| Multiple Linear Regression - Estimated Regression Equation |
| HFCE[t] = + 71477.0285422472 -421.673162748552RPI[t] -0.104860415997025`HFCE-1`[t] + 0.870028900662522`HFCE-2`[t] + 0.0742366888686009`HFCE-3`[t] + 2800.16997442852Q1[t] -13222.0530399475Q2[t] -14003.3472016326Q3[t] + 695.827997756174t + 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) | 71477.0285422472 | 11082.756006 | 6.4494 | 0 | 0 |
| RPI | -421.673162748552 | 79.354233 | -5.3138 | 1e-06 | 0 |
| `HFCE-1` | -0.104860415997025 | 0.158377 | -0.6621 | 0.509862 | 0.254931 |
| `HFCE-2` | 0.870028900662522 | 0.155598 | 5.5915 | 0 | 0 |
| `HFCE-3` | 0.0742366888686009 | 0.161787 | 0.4589 | 0.647615 | 0.323807 |
| Q1 | 2800.16997442852 | 2548.788347 | 1.0986 | 0.27531 | 0.137655 |
| Q2 | -13222.0530399475 | 2824.834412 | -4.6806 | 1.2e-05 | 6e-06 |
| Q3 | -14003.3472016326 | 2380.838002 | -5.8817 | 0 | 0 |
| t | 695.827997756174 | 124.345516 | 5.5959 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.998029220778848 |
| R-squared | 0.996062325528435 |
| Adjusted R-squared | 0.995658461480069 |
| F-TEST (value) | 2466.33076046058 |
| F-TEST (DF numerator) | 8 |
| F-TEST (DF denominator) | 78 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 2004.35192048201 |
| Sum Squared Residuals | 313359276.448913 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 123297 | 122298.601910029 | 998.398089971375 |
| 2 | 114813 | 112447.273888173 | 2365.72611182688 |
| 3 | 117925 | 118658.882445767 | -733.882445766559 |
| 4 | 126466 | 125524.265548002 | 941.73445199829 |
| 5 | 131235 | 129274.675619610 | 1960.32438039044 |
| 6 | 120546 | 120351.131002470 | 194.868997529791 |
| 7 | 123791 | 124820.387091224 | -1029.38709122434 |
| 8 | 129813 | 129769.745611712 | 43.2543882879276 |
| 9 | 133463 | 133694.153699774 | -231.153699774423 |
| 10 | 122987 | 122579.716618162 | 407.283381838195 |
| 11 | 125418 | 124854.057288611 | 563.942711389308 |
| 12 | 130199 | 129569.344325969 | 629.65567403141 |
| 13 | 133016 | 133057.995028698 | -41.9950286975279 |
| 14 | 121454 | 121481.114570997 | -27.1145709971728 |
| 15 | 122044 | 124233.156703777 | -2189.15670377696 |
| 16 | 128313 | 128767.310963161 | -454.310963161168 |
| 17 | 131556 | 130712.756330580 | 843.243669420483 |
| 18 | 120027 | 120249.138595643 | -222.138595643181 |
| 19 | 123001 | 123436.649523139 | -435.649523138921 |
| 20 | 130111 | 128076.32354789 | 2034.67645210992 |
| 21 | 132524 | 132305.351229291 | 218.648770708957 |
| 22 | 123742 | 123512.119271750 | 229.880728250156 |
| 23 | 124931 | 126047.058918214 | -1116.05891821434 |
| 24 | 133646 | 132991.425142505 | 654.574857495075 |
| 25 | 136557 | 135745.245769145 | 811.75423085505 |
| 26 | 127509 | 127699.836741347 | -190.836741346731 |
| 27 | 128945 | 130688.591587806 | -1743.59158780591 |
| 28 | 137191 | 137539.101421650 | -348.101421650137 |
| 29 | 139716 | 140368.582497518 | -652.582497517941 |
| 30 | 129083 | 131510.102019011 | -2427.10201901097 |
| 31 | 131604 | 134210.077829541 | -2606.07782954062 |
| 32 | 139413 | 139412.66099375 | 0.339006249869755 |
| 33 | 143125 | 143409.453490695 | -284.453490694735 |
| 34 | 133948 | 134337.684457606 | -389.684457606482 |
| 35 | 137116 | 138222.604904694 | -1106.60490469414 |
| 36 | 144864 | 144754.39172508 | 109.608274919903 |
| 37 | 149277 | 149133.406811198 | 143.593188802141 |
| 38 | 138796 | 139940.922684978 | -1144.92268497841 |
| 39 | 143258 | 144525.775619595 | -1267.77561959477 |
| 40 | 150034 | 149333.387498815 | 700.612501184725 |
| 41 | 154708 | 154674.670399355 | 33.3296006446181 |
| 42 | 144888 | 144873.881153612 | 14.1188463878694 |
