531563481766 | 9 | 0.425157697431217 | 0.850315394862434 | 0.574842302568783 | 10 | 0.467769714153998 | 0.935539428307995 | 0.532230285846002 | 11 | 0.461060407491732 | 0.922120814983465 | 0.538939592508268 | 12 | 0.400373179786915 | 0.80074635957383 | 0.599626820213085 | 13 | 0.321174907534732 | 0.642349815069464 | 0.678825092465268 | 14 | 0.252357501835523 | 0.504715003671046 | 0.747642498164477 | 15 | 0.190831848725076 | 0.381663697450152 | 0.809168151274924 | 16 | 0.147031848237029 | 0.294063696474059 | 0.85296815176297 | 17 | 0.110282319258264 | 0.220564638516528 | 0.889717680741736 | 18 | 0.0838173456341139 | 0.167634691268228 | 0.916182654365886 | 19 | 0.0623052923850088 | 0.124610584770018 | 0.937694707614991 | 20 | 0.053529378375405 | 0.10705875675081 | 0.946470621624595 | 21 | 0.0390930624052116 | 0.0781861248104232 | 0.960906937594788 | 22 | 0.0260383838072295 | 0.0520767676144591 | 0.97396161619277 | 23 | 0.0207702773512524 | 0.0415405547025049 | 0.979229722648748 | 24 | 0.0194576272397379 | 0.0389152544794759 | 0.980542372760262 | 25 | 0.0184746332753053 | 0.0369492665506105 | 0.981525366724695 | 26 | 0.0309149846570224 | 0.0618299693140447 | 0.969085015342978 | 27 | 0.589476690405947 | 0.821046619188106 | 0.410523309594053 | 28 | 0.661703455467988 | 0.676593089064024 | 0.338296544532012 | 29 | 0.636011791239832 | 0.727976417520336 | 0.363988208760168 | 30 | 0.581776335305686 | 0.836447329388628 | 0.418223664694314 | 31 | 0.536203620683442 | 0.927592758633117 | 0.463796379316558 | 32 | 0.523508543767727 | 0.952982912464545 | 0.476491456232273 | 33 | 0.482201915903577 | 0.964403831807153 | 0.517798084096423 | 34 | 0.437292978507324 | 0.874585957014648 | 0.562707021492676 | 35 | 0.393815197187338 | 0.787630394374675 | 0.606184802812662 | 36 | 0.353191422011923 | 0.706382844023845 | 0.646808577988077 | 37 | 0.321049862712557 | 0.642099725425114 | 0.678950137287443 | 38 | 0.282868727431107 | 0.565737454862215 | 0.717131272568893 | 39 | 0.246791864999891 | 0.493583729999781 | 0.75320813500011 | 40 | 0.236420824089226 | 0.472841648178452 | 0.763579175910774 | 41 | 0.209272478655533 | 0.418544957311066 | 0.790727521344467 | 42 | 0.179986118855433 | 0.359972237710866 | 0.820013881144567 | 43 | 0.153856121227558 | 0.307712242455116 | 0.846143878772442 | 44 | 0.130616308186698 | 0.261232616373397 | 0.869383691813302 | 45 | 0.108207474750286 | 0.216414949500572 | 0.891792525249714 | 46 | 0.0884405440894327 | 0.176881088178865 | 0.911559455910567 | 47 | 0.0725851880890993 | 0.145170376178199 | 0.9274148119109 | 48 | 0.0776704173803718 | 0.155340834760744 | 0.922329582619628 | 49 | 0.0802284896533106 | 0.160456979306621 | 0.91977151034669 | 50 | 0.095127008764692 | 0.190254017529384 | 0.904872991235308 | 51 | 0.108191344975057 | 0.216382689950114 | 0.891808655024943 | 52 | 0.114532748725215 | 0.22906549745043 | 0.885467251274785 | 53 | 0.115122176195249 | 0.230244352390497 | 0.884877823804751 | 54 | 0.105838331495145 | 0.21167666299029 | 0.894161668504855 | 55 | 0.0950381421056694 | 0.190076284211339 | 0.90496185789433 | 56 | 0.0824799311766132 | 0.164959862353226 | 0.917520068823387 | 57 | 0.0697292877188236 | 0.139458575437647 | 0.930270712281176 | 58 | 0.0681285076553798 | 0.136257015310760 | 0.93187149234462 | 59 | 0.0823595611558394 | 0.164719122311679 | 0.91764043884416 | 60 | 0.0780578767591078 | 0.156115753518216 | 0.921942123240892 | 61 | 0.0704584759582087 | 0.140916951916417 | 0.929541524041791 | 62 | 0.058640026395464 | 0.117280052790928 | 0.941359973604536 | 63 | 0.0508736572165582 | 0.101747314433116 | 0.949126342783442 | 64 | 0.0434781320886337 | 0.0869562641772673 | 0.956521867911366 | 65 | 0.0359708221095915 | 0.071941644219183 | 0.964029177890408 | 66 | 0.029562921225531 | 0.059125842451062 | 0.97043707877447 | 67 | 0.024359586865338 | 0.048719173730676 | 0.975640413134662 | 68 | 0.0204514485925772 | 0.0409028971851543 | 0.979548551407423 | 69 | 0.0175468088817615 | 0.035093617763523 | 0.982453191118238 | 70 | 0.0162157164393775 | 0.032431432878755 | 0.983784283560623 | 71 | 0.0139108419324380 | 0.0278216838648760 | 0.986089158067562 | 72 | 0.0115474990781332 | 0.0230949981562664 | 0.988452500921867 | 73 | 0.00971757803659362 | 0.0194351560731872 | 0.990282421963406 | 74 | 0.0086506910089944 | 0.0173013820179888 | 0.991349308991006 | 75 | 0.00840899468211947 | 0.0168179893642389 | 0.99159100531788 | 76 | 0.00723680757722224 | 0.0144736151544445 | 0.992763192422778 | 77 | 0.00630609287051421 | 0.0126121857410284 | 0.993693907129486 | 78 | 0.00582496057906543 | 0.0116499211581309 | 0.994175039420935 | 79 | 0.0057566857372235 | 0.011513371474447 | 0.994243314262776 | 80 | 0.00646329180713734 | 0.0129265836142747 | 0.993536708192863 | 81 | 0.00590736266214341 | 0.0118147253242868 | 0.994092637337857 | 82 | 0.00533894478534135 | 0.0106778895706827 | 0.994661055214659 | 83 | 0.00499199402322097 | 0.00998398804644194 | 0.99500800597678 | 84 | 0.00495735500715275 | 0.0099147100143055 | 0.995042644992847 | 85 | 0.00528479424117329 | 0.0105695884823466 | 0.994715205758827 | 86 | 0.0069122749300532 | 0.0138245498601064 | 0.993087725069947 | 87 | 0.00899087050721194 | 0.0179817410144239 | 0.991009129492788 | 88 | 0.0113569566856756 | 0.0227139133713512 | 0.988643043314324 | 89 | 0.0144255359200366 | 0.0288510718400732 | 0.985574464079963 | 90 | 0.0195907583876252 | 0.0391815167752504 | 0.980409241612375 | 91 | 0.0295302726947466 | 0.0590605453894932 | 0.970469727305253 | 92 | 0.0363672039395761 | 0.0727344078791523 | 0.963632796060424 | 93 | 0.042564626656456 | 0.085129253312912 | 0.957435373343544 | 94 | 0.0526377308240258 | 0.105275461648052 | 0.947362269175974 | 95 | 0.0636947938252674 | 0.127389587650535 | 0.936305206174733 | 96 | 0.072631002204781 | 0.145262004409562 | 0.927368997795219 | 97 | 0.0852279156478973 | 0.170455831295795 | 0.914772084352103 | 98 | 0.105533718959927 | 0.211067437919854 | 0.894466281040073 | 99 | 0.119245000811963 | 0.238490001623925 | 0.880754999188037 | 100 | 0.142537356707993 | 0.285074713415987 | 