| Multiple Linear Regression - Estimated Regression Equation |
| RioTinto[t] = -32.5248999044313 + 0.377868320188452Commodity[t] + 0.00535216266541196WorldLeaders[t] + e[t] |
| Multiple Linear Regression - Ordinary Least Squares | |||||
| Variable | Parameter | S.D. | T-STAT H0: parameter = 0 | 2-tail p-value | 1-tail p-value |
| (Intercept) | -32.5248999044313 | 7.551553 | -4.307 | 3.9e-05 | 2e-05 |
| Commodity | 0.377868320188452 | 0.041498 | 9.1056 | 0 | 0 |
| WorldLeaders | 0.00535216266541196 | 0.001911 | 2.8002 | 0.006153 | 0.003077 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.865918352119919 |
| R-squared | 0.749814592538075 |
| Adjusted R-squared | 0.744708767895995 |
| F-TEST (value) | 146.854748272867 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 98 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 13.1885858119561 |
| Sum Squared Residuals | 17046.0019804943 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 14.36 | 12.7742609989398 | 1.58573900106016 |
| 2 | 14.62 | 9.62546397860132 | 4.99453602139868 |
| 3 | 13.51 | 10.5000187387762 | 3.00998126122381 |
| 4 | 14.95 | 8.8125697957387 | 6.1374302042613 |
| 5 | 16.72 | 10.8514356043246 | 5.86856439567542 |
| 6 | 16.33 | 11.5949805212962 | 4.73501947870376 |
| 7 | 15.21 | 10.9987372656954 | 4.21126273430462 |
| 8 | 16.69 | 11.0578765819187 | 5.63212341808129 |
| 9 | 15.81 | 9.84546660780262 | 5.96453339219738 |
| 10 | 16.02 | 9.48299634483516 | 6.53700365516484 |
| 11 | 16.7 | 11.8661240731059 | 4.83387592689412 |
| 12 | 15.99 | 13.4469436285708 | 2.54305637142924 |
| 13 | 17.68 | 14.118003701371 | 3.561996298629 |
| 14 | 18.89 | 14.1951658889255 | 4.69483411107447 |
| 15 | 18.72 | 14.6681046161324 | 4.05189538386759 |
| 16 | 21.14 | 16.5826897173954 | 4.55731028260464 |
| 17 | 20.97 | 18.2985969045079 | 2.67140309549215 |
| 18 | 23.75 | 20.4039891409974 | 3.34601085900259 |
| 19 | 23.05 | 23.7319169106847 | -0.681916910684664 |
| 20 | 23.45 | 26.4272176443176 | -2.97721764431764 |
| 21 | 21.74 | 26.1111447783973 | -4.37114477839726 |
| 22 | 19.37 | 25.550901461072 | -6.18090146107198 |
| 23 | 21.1 | 24.0473798595960 | -2.94737985959597 |
| 24 | 21.2 | 25.3388708007858 | -4.13887080078580 |
| 25 | 22.67 | 25.4645209372585 | -2.79452093725845 |
| 26 | 22.24 | 25.3046240047401 | -3.06462400474012 |
| 27 | 23.78 | 25.962004738809 | -2.18200473880901 |
| 28 | 23.27 | 27.9639820937567 | -4.69398209375675 |
| 29 | 25.74 | 29.2914077891484 | -3.55140778914839 |
| 30 | 26.1 | 30.660131673428 | -4.56013167342803 |
| 31 | 27.49 | 32.0974443779024 | -4.60744437790239 |
| 32 | 31.41 | 33.9965242055164 | -2.58652420551636 |
| 33 | 28.79 | 34.8058150968587 | -6.01581509685867 |
| 34 | 26.76 | 33.5272575732332 | -6.76725757323325 |
| 35 | 26.41 | 32.7602131073795 | -6.35021310737953 |
| 36 | 27.05 | 33.3487020999016 | -6.29870209990163 |
| 37 | 29.43 | 34.1392264972270 | -4.70922649722696 |
| 38 | 32.1 | 35.7480869407991 | -3.64808694079915 |
| 39 | 36.84 | 36.2733254234895 | 0.566674576510471 |
| 40 | 34.22 | 36.73813467263 | -2.51813467263003 |
