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Multiple Linear Regression - Estimated Regression Equation | USA[t] = + 127.399364499604 + 1.89927769676335Colombia[t] + 2.72058738350256M1[t] + 5.08328322812179M2[t] + 1.29282804242185M3[t] + 3.57139280539231M4[t] + 4.58871546000618M5[t] + 6.9823175521443M6[t] + 15.7898723045893M7[t] + 17.1239397386148M8[t] + 13.2850232260827M9[t] + 10.2014447288555M10[t] + 2.63636461408351M11[t] + 0.148173467103375t + e[t] |
Multiple Linear Regression - Ordinary Least Squares | Variable | Parameter | S.D. | T-STAT H0: parameter = 0 | 2-tail p-value | 1-tail p-value | (Intercept) | 127.399364499604 | 9.42068 | 13.5234 | 0 | 0 | Colombia | 1.89927769676335 | 0.087266 | 21.7642 | 0 | 0 | M1 | 2.72058738350256 | 8.016357 | 0.3394 | 0.73453 | 0.367265 | M2 | 5.08328322812179 | 8.015826 | 0.6342 | 0.526398 | 0.263199 | M3 | 1.29282804242185 | 8.017056 | 0.1613 | 0.871983 | 0.435991 | M4 | 3.57139280539231 | 8.016588 | 0.4455 | 0.656237 | 0.328118 | M5 | 4.58871546000618 | 8.016216 | 0.5724 | 0.567403 | 0.283702 | M6 | 6.9823175521443 | 8.014833 | 0.8712 | 0.384263 | 0.192131 | M7 | 15.7898723045893 | 8.017549 | 1.9694 | 0.049703 | 0.024852 | M8 | 17.1239397386148 | 8.016567 | 2.1361 | 0.033375 | 0.016688 | M9 | 13.2850232260827 | 8.016201 | 1.6573 | 0.098371 | 0.049185 | M10 | 10.2014447288555 | 8.015953 | 1.2726 | 0.203999 | 0.102 | M11 | 2.63636461408351 | 8.014282 | 0.329 | 0.742386 | 0.371193 | t | 0.148173467103375 | 0.015768 | 9.3972 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | Multiple R | 0.7832915252984 | R-squared | 0.613545613604294 | Adjusted R-squared | 0.599025651109658 | F-TEST (value) | 42.2553166945808 | F-TEST (DF numerator) | 13 | F-TEST (DF denominator) | 346 | p-value | 0 | Multiple Linear Regression - Residual Statistics | Residual Standard Deviation | 31.039006205138 | Sum Squared Residuals | 333343.287546098 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error | 1 | 255 | 296.037082723707 | -41.0370827237072 | 2 | 280.2 | 298.547952035437 | -18.3479520354368 | 3 | 299.9 | 294.544807554456 | 5.3551924455444 | 4 | 339.2 | 296.648668576080 | 42.5513314239204 | 5 | 374.2 | 299.086680754628 | 75.1133192453718 | 6 | 393.5 | 307.573195504739 | 85.9268044952609 | 7 | 389.2 | 316.471945393385 | 72.7280546066153 | 8 | 381.7 | 317.213467992776 | 64.4865320072243 | 9 | 375.2 | 312.098266674774 | 63.1017333252255 | 10 | 369 | 308.004302249625 | 60.995697750375 | 11 | 357.4 | 299.580778422672 | 57.8192215773282 | 12 | 352.1 | 295.972013434601 | 56.1279865653987 | 13 | 346.5 | 297.416316012635 | 49.0836839873652 | 14 | 342.9 | 299.452365900166 | 43.4476340998335 | 15 | 340.3 | 295.012387548929 | 45.2876124510706 | 16 | 328.3 | 296.717400254233 | 31.5825997457669 | 17 | 322.9 | 297.199156405116 | 25.7008435948844 | 18 | 314.3 | 299.095177547458 | 15.2048224525425 | 19 | 308.9 | 307.443136904042 | 1.45686309595832 | 20 | 294 | 308.298616165239 | -14.2986161652386 | 21 | 285.6 | 303.221400401173 | -17.6214004011726 | 22 | 281.2 | 298.177797127641 | -16.9777971276415 | 23 | 280.3 | 289.089526106821 | -8.78952610682113 | 24 | 278.8 | 285.157883910301 | -6.35788391030083 | 25 | 274.5 | 286.678157596205 | -12.1781575962048 | 26 | 270.4 | 286.112197039171 | -15.7121970391708 | 27 | 263.4 | 264.635697747966 | -1.23569774796648 | 28 | 259.9 | 265.732941590306 | -5.83294159030594 | 29 | 258 | 269.348505940848 | -11.3485059408479 | 30 | 262.7 | 279.278471740499 | -16.5784717404988 | 31 | 284.7 | 291.747863699059 | -7.04786369905941 | 32 | 311.3 | 297.009667216747 | 14.2903327832527 | 33 | 322.1 | 300.498193865084 | 21.6018061349161 | 34 | 327 | 300.411705380105 | 26.5882946198948 | 35 | 331.3 | 295.406881407326 | 35.893118592674 | 36 | 333.3 | 294.362141309886 | 38.937858690114 | 37 | 321.4 | 297.515793815006 | 23.8842061849935 | 38 | 327 | 298.146378206933 | 28.8536217930666 | 39 | 320 | 293.307551539376 | 26.6924484606241 | 40 | 314.7 | 301.071260097355 | 13.6287399026453 | 41 | 316.7 | 300.071579644762 | 16.6284203552383 | 42 | 314.4 | 300.334221967887 | 14.0657780321127 | 43 | 321.3 | 307.884484691831 | 13.4155153081692 | 44 | 318.2 | 307.695361219808 | 10.5046387801921 | 45 | 307.2 | 302.295268247292 | 4.90473175270787 | 46 | 301.3 | 297.251664973761 | 4.04833502623902 | 47 | 287.5 | 287.68857452875 | -0.188574528749823 | 48 | 277.7 | 290.499368155739 | -12.7993681557394 | 49 | 274.4 | 292.532446819769 | -18.1324468197695 | 50 | 258.8 | 293.163031211696 | -34.3630312116964 | 51 | 253.3 | 287.963341781754 | -34.6633417817539 | 52 | 251 | 289.022600070158 | -38.0226000701581 | 53 | 248.4 | 288.7066595884 | -40.3066595883999 | 54 | 249.5 | 289.425128558749 | -39.9251285587486 | 55 | 246.1 | 296.576542966372 | -50.4765429663718 | 56 | 244.5 | 296.14051339377 | -51.6405133937697 | 57 | 243.6 | 290.588478205513 | -46.9884782055129 | 58 | 244 | 294.851335646122 | -50.8513356461221 | 59 | 240.8 | 292.049673801588 | -51.2496738015885 | 60 | 249.8 | 288.061053274165 | -38.2610532741653 | 61 | 248 | 288.726651996526 | -40.7266519965257 | 62 | 259.4 | 289.395221942388 | -29.9952219423879 | 63 | 260.5 | 292.134513284916 | -31.6345132849162 | 64 | 260.8 | 294.447294853184 | -33.6472948531842 | 65 | 261.3 | 293.6185493933 | -32.3185493932999 | 66 | 259.5 | 294.033133932166 | -34.5331339321665 | 67 | 256.6 | 301.279512224628 | -44.6795122246279 | 68 | 257.9 | 300.653554882349 | -42.7535548823494 | 69 | 256.5 | 295.196483578931 | -38.6964835789308 | 70 | 254.2 | 303.580773621516 | -49.3807736215165 | 71 | 253.3 | 293.011065997221 | -39.7110659972207 | 72 | 253.8 | 287.484030535419 | -33.6840305354192 | 73 | 255.5 | 287.978694265071 | -32.478694265071 | 74 | 257.1 | 288.096473678872 | -30.9964736788718 | 75 | 257.3 | 281.681246523001 | -24.3812465230008 | 76 | 253.2 | 287.317764060605 | -34.1177640606046 | 77 | 252.8 | 287.818512988455 | -35.0185129884547 | 78 | 252 | 287.720292549195 | -35.7202925491952 | 79 | 250.7 | 294.093003101145 | -43.3930031011454 | 80 | 252.2 | 292.726327457129 | -40.5263274571293 | 81 | 250 | 293.973706423285 | -43.9737064232852 | 82 | 251 | 292.025925795478 | -41.0259257954783 | 83 | 253.4 | 283.906286400007 | -30.5062864000073 | 84 | 251.2 | 278.645149815753 | -27.4451498157526 | 85 | 255.6 | 280.887149026427 | -25.2871490264267 | 86 | 261.1 | 280.682051231778 | -19.5820512317777 | 87 | 258.9 | 275.254448478224 | -16.3544484782236 | 88 | 259.9 | 277.624208377394 | -17.7242083773945 | 89 | 261.2 | 278.143950082212 | -16.9439500822122 | 90 | 264.7 | 279.451195138558 | -14.7511951385576 | 91 | 267.1 | 285.387071820252 | -18.2870718202522 | 92 | 266.4 | 289.699236489558 | -23.2992364895585 | 93 | 267.7 | 287.034103400382 | -19.3341034003819 | 94 | 268.6 | 281.401724040854 | -12.8017240408541 | 95 | 267.5 | 272.541366343645 | -5.04136634364543 | 96 | 268.5 | 271.515619023173 | -3.01561902317304 | 97 | 268.5 | 271.64941999044 | -3.14941999043978 | 98 | 270.5 | 270.855546109794 | -0.355546109794157 | 99 | 270.9 | 269.929231497569 | 0.970768502430785 | 100 | 270.1 | 266.297273874968 | 3.80272612503207 | 101 | 269.3 | 262.163785222715 | 7.13621477728458 | 102 | 269.8 | 267.896347312519 | 1.90365268748062 | 103 | 270.1 | 273.015534584606 | -2.9155345846058 | 104 | 264.9 | 271.306988955172 | -6.40698895517226 | 105 | 263.7 | 271.072931317853 | -7.37293131785279 | 106 | 264.8 | 264.585876994782 | 0.214123005218494 | 107 | 263.7 | 263.398601192497 | 0.301398807503297 | 108 | 255.9 | 260.872424491581 | -4.97242449158125 | 109 | 276.2 | 274.358147667094 | 1.84185233290567 | 110 | 360.1 | 295.140068421680 | 64.9599315783197 | 111 | 380.5 | 319.37918329157 | 61.1208167084304 | 112 | 373.7 | 324.48390307408 | 49.2160969259202 | 113 | 369.8 | 327.548676892560 | 42.2513231074396 | 114 | 366.6 | 328.115203647168 | 38.4847963528320 | 115 | 359.3 | 334.032087551895 | 25.2679124481050 | 116 | 345.8 | 332.570448023041 | 13.2295519769593 | 117 | 326.2 | 325.461005123438 | 0.73899487656206 | 118 | 324.5 | 320.284452411133 | 4.21554758886661 | 119 | 328.1 | 314.861787345066 | 13.2382126549337 | 120 | 327.5 | 308.97388912088 | 18.5261108791203 | 121 | 324.4 | 308.822798433632 | 15.5772015663680 | 122 | 316.5 | 308.636693415951 | 7.86330658404935 | 123 | 310.9 | 302.088516821306 | 8.8114831786938 | 124 | 301.5 | 301.761302391073 | -0.261302391073139 | 125 | 291.7 | 300.172845852483 | -8.47284585248351 | 126 | 290.4 | 300.264553182900 | -9.86455318290036 | 127 | 287.4 | 306.732227619689 | -19.3322276196888 | 128 | 277.7 | 306.011306392572 | -28.3113063925721 | 129 | 281.6 | 300.345314542509 | -18.7453145425094 | 130 | 288 | 300.239833280563 | -12.2398332805630 | 131 | 276 | 295.956734832554 | -19.956734832554 | 132 | 272.9 | 291.588258765778 | -18.6882587657781 | 133 | 283 | 294.684932939996 | -11.6849329399956 | 134 | 283.3 | 300.842415429504 | -17.5424154295039 | 135 | 276.8 | 293.971361626410 | -17.1713616264096 | 136 | 284.5 | 297.955507567829 | -13.4555075678294 | 137 | 282.7 | 297.867480409683 | -15.1674804096828 | 138 | 281.2 | 297.256454992297 | -16.0564549922972 | 139 | 287.4 | 303.401252220636 | -16.0012522206359 | 140 | 283.1 | 302.148533238425 | -19.0485332384254 | 141 | 284 | 295.646859201787 | -11.6468592017870 | 142 | 285.5 | 295.313464616229 | -9.81346461622892 | 143 | 289.2 | 296.120430395546 | -6.92043039554565 | 144 | 292.5 | 290.916272142194 | 1.58372785780611 | 145 | 296.4 | 293.917982431573 | 2.48201756842669 | 146 | 305.2 | 290.674040322103 | 14.5259596778970 | 147 | 303.9 | 285.341401453387 | 18.5585985466130 | 148 | 311.5 | 300.037473604552 | 11.4625263954480 | 149 | 316.3 | 297.993190418739 | 18.3068095812608 | 150 | 316.7 | 302.092373689327 | 14.6076263106733 | 151 | 322.5 | 310.041484729590 | 12.4585152704095 | 152 | 317.1 | 308.674809085574 | 8.4251909144257 | 153 | 309.8 | 302.040185610162 | 7.75981438983762 | 154 | 303.8 | 298.402047832236 | 5.39795216776386 | 155 | 290.3 | 291.953772809917 | -1.65377280991684 | 156 | 293.7 | 286.369759017212 | 7.33024098278754 | 157 | 291.7 | 285.914783898483 | 5.78521610151744 | 158 | 296.5 | 285.006953356031 | 11.4930466439688 | 159 | 289.1 | 285.125241477026 | 3.97475852297404 | 160 | 288.5 | 291.730390639979 | -3.23039063997917 | 161 | 293.8 | 289.686107454166 | 4.11389254583367 | 162 | 297.7 | 289.170045921619 | 8.5299540783811 | 163 | 305.4 | 295.29585037299 | 10.1041496270101 | 164 | 302.7 | 293.929174728974 | 8.77082527102625 | 165 | 302.5 | 302.184888396186 | 0.315111603813589 | 166 | 303 | 297.692075654717 | 5.30792434528333 | 167 | 294.5 | 287.597187454612 | 6.90281254538824 | 168 | 294.1 | 282.279072539454 | 11.8209274605458 | 169 | 294.5 | 282.716757938203 | 11.7832420617969 | 170 | 297.1 | 283.043457898648 | 14.0565421013522 | 171 | 289.4 | 281.756280524038 | 7.64371947596215 | 172 | 292.4 | 291.134375124265 | 1.26562487573449 | 173 | 287.9 | 290.096709117737 | -2.19670911773726 | 174 | 286.6 | 290.435322548733 | -3.83532254873328 | 175 | 280.5 | 297.282852524874 | -16.7828525248744 | 176 | 272.4 | 296.54293852079 | -24.1429385207901 | 177 | 269.2 | 290.003278930216 | -20.8032789302163 | 178 | 270.6 | 290.429595423364 | -19.8295954233636 | 179 | 267.3 | 281.854129380669 | -14.5541293806694 | 180 | 262.5 | 276.9538555588 | -14.4538555587998 | 181 | 266.8 | 279.822616409406 | -13.0226164094057 | 182 | 268.8 | 275.192201581298 | -6.39220158129817 | 183 | 263.1 | 268.017263346722 | -4.91726334672179 | 184 | 261.2 | 269.190478296932 | -7.99047829693184 | 185 | 266 | 269.121443915753 | -3.12144391575288 | 186 | 262.5 | 270.409696195131 | -7.9096961951306 | 187 | 265.2 | 272.148169166978 | -6.94816916697829 | 188 | 261.3 | 267.26782978395 | -5.9678297839499 | 189 | 253.7 | 262.513491228334 | -8.8134912283337 | 190 | 249.2 | 258.514490688022 | -9.31449068802242 | 191 | 239.1 | 250.071974084102 | -10.9719740841016 | 192 | 236.4 | 246.520187426934 | -10.1201874269340 | 193 | 235.2 | 248.439309429158 | -13.2393094291583 | 194 | 245.2 | 250.038525446434 | -4.83852544643447 | 195 | 246.2 | 245.503583210359 | 0.696416789640858 | 196 | 247.7 | 252.887436228985 | -5.18743622898529 | 197 | 251.4 | 254.679693990634 | -3.27969399063439 | 198 | 253.3 | 255.891975162142 | -2.59197516214159 | 199 | 254.8 | 263.898064533308 | -9.0980645333083 | 200 | 250 | 277.364747701014 | -27.3647477010139 | 201 | 249.3 | 272.629401922365 | -23.3294019223653 | 202 | 241.5 | 268.649394159022 | -27.1493941590216 | 203 | 243.3 | 260.700689756259 | -17.4006897562593 | 204 | 248 | 256.712069228836 | -8.7120692288361 | 205 | 253 | 258.688169561963 | -5.68816956196327 | 206 | 252.9 | 274.209091096515 | -21.3090910965148 | 207 | 251.5 | 307.887616119318 | -56.387616119318 | 208 | 251.6 | 308.092199444179 | -56.4921994441787 | 209 | 253.5 | 307.662302300615 | -54.1623023006147 | 210 | 259.8 | 312.027384448749 | -52.227384448749 | 211 | 334.1 | 318.55203721644 | 15.5479627835597 | 212 | 448 | 357.260120974131 | 90.7398790258693 | 213 | 445.8 | 380.539121222741 | 65.2608787772585 | 214 | 445 | 382.56083098117 | 62.43916901883 | 215 | 448.2 | 374.631119355375 | 73.5688806446247 | 216 | 438.2 | 364.393875205601 | 73.8061247943993 | 217 | 439.8 | 363.521058993583 | 76.2789410064172 | 218 | 423.4 | 364.322578378219 | 59.0774216217815 | 219 | 410.8 | 356.729799050354 | 54.0702009496459 | 220 | 408.4 | 357.675100676953 | 50.7248993230474 | 221 | 406.7 | 364.595408219863 | 42.1045917801373 | 222 | 405.9 | 360.717625164044 | 45.1823748359558 | 223 | 402.7 | 365.950769097936 | 36.7492309020636 | 224 | 405.1 | 360.481653628911 | 44.6183463710886 | 225 | 399.6 | 353.998972369241 | 45.6010276307595 | 226 | 386.5 | 344.890914824636 | 41.6090851753642 | 227 | 381.4 | 337.701921500579 | 43.6980784994212 | 228 | 375.2 | 335.04279536089 | 40.15720463911 | 229 | 357.7 | 325.927113944919 | 31.7728860550808 | 230 | 359 | 333.376105268227 | 25.6238947317735 | 231 | 355 | 328.879148586087 | 26.1208514139135 | 232 | 352.7 | 325.722010387676 | 26.9779896123239 | 233 | 344.4 | 328.311964781966 | 16.0880352180342 | 234 | 343.8 | 328.650578212962 | 15.1494217870382 | 235 | 338 | 342.734356213771 | -4.73435621377126 | 236 | 339 | 374.206191946793 | -35.2061919467933 | 237 | 333.3 | 374.181054856118 | -40.8810548561178 | 238 | 334.4 | 376.050822398805 | -41.6508223988053 | 239 | 328.3 | 368.709886859007 | -40.4098868590072 | 240 | 330.7 | 351.483300785144 | -20.7833007851435 | 241 | 330 | 345.216535914318 | -15.2165359143178 | 242 | 331.6 | 383.794688687576 | -52.1946886875763 | 243 | 351.2 | 463.511705079923 | -112.311705079923 | 244 | 389.4 | 447.040630227201 | -57.6406302272015 | 245 | 410.9 | 494.757422696588 | -83.8574226965883 | 246 | 442.8 | 497.413154917636 | -54.6131549176356 | 247 | 462.8 | 431.841226316190 | 30.9587736838096 | 248 | 466.9 | 420.617299425972 | 46.2827005740276 | 249 | 461.7 | 407.734052328209 | 53.9659476717909 | 250 | 439.2 | 393.915786095631 | 45.2842139043687 | 251 | 430.3 | 377.059469295049 | 53.2405307049511 | 252 | 416.1 | 388.568954773215 | 27.5310452267855 | 253 | 402.5 | 391.019874530533 | 11.4801254694674 | 254 | 397.3 | 406.863673273534 | -9.5636732735339 | 255 | 403.3 | 374.618269441681 | 28.6817305583186 | 256 | 395.9 | 380.235794202318 | 15.6642057976824 | 257 | 387.8 | 359.578589588224 | 28.2214104117760 | 258 | 378.6 | 359.138499163547 | 19.4615008364530 | 259 | 377.1 | 369.974512302891 | 7.12548769710884 | 260 | 370.4 | 369.120641637001 | 1.27935836299887 | 261 | 362 | 349.437980384825 | 12.562019615175 | 262 | 350.3 | 343.387759932009 | 6.91224006799073 | 263 | 348.2 | 346.283931177766 | 1.91606882223432 | 264 | 344.6 | 345.84695994329 | -1.24695994328989 | 265 | 343.5 | 346.398602003845 | -2.89860200384459 | 266 | 342.8 | 343.382573217986 | -0.582573217985868 | 267 | 347.6 | 341.962446404602 | 5.63755359539762 | 268 | 346.6 | 341.578253643466 | 5.02174635653353 | 269 | 349.5 | 339.647927119459 | 9.85207288054055 | 270 | 342.1 | 342.303659340507 | -0.203659340506761 | 271 | 342 | 339.920699710378 | 2.079300289622 | 272 | 342.8 | 336.55978248476 | 6.24021751523969 | 273 | 339.3 | 324.892073112926 | 14.4079268870745 | 274 | 348.2 | 321.899689751899 | 26.3003102481012 | 275 | 333.7 | 331.272397943618 | 2.42760205638179 | 276 | 334.7 | 352.012373028054 | -17.3123730280538 | 277 | 354 | 337.312815183599 | 16.6871848164012 | 278 | 367.7 | 330.156361018796 | 37.5436389812040 | 279 | 363.3 | 328.584291989671 | 34.7157080103286 | 280 | 358.4 | 323.091042224242 | 35.3089577757579 | 281 | 353.1 | 322.072368994681 | 31.0276310053186 | 282 | 343.1 | 314.377037768369 | 28.7229622316314 | 283 | 344.6 | 322.724997124953 | 21.8750028750473 | 284 | 344.4 | 316.629120015996 | 27.7708799840042 | 285 | 333.9 | 311.342983705286 | 22.5570162947141 | 286 | 331.7 | 310.572755249472 | 21.1272447505277 | 287 | 324.3 | 305.643902384564 | 18.6560976154364 | 288 | 321.2 | 300.268809138503 | 20.9311908614968 | 289 | 322.4 | 296.964917474628 | 25.4350825253717 | 290 | 321.7 | 287.434366188871 | 34.2656338111287 | 291 | 320.5 | 284.190932786595 | 36.309067213405 | 292 | 312.8 | 292.695359646312 | 20.1046403536885 | 293 | 309.7 | 301.287031562373 | 8.41296843762655 | 294 | 315.6 | 283.582506874118 | 32.0174931258823 | 295 | 309.7 | 291.797516791928 | 17.9024832080716 | 296 | 304.6 | 294.457309865051 | 10.1426901349495 | 297 | 302.5 | 292.475916746709 | 10.0240832532912 | 298 | 301.5 | 278.410744413552 | 23.0892555864482 | 299 | 298.8 | 276.672678079206 | 22.1273219207944 | 300 | 291.3 | 272.418158674235 | 18.8818413257645 | 301 | 293.6 | 279.332381018947 | 14.2676189810526 | 302 | 294.6 | 279.051312116428 | 15.5486878835721 | 303 | 285.9 | 285.228296090098 | 0.67170390990217 | 304 | 297.6 | 293.485816849235 | 4.11418315076494 | 305 | 301.1 | 283.369603452178 | 17.7303965478220 | 306 | 293.8 | 280.992249776803 | 12.8077502231975 | 307 | 297.7 | 276.823969111716 | 20.8760308882838 | 308 | 292.9 | 274.811539050800 | 18.0884609491995 | 309 | 292.1 | 281.433873898797 | 10.6661261012033 | 310 | 287.2 | 278.498468868673 | 8.7015311313271 | 311 | 288.2 | 277.463135282129 | 10.7368647178709 | 312 | 283.8 | 261.433094157226 | 22.3669058427737 | 313 | 299.9 | 272.316806888174 | 27.5831931118264 | 314 | 292.4 | 272.206672978363 | 20.1933270216372 | 315 | 293.3 | 262.448717076188 | 30.8512829238117 | 316 | 300.8 | 269.813577317847 | 30.9864226821532 | 317 | 293.7 | 273.846982761677 | 19.8530172383233 | 318 | 293.1 | 269.87423582102 | 23.2257641789801 | 319 | 294.4 | 286.389089273686 | 8.01091072631358 | 320 | 292.1 | 282.306446523299 | 9.79355347670137 | 321 | 291.9 | 279.508363995349 | 12.3916360046513 | 322 | 282.5 | 274.274832952141 | 8.22516704785877 | 323 | 277.9 | 268.434326792786 | 9.46567320721377 | 324 | 287.5 | 268.776059413983 | 18.7239405860166 | 325 | 289.2 | 283.762211969940 | 5.43778803006047 | 326 | 285.6 | 286.804879036756 | -1.20487903675584 | 327 | 293.2 | 287.720863790391 | 5.47913620960865 | 328 | 290.8 | 286.292068296036 | 4.50793170396446 | 329 | 283.1 | 290.458423178639 | -7.35842317863887 | 330 | 275 | 303.294283854338 | -28.2942838543377 | 331 | 287.8 | 296.239101090171 | -8.43910109017111 | 332 | 287.8 | 299.582634134128 | -11.7826341341280 | 333 | 287.4 | 308.80697942669 | -21.4069794266901 | 334 | 284 | 303.687405045288 | -19.6874050452884 | 335 | 277.8 | 311.863568288047 | -34.0635682880468 | 336 | 277.6 | 327.665421360898 | -50.0654213608977 | 337 | 304.9 | 331.996626038011 | -27.0966260380115 | 338 | 294 | 360.489614241457 | -66.4896142414566 | 339 | 300.9 | 383.342256392709 | -82.4422563927087 | 340 | 324 | 371.619375781896 | -47.6193757818956 | 341 | 332.9 | 367.314952136934 | -34.4149521369344 | 342 | 341.6 | 356.846675473347 | -15.246675473347 | 343 | 333.4 | 347.170489487647 | -13.7704894876470 | 344 | 348.2 | 348.53877372697 | -0.338773726970039 | 345 | 344.7 | 335.807468844948 | 8.89253115505222 | 346 | 344.7 | 351.428006912202 | -6.72800691220185 | 347 | 329.3 | 351.152384404363 | -21.8523844043634 | 348 | 323.5 | 348.797142696157 | -25.2971426961567 | 349 | 323.2 | 380.743845084209 | -57.5438450842095 | 350 | 317.4 | 365.382511269389 | -47.982511269389 | 351 | 330.1 | 350.249599485374 | -20.1495994853742 | 352 | 329.2 | 354.898492620661 | -25.6984926206611 | 353 | 334.9 | 349.473495134610 | -14.5734951346096 | 354 | 315.8 | 338.739319593475 | -22.9393195934753 | 355 | 315.4 | 350.05015215701 | -34.6501521570102 | 356 | 319.6 | 363.174965339298 | -43.5749653392984 | 357 | 317.3 | 352.437902038878 | -35.1379020388776 | 358 | 313.8 | 346.80552267935 | -33.0055226793498 | 359 | 315.8 | 362.521818378259 | -46.7218183782588 | 360 | 311.3 | 374.810007712097 | -63.5100077120975 |
Goldfeld-Quandt test for Heteroskedasticity | p-values | Alternative Hypothesis | breakpoint index | greater | 2-sided | less | 17 | 0.156938236245337 | 0.313876472490674 | 0.843061763754663 | 18 | 0.603874457264866 | 0.792251085470269 | 0.396125542735134 | 19 | 0.49150418377059 | 0.98300836754118 | 0.50849581622941 | 20 | 0.362762370690291 | 0.725524741380582 | 0.637237629309709 | 21 | 0.253764393571779 | 0.507528787143559 | 0.74623560642822 | 22 | 0.178799903968546 | 0.357599807937092 | 0.821200096031454 | 23 | 0.149401285814679 | 0.298802571629358 | 0.850598714185321 | 24 | 0.128876839384905 | 0.257753678769810 | 0.871123160615095 | 25 | 0.188942609214907 | 0.377885218429814 | 0.811057390785093 | 26 | 0.280081603189733 | 0.560163206379465 | 0.719918396810267 | 27 | 0.892661251211966 | 0.214677497576068 | 0.107338748788034 | 28 | 0.893008116919763 | 0.213983766160473 | 0.106991883080236 | 29 | 0.85664643928392 | 0.286707121432160 | 0.143353560716080 | 30 | 0.814785900102376 | 0.370428199795249 | 0.185214099897624 | 31 | 0.76560845789007 | 0.468783084219861 | 0.234391542109931 | 32 | 0.739838662491206 | 0.520322675017588 | 0.260161337508794 | 33 | 0.695802962380203 | 0.608394075239594 | 