0.857462643292006 | 101 | 0.172718707506614 | 0.345437415013227 | 0.827281292493387 | 102 | 0.191655070052229 | 0.383310140104458 | 0.808344929947771 | 103 | 0.213796197466223 | 0.427592394932446 | 0.786203802533777 | 104 | 0.22597336169399 | 0.45194672338798 | 0.77402663830601 | 105 | 0.227715896149987 | 0.455431792299974 | 0.772284103850013 | 106 | 0.231474049854235 | 0.462948099708469 | 0.768525950145765 | 107 | 0.226566241805518 | 0.453132483611035 | 0.773433758194482 | 108 | 0.215099017693108 | 0.430198035386217 | 0.784900982306892 | 109 | 0.216561355101023 | 0.433122710202045 | 0.783438644898977 | 110 | 0.465767895550886 | 0.931535791101771 | 0.534232104449114 | 111 | 0.604905844887352 | 0.790188310225295 | 0.395094155112648 | 112 | 0.642437788704461 | 0.715124422591078 | 0.357562211295539 | 113 | 0.645829981390068 | 0.708340037219864 | 0.354170018609932 | 114 | 0.642169341893849 | 0.715661316212302 | 0.357830658106151 | 115 | 0.630506299239993 | 0.738987401520014 | 0.369493700760007 | 116 | 0.606326173681176 | 0.787347652637648 | 0.393673826318824 | 117 | 0.575653045446443 | 0.848693909107115 | 0.424346954553557 | 118 | 0.544203809664939 | 0.911592380670122 | 0.455796190335061 | 119 | 0.512747352637815 | 0.97450529472437 | 0.487252647362185 | 120 | 0.481989709599605 | 0.96397941919921 | 0.518010290400395 | 121 | 0.451867174856427 | 0.903734349712854 | 0.548132825143573 | 122 | 0.420683890168647 | 0.841367780337294 | 0.579316109831353 | 123 | 0.389902293147567 | 0.779804586295134 | 0.610097706852433 | 124 | 0.360311874169973 | 0.720623748339946 | 0.639688125830027 | 125 | 0.334152933461647 | 0.668305866923293 | 0.665847066538353 | 126 | 0.307993583008748 | 0.615987166017497 | 0.692006416991252 | 127 | 0.283009450915522 | 0.566018901831044 | 0.716990549084478 | 128 | 0.262960142610631 | 0.525920285221263 | 0.737039857389369 | 129 | 0.240889033879243 | 0.481778067758486 | 0.759110966120757 | 130 | 0.218958499410143 | 0.437916998820286 | 0.781041500589857 | 131 | 0.208456045616269 | 0.416912091232538 | 0.791543954383731 | 132 | 0.198943355141920 | 0.397886710283840 | 0.80105664485808 | 133 | 0.182322804651478 | 0.364645609302956 | 0.817677195348522 | 134 | 0.169654751991416 | 0.339309503982832 | 0.830345248008584 | 135 | 0.159415919558883 | 0.318831839117766 | 0.840584080441117 | 136 | 0.146108772692146 | 0.292217545384293 | 0.853891227307854 | 137 | 0.133905088073953 | 0.267810176147906 | 0.866094911926047 | 138 | 0.121766029041403 | 0.243532058082806 | 0.878233970958597 | 139 | 0.109462119352232 | 0.218924238704465 | 0.890537880647768 | 140 | 0.0986307195312217 | 0.197261439062443 | 0.901369280468778 | 141 | 0.0895610375857264 | 0.179122075171453 | 0.910438962414274 | 142 | 0.0803393350165969 | 0.160678670033194 | 0.919660664983403 | 143 | 0.0713674044142128 | 0.142734808828426 | 0.928632595585787 | 144 | 0.062917785187203 | 0.125835570374406 | 0.937082214812797 | 145 | 0.0553671599547626 | 0.110734319909525 | 0.944632840045237 | 146 | 0.0530953091090177 | 0.106190618218035 | 0.946904690890982 | 147 | 0.0512263484480594 | 0.102452696896119 | 0.94877365155194 | 148 | 0.0449112235530831 | 0.0898224471061662 | 0.955088776446917 | 149 | 0.0414381382168379 | 0.0828762764336759 | 0.958561861783162 | 150 | 0.0373719057997908 | 0.0747438115995816 | 0.96262809420021 | 151 | 0.0354659257307749 | 0.0709318514615497 | 0.964534074269225 | 152 | 0.0332763237087076 | 0.0665526474174151 | 0.966723676291292 | 153 | 0.0305105018474347 | 0.0610210036948695 | 0.969489498152565 | 154 | 0.0270012749466361 | 0.0540025498932722 | 0.972998725053364 | 155 | 0.0230711840747627 | 0.0461423681495253 | 0.976928815925237 | 156 | 0.0198234141336328 | 0.0396468282672655 | 0.980176585866367 | 157 | 0.0172338528727159 | 0.0344677057454318 | 0.982766147127284 | 158 | 0.0158819633040595 | 0.0317639266081191 | 0.98411803669594 | 159 | 0.0135525427880079 | 0.0271050855760157 | 0.986447457211992 | 160 | 0.0114313330552044 | 0.0228626661104087 | 0.988568666944796 | 161 | 0.00971083153290665 | 0.0194216630658133 | 0.990289168467093 | 162 | 0.00860708381723446 | 0.0172141676344689 | 0.991392916182766 | 163 | 0.00853861538417739 | 0.0170772307683548 | 0.991461384615823 | 164 | 0.00859681609638434 | 0.0171936321927687 | 0.991403183903616 | 165 | 0.00718181638931537 | 0.0143636327786307 | 0.992818183610685 | 166 | 0.00605138432385323 | 0.0121027686477065 | 0.993948615676147 | 167 | 0.0050204952619366 | 0.0100409905238732 | 0.994979504738063 | 168 | 0.00422379329246339 | 0.00844758658492678 | 0.995776206707537 | 169 | 0.00362877709441722 | 0.00725755418883443 | 0.996371222905583 | 170 | 0.00325338165880756 | 0.00650676331761512 | 0.996746618341192 | 171 | 0.00269079252302964 | 0.00538158504605927 | 0.99730920747697 | 172 | 0.0021685004362273 | 0.0043370008724546 | 0.997831499563773 | 173 | 0.00175444954541032 | 0.00350889909082064 | 0.99824555045459 | 174 | 0.00141746468389718 | 0.00283492936779436 | 0.998582535316103 | 175 | 0.00115804606789543 | 0.00231609213579086 | 0.998841953932105 | 176 | 0.000976571040594084 | 0.00195314208118817 | 0.999023428959406 | 177 | 0.000828534287138166 | 0.00165706857427633 | 0.999171465712862 | 178 | 0.00071662337974381 | 0.00143324675948762 | 0.999283376620256 | 179 | 0.00063568103961206 | 0.00127136207922412 | 0.999364318960388 | 180 | 0.000581746882639965 | 0.00116349376527993 | 0.99941825311736 | 181 | 0.000513754670718936 | 0.00102750934143787 | 0.999486245329281 | 182 | 0.000442125044345782 | 0.000884250088691563 | 0.999557874955654 | 183 | 0.000389457586616742 | 0.000778915173233484 | 0.999610542413383 | 184 | 0.000346882405261242 | 0.000693764810522485 | 0.999653117594739 | 185 | 0.000309828446674369 | 0.000619656893348737 | 0.999690171553326 | 186 | 0.000278843354011913 | 0.000557686708023827 | 0.999721156645988 | 187 | 0.000274214274508251 | 0.000548428549016501 | 0.999725785725492 | 188 | 0.000288961230965323 | 0.000577922461930645 | 0.999711038769035 | 189 | 0.000287388320331862 | 0.000574776640663723 | 0.999712611679668 | 190 | 0.000282949539855448 | 0.000565899079710897 | 0.999717050460145 | 191 | 0.000287382800851859 | 0.000574765601703718 | 0.999712617199148 | 192 | 0.000302259374470526 | 0.000604518748941051 | 0.99969774062553 | 193 | 0.000327984657083490 | 0.000655969314166981 | 0.999672015342916 | 194 | 0.000344698961085209 | 0.000689397922170419 | 0.999655301038915 | 195 | 0.000366304620200327 | 0.000732609240400653 | 0.9996336953798 | 196 | 0.00038653152183271 | 0.00077306304366542 | 0.999613468478167 | 197 | 0.000407494327770643 | 0.000814988655541287 | 0.99959250567223 | 198 | 0.000435158602512202 | 0.000870317205024405 | 0.999564841397488 | 199 | 0.00047165635584157 | 0.00094331271168314 | 0.999528343644158 | 200 | 0.000583351590067642 | 0.00116670318013528 | 0.999416648409932 | 201 | 0.00075809457049129 | 0.00151618914098258 | 0.999241905429509 | 202 | 0.00120611893110204 | 0.00241223786220409 | 0.998793881068898 | 203 | 0.00196969766114146 | 0.00393939532228291 | 0.998030302338859 | 204 | 0.00309010411968798 | 0.00618020823937595 | 0.996909895880312 | 205 | 0.00473794364241047 | 0.00947588728482093 | 0.99526205635759 | 206 | 0.0093793710320847 | 0.0187587420641694 | 0.990620628967915 | 207 | 0.0591346797989439 | 0.118269359597888 | 0.940865320201056 | 208 | 0.230978918643821 | 0.461957837287642 | 0.769021081356179 | 209 | 0.555372771249563 | 0.889254457500875 | 0.444627228750437 | 210 | 0.854505370153457 | 0.290989259693086 | 0.145494629846543 | 211 | 0.868207390931851 | 0.263585218136297 | 0.131792609068149 | 212 | 0.947087118512766 | 0.105825762974467 | 0.0529128814872337 | 213 | 0.95889652234649 | 0.0822069553070203 | 0.0411034776535101 | 214 | 0.965494197741067 | 0.069011604517865 | 0.0345058022589325 | 215 | 0.973874856985029 | 0.0522502860299424 | 0.0261251430149712 | 216 | 0.979090114184645 | 0.0418197716307109 | 0.0209098858153555 | 217 | 0.985559694117652 | 0.0288806117646967 | 0.0144403058823484 | 218 | 0.986559158258623 | 0.0268816834827541 | 0.0134408417413770 | 219 | 0.985708638218508 | 0.0285827235629845 | 0.0142913617814923 | 220 | 0.984728417118478 | 0.0305431657630445 | 0.0152715828815222 | 221 | 0.983164200445478 | 0.0336715991090433 | 0.0168357995545216 | 222 | 0.982019710205455 | 0.0359605795890896 | 0.0179802897945448 | 223 | 0.980820983972 | 0.0383580320560012 | 0.0191790160280006 | 224 | 0.981890942625923 | 0.036218114748154 | 0.018109057374077 | 225 | 0.982169635769073 | 0.035660728461853 | 0.0178303642309265 | 226 | 0.980479946135054 | 0.0390401077298923 | 0.0195200538649461 | 227 | 0.977660186708342 | 0.0446796265833165 | 0.0223398132916583 | 228 | 0.973623329508868 | 0.052753340982265 | 0.0263766704911325 | 229 | 0.968405688770923 | 0.0631886224581533 | 0.0315943112290766 | 230 | 0.962407645162287 | 0.0751847096754262 | 0.0375923548377131 | 231 | 0.95584044809226 | 0.0883191038154803 | 0.0441595519077402 | 232 | 0.948076318327953 | 0.103847363344094 | 0.0519236816720468 | 233 | 0.941679289215591 | 0.116641421568818 | 0.0583207107844091 | 234 | 0.934227073473157 | 