| 41 | 36.53 | 39.0555394255468 | -2.52553942554675 |
| 42 | 40.99 | 42.5832287865419 | -1.59322878654192 |
| 43 | 45.97 | 47.0355275728812 | -1.06552757288119 |
| 44 | 43.6 | 48.4356550815049 | -4.8356550815049 |
| 45 | 47.84 | 49.7013443716397 | -1.86134437163967 |
| 46 | 51.47 | 57.7272611196563 | -6.2572611196563 |
| 47 | 51.31 | 64.4643806526226 | -13.1543806526226 |
| 48 | 48.47 | 58.6267128001913 | -10.1567128001913 |
| 49 | 48.28 | 62.6833290186818 | -14.4033290186818 |
| 50 | 46.56 | 64.0441933960584 | -17.4841933960584 |
| 51 | 43.83 | 64.6984471144882 | -20.8684471144882 |
| 52 | 51.17 | 68.6014891060444 | -17.4314891060444 |
| 53 | 49.59 | 69.3410537611562 | -19.7510537611562 |
| 54 | 49.11 | 71.2193361554943 | -22.1093361554943 |
| 55 | 49.97 | 69.0832206413275 | -19.1132206413275 |
| 56 | 50.07 | 69.6022273549807 | -19.5322273549807 |
| 57 | 53.3 | 73.8618544849765 | -20.5618544849765 |
| 58 | 57.08 | 82.2647667540992 | -25.1847667540992 |
| 59 | 68.54 | 84.8754532862241 | -16.3354532862241 |
| 60 | 71.62 | 81.5500987170752 | -9.93009871707516 |
| 61 | 67.64 | 80.1382577540029 | -12.4982577540029 |
| 62 | 64.79 | 74.1833801840295 | -9.39338018402952 |
| 63 | 80.97 | 74.2050812207982 | 6.76491877920178 |
| 64 | 88.42 | 77.1320574147294 | 11.2879425852706 |
| 65 | 110.22 | 72.7227773997456 | 37.4972226002544 |
| 66 | 99 | 68.2421782893808 | 30.7578217106192 |
| 67 | 95.95 | 71.5525480593663 | 24.3974519406337 |
| 68 | 107.94 | 75.5351516499829 | 32.4048483500171 |
| 69 | 97.82 | 78.780246995419 | 19.0397530045810 |
| 70 | 111.64 | 80.0078498933172 | 31.6321501066828 |
| 71 | 114.73 | 76.7562347724474 | 37.9737652275526 |
| 72 | 117.58 | 72.1759159831071 | 45.4040840168929 |
| 73 | 99.19 | 72.0894559679422 | 27.1005440320578 |
| 74 | 90.19 | 66.7311615553386 | 23.4588384446614 |
| 75 | 59.74 | 59.5551666768839 | 0.184833323116091 |
| 76 | 44.51 | 41.7504142815143 | 2.75958571848568 |
| 77 | 23.94 | 34.3074819706895 | -10.3674819706894 |
| 78 | 21.29 | 30.0291269974246 | -8.73912699742464 |
| 79 | 20.77 | 25.0972005809235 | -4.32720058092348 |
| 80 | 25.07 | 21.581111451984 | 3.48888854801599 |
| 81 | 32.95 | 24.0460979177046 | 8.9039020822954 |
| 82 | 40.05 | 29.0538338920158 | 10.9961661079842 |
| 83 | 44.59 | 33.0350355377972 | 11.5549644622028 |
| 84 | 40.28 | 35.7716220170184 | 4.50837798298164 |
| 85 | 41.19 | 39.144993137967 | 2.04500686203296 |
| 86 | 38.14 | 45.6404098944419 | -7.50040989444192 |
| 87 | 41.85 | 45.5567842065367 | -3.70678420653673 |
| 88 | 43.76 | 46.4222272832796 | -2.66222728327957 |
| 89 | 50.16 | 49.2012726277698 | 0.958727372230181 |
| 90 | 52.94 | 51.9985797285435 | 0.941420271456505 |
| 91 | 47.69 | 52.7046022777469 | -5.01460227774689 |
| 92 | 51.52 | 49.8005768254575 | 1.71942317454254 |
| 93 | 58.69 | 55.2259083655863 | 3.46409163441374 |
| 94 | 50.44 | 62.4457671098739 | -12.0057671098739 |
| 95 | 45.72 | 53.1945640465843 | -7.47456404658432 |
| 96 | 43.24 | 49.1131743599659 | -5.87317435996587 |
| 97 | 51.49 | 55.5945473152185 | -4.10454731521849 |
| 98 | 50.43 | 58.863777705844 | -8.43377770584405 |