0.304197037619797 | 34 | 0.644604442207756 | 0.710791115584488 | 0.355395557792244 | 35 | 0.593374630092308 | 0.813250739815385 | 0.406625369907692 | 36 | 0.542369003454594 | 0.915261993090811 | 0.457630996545406 | 37 | 0.487988935850591 | 0.975977871701182 | 0.512011064149409 | 38 | 0.436915412335886 | 0.873830824671771 | 0.563084587664114 | 39 | 0.403395234487448 | 0.806790468974895 | 0.596604765512552 | 40 | 0.446712977732706 | 0.893425955465412 | 0.553287022267294 | 41 | 0.445720097218838 | 0.891440194437676 | 0.554279902781162 | 42 | 0.407313748274391 | 0.814627496548782 | 0.592686251725609 | 43 | 0.358713020052216 | 0.717426040104433 | 0.641286979947784 | 44 | 0.310913114162423 | 0.621826228324846 | 0.689086885837577 | 45 | 0.265657662666926 | 0.531315325333852 | 0.734342337333074 | 46 | 0.223985543760347 | 0.447971087520693 | 0.776014456239653 | 47 | 0.187555407543997 | 0.375110815087995 | 0.812444592456003 | 48 | 0.181002344238574 | 0.362004688477147 | 0.818997655761426 | 49 | 0.149424070760969 | 0.298848141521938 | 0.85057592923903 | 50 | 0.139047764379261 | 0.278095528758523 | 0.860952235620739 | 51 | 0.153133049105945 | 0.306266098211889 | 0.846866950894055 | 52 | 0.164002800696069 | 0.328005601392138 | 0.835997199303931 | 53 | 0.181761041451647 | 0.363522082903293 | 0.818238958548353 | 54 | 0.175447788625412 | 0.350895577250823 | 0.824552211374588 | 55 | 0.173543961112029 | 0.347087922224058 | 0.826456038887971 | 56 | 0.164613691412265 | 0.329227382824531 | 0.835386308587735 | 57 | 0.145004476481809 | 0.290008952963617 | 0.854995523518191 | 58 | 0.146334805308640 | 0.292669610617279 | 0.85366519469136 | 59 | 0.167381031563340 | 0.334762063126681 | 0.83261896843666 | 60 | 0.152037686939956 | 0.304075373879913 | 0.847962313060044 | 61 | 0.131875844807097 | 0.263751689614194 | 0.868124155192903 | 62 | 0.117141118035040 | 0.234282236070079 | 0.88285888196496 | 63 | 0.100249145753573 | 0.200498291507146 | 0.899750854246427 | 64 | 0.0859863907050261 | 0.171972781410052 | 0.914013609294974 | 65 | 0.07285571866388 | 0.145711437327760 | 0.92714428133612 | 66 | 0.0604527540049793 | 0.120905508009959 | 0.93954724599502 | 67 | 0.0514895425069936 | 0.102979085013987 | 0.948510457493006 | 68 | 0.0431798223054954 | 0.0863596446109908 | 0.956820177694505 | 69 | 0.0361429012365744 | 0.0722858024731488 | 0.963857098763426 | 70 | 0.0341848917982325 | 0.0683697835964649 | 0.965815108201768 | 71 | 0.0285049119935897 | 0.0570098239871795 | 0.97149508800641 | 72 | 0.0232350461689517 | 0.0464700923379033 | 0.976764953831048 | 73 | 0.0240385635400349 | 0.0480771270800698 | 0.975961436459965 | 74 | 0.0244784638580329 | 0.0489569277160659 | 0.975521536141967 | 75 | 0.0243164823283991 | 0.0486329646567981 | 0.9756835176716 | 76 | 0.0208791033050199 | 0.0417582066100398 | 0.97912089669498 | 77 | 0.0174103178327702 | 0.0348206356655403 | 0.98258968216723 | 78 | 0.0151662212340817 | 0.0303324424681634 | 0.984833778765918 | 79 | 0.013970509129817 | 0.027941018259634 | 0.986029490870183 | 80 | 0.0137443816313153 | 0.0274887632626306 | 0.986255618368685 | 81 | 0.0121918092570259 | 0.0243836185140517 | 0.987808190742974 | 82 | 0.0113311465834910 | 0.0226622931669820 | 0.98866885341651 | 83 | 0.0110051799376250 | 0.0220103598752499 | 0.988994820062375 | 84 | 0.0113476786014192 | 0.0226953572028385 | 0.98865232139858 | 85 | 0.0168046983549130 | 0.0336093967098261 | 0.983195301645087 | 86 | 0.0252863380202926 | 0.0505726760405851 | 0.974713661979707 | 87 | 0.0318526352816407 | 0.0637052705632814 | 0.96814736471836 | 88 | 0.0389811561070874 | 0.0779623122141748 | 0.961018843892913 | 89 | 0.0440121034000915 | 0.088024206800183 | 0.955987896599908 | 90 | 0.0525123197275493 | 0.105024639455099 | 0.94748768027245 | 91 | 0.0666149926566956 | 0.133229985313391 | 0.933385007343304 | 92 | 0.07249001830454 | 0.14498003660908 | 0.92750998169546 | 93 | 0.0795906608761894 | 0.159181321752379 | 0.92040933912381 | 94 | 0.100014331823989 | 0.200028663647979 | 0.89998566817601 | 95 | 0.125202883827726 | 0.250405767655452 | 0.874797116172274 | 96 | 0.145819529330883 | 0.291639058661766 | 0.854180470669117 | 97 | 0.195838016334499 | 0.391676032668997 | 0.804161983665502 | 98 | 0.246028706581665 | 0.492057413163329 | 0.753971293418335 | 99 | 0.273208077131509 | 0.546416154263019 | 0.72679192286849 | 100 | 0.313667263526253 | 0.627334527052507 | 0.686332736473747 | 101 | 0.351304509872738 | 0.702609019745476 | 0.648695490127262 | 102 | 0.36864924530441 | 0.73729849060882 | 0.63135075469559 | 103 | 0.385101189557048 | 0.770202379114096 | 0.614898810442952 | 104 | 0.391231701238597 | 0.782463402477193 | 0.608768298761403 | 105 | 0.390197664862494 | 0.780395329724989 | 0.609802335137506 | 106 | 0.395174894364417 | 0.790349788728835 | 0.604825105635583 | 107 | 0.390143078505887 | 0.780286157011774 | 0.609856921494113 | 108 | 0.374189126430159 | 0.748378252860318 | 0.625810873569841 | 109 | 0.394462986198758 | 0.788925972397516 | 0.605537013801242 | 110 | 0.670591723537538 | 0.658816552924924 | 0.329408276462462 | 111 | 0.789063465629513 | 0.421873068740974 | 0.210936534370487 | 112 | 0.816510576232879 | 0.366978847534243 | 0.183489423767121 | 113 | 0.816622423792564 | 0.366755152414872 | 0.183377576207436 | 114 | 0.811045516817285 | 0.37790896636543 | 0.188954483182715 | 115 | 0.793715974716774 | 0.412568050566452 | 0.206284025283226 | 116 | 0.769666798947928 | 0.460666402104145 | 0.230333201052072 | 117 | 