0.131545853053686 | 0.065772926526843 | 235 | 0.932407342743283 | 0.135185314513434 | 0.067592657256717 | 236 | 0.959351138558136 | 0.0812977228837281 | 0.0406488614418641 | 237 | 0.982441281210163 | 0.0351174375796735 | 0.0175587187898367 | 238 | 0.993929722733908 | 0.0121405545321844 | 0.00607027726609222 | 239 | 0.998655871950857 | 0.00268825609828602 | 0.00134412804914301 | 240 | 0.99945565842272 | 0.00108868315455905 | 0.000544341577279524 | 241 | 0.999728384375027 | 0.000543231249946219 | 0.000271615624973110 | 242 | 0.999979562683671 | 4.08746326575866e-05 | 2.04373163287933e-05 | 243 | 0.999999998862264 | 2.27547137482008e-09 | 1.13773568741004e-09 | 244 | 0.99999999994277 | 1.14459058666848e-10 | 5.72295293334241e-11 | 245 | 0.999999999999734 | 5.31491485492497e-13 | 2.65745742746249e-13 | 246 | 0.999999999999948 | 1.03286188487570e-13 | 5.16430942437851e-14 | 247 | 0.999999999999978 | 4.40190606597391e-14 | 2.20095303298695e-14 | 248 | 0.999999999999999 | 2.36051198037948e-15 | 1.18025599018974e-15 | 249 | 1 | 3.75838125386545e-17 | 1.87919062693272e-17 | 250 | 1 | 3.19459164802969e-18 | 1.59729582401484e-18 | 251 | 1 | 2.20149388536650e-19 | 1.10074694268325e-19 | 252 | 1 | 2.03653149227817e-19 | 1.01826574613908e-19 | 253 | 1 | 3.99344484812625e-19 | 1.99672242406312e-19 | 254 | 1 | 8.58406383952805e-19 | 4.29203191976403e-19 | 255 | 1 | 8.1172996894065e-19 | 4.05864984470325e-19 | 256 | 1 | 1.32678453559517e-18 | 6.63392267797587e-19 | 257 | 1 | 1.43283441754056e-18 | 7.1641720877028e-19 | 258 | 1 | 2.37910042201582e-18 | 1.18955021100791e-18 | 259 | 1 | 4.27003021095118e-18 | 2.13501510547559e-18 | 260 | 1 | 9.10154924829763e-18 | 4.55077462414882e-18 | 261 | 1 | 1.8316538233479e-17 | 9.1582691167395e-18 | 262 | 1 | 4.21577156212684e-17 | 2.10788578106342e-17 | 263 | 1 | 8.21194502720864e-17 | 4.10597251360432e-17 | 264 | 1 | 1.24402878925101e-16 | 6.22014394625504e-17 | 265 | 1 | 1.84419998042294e-16 | 9.2209999021147e-17 | 266 | 1 | 3.04536804962818e-16 | 1.52268402481409e-16 | 267 | 1 | 5.80447364964524e-16 | 2.90223682482262e-16 | 268 | 1 | 1.11688858205391e-15 | 5.58444291026957e-16 | 269 | 0.999999999999999 | 2.41933361784646e-15 | 1.20966680892323e-15 | 270 | 0.999999999999998 | 4.0566872895425e-15 | 2.02834364477125e-15 | 271 | 0.999999999999996 | 8.359669744767e-15 | 4.1798348723835e-15 | 272 | 0.999999999999991 | 1.79134030036395e-14 | 8.95670150181976e-15 | 273 | 0.999999999999981 | 3.76669545592898e-14 | 1.88334772796449e-14 | 274 | 0.999999999999967 | 6.60523110442055e-14 | 3.30261555221027e-14 | 275 | 0.999999999999953 | 9.38526587652703e-14 | 4.69263293826352e-14 | 276 | 0.999999999999983 | 3.42551426640368e-14 | 1.71275713320184e-14 | 277 | 0.999999999999962 | 7.56237602861695e-14 | 3.78118801430847e-14 | 278 | 0.999999999999963 | 7.37601204588293e-14 | 3.68800602294146e-14 | 279 | 0.999999999999953 | 9.39154176217899e-14 | 4.69577088108949e-14 | 280 | 0.99999999999995 | 1.01917403179689e-13 | 5.09587015898446e-14 | 281 | 0.999999999999937 | 