| 43 | 148762 | 149122.667671999 | -360.667671998551 |
| 44 | 156500 | 155008.075517706 | 1491.92448229352 |
| 45 | 161088 | 160038.980053459 | 1049.01994654085 |
| 46 | 152772 | 151546.533228173 | 1225.46677182748 |
| 47 | 158011 | 156140.210685432 | 1870.78931456771 |
| 48 | 163318 | 163353.292439757 | -35.2924397574393 |
| 49 | 169969 | 169727.517494887 | 241.482505112679 |
| 50 | 162269 | 158414.694026346 | 3854.3059736541 |
| 51 | 165765 | 164010.002587206 | 1754.99741279439 |
| 52 | 170600 | 172010.609506008 | -1410.60950600789 |
| 53 | 174681 | 177005.765420252 | -2324.76542025151 |
| 54 | 166364 | 165801.890877485 | 562.109122514546 |
| 55 | 170240 | 169612.557485915 | 627.44251408479 |
| 56 | 176150 | 176930.055957087 | -780.055957087267 |
| 57 | 182056 | 182645.468980927 | -589.46898092703 |
| 58 | 172218 | 172087.213240124 | 130.786759875881 |
| 59 | 177856 | 177724.979725528 | 131.020274471795 |
| 60 | 182253 | 183459.045561617 | -1206.04556161673 |
| 61 | 188090 | 189994.177621111 | -1904.17762111082 |
| 62 | 176863 | 177878.102721622 | -1015.10272162209 |
| 63 | 183273 | 183489.168220442 | -216.168220442115 |
| 64 | 187969 | 187970.856657104 | -1.85665710360944 |
| 65 | 194650 | 195254.019584062 | -604.019584061857 |
| 66 | 183036 | 183409.059174851 | -373.059174851137 |
| 67 | 189516 | 189648.537551693 | -132.537551693487 |
| 68 | 193805 | 193595.836442435 | 209.163557565243 |
| 69 | 200499 | 200658.678769234 | -159.678769234043 |
| 70 | 188142 | 188632.119245366 | -490.119245365938 |
| 71 | 193732 | 195057.106903458 | -1325.10690345774 |
| 72 | 197126 | 198620.934433299 | -1494.93443329882 |
| 73 | 205140 | 205243.314464920 | -103.314464920399 |
| 74 | 191751 | 192233.592672750 | -482.592672750217 |
| 75 | 196700 | 199342.78479719 | -2642.78479718981 |
| 76 | 199784 | 201752.277294759 | -1968.27729475926 |
| 77 | 207360 | 207351.190104354 | 8.80989564570689 |
| 78 | 196101 | 193606.262018597 | 2494.73798140276 |
| 79 | 200824 | 200130.182741199 | 693.817258801417 |
| 80 | 205743 | 204763.525427944 | 979.474572056214 |
| 81 | 212489 | 209878.513092276 | 2610.48690772446 |
| 82 | 200810 | 197926.846641652 | 2883.15335834799 |
| 83 | 203683 | 203529.403229022 | 153.596770977609 |
| 84 | 207286 | 207381.53398375 | -95.533983749771 |
| 85 | 210910 | 212933.481628626 | -2023.48162862647 |
| 86 | 194915 | 202514.765149283 | -7599.76514928332 |
| 87 | 217920 | 206810.156488549 | 11109.8435114512 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 12 | 0.0725192801799515 | 0.145038560359903 | 0.927480719820049 |
| 13 | 0.0226988108189551 | 0.0453976216379103 | 0.977301189181045 |
| 14 | 0.0065336173472354 | 0.0130672346944708 | 0.993466382652765 |
| 15 | 0.00182525292556823 | 0.00365050585113647 | 0.998174747074432 |
| 16 | 0.00199463432261179 | 0.00398926864522358 | 0.998005365677388 |
| 17 | 0.000868920070575887 | 0.00173784014115177 | 0.999131079929424 |
| 18 | 0.000274454076932242 | 0.000548908153864485 | 0.999725545923068 |
| 19 | 0.000272254202437409 | 0.000544508404874817 | 0.999727745797563 |
| 20 | 0.000187361300102017 | 0.000374722600204034 | 0.999812638699898 |
| 21 | 9.98074989927117e-05 | 0.000199614997985423 | 0.999900192501007 |
| 22 | 7.55750785327577e-05 | 0.000151150157065515 | 0.999924424921467 |
| 23 | 7.06770424835579e-05 | 0.000141354084967116 | 0.999929322957516 |
| 24 | 4.74754385948592e-05 | 9.49508771897184e-05 | 0.999952524561405 |
| 25 | 2.00542256163889e-05 | 4.01084512327779e-05 | 0.999979945774384 |
| 26 | 7.39743552483052e-06 | 1.47948710496610e-05 | 0.999992602564475 |
| 27 | 3.30913344421007e-06 | 6.61826688842014e-06 | 0.999996690866556 |
