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Multiple Linear Regression - Estimated Regression Equation | Amerika[t] = + 235.738979446839 + 1.01224880651333Japan[t] -0.231107287068407t + e[t] |
Multiple Linear Regression - Regression Statistics | Multiple R | 0.958941369643888 | R-squared | 0.919568550414496 | Adjusted R-squared | 0.919158185875795 | F-TEST (value) | 2240.85773425779 | F-TEST (DF numerator) | 2 | F-TEST (DF denominator) | 392 | p-value | 0 | Multiple Linear Regression - Residual Statistics | Residual Standard Deviation | 11.8867463833538 | Sum Squared Residuals | 55387.537916212 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error | 1 | 358.59 | 359.366636124739 | -0.776636124738803 | 2 | 362.96 | 360.117410179992 | 2.84258982000813 | 3 | 362.42 | 359.592750739034 | 2.82724926096589 | 4 | 364.97 | 360.869894173671 | 4.10010582632921 | 5 | 364.04 | 361.24613617051 | 2.79386382948961 | 6 | 361.06 | 361.743848024132 | -0.683848024131606 | 7 | 358.48 | 362.170702461297 | -3.69070246129686 | 8 | 352.96 | 361.969962638424 | -9.00996263842389 | 9 | 359.59 | 362.285469706873 | -2.69546970687268 | 10 | 360.39 | 359.503495427391 | 0.886504572609335 | 11 | 357.4 | 359.626675222602 | -2.22667522260194 | 12 | 362.93 | 358.808463627756 | 4.12153637224425 | 13 | 364.55 | 357.079228107048 | 7.47077189295239 | 14 | 365.73 | 357.323877759040 | 8.40612224095953 | 15 | 364.7 | 357.092770471972 | 7.6072295280279 | 16 | 364.65 | 358.440771323064 | 6.2092286769355 | 17 | 359.43 | 357.976846810498 | 1.45315318950201 | 18 | 362.14 | 357.836841916016 | 4.30315808398419 | 19 | 356.97 | 357.777816926055 | -0.807816926054633 | 20 | 354.82 | 356.676175665385 | -1.85617566538479 | 21 | 353.17 | 355.675759285366 | -2.50575928536622 | 22 | 357.06 | 356.031756306076 | 1.02824369392444 | 23 | 356.18 | 354.211418392781 | 1.96858160721878 | 24 | 355.01 | 355.802358957437 | -0.792358957436827 | 25 | 355.65 | 356.026763633299 | -0.376763633299435 | 26 | 357.31 | 356.919252521461 | 0.390747478539191 | 27 | 357.07 | 356.738757674718 | 0.331242325281925 | 28 | 357.91 | 356.335568090542 | 1.57443190945763 | 29 | 358.48 | 356.185440707995 | 2.29455929200497 | 30 | 358.97 | 355.893598492536 | 3.07640150746419 | 31 | 351.77 | 355.520776372556 | -3.75077637255558 | 32 | 352.16 | 357.506493971751 | -5.34649397175134 | 33 | 359.08 | 354.319620169664 | 4.76037983033596 | 34 | 360.35 | 353.815205704837 | 6.53479429516301 | 35 | 359.53 | 355.628841006926 | 3.90115899307442 | 36 | 359.3 | 355.347121279531 | 3.95287872046854 | 37 | 358.41 | 354.508664708555 | 3.90133529144496 | 38 | 359.68 | 353.184328710452 | 6.49567128954776 | 39 | 355.31 | 353.327753481794 | 1.98224651820623 | 40 | 357.08 | 353.278850979898 | 3.80114902010222 | 41 | 349.71 | 354.394034605492 | -4.68403460549212 | 42 | 354.13 | 354.719664162006 | -0.589664162006028 | 43 | 345.49 | 353.162510938405 | -7.67251093840514 | 44 | 341.69 | 350.785436181528 | -9.09543618152848 | 45 | 344.25 | 351.252780570954 | -7.00278057095427 | 46 | 340.17 | 350.323221607392 | -10.1532216073916 | 47 | 342.47 | 350.820933461013 | -8.35093346101283 | 48 | 344.43 | 347.178547695994 | -2.74854769599450 | 49 | 333.23 | 346.917072944731 | -13.6870729447307 | 50 | 339.72 | 348.923035520057 | -9.20303552005674 | 51 | 342.61 | 346.758533012548 | -4.14853301254786 | 52 | 346.36 | 346.112403714809 | 0.24759628519101 | 53 | 339.09 | 345.688969154503 | -6.59896915450309 | 54 | 339.73 | 348.079586276304 | -8.34958627630419 | 55 | 341.12 | 344.072790940941 | -2.95279094094104 | 56 | 335.94 | 343.791071213547 | -7.85107121354698 | 57 | 333.46 | 344.632947661383 | -11.1729476613827 | 58 | 335.66 | 342.417832713548 | -6.75783271354813 | 59 | 341.12 | 342.024765617438 | -0.904765617437614 | 60 | 342.21 | 335.05208127899 | 7.15791872100958 | 61 | 342.62 | 337.756495530811 | 4.86350446918935 | 62 | 346.06 | 340.187602604872 | 5.87239739512767 | 63 | 344.43 | 338.367264691578 | 6.06273530842203 | 64 | 346.65 | 340.778126789509 | 5.87187321049060 | 65 | 343.74 | 340.000405146924 | 3.73959485307624 | 66 | 335.67 | 340.771424178304 | -5.10142417830355 | 67 | 342.75 | 341.744892970986 | 1.00510702901397 | 68 | 341.77 | 337.657117731102 | 4.11288226889818 | 69 | 345.84 | 338.3066669057 | 7.53333309429997 | 70 | 346.52 | 341.233775894953 | 5.28622410504677 | 71 | 350.79 | 340.628136549475 | 10.1618634505252 | 72 | 345.44 | 339.475882848479 | 5.96411715152067 | 73 | 345.87 | 338.343874123614 | 7.52612587638595 | 74 | 338.48 | 337.788847218461 | 0.691152781538651 | 75 | 337.21 | 339.420277735378 | -2.21027773537753 | 76 | 340.81 | 335.727279530033 | 5.08272046996652 | 77 | 339.86 | 335.334212433923 | 4.52578756607707 | 78 | 342.86 | 335.123350122985 | 7.73664987701521 | 79 | 343.33 | 333.849626565208 | 9.48037343479233 | 80 | 341.73 | 335.136892487909 | 6.59310751209076 | 81 | 351.38 | 334.996887593427 | 16.3831124065729 | 82 | 351.13 | 331.222909483562 | 19.9070905164380 | 83 | 345.99 | 335.435574457087 | 10.5544255429129 | 84 | 347.55 | 336.621615499137 | 10.9283845008626 | 85 | 346.02 | 334.588705336475 | 11.4312946635248 | 86 | 345.29 | 334.843477476533 | 10.4465225234668 | 87 | 347.03 | 336.404050576993 | 10.6259494230066 | 88 | 348.01 | 335.575716494082 | 12.4342835059178 | 89 | 345.48 | 338.209273329446 | 7.27072667055355 | 90 | 349.4 | 339.051149777282 | 10.3488502227178 | 91 | 351.05 | 337.726813779179 | 13.3231862208206 | 92 | 349.7 | 339.297509367705 | 10.4024906322953 | 93 | 350.86 | 339.835711173586 | 11.0242888264136 | 94 | 354.45 | 339.118724459392 | 15.3312755406083 | 95 | 355.3 | 338.260022912285 | 17.0399770877150 | 96 | 357.48 | 338.281977826845 | 19.1980221731551 | 97 | 