1.26857811156206e-13 | 6.3428905578103e-14 | 282 | 0.99999999999991 | 1.80876006907715e-13 | 9.04380034538576e-14 | 283 | 0.9999999999999 | 2.01926725246475e-13 | 1.00963362623237e-13 | 284 | 0.999999999999936 | 1.28165070247340e-13 | 6.40825351236698e-14 | 285 | 0.99999999999992 | 1.59108444357248e-13 | 7.95542221786239e-14 | 286 | 0.999999999999889 | 2.22554366847883e-13 | 1.11277183423941e-13 | 287 | 0.999999999999776 | 4.48276508233953e-13 | 2.24138254116977e-13 | 288 | 0.99999999999954 | 9.18498332585964e-13 | 4.59249166292982e-13 | 289 | 0.99999999999925 | 1.49949019843212e-12 | 7.49745099216061e-13 | 290 | 0.999999999999208 | 1.58383309597335e-12 | 7.91916547986677e-13 | 291 | 0.99999999999918 | 1.64048550053432e-12 | 8.20242750267162e-13 | 292 | 0.999999999998495 | 3.01021017107879e-12 | 1.50510508553940e-12 | 293 | 0.999999999996738 | 6.52380740784704e-12 | 3.26190370392352e-12 | 294 | 0.99999999999691 | 6.1794192773749e-12 | 3.08970963868745e-12 | 295 | 0.999999999995958 | 8.08399576522583e-12 | 4.04199788261292e-12 | 296 | 0.999999999993085 | 1.38294761600739e-11 | 6.91473808003694e-12 | 297 | 0.999999999987126 | 2.57475345135319e-11 | 1.28737672567659e-11 | 298 | 0.999999999980207 | 3.95855734611037e-11 | 1.97927867305519e-11 | 299 | 0.999999999963029 | 7.39422737926421e-11 | 3.69711368963211e-11 | 300 | 0.999999999918479 | 1.63042968935177e-10 | 8.15214844675886e-11 | 301 | 0.999999999824341 | 3.51317119761513e-10 | 1.75658559880756e-10 | 302 | 0.999999999640697 | 7.18606172838802e-10 | 3.59303086419401e-10 | 303 | 0.999999999268877 | 1.46224552785131e-09 | 7.31122763925657e-10 | 304 | 0.999999998464971 | 3.07005798586133e-09 | 1.53502899293066e-09 | 305 | 0.999999997413658 | 5.17268503776017e-09 | 2.58634251888008e-09 | 306 | 0.999999994860769 | 1.02784626455567e-08 | 5.13923132277836e-09 | 307 | 0.99999999263465 | 1.47307019263892e-08 | 7.36535096319461e-09 | 308 | 0.9999999877314 | 2.45371994155413e-08 | 1.22685997077706e-08 | 309 | 0.999999976956115 | 4.60877695195836e-08 | 2.30438847597918e-08 | 310 | 0.999999952772902 | 9.44541952444921e-08 | 4.72270976222461e-08 | 311 | 0.999999903520717 | 1.92958566016419e-07 | 9.64792830082094e-08 | 312 | 0.999999804561733 | 3.90876533135911e-07 | 1.95438266567956e-07 | 313 | 0.999999730459079 | 5.39081843024156e-07 | 2.69540921512078e-07 | 314 | 0.999999523926038 | 9.52147923560824e-07 | 4.76073961780412e-07 | 315 | 0.99999923645949 | 1.52708102094801e-06 | 7.63540510474005e-07 | 316 | 0.999999126352635 | 1.74729472977426e-06 | 8.73647364887128e-07 | 317 | 0.999998591500862 | 2.81699827561681e-06 | 1.40849913780841e-06 | 318 | 0.999997850304754 | 4.29939049292595e-06 | 2.14969524646297e-06 | 319 | 0.999996723435215 | 6.55312956935623e-06 | 3.27656478467812e-06 | 320 | 0.99999490443935 | 1.01911213020625e-05 | 5.09556065103126e-06 | 321 | 0.999992106780136 | 1.57864397275006e-05 | 7.89321986375028e-06 | 322 | 0.999984984151063 | 3.00316978741216e-05 | 1.50158489370608e-05 | 323 | 0.999971491136388 | 5.70177272231183e-05 | 