| 28 | 1.17629370834936e-06 | 2.35258741669871e-06 | 0.999998823706292 |
| 29 | 5.21892190929217e-07 | 1.04378438185843e-06 | 0.999999478107809 |
| 30 | 4.83192267974532e-07 | 9.66384535949063e-07 | 0.999999516807732 |
| 31 | 1.64789645768043e-07 | 3.29579291536086e-07 | 0.999999835210354 |
| 32 | 7.31198413336719e-08 | 1.46239682667344e-07 | 0.999999926880159 |
| 33 | 2.49329138049039e-08 | 4.98658276098079e-08 | 0.999999975067086 |
| 34 | 1.42147205388678e-08 | 2.84294410777356e-08 | 0.99999998578528 |
| 35 | 1.21874322154418e-08 | 2.43748644308837e-08 | 0.999999987812568 |
| 36 | 4.60648940167522e-09 | 9.21297880335043e-09 | 0.99999999539351 |
| 37 | 2.35840265154597e-09 | 4.71680530309194e-09 | 0.999999997641597 |
| 38 | 8.17807810211445e-10 | 1.63561562042289e-09 | 0.999999999182192 |
| 39 | 1.65029606767771e-09 | 3.30059213535542e-09 | 0.999999998349704 |
| 40 | 6.13997130505105e-10 | 1.22799426101021e-09 | 0.999999999386003 |
| 41 | 3.05871321283437e-10 | 6.11742642566875e-10 | 0.999999999694129 |
| 42 | 1.49757838197939e-10 | 2.99515676395879e-10 | 0.999999999850242 |
| 43 | 3.19187402645567e-10 | 6.38374805291133e-10 | 0.999999999680813 |
| 44 | 1.93428854482545e-10 | 3.86857708965091e-10 | 0.999999999806571 |
| 45 | 9.24310412399491e-11 | 1.84862082479898e-10 | 0.999999999907569 |
| 46 | 8.4732741324961e-11 | 1.69465482649922e-10 | 0.999999999915267 |
| 47 | 3.79350052273352e-10 | 7.58700104546703e-10 | 0.99999999962065 |
| 48 | 1.00883063706315e-09 | 2.01766127412629e-09 | 0.99999999899117 |
| 49 | 3.86411488055981e-10 | 7.72822976111961e-10 | 0.999999999613588 |
| 50 | 2.15927901678716e-09 | 4.31855803357431e-09 | 0.99999999784072 |
| 51 | 9.8325007440201e-10 | 1.96650014880402e-09 | 0.99999999901675 |
| 52 | 7.59156197428184e-09 | 1.51831239485637e-08 | 0.999999992408438 |
| 53 | 9.88689326604604e-09 | 1.97737865320921e-08 | 0.999999990113107 |
| 54 | 4.10450668708562e-09 | 8.20901337417125e-09 | 0.999999995895493 |
| 55 | 1.92029747844126e-09 | 3.84059495688253e-09 | 0.999999998079703 |
| 56 | 1.55614008162405e-09 | 3.11228016324810e-09 | 0.99999999844386 |
| 57 | 6.76502635558374e-10 | 1.35300527111675e-09 | 0.999999999323497 |
| 58 | 3.48630748263141e-10 | 6.97261496526281e-10 | 0.99999999965137 |
| 59 | 2.71947115924948e-10 | 5.43894231849897e-10 | 0.999999999728053 |
| 60 | 7.3166130241806e-10 | 1.46332260483612e-09 | 0.999999999268339 |
| 61 | 3.64189904698123e-10 | 7.28379809396245e-10 | 0.99999999963581 |
| 62 | 2.27966179177347e-10 | 4.55932358354695e-10 | 0.999999999772034 |
| 63 | 5.65477209248383e-10 | 1.13095441849677e-09 | 0.999999999434523 |
| 64 | 4.10413636503102e-10 | 8.20827273006203e-10 | 0.999999999589586 |
| 65 | 2.52059574222443e-10 | 5.04119148444887e-10 | 0.99999999974794 |
| 66 | 1.25652003577676e-10 | 2.51304007155352e-10 | 0.999999999874348 |
| 67 | 7.55006972673888e-10 | 1.51001394534778e-09 | 0.999999999244993 |
| 68 | 1.78135085682623e-09 | 3.56270171365247e-09 | 0.99999999821865 |
| 69 | 1.62514006563992e-09 | 3.25028013127983e-09 | 0.99999999837486 |
| 70 | 5.97661316806998e-10 | 1.19532263361400e-09 | 0.999999999402339 |
| 71 | 4.68921464210029e-10 | 9.37842928420059e-10 | 0.999999999531079 |
| 72 | 3.00771788256793e-10 | 6.01543576513586e-10 | 0.999999999699228 |
| 73 | 2.16630243737373e-10 | 4.33260487474747e-10 | 0.99999999978337 |
| 74 | 1.97753013229126e-10 | 3.95506026458252e-10 | 0.999999999802247 |
| 75 | 1.12866245505971e-10 | 2.25732491011942e-10 | 0.999999999887134 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 61 | 0.953125 | NOK |
| 5% type I error level | 63 | 0.984375 | NOK |
| 10% type I error level | 63 | 0.984375 | NOK |