| 99 | 58.73 | 63.287782476395 | -4.55778247639503 |
| 100 | 65.12 | 65.8922254038609 | -0.7722254038609 |
| 101 | 64.13 | 65.6460423743079 | -1.51604237430787 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 3.31381938265085e-05 | 6.6276387653017e-05 | 0.999966861806173 |
| 7 | 7.02952933105933e-05 | 0.000140590586621187 | 0.99992970470669 |
| 8 | 4.76784671658683e-06 | 9.53569343317365e-06 | 0.999995232153283 |
| 9 | 3.88713026898309e-07 | 7.77426053796619e-07 | 0.999999611286973 |
| 10 | 2.47258176414310e-08 | 4.94516352828621e-08 | 0.999999975274182 |
| 11 | 1.59296280506289e-09 | 3.18592561012579e-09 | 0.999999998407037 |
| 12 | 9.42289907103886e-11 | 1.88457981420777e-10 | 0.999999999905771 |
| 13 | 9.7760762149047e-12 | 1.95521524298094e-11 | 0.999999999990224 |
| 14 | 1.86088356200232e-12 | 3.72176712400463e-12 | 0.99999999999814 |
| 15 | 1.61534637052527e-13 | 3.23069274105054e-13 | 0.999999999999838 |
| 16 | 2.16052357460769e-14 | 4.32104714921539e-14 | 0.999999999999978 |
| 17 | 1.54165685175535e-15 | 3.08331370351069e-15 | 0.999999999999998 |
| 18 | 9.19988990409818e-17 | 1.83997798081964e-16 | 1 |
| 19 | 1.50590929199138e-16 | 3.01181858398276e-16 | 1 |
| 20 | 2.29021230924293e-16 | 4.58042461848586e-16 | 1 |
| 21 | 6.74564162733754e-16 | 1.34912832546751e-15 | 1 |
| 22 | 4.28279104554939e-15 | 8.56558209109877e-15 | 0.999999999999996 |
| 23 | 5.59616966905066e-16 | 1.11923393381013e-15 | 1 |
| 24 | 8.43545883698301e-17 | 1.68709176739660e-16 | 1 |
| 25 | 8.82290863193964e-18 | 1.76458172638793e-17 | 1 |
| 26 | 9.1394007142471e-19 | 1.82788014284942e-18 | 1 |
| 27 | 1.06805553909613e-19 | 2.13611107819225e-19 | 1 |
| 28 | 1.12027714543572e-20 | 2.24055429087144e-20 | 1 |
| 29 | 1.64756908776565e-21 | 3.29513817553130e-21 | 1 |
| 30 | 2.04304986214598e-22 | 4.08609972429196e-22 | 1 |
| 31 | 2.81360799279083e-23 | 5.62721598558166e-23 | 1 |
| 32 | 6.50254789892538e-23 | 1.30050957978508e-22 | 1 |
| 33 | 6.58390652917612e-24 | 1.31678130583522e-23 | 1 |
| 34 | 8.53181591963037e-25 | 1.70636318392607e-24 | 1 |
| 35 | 9.40036337795445e-26 | 1.88007267559089e-25 | 1 |
| 36 | 9.3725139525155e-27 | 1.8745027905031e-26 | 1 |
| 37 | 1.59692236202637e-27 | 3.19384472405275e-27 | 1 |
| 38 | 1.08731425365316e-27 | 2.17462850730631e-27 | 1 |
| 39 | 3.35483432306142e-25 | 6.70966864612283e-25 | 1 |
| 40 | 1.78420348179167e-25 | 3.56840696358333e-25 | 1 |
| 41 | 1.22682147172868e-25 | 2.45364294345736e-25 | 1 |
| 42 | 1.69280011668667e-25 | 3.38560023337333e-25 | 1 |
| 43 | 3.3586792612263e-25 | 6.7173585224526e-25 | 1 |
| 44 | 4.78103628253307e-26 | 9.56207256506614e-26 | 1 |
| 45 | 2.16092550494429e-26 | 4.32185100988857e-26 | 1 |
| 46 | 3.26562760759716e-27 | 6.53125521519432e-27 | 1 |
| 47 | 5.16339847283092e-26 | 1.03267969456618e-25 | 1 |
| 48 | 1.33311267215861e-26 | 2.66622534431722e-26 | 1 |
| 49 | 1.44159321712410e-26 | 2.88318643424820e-26 | 1 |
| 50 | 4.68057333124504e-26 | 9.36114666249008e-26 | 1 |
| 51 | 7.44532981811592e-25 | 1.48906596362318e-24 | 1 |
| 52 | 3.6852839626275e-25 | 7.370567925255e-25 | 1 |
| 53 | 4.37451816554986e-25 | 8.74903633109972e-25 | 1 |