2.85088636115591e-05 | 324 | 0.99994901624389 | 0.000101967512221351 | 5.09837561106753e-05 | 325 | 0.999908511998062 | 0.000182976003875125 | 9.14880019375623e-05 | 326 | 0.99983368511037 | 0.000332629779260524 | 0.000166314889630262 | 327 | 0.999717146441544 | 0.000565707116911737 | 0.000282853558455869 | 328 | 0.99951394748524 | 0.000972105029521202 | 0.000486052514760601 | 329 | 0.999174338491897 | 0.00165132301620578 | 0.000825661508102888 | 330 | 0.998998272676159 | 0.00200345464768207 | 0.00100172732384103 | 331 | 0.998294664346937 | 0.00341067130612678 | 0.00170533565306339 | 332 | 0.997207141839954 | 0.00558571632009286 | 0.00279285816004643 | 333 | 0.995968351544944 | 0.00806329691011183 | 0.00403164845505592 | 334 | 0.995592316638619 | 0.00881536672276272 | 0.00440768336138136 | 335 | 0.998531624355842 | 0.00293675128831611 | 0.00146837564415806 | 336 | 0.999942802012115 | 0.000114395975769793 | 5.71979878848966e-05 | 337 | 0.999986760771728 | 2.64784565434976e-05 | 1.32392282717488e-05 | 338 | 0.999999838584183 | 3.22831633310688e-07 | 1.61415816655344e-07 | 339 | 0.9999999962092 | 7.58159858142675e-09 | 3.79079929071337e-09 | 340 | 0.999999997024752 | 5.95049593250743e-09 | 2.97524796625371e-09 | 341 | 0.999999991738527 | 1.65229461143204e-08 | 8.26147305716022e-09 | 342 | 0.99999996179703 | 7.64059416697612e-08 | 3.82029708348806e-08 | 343 | 0.999999929385332 | 1.41229336905446e-07 | 7.06146684527232e-08 | 344 | 0.999999794209615 | 4.11580769051403e-07 | 2.05790384525701e-07 | 345 | 0.999999323877755 | 1.35224448963857e-06 | 6.76122244819287e-07 | 346 | 0.999999468066366 | 1.0638672687497e-06 | 5.3193363437485e-07 | 347 | 0.999997243186445 | 5.51362710998822e-06 | 2.75681355499411e-06 | 348 | 0.99998926228814 | 2.14754237182049e-05 | 1.07377118591024e-05 | 349 | 0.999958646264932 | 8.27074701365488e-05 | 4.13537350682744e-05 | 350 | 0.999990086396503 | 1.98272069930427e-05 | 9.91360349652136e-06 | 351 | 0.999939817828316 | 0.000120364343367269 | 6.01821716836345e-05 | 352 | 0.999669682352602 | 0.000660635294796541 | 0.000330317647398270 | 353 | 0.999887727210634 | 0.000224545578731656 | 0.000112272789365828 | 354 | 0.999029485274074 | 0.00194102945185158 | 0.000970514725925788 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | Description | # significant tests | % significant tests | OK/NOK | 1% type I error level | 156 | 0.446991404011461 | NOK | 5% type I error level | 210 | 0.601719197707736 | NOK | 10% type I error level | 234 | 0.670487106017192 | NOK |
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| | Parameters (Session): | par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ; | | Parameters (R input): | par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ; | | R code (references can be found in the software module): | library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
| |
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Software written by Ed van Stee & Patrick Wessa
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