0.744395432725714 | 0.511209134548572 | 0.255604567274286 | 118 | 0.716845142554154 | 0.566309714891691 | 0.283154857445846 | 119 | 0.689151135881997 | 0.621697728236006 | 0.310848864118003 | 120 | 0.663753955489219 | 0.672492089021561 | 0.336246044510781 | 121 | 0.639966380106168 | 0.720067239787665 | 0.360033619893832 | 122 | 0.609025181874288 | 0.781949636251423 | 0.390974818125712 | 123 | 0.577899114034136 | 0.844201771931727 | 0.422100885965864 | 124 | 0.545424116088849 | 0.909151767822302 | 0.454575883911151 | 125 | 0.515804091141924 | 0.968391817716151 | 0.484195908858076 | 126 | 0.485680509633199 | 0.971361019266398 | 0.514319490366801 | 127 | 0.462217579611332 | 0.924435159222665 | 0.537782420388668 | 128 | 0.449775766975034 | 0.899551533950067 | 0.550224233024966 | 129 | 0.426761064369947 | 0.853522128739895 | 0.573238935630053 | 130 | 0.400234008483323 | 0.800468016966646 | 0.599765991516677 | 131 | 0.380075365464697 | 0.760150730929395 | 0.619924634535303 | 132 | 0.358826166374187 | 0.717652332748375 | 0.641173833625813 | 133 | 0.334467626749836 | 0.668935253499672 | 0.665532373250164 | 134 | 0.314348283624091 | 0.628696567248183 | 0.685651716375909 | 135 | 0.293786794312232 | 0.587573588624463 | 0.706213205687768 | 136 | 0.271259272863944 | 0.542518545727888 | 0.728740727136056 | 137 | 0.25092202407684 | 0.50184404815368 | 0.74907797592316 | 138 | 0.231443355492412 | 0.462886710984825 | 0.768556644507588 | 139 | 0.214571261480129 | 0.429142522960257 | 0.785428738519871 | 140 | 0.201657055831683 | 0.403314111663366 | 0.798342944168317 | 141 | 0.188358778324421 | 0.376717556648843 | 0.811641221675579 | 142 | 0.174139264406651 | 0.348278528813302 | 0.82586073559335 | 143 | 0.157159682896058 | 0.314319365792116 | 0.842840317103942 | 144 | 0.141619713631845 | 0.283239427263691 | 0.858380286368155 | 145 | 0.130244344555003 | 0.260488689110005 | 0.869755655444997 | 146 | 0.125230062150458 | 0.250460124300916 | 0.874769937849542 | 147 | 0.122038251662840 | 0.244076503325680 | 0.87796174833716 | 148 | 0.109424252747483 | 0.218848505494965 | 0.890575747252518 | 149 | 0.101383964649309 | 0.202767929298618 | 0.898616035350691 | 150 | 0.0916959192427699 | 0.183391838485540 | 0.90830408075723 | 151 | 0.083654206277466 | 0.167308412554932 | 0.916345793722534 | 152 | 0.0762731312415369 | 0.152546262483074 | 0.923726868758463 | 153 | 0.06968674206846 | 0.13937348413692 | 0.93031325793154 | 154 | 0.0628884425156108 | 0.125776885031222 | 0.937111557484389 | 155 | 0.0550031250156442 | 0.110006250031288 | 0.944996874984356 | 156 | 0.0488007000860415 | 0.097601400172083 | 0.951199299913958 | 157 | 0.0448544267207594 | 0.0897088534415189 | 0.95514557327924 | 158 | 0.0413630911855423 | 0.0827261823710846 | 0.958636908814458 | 159 | 0.0355018202963288 | 0.0710036405926576 | 0.964498179703671 | 160 | 0.0301377731790164 | 0.0602755463580327 | 0.969862226820984 | 161 | 0.0256539729673634 | 0.0513079459347269 | 0.974346027032637 | 162 | 0.0225448529104803 | 0.0450897058209605 | 0.97745514708952 | 163 | 0.0208703183292362 | 0.0417406366584723 | 0.979129681670764 | 164 | 0.0197238949389948 | 0.0394477898779897 | 0.980276105061005 | 165 | 0.0168355308485653 | 0.0336710616971306 | 0.983164469151435 | 166 | 0.0144766091422563 | 0.0289532182845127 | 0.985523390857744 | 167 | 0.0124939426525604 | 0.0249878853051209 | 0.98750605734744 | 168 | 0.0109469714363189 | 0.0218939428726378 | 0.989053028563681 | 169 | 0.0100337871953563 | 0.0200675743907125 | 0.989966212804644 | 170 | 0.00896606145326906 | 0.0179321229065381 | 0.99103393854673 | 171 | 0.00746355269636122 | 0.0149271053927224 | 0.992536447303639 | 172 | 0.00605777983692504 | 0.0121155596738501 | 0.993942220163075 | 173 | 0.00488832263803056 | 0.00977664527606113 | 0.99511167736197 | 174 | 0.00395508134045288 | 0.00791016268090575 | 0.996044918659547 | 175 | 0.00346748884816419 | 0.00693497769632837 | 0.996532511151836 | 176 | 0.00333313808558399 | 0.00666627617116799 | 0.996666861914416 | 177 | 0.00311065004494645 | 0.0062213000898929 | 0.996889349955054 | 178 | 0.00286832689655923 | 0.00573665379311847 | 0.99713167310344 | 179 | 0.00250922715413026 | 0.00501845430826051 | 0.99749077284587 | 180 | 0.00216815829393361 | 0.00433631658786721 | 0.997831841706066 | 181 | 0.00191211687421632 | 0.00382423374843265 | 0.998087883125784 | 182 | 0.00159115481276637 | 0.00318230962553275 | 0.998408845187234 | 183 | 0.00131825549681732 | 0.00263651099363465 | 0.998681744503183 | 184 | 0.00113817409512468 | 0.00227634819024937 | 0.998861825904875 | 185 | 0.00096829225310929 | 0.00193658450621858 | 0.99903170774689 | 186 | 0.000836354386402556 | 0.00167270877280511 | 0.999163645613597 | 187 | 0.00081330435513349 | 0.00162660871026698 | 0.999186695644867 | 188 | 0.00087809526365366 | 0.00175619052730732 | 0.999121904736346 | 189 | 0.000948325309512614 | 0.00189665061902523 | 0.999051674690487 | 190 | 0.00101187350611413 | 0.00202374701222826 | 0.998988126493886 | 191 | 0.00105152366956465 | 0.00210304733912929 | 0.998948476330435 | 192 | 0.00105270247140201 | 0.00210540494280401 | 0.998947297528598 | 193 | 0.00115614567307175 | 0.00231229134614351 | 0.998843854326928 | 194 | 0.00110961918689183 | 0.00221923837378365 | 0.998890380813108 | 195 | 0.00104271784931481 | 0.00208543569862963 | 0.998957282150685 | 196 | 0.00101955680078002 | 0.00203911360156004 | 0.99898044319922 | 197 | 0.000968152370517179 | 0.00193630474103436 | 0.999031847629483 | 