| 54 | 1.40287411566083e-24 | 2.80574823132165e-24 | 1 |
| 55 | 1.68425801158026e-24 | 3.36851602316053e-24 | 1 |
| 56 | 2.6198167811415e-24 | 5.239633562283e-24 | 1 |
| 57 | 5.49724690675642e-24 | 1.09944938135128e-23 | 1 |
| 58 | 6.6651580483602e-23 | 1.33303160967204e-22 | 1 |
| 59 | 2.63835896471265e-21 | 5.27671792942529e-21 | 1 |
| 60 | 1.29529755685769e-18 | 2.59059511371538e-18 | 1 |
| 61 | 1.00621868174587e-16 | 2.01243736349174e-16 | 1 |
| 62 | 3.25494767882872e-14 | 6.50989535765743e-14 | 0.999999999999967 |
| 63 | 7.38021355238883e-09 | 1.47604271047777e-08 | 0.999999992619786 |
| 64 | 8.43026651245552e-05 | 0.000168605330249110 | 0.999915697334875 |
| 65 | 0.0981042865769474 | 0.196208573153895 | 0.901895713423053 |
| 66 | 0.344749811638908 | 0.689499623277817 | 0.655250188361092 |
| 67 | 0.621166043940163 | 0.757667912119673 | 0.378833956059837 |
| 68 | 0.868656740454813 | 0.262686519090374 | 0.131343259545187 |
| 69 | 0.902376951566535 | 0.195246096866930 | 0.0976230484334652 |
| 70 | 0.940671351510441 | 0.118657296979117 | 0.0593286484895586 |
| 71 | 0.969341724440544 | 0.0613165511189112 | 0.0306582755594556 |
| 72 | 0.999356460705918 | 0.00128707858816329 | 0.000643539294081643 |
| 73 | 0.999926231784928 | 0.000147536430143438 | 7.37682150717189e-05 |
| 74 | 0.999997985225683 | 4.02954863346795e-06 | 2.01477431673398e-06 |
| 75 | 0.999995314234204 | 9.37153159121791e-06 | 4.68576579560896e-06 |
| 76 | 0.999989757595779 | 2.04848084427841e-05 | 1.02424042213920e-05 |
| 77 | 0.999995127068816 | 9.74586236878838e-06 | 4.87293118439419e-06 |
| 78 | 0.999998827678088 | 2.34464382442220e-06 | 1.17232191221110e-06 |
| 79 | 0.999999447520482 | 1.10495903563028e-06 | 5.5247951781514e-07 |
| 80 | 0.999998669724075 | 2.66055184990029e-06 | 1.33027592495014e-06 |
| 81 | 0.999995985644298 | 8.02871140425528e-06 | 4.01435570212764e-06 |
| 82 | 0.999994701964944 | 1.05960701120903e-05 | 5.29803505604516e-06 |
| 83 | 0.999998100631626 | 3.79873674718766e-06 | 1.89936837359383e-06 |
| 84 | 0.999998812105567 | 2.37578886555616e-06 | 1.18789443277808e-06 |
| 85 | 0.99999790917275 | 4.18165450091320e-06 | 2.09082725045660e-06 |
| 86 | 0.99999600997608 | 7.9800478382341e-06 | 3.99002391911705e-06 |
| 87 | 0.99998959633328 | 2.08073334406710e-05 | 1.04036667203355e-05 |
| 88 | 0.9999620439512 | 7.59120976014086e-05 | 3.79560488007043e-05 |
| 89 | 0.999854172632031 | 0.00029165473593799 | 0.000145827367968995 |
| 90 | 0.999456939692716 | 0.00108612061456733 | 0.000543060307283663 |
| 91 | 0.998385547848512 | 0.00322890430297575 | 0.00161445215148788 |
| 92 | 0.995131024303805 | 0.0097379513923898 | 0.0048689756961949 |
| 93 | 0.993422888977734 | 0.0131542220445313 | 0.00657711102226566 |
| 94 | 0.999350700572076 | 0.00129859885584776 | 0.000649299427923881 |
| 95 | 0.996602399680105 | 0.00679520063978986 | 0.00339760031989493 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 82 | 0.911111111111111 | NOK |
| 5% type I error level | 83 | 0.922222222222222 | NOK |
| 10% type I error level | 84 | 0.933333333333333 | NOK |