355.24 | 337.868665754604 | 17.3713342453959 | 98 | 351.79 | 337.556578563015 | 14.2334214369854 | 99 | 355.22 | 337.173633954969 | 18.0463660450308 | 100 | 351.02 | 336.942526667901 | 14.0774733320992 | 101 | 350.28 | 336.519092107595 | 13.7609078924051 | 102 | 350.17 | 334.465936968802 | 15.7040630311976 | 103 | 348.16 | 332.80755886455 | 15.3524411354498 | 104 | 340.3 | 334.752786511486 | 5.54721348851451 | 105 | 343.75 | 334.552046688613 | 9.1979533113875 | 106 | 344.71 | 331.193090589418 | 13.5169094105821 | 107 | 344.13 | 331.235290480108 | 12.8947095198919 | 108 | 342.14 | 331.095285585626 | 11.0447144143741 | 109 | 345.04 | 329.588744802351 | 15.4512551976494 | 110 | 346.02 | 331.685809770263 | 14.3341902297371 | 111 | 346.43 | 333.408342679765 | 13.0216573202348 | 112 | 347.07 | 333.187357880762 | 13.882642119238 | 113 | 339.33 | 333.239680259517 | 6.09031974048267 | 114 | 339.1 | 333.008572972449 | 6.09142702755112 | 115 | 337.19 | 332.008156592430 | 5.18184340756964 | 116 | 339.58 | 330.056226334289 | 9.5237736657107 | 117 | 327.85 | 329.480954453006 | -1.63095445300631 | 118 | 326.81 | 330.302585924712 | -3.4925859247118 | 119 | 321.73 | 326.731057576149 | -5.00105757614937 | 120 | 320.45 | 326.925094787817 | -6.47509478781659 | 121 | 327.69 | 324.790959744503 | 2.89904025549690 | 122 | 323.95 | 322.798539534102 | 1.15146046589850 | 123 | 320.47 | 325.664913594964 | -5.19491359496386 | 124 | 322.13 | 326.273972817302 | -4.14397281730155 | 125 | 316.34 | 326.042865530233 | -9.70286553023317 | 126 | 314.78 | 323.341871155272 | -8.56187115527223 | 127 | 308.9 | 324.092645210522 | -15.1926452105217 | 128 | 308.62 | 322.788554188549 | -14.1685541885492 | 129 | 314.41 | 322.992713888282 | -8.58271388828149 | 130 | 306.88 | 322.214992245696 | -15.3349922456959 | 131 | 310.6 | 325.587490709815 | -14.9874907098149 | 132 | 321.6 | 324.718666674643 | -3.11866667464314 | 133 | 321.5 | 322.928696225544 | -1.42869622554421 | 134 | 325.68 | 326.017765023840 | -0.337765023839547 | 135 | 324.35 | 325.958740033878 | -1.60874003387839 | 136 | 320.01 | 326.152777245546 | -6.14277724554562 | 137 | 326.88 | 325.334565650699 | 1.54543434930053 | 138 | 332.39 | 324.739048793286 | 7.65095120671373 | 139 | 331.48 | 326.157907060835 | 5.32209293916544 | 140 | 332.62 | 326.615128962195 | 6.00487103780476 | 141 | 324.79 | 325.726059950893 | -0.93605995089315 | 142 | 327.12 | 327.39798042007 | -0.277980420069828 | 143 | 328.91 | 324.666618580914 | 4.24338141908654 | 144 | 328.37 | 321.074845256221 | 7.2951547437792 | 145 | 324.83 | 318.667403035149 | 6.16259696485126 | 146 | 325.9 | 316.745840241203 | 9.15415975879693 | 147 | 326.18 | 315.735301373119 | 10.4446986268806 | 148 | 328.94 | 314.552680207928 | 14.3873197920716 | 149 | 333.78 | 314.655615027009 | 19.1243849729905 | 150 | 328.06 | 317.349906790765 | 10.7100932092354 | 151 | 325.87 | 316.916349742393 | 8.95365025760652 | 152 | 325.41 | 316.098138147547 | 9.31186185245268 | 153 | 318.86 | 316.555360048908 | 2.30463995109202 | 154 | 319.13 | 318.63218004069 | 0.497819959310001 | 155 | 310.16 | 318.573155050729 | -8.41315505072883 | 156 | 311.73 | 314.252562585347 | -2.52256258534656 | 157 | 306.54 | 311.764140459753 | -5.22414045975341 | 158 | 311.16 | 312.737609252436 | -1.57760925243587 | 159 | 311.98 | 313.093606273145 | -1.1136062731452 | 160 | 306.72 | 310.119304720426 | -3.39930472042565 | 161 | 308.05 | 310.171627099181 | -2.12162709918099 | 162 | 300.76 | 310.396031775044 | -9.6360317750436 | 163 | 301.9 | 309.739779989240 | -7.8397799892396 | 164 | 293.09 | 305.024410489317 | -11.9344104893171 | 165 | 292.76 | 307.91102952631 | -15.1510295263098 | 166 | 294.58 | 308.054454297651 | -13.4744542976513 | 167 | 289.9 | 305.019417816541 | -15.1194178165410 | 168 | 296.69 | 297.621588979358 | -0.931588979358118 | 169 | 297.21 | 299.738898923401 | -2.52889892340067 | 170 | 293.31 | 302.018168676485 | -8.70816867648532 | 171 | 296.25 | 307.293694896849 | -11.0436948968495 | 172 | 298.6 | 302.335385683364 | -3.73538568336375 | 173 | 296.87 | 305.049922423249 | -8.17992242324916 | 174 | 301.02 | 304.980774945223 | -3.96077494522291 | 175 | 304.73 | 306.500858093423 | -1.77085809342254 | 176 | 301.92 | 305.348604392427 | -3.42860439242701 | 177 | 295.72 | 307.395056920014 | -11.6750569200136 | 178 | 293.18 | 306.647702741623 | -13.4677027416234 | 179 | 298.35 | 301.770373432659 | -3.42037343265876 | 180 | 297.99 | 301.114121646855 | -3.12412164685478 | 181 | 299.85 | 299.303906221626 | 0.546093778374446 | 182 | 299.85 | 299.6700257304 | 0.179974269599995 | 183 | 304.45 | 299.023896432661 | 5.42610356733883 | 184 | 299.45 | 298.003235076512 | 1.44676492348764 | 185 | 298.14 | 302.064062729060 | -3.92406272906051 | 186 | 298.78 | 301.873445394253 | -3.09344539425264 | 187 | 297.02 | 301.136213703928 | -4.11621370392755 | 188 | 301.33 | 302.261519817587 | -0.931519817587017 | 189 | 294.96 | 298.376194339005 | -3.41619433900547 | 190 | 296.69 | 301.455140649236 | -4.76514064923565 | 191 | 300.73 | 300.120682163068 | 0.609317836932316 | 192 | 301.96 | 301.974807417417 | -0.0148074174167898 | 193 | 297.38 | 301.976517355846 | -4.59651735584644 | 194 | 293.87 | 303.952112466977 | -10.0821124669771 | 195 | 285.96 | 303.842475036690 | -17.8824750366903 | 196 | 285.41 | 303.560755309296 | -18.1507553092962 | 197 | 283.7 | 298.197546573205 | -14.4975465732052 | 198 | 284.76 | 297.652642156118 | -12.8926421561177 | 199 | 277.11 | 296.804063097076 | -19.6940630970761 | 200 | 274.73 | 299.862764431176 | -25.1327644311760 | 201 | 274.73 | 299.631657144108 | -24.9016571441076 | 202 | 274.73 | 299.400549857039 | -24.6705498570392 | 203 | 274.73 | 299.169442569971 | -24.4394425699708 | 204 | 274.69 | 297.602166858305 | -22.9121668583048 | 205 | 275.42 | 294.840437554953 | -19.4204375549531 | 206 | 264.15 | 294.902882421774 | -30.7528824217736 | 207 | 276.24 | 291.371844025472 | -15.1318440254716 | 208 | 268.88 | 289.440158743461 | -20.5601587434608 | 209 | 277.97 | 293.723681133442 | -15.7536811334419 | 210 | 280.49 | 293.937963321239 | -13.4479633212394 | 211 | 281.09 | 296.186865610129 | -15.0968656101287 | 212 | 276.16 | 296.714944927945 | -20.5549449279452 | 213 | 272.58 | 294.520074956241 | -21.9400749562410 | 214 | 270.94 | 296.718364804805 | -25.7783648048045 | 215 | 284.31 | 292.569854636530 | -8.25985463652953 | 216 | 283.94 | 295.557698554174 | -11.6176985541735 | 217 | 284.18 | 295.721368301645 | -11.5413683016453 | 218 | 282.83 | 297.099736616933 | -14.2697366169331 | 219 | 283.84 | 296.696547032757 | -12.8565470327575 | 220 | 282.71 | 297.113278981858 | -14.4032789818576 | 221 | 279.29 | 294.574244415939 | -15.2842444159387 | 222 | 280.7 | 293.452358179139 | -12.7523581791386 | 223 | 274.47 | 292.128022181036 | -17.6580221810358 | 224 | 273.44 | 295.156356050940 | -21.7163560509404 | 225 | 275.49 | 292.212421962416 | -16.7224219624162 | 226 | 279.46 | 292.082539555999 | -12.6225395559992 | 227 | 280.19 | 293.30907055031 | -13.1190705503099 | 228 | 288.21 | 294.242049390732 | -6.03204939073187 | 229 | 284.8 | 293.565552628798 | -8.76555262879756 | 230 | 281.41 | 296.320579320944 | -14.9105793209435 | 231 | 283.39 | 294.743181121212 | -11.3531811212124 | 232 | 287.97 | 294.147664263799 | -6.17766426379913 | 233 | 290.77 | 292.438673719221 | -1.66867371922129 | 234 | 290.6 | 296.631093716616 | -6.03109371661612 | 235 | 289.67 | 296.703661071502 | -7.03366107150172 | 236 | 289.84 | 296.675003545736 | -6.83500354573603 | 237 | 298.55 | 294.672460847269 | 3.87753915273075 | 238 | 296.07 | 296.050829162557 | 0.0191708374429372 | 239 | 297.14 | 296.31572379068 | 0.824276209319809 | 240 | 295.34 | 296.246576312654 | -0.906576312653924 | 241 | 296.25 | 296.805023094666 | -0.555023094665902 | 242 | 294.3 | 294.326723457138 | -0.0267234571378758 | 243 | 296.15 | 294.257575979112 | 1.89242402088835 | 244 | 296.49 | 293.287527063288 | 3.20247293671153 | 245 | 298.05 | 293.562544179477 | 4.48745582052327 | 246 | 301.03 | 293.736336415014 | 7.29366358498631 | 247 | 300.52 | 295.458869324516 | 5.06113067548398 | 248 | 301.5 | 296.472828069459 | 5.027171930541 | 249 | 296.93 | 296.666865281126 | 0.263134718873819 | 250 | 289.84 | 296.820412540533 | -6.98041254053287 | 251 | 291.44 | 294.767257401740 | -3.32725740174044 | 252 | 286.88 | 294.070515663676 | -7.1905156636759 | 253 | 286.74 | 294.375900244060 | -7.63590024405954 | 254 | 288.93 | 291.270006346493 | -2.34000634649326 | 255 | 292.19 | 292.253597627241 | -0.0635976272408678 | 256 | 295.39 | 289.94738028682 | 5.44261971317986 | 257 | 295.86 | 291.477585923085 | 4.3824140769151 | 258 | 293.36 | 293.79734562843 | -0.437345628430114 | 259 | 292.86 | 295.965268012798 | -3.10526801279831 | 260 | 292.73 | 293.567948279791 | -0.83794827979135 | 261 | 296.73 | 295.098153916056 | 1.63184608394385 | 262 | 285.02 | 293.449898299869 | -8.4298982998691 | 263 | 285.24 | 295.233166137762 | -9.9931661377622 | 264 | 288.62 | 290.487429173644 | -1.86742917364433 | 265 | 283.36 | 287.887659679335 | -4.52765967933471 | 266 | 285.84 | 288.891495936213 | -3.05149593621261 | 267 | 291.48 | 285.127640314413 | 6.35235968558738 | 268 | 291.41 | 285.483637335122 | 5.92636266487806 | 269 | 287.77 | 287.813519528532 | -0.0435195285323185 | 270 | 284.97 | 287.764617026636 | -2.79461702663627 | 271 | 286.05 | 288.302818832518 | -2.25281883251801 | 272 | 278.19 | 285.136190006561 | -6.94619000656095 | 273 | 281.21 | 283.95356884137 | -2.74356884137001 | 274 | 277.92 | 282.436905570030 | -4.51690557002964 | 275 | 280.08 | 282.357635603938 | -2.27763560393826 | 276 | 269.24 | 281.75199625846 | -12.5119962584599 | 277 | 268.48 | 281.115989448786 | -12.6359894487861 | 278 | 268.83 | 280.753289816871 | -11.9232898168710 | 279 | 269.54 | 280.69426482691 | -11.1542648269099 | 280 | 262.37 | 280.463157539841 | -18.0931575398415 | 281 | 265.12 | 278.916126804306 | -13.7961268043057 | 282 | 265.34 | 277.439953485226 | -12.0999534852259 | 283 | 263.32 | 277.239213662353 | -13.9192136623529 | 284 | 267.18 | 277.929252789212 | -10.7492527892116 | 285 | 260.75 | 275.005563676818 | -14.2555636768178 | 286 | 261.78 | 275.523520506569 | -13.7435205065692 | 287 | 257.27 | 275.424005564348 | -18.1540055643476 | 288 | 255.63 | 275.587675311819 | -19.9576753118194 | 289 | 251.39 | 274.992158454406 | -23.6021584544062 | 290 | 259.49 | 273.839904753411 | -14.3499047534106 | 291 | 261.18 | 273.588552490212 | -12.4085524902119 | 292 | 261.65 | 272.739973431170 | -11.0899734311704 | 293 | 262.01 | 270.909513029811 | -8.8995130298109 | 294 | 265.23 | 271.174407657934 | -5.944407657934 | 295 | 268.1 | 273.170247745195 | -5.07024774519493 | 296 | 262.27 | 273.536367253969 | -11.2663672539694 | 297 | 263.59 | 276.200291553529 | -12.6102915535292 | 298 | 257.85 | 272.638885693032 | -14.7888856930318 | 299 | 265.69 | 270.697077922956 | -5.00707792295592 | 300 | 271.15 | 270.526705564278 | 0.623294435721659 | 301 | 266.69 | 271.965808807957 | -5.27580880795692 | 302 | 265.77 | 271.957396258321 | -6.18739625832146 | 303 | 262.32 | 269.549954037249 | -7.22995403724936 | 304 | 270.48 | 266.636387412921 | 3.8436125870794 | 305 | 273.03 | 267.903408359492 | 5.12659164050804 | 306 | 269.13 | 267.307891502079 | 1.82210849792126 | 307 | 280.65 | 265.872208135259 | 14.7777918647405 | 308 | 282.75 | 266.906411856333 | 15.8435881436673 | 309 | 281.44 | 266.452609831831 | 