198 | 0.000950850092803903 | 0.00190170018560781 | 0.999049149907196 | 199 | 0.00108600116809164 | 0.00217200233618328 | 0.998913998831908 | 200 | 0.00175994581650774 | 0.00351989163301547 | 0.998240054183492 | 201 | 0.00278694456230563 | 0.00557388912461125 | 0.997213055437694 | 202 | 0.00497892989256186 | 0.00995785978512371 | 0.995021070107438 | 203 | 0.00757545516008799 | 0.0151509103201760 | 0.992424544839912 | 204 | 0.0102496945997546 | 0.0204993891995091 | 0.989750305400245 | 205 | 0.0148024301730777 | 0.0296048603461555 | 0.985197569826922 | 206 | 0.0240363731447214 | 0.0480727462894429 | 0.975963626855278 | 207 | 0.0988510744684041 | 0.197702148936808 | 0.901148925531596 | 208 | 0.302874550545813 | 0.605749101091627 | 0.697125449454187 | 209 | 0.619705441334556 | 0.760589117330887 | 0.380294558665444 | 210 | 0.883367244292883 | 0.233265511414234 | 0.116632755707117 | 211 | 0.897425580517957 | 0.205148838964086 | 0.102574419482043 | 212 | 0.947857280608515 | 0.104285438782971 | 0.0521427193914854 | 213 | 0.954053037092754 | 0.0918939258144928 | 0.0459469629072464 | 214 | 0.95871649748139 | 0.082567005037221 | 0.0412835025186105 | 215 | 0.971275459222756 | 0.0574490815544875 | 0.0287245407772437 | 216 | 0.98076234544848 | 0.0384753091030401 | 0.0192376545515201 | 217 | 0.988424743503602 | 0.0231505129927955 | 0.0115752564963978 | 218 | 0.990544530690292 | 0.0189109386194159 | 0.00945546930970797 | 219 | 0.99093980281072 | 0.0181203943785607 | 0.00906019718928036 | 220 | 0.990404838410337 | 0.0191903231793264 | 0.0095951615896632 | 221 | 0.989370063692009 | 0.0212598726159819 | 0.0106299363079910 | 222 | 0.988363600521748 | 0.0232727989565035 | 0.0116363994782517 | 223 | 0.986350068861797 | 0.0272998622764053 | 0.0136499311382026 | 224 | 0.984941747926321 | 0.0301165041473576 | 0.0150582520736788 | 225 | 0.983471798602171 | 0.0330564027956588 | 0.0165282013978294 | 226 | 0.981092695723415 | 0.0378146085531695 | 0.0189073042765848 | 227 | 0.979200249147319 | 0.0415995017053626 | 0.0207997508526813 | 228 | 0.976750014376444 | 0.0464999712471115 | 0.0232499856235558 | 229 | 0.972015049709198 | 0.0559699005816047 | 0.0279849502908024 | 230 | 0.966586520555762 | 0.0668269588884763 | 0.0334134794442381 | 231 | 0.960013330812419 | 0.079973338375163 | 0.0399866691875815 | 232 | 0.952533120769878 | 0.0949337584602448 | 0.0474668792301224 | 233 | 0.946019807059367 | 0.107960385881266 | 0.0539801929406332 | 234 | 0.939241406618208 | 0.121517186763584 | 0.060758593381792 | 235 | 0.94583683664957 | 0.108326326700861 | 0.0541631633504307 | 236 | 0.977880623469555 | 0.0442387530608896 | 0.0221193765304448 | 237 | 0.993877487380068 | 0.0122450252398631 | 0.00612251261993157 | 238 | 0.99859392155312 | 0.0028121568937618 | 0.0014060784468809 | 239 | 0.999701348884668 | 0.000597302230664601 | 0.000298651115332300 | 240 | 0.999844605185684 | 0.000310789628631667 | 0.000155394814315834 | 241 | 0.999912208668866 | 0.000175582662268876 | 8.7791331134438e-05 | 242 | 0.999992464872167 | 1.50702556656575e-05 | 7.53512783282877e-06 | 243 | 0.999999999531196 | 9.37607838870596e-10 | 4.68803919435298e-10 | 244 | 0.99999999997801 | 4.39805552476716e-11 | 2.19902776238358e-11 | 245 | 0.999999999999943 | 1.13684835058987e-13 | 5.68424175294936e-14 | 246 | 0.999999999999993 | 1.47677906970995e-14 | 7.38389534854975e-15 | 247 | 0.999999999999994 | 1.19572973844443e-14 | 5.97864869222217e-15 | 248 | 0.999999999999999 | 2.19501906389209e-15 | 1.09750953194604e-15 | 249 | 1 | 1.32437418951143e-16 | 6.62187094755714e-17 | 250 | 1 | 2.62549238396888e-17 | 1.31274619198444e-17 | 251 | 1 | 7.32754877220696e-19 | 3.66377438610348e-19 | 252 | 1 | 2.20300697494243e-19 | 1.10150348747122e-19 | 253 | 1 | 3.83885046254580e-19 | 1.91942523127290e-19 | 254 | 1 | 8.83476074526285e-19 | 4.41738037263143e-19 | 255 | 1 | 6.41216364957608e-19 | 3.20608182478804e-19 | 256 | 1 | 1.19270329049175e-18 | 5.96351645245876e-19 | 257 | 1 | 1.61550449153557e-18 | 8.07752245767783e-19 | 258 | 1 | 3.20520731174024e-18 | 1.60260365587012e-18 | 259 | 1 | 7.78892112711224e-18 | 3.89446056355612e-18 | 260 | 1 | 1.88620057270521e-17 | 9.43100286352607e-18 | 261 | 1 | 4.57854552489302e-17 | 2.28927276244651e-17 | 262 | 1 | 9.85152220066135e-17 | 4.92576110033067e-17 | 263 | 1 | 2.28484565175517e-16 | 1.14242282587759e-16 | 264 | 1 | 5.18433824197067e-16 | 2.59216912098533e-16 | 265 | 1 | 8.88547902787122e-16 | 4.44273951393561e-16 | 266 | 1 | 1.69237585396081e-15 | 8.46187926980404e-16 | 267 | 0.999999999999998 | 3.59254432960335e-15 | 1.79627216480167e-15 | 268 | 0.999999999999997 | 6.50458148700456e-15 | 3.25229074350228e-15 | 269 | 0.999999999999993 | 1.34349898572055e-14 | 6.71749492860274e-15 | 270 | 0.99999999999999 | 1.86503128829215e-14 | 9.32515644146073e-15 | 271 | 0.999999999999986 | 2.8221042188453e-14 | 1.41105210942265e-14 | 272 | 0.999999999999977 | 4.63235322684322e-14 | 2.31617661342161e-14 | 273 | 0.999999999999956 | 8.88466041210958e-14 | 4.44233020605479e-14 | 274 | 0.999999999999906 | 1.8794350317948e-13 | 9.397175158974e-14 | 275 | 0.999999999999834 | 3.31017741508635e-13 | 1.65508870754318e-13 | 276 | 0.999999999999874 | 2.52033636189922e-13 | 1.26016818094961e-13 | 277 | 0.999999999999713 | 5.73177032401128e-13 | 2.86588516200564e-13 | 278 | 0.99999999999982 | 3.61300516038049e-13 | 1.80650258019024e-13 | 279 | 0.999999999999837 | 3.26906092255719e-13 | 1.63453046127859e-13 | 280 | 0.999999999999812 | 