14.9873901681686 | 310 | 281.99 | 266.423952306066 | 15.5660476939344 | 311 | 282.86 | 263.37879333689 | 19.4812066631099 | 312 | 287.21 | 262.914868824324 | 24.2951311756763 | 313 | 283.11 | 264.17176728283 | 18.9382327171701 | 314 | 280.66 | 264.011517412217 | 16.6484825877826 | 315 | 282.39 | 261.502850310494 | 20.887149689506 | 316 | 280.83 | 262.071419580571 | 18.7585804194289 | 317 | 284.71 | 261.658107508330 | 23.0518924916697 | 318 | 279.99 | 261.599082518369 | 18.3909174816308 | 319 | 283.5 | 260.305113984462 | 23.1948860155382 | 320 | 284.88 | 260.215721530305 | 24.6642784696948 | 321 | 288.6 | 259.437999887720 | 29.1620001122804 | 322 | 284.8 | 259.146157672260 | 25.6538423277396 | 323 | 287.2 | 262.974168099310 | 24.2258319006895 | 324 | 286.22 | 258.79529046684 | 27.4247095331600 | 325 | 286.54 | 259.56630949822 | 26.9736905017802 | 326 | 279.58 | 259.517406996324 | 20.0625930036761 | 327 | 283.08 | 259.711444207991 | 23.3685557920089 | 328 | 288.88 | 254.925217291613 | 33.9547827083874 | 329 | 280.18 | 258.702615278337 | 21.4773847216630 | 330 | 284.16 | 256.851909900847 | 27.3080900991527 | 331 | 290.57 | 256.408230364411 | 34.1617696355889 | 332 | 286.82 | 255.357201544067 | 31.4627984559331 | 333 | 273 | 255.905525838014 | 17.0944741619863 | 334 | 278.69 | 251.908852990716 | 26.7811470092843 | 335 | 264.54 | 251.222233740716 | 13.3177662592837 | 336 | 271.92 | 252.195702533399 | 19.7242974666013 | 337 | 283.6 | 248.715276577423 | 34.8847234225775 | 338 | 269.25 | 251.642385566676 | 17.6076144333243 | 339 | 263.58 | 254.802311781427 | 8.77768821857297 | 340 | 264.16 | 254.125815019493 | 10.0341849805073 | 341 | 268.85 | 252.05241490457 | 16.7975850954300 | 342 | 269.67 | 251.750450201046 | 17.9195497989543 | 343 | 249.41 | 251.215668272023 | -1.80566827202331 | 344 | 268.99 | 251.3489705553 | 17.6410294447003 | 345 | 268.65 | 245.783312057906 | 22.8666879420940 | 346 | 260.16 | 245.430734914056 | 14.729265085944 | 347 | 256.55 | 242.213493647773 | 14.3365063522267 | 348 | 251.47 | 242.620103108808 | 8.84989689119174 | 349 | 234.93 | 241.457726919748 | -6.52772691974758 | 350 | 232.96 | 239.202122019653 | -6.2421220196525 | 351 | 215.49 | 233.353033856435 | -17.8630338564351 | 352 | 213.68 | 234.053195471359 | -20.3731954713589 | 353 | 236.07 | 227.090633620977 | 8.97936637902315 | 354 | 235.41 | 235.666090950574 | -0.256090950574472 | 355 | 214.77 | 236.103067875805 | -21.3330678758049 | 356 | 225.85 | 237.127149108813 | -11.277149108813 | 357 | 224.64 | 230.012749937454 | -5.37274993745392 | 358 | 238.26 | 229.629805329408 | 8.63019467059149 | 359 | 232.44 | 231.979932498949 | 0.460067501050901 | 360 | 222.5 | 230.898536214409 | -8.39853621440949 | 361 | 225.28 | 230.090447107628 | -4.81044710762848 | 362 | 220.49 | 227.237615411691 | -6.74761541169052 | 363 | 216.86 | 227.715082289181 | -10.8550822891815 | 364 | 234.7 | 221.238399865926 | 13.4616001340742 | 365 | 230.06 | 225.491554791711 | 4.56844520828857 | 366 | 238.27 | 225.311059944969 | 12.9589400550313 | 367 | 238.56 | 230.556218701137 | 8.00378129886256 | 368 | 242.7 | 227.247875042268 | 15.4521249577315 | 369 | 249.14 | 226.368928519032 | 22.7710714809684 | 370 | 234.89 | 235.126590633802 | -0.236590633801577 | 371 | 227.78 | 230.593425919051 | -2.81342591905148 | 372 | 234.04 | 230.878565523305 | 3.16143447669512 | 373 | 230.7 | 230.272926177827 | 0.427073822173445 | 374 | 230.17 | 228.462710752597 | 1.70728924740267 | 375 | 218.23 | 228.079766144552 | -9.84976614455192 | 376 | 232.2 | 228.860907663997 | 3.33909233600314 | 377 | 220.76 | 222.829614715607 | -2.06961471560703 | 378 | 215.6 | 224.471167720588 | -8.87116772058829 | 379 | 217.69 | 222.306665213079 | -4.61666521307942 | 380 | 204.35 | 222.541192377007 | -18.1911923770071 | 381 | 191.44 | 222.158247768962 | -30.7182477689617 | 382 | 203.84 | 218.920761526549 | -15.0807615265487 | 383 | 211.86 | 219.347615963714 | -7.48761596371397 | 384 | 210.57 | 222.12288763199 | -11.5528876319902 | 385 | 219.57 | 220.980756419060 | -1.41075641905977 | 386 | 219.98 | 220.435852001972 | -0.455852001972238 | 387 | 226.01 | 221.41944328272 | 4.59055671728018 | 388 | 207.04 | 222.311932170881 | -15.2719321708812 | 389 | 212.52 | 218.44685166843 | -5.92685166842993 | 390 | 217.92 | 218.428316630729 | -0.508316630729335 | 391 | 210.45 | 219.209458150174 | -8.75945815017427 | 392 | 218.53 | 218.502593924045 | 0.0274060759554299 | 393 | 223.32 | 217.734994769524 | 5.58500523047589 | 394 | 218.76 | 219.892794665827 | -1.13279466582717 | 395 | 217.63 | 219.661687378759 | -2.03168737875876 |
Goldfeld-Quandt test for Heteroskedasticity | p-values | Alternative Hypothesis | breakpoint index | greater | 2-sided | less | 6 | 0.0143345065447606 | 0.0286690130895212 | 0.98566549345524 | 7 | 0.00818661833617924 | 0.0163732366723585 | 0.99181338166382 | 8 | 0.00642989915699999 | 0.0128597983140000 | 0.993570100843 | 9 | 0.00259005332814887 | 0.00518010665629774 | 0.997409946671851 | 10 | 0.00107963092742759 | 0.00215926185485517 | 0.998920369072572 | 11 | 0.000302324358686327 | 0.000604648717372655 | 0.999697675641314 | 12 | 0.000136388060484332 | 0.000272776120968664 | 0.999863611939516 | 13 | 4.38171326346549e-05 | 8.76342652693097e-05 | 0.999956182867365 | 14 | 1.51225279327809e-05 | 3.02450558655618e-05 | 0.999984877472067 | 15 | 3.89423532115813e-06 | 7.78847064231625e-06 | 0.999996105764679 | 16 | 1.20167676884055e-06 | 2.40335353768109e-06 | 0.999998798323231 | 17 | 5.19799820408613e-07 | 1.03959964081723e-06 | 0.99999948020018 | 18 | 1.24840608317637e-07 | 2.49681216635275e-07 | 0.999999875159392 | 19 | 9.73216452501917e-08 | 1.94643290500383e-07 | 0.999999902678355 | 20 | 1.93986671748058e-07 | 3.87973343496117e-07 | 0.999999806013328 | 21 | 4.30333441868043e-07 | 8.60666883736086e-07 | 0.999999569666558 | 22 | 1.45729049371838e-07 | 2.91458098743676e-07 | 0.99999985427095 | 23 | 6.22341016444861e-08 | 1.24468203288972e-07 | 0.999999937765898 | 24 | 2.21247981079946e-08 | 4.42495962159893e-08 | 0.999999977875202 | 25 | 6.53809877859921e-09 | 1.30761975571984e-08 | 0.999999993461901 | 26 | 2.03808975548374e-09 | 4.07617951096747e-09 | 0.99999999796191 | 27 | 6.06531868420063e-10 | 1.21306373684013e-09 | 0.999999999393468 | 28 | 1.95033124164435e-10 | 3.90066248328870e-10 | 0.999999999804967 | 29 | 6.77252581763186e-11 | 1.35450516352637e-10 | 0.999999999932275 | 30 | 2.47804949856158e-11 | 4.95609899712316e-11 | 0.99999999997522 | 31 | 1.36985507775012e-11 | 2.73971015550024e-11 | 0.999999999986301 | 32 | 4.32907805584442e-12 | 8.65815611168884e-12 | 0.99999999999567 | 33 | 1.88595180094111e-12 | 3.77190360188222e-12 | 0.999999999998114 | 34 | 1.06000711097655e-12 | 2.12001422195311e-12 | 0.99999999999894 | 35 | 6.20911201020112e-13 | 1.24182240204022e-12 | 0.99999999999938 | 36 | 2.93147504875948e-13 | 5.86295009751896e-13 | 0.999999999999707 | 37 | 9.8256309554895e-14 | 1.9651261910979e-13 | 0.999999999999902 | 38 | 3.7067953954895e-14 | 7.413590790979e-14 | 0.999999999999963 | 39 | 1.05712151547570e-14 | 2.11424303095140e-14 | 0.99999999999999 | 40 | 2.85446320739083e-15 | 5.70892641478166e-15 | 0.999999999999997 | 41 | 2.64076394133862e-15 | 5.28152788267725e-15 | 0.999999999999997 | 42 | 7.00030773454134e-16 | 1.40006154690827e-15 | 1 | 43 | 4.80687886090848e-15 | 9.61375772181695e-15 | 0.999999999999995 | 44 | 2.05685900873982e-13 | 4.11371801747963e-13 | 0.999999999999794 | 45 | 3.92434904545249e-13 | 7.84869809090498e-13 | 0.999999999999608 | 46 | 2.09234117199993e-12 | 4.18468234399985e-12 | 0.999999999997908 | 47 | 2.34730782826030e-12 | 4.69461565652061e-12 | 0.999999999997653 | 48 | 9.9950002801515e-13 | 1.9990000560303e-12 | 0.999999999999 | 49 | 5.89163064878997e-12 | 1.17832612975799e-11 | 0.999999999994108 | 50 | 4.01382925367317e-12 | 8.02765850734634e-12 | 0.999999999995986 | 51 | 1.51843526395583e-12 | 3.03687052791167e-12 | 0.999999999998482 | 52 | 7.98724230170855e-13 | 1.59744846034171e-12 | 0.999999999999201 | 53 | 3.40907296017998e-13 | 6.81814592035995e-13 | 0.99999999999966 | 54 | 1.73489849680170e-13 | 3.46979699360340e-13 | 0.999999999999827 | 55 | 6.79886177528898e-14 | 1.35977235505780e-13 | 0.999999999999932 | 56 | 2.98444161362070e-14 | 5.96888322724139e-14 | 0.99999999999997 | 57 | 2.11573082626292e-14 | 4.23146165252583e-14 | 0.999999999999979 | 58 | 7.86593713937448e-15 | 1.57318742787490e-14 | 0.999999999999992 | 59 | 4.9401047291702e-15 | 9.8802094583404e-15 | 0.999999999999995 | 60 | 1.60754702565920e-14 | 3.21509405131841e-14 | 0.999999999999984 | 61 | 1.36244382600189e-14 | 2.72488765200378e-14 | 0.999999999999986 | 62 | 1.67517185230434e-14 | 3.35034370460867e-14 | 0.999999999999983 | 63 | 1.41702713576236e-14 | 2.83405427152471e-14 | 0.999999999999986 | 64 | 1.52307559635575e-14 | 3.04615119271150e-14 | 0.999999999999985 | 65 | 8.90097319579419e-15 | 1.78019463915884e-14 | 0.99999999999999 | 66 | 4.08230809478066e-15 | 8.16461618956132e-15 | 0.999999999999996 | 67 | 2.05126436766485e-15 | 4.10252873532970e-15 | 0.999999999999998 | 68 | 1.06412258192680e-15 | 2.12824516385360e-15 | 0.999999999999999 | 69 | 1.20438490167546e-15 | 2.40876980335092e-15 | 0.999999999999999 | 70 | 1.27632435177126e-15 | 2.55264870354252e-15 | 0.999999999999999 | 71 | 4.77169350430311e-15 | 9.54338700860623e-15 | 0.999999999999995 | 72 | 3.74919157601223e-15 | 7.49838315202447e-15 | 0.999999999999996 | 73 | 3.35248087817362e-15 | 6.70496175634724e-15 | 0.999999999999997 | 74 | 1.35645806718066e-15 | 2.71291613436132e-15 | 0.999999999999999 | 75 | 5.59005932178543e-16 | 1.11801186435709e-15 | 1 | 76 | 2.68446615861273e-16 | 5.36893231722545e-16 | 1 | 77 | 1.19403401970555e-16 | 2.38806803941111e-16 | 1 | 78 | 7.97236562922924e-17 | 1.59447312584585e-16 | 1 | 79 | 6.04906840742212e-17 | 1.20981368148442e-16 | 1 | 80 | 3.32101692939033e-17 | 6.64203385878066e-17 | 1 | 81 | 2.5839069594042e-16 | 5.1678139188084e-16 | 1 | 82 | 1.52834040823049e-15 | 3.05668081646098e-15 | 0.999999999999998 | 83 | 1.55087137138053e-15 | 3.10174274276106e-15 | 0.999999999999998 | 84 | 2.10887011204212e-15 | 4.21774022408425e-15 | 0.999999999999998 | 85 | 2.07058904380221e-15 | 4.14117808760442e-15 | 0.999999999999998 | 86 | 1.73761717157565e-15 | 3.4752343431513e-15 | 0.999999999999998 | 87 | 1.89839369434612e-15 | 3.79678738869225e-15 | 0.999999999999998 | 88 | 2.50455682565262e-15 | 5.00911365130525e-15 | 0.999999999999998 | 89 | 1.73807533966187e-15 | 3.47615067932374e-15 | 0.999999999999998 | 90 | 2.13000978777632e-15 | 4.26001957555263e-15 | 0.999999999999998 | 91 | 3.59035693948088e-15 | 7.18071387896177e-15 | 0.999999999999996 | 92 | 3.3462164515877e-15 | 6.6924329031754e-15 | 0.999999999999997 | 93 | 3.19854114059545e-15 | 6.3970822811909e-15 | 0.999999999999997 | 94 | 5.98388042784752e-15 | 1.19677608556950e-14 | 0.999999999999994 | 95 | 1.26132982998659e-14 | 2.52265965997318e-14 | 0.999999999999987 | 96 | 3.57295819550686e-14 | 7.14591639101372e-14 | 0.999999999999964 | 97 | 5.30523999886051e-14 | 1.06104799977210e-13 | 0.999999999999947 | 98 | 4.30531902403304e-14 | 8.61063804806609e-14 | 0.999999999999957 | 99 | 5.97672949300136e-14 | 1.19534589860027e-13 | 0.99999999999994 | 100 | 4.39293431664299e-14 | 8.78586863328599e-14 | 0.999999999999956 | 101 | 3.08237614846064e-14 | 6.16475229692129e-14 | 0.99999999999997 | 102 | 2.65969426312558e-14 | 5.31938852625115e-14 | 0.999999999999973 | 103 | 2.19547017107645e-14 | 4.3909403421529e-14 | 0.999999999999978 | 104 | 1.56265149382028e-14 | 3.12530298764056e-14 | 0.999999999999984 | 105 | 9.35559106501702e-15 | 1.87111821300340e-14 | 0.99999999999999 | 106 | 6.60395695817254e-15 | 1.32079139163451e-14 | 0.999999999999993 | 107 | 4.47678530663146e-15 | 8.95357061326292e-15 | 0.999999999999996 | 108 | 2.83239417351484e-15 | 5.66478834702969e-15 | 0.999999999999997 | 109 | 2.44258000552974e-15 | 4.88516001105947e-15 | 0.999999999999998 | 110 | 1.86118695374884e-15 | 3.72237390749769e-15 | 0.999999999999998 | 111 | 1.29190930542833e-15 | 2.58381861085666e-15 | 0.999999999999999 | 112 | 9.52524367575764e-16 | 1.90504873515153e-15 | 1 | 113 | 8.13737212254664e-16 | 1.62747442450933e-15 | 1 | 114 | 6.837316562848e-16 | 1.3674633125696e-15 | 1 | 115 | 6.23798330630879e-16 | 1.24759666126176e-15 | 1 | 116 | 4.36867772575929e-16 | 8.73735545151859e-16 | 1 | 117 | 1.31821456307312e-15 | 2.63642912614623e-15 | 0.999999999999999 | 118 | 5.19105920893444e-15 | 1.03821184178689e-14 | 0.999999999999995 | 119 | 2.5672398142976e-14 | 5.1344796285952e-14 | 0.999999999999974 | 120 | 1.41856501370833e-13 | 2.83713002741666e-13 | 0.999999999999858 | 121 | 1.33633609466428e-13 | 2.67267218932856e-13 | 0.999999999999866 | 122 | 1.47674833226616e-13 | 2.95349666453232e-13 | 0.999999999999852 | 123 | 4.24294746801821e-13 | 8.48589493603642e-13 | 0.999999999999576 | 124 | 8.72582116858242e-13 | 1.74516423371648e-12 | 0.999999999999127 | 125 | 4.90636157862709e-12 | 9.81272315725419e-12 | 0.999999999995094 | 126 | 1.62449466316241e-11 | 3.24898932632482e-11 | 0.999999999983755 | 127 | 1.88549767426014e-10 | 3.77099534852028e-10 | 0.99999999981145 | 128 | 1.09614539141732e-09 | 2.19229078283463e-09 | 0.999999998903855 | 129 | 1.95455827103661e-09 | 3.90911654207323e-09 | 0.999999998045442 | 130 | 8.97666849088752e-09 | 1.79533369817750e-08 | 0.999999991023331 | 131 | 3.48618905267575e-08 | 6.9723781053515e-08 | 0.99999996513811 | 132 | 3.02881465744483e-08 | 6.05762931488966e-08 | 0.999999969711853 | 133 | 2.36002976916451e-08 | 4.72005953832903e-08 | 0.999999976399702 | 134 | 1.79223337522817e-08 | 3.58446675045634e-08 | 0.999999982077666 | 135 | 1.41604343959847e-08 | 2.83208687919693e-08 | 0.999999985839566 | 136 | 1.46786410548504e-08 | 2.93572821097008e-08 | 0.99999998532136 | 137 | 1.03878947578579e-08 | 2.07757895157159e-08 | 0.999999989612105 | 138 | 8.25588430943502e-09 | 1.65117686188700e-08 | 0.999999991744116 | 139 | 5.99160156882957e-09 | 1.19832031376591e-08 | 0.999999994008398 | 140 | 4.41942179924282e-09 | 8.83884359848564e-09 | 0.999999995580578 | 141 | 3.33081481747388e-09 | 6.66162963494776e-09 | 0.999999996669185 | 142 | 2.43514083458830e-09 | 4.87028166917661e-09 | 0.99999999756486 | 143 | 1.73499861577080e-09 | 3.46999723154161e-09 | 0.999999998265001 | 144 | 1.40790188352022e-09 | 2.81580376704044e-09 | 0.999999998592098 | 145 | 1.10698794645704e-09 | 2.21397589291408e-09 | 0.999999998893012 | 146 | 1.05976167434695e-09 | 2.11952334869389e-09 | 0.999999998940238 | 147 | 1.14347468352303e-09 | 2.28694936704605e-09 | 0.999999998856525 | 148 | 1.89734638785369e-09 | 3.79469277570737e-09 | 0.999999998102654 | 149 | 6.08249994664854e-09 | 1.21649998932971e-08 | 0.9999999939175 | 150 | 6.76919838422753e-09 | 1.35383967684551e-08 | 0.999999993230802 | 151 | 6.7606435021943e-09 | 1.35212870043886e-08 | 0.999999993239357 | 152 | 7.06496216290789e-09 | 1.41299243258158e-08 | 0.999999992935038 | 153 | 5.89360220408853e-09 | 1.17872044081771e-08 | 0.999999994106398 | 154 | 4.88386622729565e-09 | 9.7677324545913e-09 | 0.999999995116134 | 155 | 6.75826081348329e-09 | 1.35165216269666e-08 | 0.99999999324174 | 156 | 6.23402466980129e-09 | 1.24680493396026e-08 | 0.999999993765975 | 157 | 6.62714610029772e-09 | 1.32542922005954e-08 | 0.999999993372854 | 158 | 5.79255355383343e-09 | 1.15851071076669e-08 | 0.999999994207446 | 159 | 4.95558713514607e-09 | 9.91117427029215e-09 | 0.999999995044413 | 160 | 4.57488097515781e-09 | 9.14976195031561e-09 | 0.99999999542512 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189 | 9.0925158421455e-09 | 1.8185031684291e-08 | 0.999999990907484 | 190 | 8.72227006990382e-09 | 1.74445401398076e-08 | 0.99999999127773 | 191 | 1.13376546020437e-08 | 2.26753092040875e-08 | 0.999999988662345 | 192 | 1.33483783490848e-08 | 2.66967566981695e-08 | 0.999999986651622 | 193 | 1.34580287660774e-08 | 2.69160575321548e-08 | 0.999999986541971 | 194 | 1.43542819505427e-08 | 2.87085639010854e-08 | 0.999999985645718 | 195 | 2.67410191125481e-08 | 5.34820382250961e-08 | 0.99999997325898 | 196 | 4.71786052577812e-08 | 9.43572105155624e-08 | 0.999999952821395 | 197 | 5.30117979035214e-08 | 1.06023595807043e-07 | 0.999999946988202 | 198 | 5.50395757535076e-08 | 1.10079151507015e-07 | 0.999999944960424 | 199 | 8.0418774447866e-08 | 1.60837548895732e-07 | 0.999999919581225 | 200 | 2.24940624822330e-07 | 4.49881249644659e-07 | 0.999999775059375 | 201 | 5.40543801087549e-07 | 1.08108760217510e-06 | 0.9999994594562 | 202 | 1.14322615217638e-06 | 2.28645230435277e-06 | 0.999998856773848 | 203 | 2.16989951621074e-06 | 4.33979903242149e-06 | 0.999997830100484 | 204 | 3.17266719892082e-06 | 6.34533439784164e-06 | 0.9999968273328 | 205 | 3.30609612812272e-06 | 6.61219225624544e-06 | 0.999996693903872 | 206 | 8.6655406415406e-06 | 1.73310812830812e-05 | 0.999991334459359 | 207 | 7.42736342057198e-06 | 1.48547268411440e-05 | 0.99999257263658 | 208 | 6.981655650121e-06 | 1.3963311300242e-05 | 0.99999301834435 | 209 | 5.95538283387009e-06 | 1.19107656677402e-05 | 0.999994044617166 | 210 | 4.91803480322089e-06 | 