3.75642662024854e-13 | 1.87821331012427e-13 | 281 | 0.999999999999722 | 5.55811924938153e-13 | 2.77905962469076e-13 | 282 | 0.999999999999499 | 1.00236501361782e-12 | 5.01182506808911e-13 | 283 | 0.99999999999901 | 1.97950507555796e-12 | 9.89752537778979e-13 | 284 | 0.999999999998426 | 3.14742285627981e-12 | 1.57371142813990e-12 | 285 | 0.999999999996785 | 6.42928936980996e-12 | 3.21464468490498e-12 | 286 | 0.999999999993632 | 1.27353581539909e-11 | 6.36767907699546e-12 | 287 | 0.999999999988079 | 2.38428682317098e-11 | 1.19214341158549e-11 | 288 | 0.99999999998113 | 3.77382521826151e-11 | 1.88691260913075e-11 | 289 | 0.999999999970998 | 5.8003669194426e-11 | 2.9001834597213e-11 | 290 | 0.999999999982094 | 3.58114680647222e-11 | 1.79057340323611e-11 | 291 | 0.999999999987797 | 2.44064897019002e-11 | 1.22032448509501e-11 | 292 | 0.999999999974463 | 5.10734474365915e-11 | 2.55367237182957e-11 | 293 | 0.999999999940232 | 1.19536556940986e-10 | 5.97682784704931e-11 | 294 | 0.999999999924276 | 1.51448886995360e-10 | 7.57244434976801e-11 | 295 | 0.999999999844007 | 3.11986924425287e-10 | 1.55993462212643e-10 | 296 | 0.999999999640683 | 7.18633889149318e-10 | 3.59316944574659e-10 | 297 | 0.999999999180828 | 1.6383431625136e-09 | 8.191715812568e-10 | 298 | 0.999999998430817 | 3.13836546500972e-09 | 1.56918273250486e-09 | 299 | 0.99999999752321 | 4.95357945114213e-09 | 2.47678972557106e-09 | 300 | 0.999999995560023 | 8.87995492534818e-09 | 4.43997746267409e-09 | 301 | 0.999999990454474 | 1.90910512724550e-08 | 9.54552563622748e-09 | 302 | 0.999999984760476 | 3.04790483686344e-08 | 1.52395241843172e-08 | 303 | 0.99999996715152 | 6.56969603854876e-08 | 3.28484801927438e-08 | 304 | 0.99999992908838 | 1.41823242139719e-07 | 7.09116210698594e-08 | 305 | 0.999999856316585 | 2.87366830463241e-07 | 1.43683415231621e-07 | 306 | 0.99999970163251 | 5.9673497783739e-07 | 2.98367488918695e-07 | 307 | 0.99999944512689 | 1.10974621868612e-06 | 5.54873109343061e-07 | 308 | 0.999998870594587 | 2.25881082524872e-06 | 1.12940541262436e-06 | 309 | 0.999997702328767 | 4.59534246601763e-06 | 2.29767123300881e-06 | 310 | 0.999995386241098 | 9.22751780330922e-06 | 4.61375890165461e-06 | 311 | 0.999991633127803 | 1.67337443944302e-05 | 8.36687219721508e-06 | 312 | 0.9999864857654 | 2.7028469199326e-05 | 1.3514234599663e-05 | 313 | 0.999982879640643 | 3.42407187135129e-05 | 1.71203593567565e-05 | 314 | 0.999980004708498 | 3.99905830031297e-05 | 1.99952915015648e-05 | 315 | 0.999973866892008 | 5.22662159848674e-05 | 2.61331079924337e-05 | 316 | 0.999964201926092 | 7.15961478165233e-05 | 3.57980739082616e-05 | 317 | 0.999933901446877 | 0.000132197106246205 | 6.60985531231025e-05 | 318 | 0.999895780336128 | 0.000208439327743923 | 0.000104219663871962 | 319 | 0.999813502501912 | 0.00037299499617554 | 0.00018649749808777 | 320 | 0.999652666390409 | 0.000694667219182564 | 0.000347333609591282 | 321 | 0.99937247938726 | 0.00125504122548067 | 0.000627520612740337 | 322 | 0.998861312672313 | 0.00227737465537431 | 0.00113868732768715 | 323 | 0.998059043263299 | 0.00388191347340226 | 0.00194095673670113 | 324 | 0.997981658234635 | 0.00403668353073085 | 0.00201834176536542 | 325 | 0.99685188155281 | 0.00629623689438082 | 0.00314811844719041 | 326 | 0.996084242946494 | 0.00783151410701226 | 0.00391575705350613 | 327 | 0.995656497445514 | 0.00868700510897177 | 0.00434350255448588 | 328 | 0.993493180668515 | 0.0130136386629707 | 0.00650681933148536 | 329 | 0.988872283072729 | 0.0222554338545424 | 0.0111277169272712 | 330 | 0.986549427079218 | 0.0269011458415649 | 0.0134505729207825 | 331 | 0.977369578261893 | 0.0452608434762135 | 0.0226304217381067 | 332 | 0.965448580534468 | 0.0691028389310637 | 0.0345514194655319 | 333 | 0.957730784830822 | 0.0845384303383554 | 0.0422692151691777 | 334 | 0.950952075479392 | 0.0980958490412168 | 0.0490479245206084 | 335 | 0.958749127375562 | 0.082501745248876 | 0.041250872624438 | 336 | 0.984777297007493 | 0.0304454059850133 | 0.0152227029925067 | 337 | 0.992885262947417 | 0.0142294741051663 | 0.00711473705258317 | 338 | 0.997658882665837 | 0.00468223466832525 | 0.00234111733416263 | 339 | 0.998711372164136 | 0.00257725567172729 | 0.00128862783586364 | 340 | 0.99839564568675 | 0.00320870862650192 | 0.00160435431325096 | 341 | 0.999566928197041 | 0.000866143605917777 | 0.000433071802958888 | 342 | 0.99761415247143 | 0.00477169505714024 | 0.00238584752857012 | 343 | 0.990793655862247 | 0.0184126882755059 | 0.00920634413775294 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | Description | # significant tests | % significant tests | OK/NOK | 1% type I error level | 125 | 0.382262996941896 | NOK | 5% type I error level | 176 | 0.53822629969419 | NOK | 10% type I error level | 201 | 0.614678899082569 | NOK |
| Charts produced by software: | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227809493e9horj5n2ty9vda/109cda1227809406.png (open in new window) | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227809493e9horj5n2ty9vda/109cda1227809406.ps (open in new window) |
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| | Parameters (Session): | par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; | | Parameters (R input): | par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; | | R code (references can be found in the software module): | library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
| |
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