9.83606960644178e-06 | 0.999995081965197 | 211 | 4.17114812442123e-06 | 8.34229624884247e-06 | 0.999995828851876 | 212 | 4.49143625510091e-06 | 8.98287251020182e-06 | 0.999995508563745 | 213 | 4.84669306829607e-06 | 9.69338613659214e-06 | 0.999995153306932 | 214 | 7.60374767661353e-06 | 1.52074953532271e-05 | 0.999992396252323 | 215 | 6.40954655874727e-06 | 1.28190931174945e-05 | 0.999993590453441 | 216 | 4.96069792955011e-06 | 9.92139585910022e-06 | 0.99999503930207 | 217 | 3.81379581300682e-06 | 7.62759162601363e-06 | 0.999996186204187 | 218 | 3.04901671083014e-06 | 6.09803342166027e-06 | 0.99999695098329 | 219 | 2.33970146998700e-06 | 4.67940293997401e-06 | 0.99999766029853 | 220 | 1.85512028261768e-06 | 3.71024056523537e-06 | 0.999998144879717 | 221 | 1.45469329756863e-06 | 2.90938659513725e-06 | 0.999998545306702 | 222 | 1.08363105640168e-06 | 2.16726211280336e-06 | 0.999998916368944 | 223 | 8.76609913685256e-07 | 1.75321982737051e-06 | 0.999999123390086 | 224 | 9.52853306893378e-07 | 1.90570661378676e-06 | 0.999999047146693 | 225 | 7.4088119570085e-07 | 1.4817623914017e-06 | 0.999999259118804 | 226 | 5.33117451561304e-07 | 1.06623490312261e-06 | 0.999999466882548 | 227 | 3.83078226568157e-07 | 7.66156453136314e-07 | 0.999999616921773 | 228 | 2.86449485986621e-07 | 5.72898971973241e-07 | 0.999999713550514 | 229 | 2.03414689519427e-07 | 4.06829379038854e-07 | 0.99999979658531 | 230 | 1.58863669198310e-07 | 3.17727338396619e-07 | 0.99999984113633 | 231 | 1.10167556251878e-07 | 2.20335112503756e-07 | 0.999999889832444 | 232 | 7.87562177252422e-08 | 1.57512435450484e-07 | 0.999999921243782 | 233 | 7.25759468364419e-08 | 1.45151893672884e-07 | 0.999999927424053 | 234 | 4.96879739190732e-08 | 9.93759478381463e-08 | 0.999999950312026 | 235 | 3.34011301141588e-08 | 6.68022602283176e-08 | 0.99999996659887 | 236 | 2.23117403124183e-08 | 4.46234806248367e-08 | 0.99999997768826 | 237 | 2.62140857470646e-08 | 5.24281714941292e-08 | 0.999999973785914 | 238 | 2.13426343790362e-08 | 4.26852687580725e-08 | 0.999999978657366 | 239 | 1.76457601259026e-08 | 3.52915202518053e-08 | 0.99999998235424 | 240 | 1.31955949752615e-08 | 2.6391189950523e-08 | 0.999999986804405 | 241 | 9.65939958626936e-09 | 1.93187991725387e-08 | 0.9999999903406 | 242 | 7.86555641589624e-09 | 1.57311128317925e-08 | 0.999999992134444 | 243 | 7.12513064011509e-09 | 1.42502612802302e-08 | 0.99999999287487 | 244 | 7.49156637409858e-09 | 1.49831327481972e-08 | 0.999999992508434 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0.99999999956077 | 259 | 3.02731360628570e-10 | 6.05462721257141e-10 | 0.99999999969727 | 260 | 1.91477117159759e-10 | 3.82954234319517e-10 | 0.999999999808523 | 261 | 1.22912730317170e-10 | 2.45825460634339e-10 | 0.999999999877087 | 262 | 1.06005156240241e-10 | 2.12010312480482e-10 | 0.999999999893995 | 263 | 1.36430868055573e-10 | 2.72861736111146e-10 | 0.999999999863569 | 264 | 8.65546563287484e-11 | 1.73109312657497e-10 | 0.999999999913445 | 265 | 5.38722994812727e-11 | 1.07744598962545e-10 | 0.999999999946128 | 266 | 3.39128070770687e-11 | 6.78256141541374e-11 | 0.999999999966087 | 267 | 3.99532384218830e-11 | 7.99064768437661e-11 | 0.999999999960047 | 268 | 4.14923422705771e-11 | 8.29846845411541e-11 | 0.999999999958508 | 269 | 2.65132089655289e-11 | 5.30264179310578e-11 | 0.999999999973487 | 270 | 1.68493552185676e-11 | 3.36987104371353e-11 | 0.99999999998315 | 271 | 1.10114820986225e-11 | 2.20229641972450e-11 | 0.999999999988989 | 272 | 7.26288022309823e-12 | 1.45257604461965e-11 | 0.999999999992737 | 273 | 4.49100699249523e-12 | 8.98201398499045e-12 | 0.99999999999551 | 274 | 2.7279813507735e-12 | 5.455962701547e-12 | 0.999999999997272 | 275 | 1.69749138357962e-12 | 3.39498276715924e-12 | 0.999999999998302 | 276 | 1.38066842556501e-12 | 2.76133685113002e-12 | 0.99999999999862 | 277 | 1.14082853523901e-12 | 2.28165707047803e-12 | 0.99999999999886 | 278 | 9.27115234748108e-13 | 1.85423046949622e-12 | 0.999999999999073 | 279 | 7.62296400246368e-13 | 1.52459280049274e-12 | 0.999999999999238 | 280 | 1.39504301256578e-12 | 2.79008602513156e-12 | 0.999999999998605 | 281 | 1.41762606258913e-12 | 2.83525212517825e-12 | 0.999999999998582 | 282 | 1.18214170083673e-12 | 2.36428340167345e-12 | 0.999999999998818 | 283 | 1.22300674317717e-12 | 2.44601348635433e-12 | 0.999999999998777 | 284 | 1.16587694730429e-12 | 2.33175389460858e-12 | 0.999999999998834 | 285 | 1.19778233141056e-12 | 2.39556466282111e-12 | 0.999999999998802 | 286 | 1.41064663278050e-12 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8.77471808316127e-06 | 1.75494361663225e-05 | 0.999991225281917 | 301 | 3.72033832385445e-05 | 7.4406766477089e-05 | 0.999962796616761 | 302 | 0.000205883020266987 | 0.000411766040533973 | 0.999794116979733 | 303 | 0.00114997870684923 | 0.00229995741369846 | 0.998850021293151 | 304 | 0.00230987716830233 | 0.00461975433660467 | 0.997690122831698 | 305 | 0.00474317472102382 | 0.00948634944204764 | 0.995256825278976 | 306 | 0.0116381158929855 | 0.0232762317859709 | 0.988361884107015 | 307 | 0.0186933637186592 | 0.0373867274373185 | 0.98130663628134 | 308 | 0.0286152900167069 | 0.0572305800334138 | 0.971384709983293 | 309 | 0.0417940577919633 | 0.0835881155839266 | 0.958205942208037 | 310 | 0.0587249476418738 | 0.117449895283748 | 0.941275052358126 | 311 | 0.079894194662804 | 0.159788389325608 | 0.920105805337196 | 312 | 0.112816467131391 | 0.225632934262782 | 0.88718353286861 | 313 | 0.136993894707200 | 0.273987789414399 | 0.8630061052928 | 314 | 0.161759612857453 | 0.323519225714905 | 0.838240387142547 | 315 | 0.18889089546214 | 0.37778179092428 | 0.81110910453786 | 316 | 0.211787808091485 | 0.423575616182969 | 0.788212191908515 | 317 | 0.240428178332617 | 0.480856356665235 | 0.759571821667383 | 318 | 0.259391438579820 | 0.518782877159641 | 0.74060856142018 | 319 | 0.283899669112147 | 0.567799338224293 | 0.716100330887853 | 320 | 0.310305926557582 | 0.620611853115163 | 0.689694073442418 | 321 | 0.359890379334305 | 0.719780758668609 | 0.640109620665695 | 322 | 0.384763373920256 | 0.769526747840512 | 0.615236626079744 | 323 | 0.397182452642071 | 0.794364905284142 | 0.602817547357929 | 324 | 0.426062416027581 | 0.852124832055162 | 0.573937583972419 | 325 | 0.447492983468136 | 0.894985966936271 | 0.552507016531864 | 326 | 0.441108768919287 | 0.882217537838575 | 0.558891231080713 | 327 | 0.440769137563049 | 0.881538275126099 | 0.559230862436951 | 328 | 0.53315843939721 | 0.93368312120558 | 0.46684156060279 | 329 | 0.52227128608002 | 0.95545742783996 | 0.47772871391998 | 330 | 0.541882193555666 | 0.916235612888669 | 0.458117806444334 | 331 | 0.628575620341462 | 0.742848759317077 | 0.371424379658538 | 332 | 0.692561118073557 | 0.614877763852886 | 0.307438881926443 | 333 | 0.668552124313926 | 0.662895751372149 | 0.331447875686074 | 334 | 0.704982541773572 | 0.590034916452857 | 0.295017458226428 | 335 | 0.674491758555241 | 0.651016482889519 | 0.325508241444759 | 336 | 0.664175676143083 | 0.671648647713834 | 0.335824323856917 | 337 | 0.81409271074817 | 0.371814578503661 | 0.185907289251830 | 338 | 0.80494986656465 | 0.390100266870702 | 0.195050133435351 | 339 | 0.776185873059438 | 0.447628253881124 | 0.223814126940562 | 340 | 0.744732955543363 | 0.510534088913274 | 0.255267044456637 | 341 | 0.730469683574006 | 0.539060632851989 | 0.269530316425994 | 342 | 0.728580694892202 | 0.542838610215596 | 0.271419305107798 | 343 | 0.711628799482764 | 0.576742401034471 | 0.288371200517236 | 344 | 0.711170287059313 | 0.577659425881375 | 0.288829712940687 | 345 | 0.788508215052727 | 0.422983569894546 | 0.211491784947273 | 346 | 0.813547198771858 | 0.372905602456283 | 0.186452801228142 | 347 | 0.848598794425773 | 0.302802411148455 | 0.151401205574227 | 348 | 0.863673899648315 | 0.272652200703370 | 0.136326100351685 | 349 | 0.83997802422052 | 0.320043951558960 | 0.160021975779480 | 350 | 0.813540372471913 | 0.372919255056175 | 0.186459627528087 | 351 | 0.854738516774166 | 0.290522966451669 | 0.145261483225834 | 352 | 0.910895632061552 | 0.178208735876897 | 0.0891043679384485 | 353 | 0.8946865756612 | 0.2106268486776 | 0.1053134243388 | 354 | 0.870741107668921 | 0.258517784662158 | 0.129258892331079 | 355 | 0.927417746489603 | 0.145164507020794 | 0.0725822535103968 | 356 | 0.932595994794373 | 0.134808010411253 | 0.0674040052056267 | 357 | 0.92514993437618 | 0.149700131247640 | 0.0748500656238198 | 358 | 0.910540892057444 | 0.178918215885112 | 0.0894591079425559 | 359 | 0.887244875306424 | 0.225510249387153 | 0.112755124693576 | 360 | 0.88718900066984 | 0.225621998660319 | 0.112810999330160 | 361 | 0.874781142570433 | 0.250437714859133 | 0.125218857429567 | 362 | 0.875323226124572 | 0.249353547750855 | 0.124676773875428 | 363 | 0.909635196862571 | 0.180729606274858 | 0.0903648031374288 | 364 | 0.89398498548889 | 0.212030029022220 | 0.106015014511110 | 365 | 0.864189830906298 | 0.271620338187404 | 0.135810169093702 | 366 | 0.858621330253041 | 0.282757339493917 | 0.141378669746959 | 367 | 0.832844937088189 | 0.334310125823623 | 0.167155062911811 | 368 | 0.87760269088303 | 0.244794618233941 | 0.122397309116971 | 369 | 0.991636140800452 | 0.0167277183990964 | 0.00836385919954822 | 370 | 0.987347917029351 | 0.0253041659412977 | 0.0126520829706489 | 371 | 0.980334232229652 | 0.0393315355406967 | 0.0196657677703484 | 372 | 0.973377540162255 | 0.0532449196754895 | 0.0266224598377448 | 373 | 0.962434642736287 | 0.0751307145274263 | 0.0375653572637131 | 374 | 0.95861371654469 | 0.0827725669106188 | 0.0413862834553094 | 375 | 0.94031375163249 | 0.119372496735020 | 0.0596862483675098 | 376 | 0.957216570376628 | 0.0855668592467434 | 0.0427834296233717 | 377 | 0.966722242200898 | 0.0665555155982034 | 0.0332777577991017 | 378 | 0.963620925289755 | 0.0727581494204892 | 0.0363790747102446 | 379 | 0.975652394824773 | 0.0486952103504547 | 0.0243476051752273 | 380 | 0.959783145401061 | 0.0804337091978775 | 0.0402168545989387 | 381 | 0.99158565305089 | 0.0168286938982211 | 0.00841434694911057 | 382 | 0.992644557513593 | 0.0147108849728141 | 0.00735544248640703 | 383 | 0.98735236653947 | 0.0252952669210594 | 0.0126476334605297 | 384 | 0.97960692627952 | 0.0407861474409583 | 0.0203930737204791 | 385 | 0.95969441782723 | 0.0806111643455415 | 0.0403055821727707 | 386 | 0.928478620454755 | 0.143042759090489 | 0.0715213795452445 | 387 | 0.99718741470327 | 0.00562517059346127 | 0.00281258529673064 | 388 | 0.995861213923248 | 0.00827757215350321 | 0.00413878607675161 | 389 | 0.980337557600467 | 0.0393248847990665 | 0.0196624423995332 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | Description | # significant tests | % significant tests | OK/NOK | 1% type I error level | 299 | 0.778645833333333 | NOK | 5% type I error level | 313 | 0.815104166666667 | NOK | 10% type I error level | 323 | 0.841145833333333 | NOK |
| Charts produced by software: | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289239839li8ei2riwqqc8c/10h6601228923785.png (open in new window) | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289239839li8ei2riwqqc8c/10h6601228923785.ps (open in new window) |
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| | Parameters (Session): | par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ; | | Parameters (R input): | par1 = 1 ; 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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