| Multiple Linear Regression - Estimated Regression Equation |
| HFCE[t] = + 74688.2221859923 -442.983839249867RPI[t] + 0.630377456292092`HFCE-2`[t] + 0.211331462128754`HFCE-4`[t] -12639.0030914300Q1[t] -11436.7551722576Q2[t] -1206.43033445861Q3[t] + 720.266859665427t + 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) | 74688.2221859923 | 10682.706333 | 6.9915 | 0 | 0 |
| RPI | -442.983839249867 | 79.24004 | -5.5904 | 0 | 0 |
| `HFCE-2` | 0.630377456292092 | 0.159069 | 3.9629 | 0.000163 | 8.1e-05 |
| `HFCE-4` | 0.211331462128754 | 0.149661 | 1.4121 | 0.161906 | 0.080953 |
| Q1 | -12639.0030914300 | 2487.099896 | -5.0818 | 2e-06 | 1e-06 |
| Q2 | -11436.7551722576 | 2762.014669 | -4.1407 | 8.7e-05 | 4.3e-05 |
| Q3 | -1206.43033445861 | 645.142892 | -1.87 | 0.065233 | 0.032616 |
| t | 720.266859665427 | 119.451131 | 6.0298 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.998043546349196 |
| R-squared | 0.99609092040928 |
| Adjusted R-squared | 0.995740105574216 |
| F-TEST (value) | 2839.36373507684 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 78 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1980.38801473839 |
| Sum Squared Residuals | 305911061.735718 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 114813 | 112735.23404973 | 2077.76595027006 |
| 2 | 117925 | 118485.144903508 | -560.144903507992 |
| 3 | 126466 | 124923.803215492 | 1542.19678450810 |
| 4 | 131235 | 129279.162510427 | 1955.83748957257 |
| 5 | 120546 | 120154.173097504 | 391.826902496483 |
| 6 | 123791 | 124323.073189943 | -532.073189943426 |
| 7 | 129813 | 129853.260051969 | -40.2600519685351 |
| 8 | 133463 | 133814.509004378 | -351.509004377733 |
| 9 | 122987 | 122502.717753285 | 484.282246714847 |
| 10 | 125418 | 124931.171342398 | 486.828657602327 |
| 11 | 130199 | 129620.300810261 | 578.699189739208 |
| 12 | 133016 | 132964.837758901 | 51.1622410988788 |
| 13 | 121454 | 121535.939060933 | -81.9390609332829 |
| 14 | 122044 | 124507.619168681 | -2463.61916868131 |
| 15 | 128313 | 128914.372133384 | -601.372133384241 |
| 16 | 131556 | 131232.433764512 | 323.566235487521 |
| 17 | 120027 | 120512.030753635 | -485.030753635457 |
| 18 | 123001 | 123318.89205206 | -317.892052059885 |
| 19 | 130111 | 128370.997375943 | 1740.00262405706 |
| 20 | 132524 | 132591.994753213 | -67.9947532132893 |
| 21 | 123742 | 123117.487264128 | 624.512735872052 |
| 22 | 124931 | 126215.038167020 | -1284.03816701980 |
| 23 | 133646 | 132955.028203363 | 690.971796637425 |
| 24 | 136557 | 135919.695091510 | 637.304908490343 |
| 25 | 127509 | 127550.188723066 | -41.1887230659590 |
| 26 | 128945 | 130451.545787516 | -1506.54578751649 |
| 27 | 137191 | 137495.937568977 | -304.937568977185 |
| 28 | 139716 | 140544.357221269 | -828.357221268587 |
| 29 | 129083 | 131335.707433723 | -2252.70743372279 |
| 30 | 131604 | 133957.340903340 | -2353.3409033404 |
| 31 | 139413 | 139770.574809065 | -357.57480906478 |
| 32 | 143125 | 143731.468744526 | -606.468744526318 |
| 33 | 133948 | 134133.875560732 | -185.875560731733 |
| 34 | 137116 | 138087.448778778 | -971.448778777643 |
| 35 | 144864 | 144770.458795838 | 93.541204161959 |
| 36 | 149277 | 149079.968703592 | 197.031296407523 |
| 37 | 138796 | 139707.322719899 | -911.322719898554 |
| 38 | 143258 | 144195.223606878 | -937.223606877547 |
| 39 | 150034 | 149511.749594643 | 522.250405356648 |
| 40 | 154708 | 154607.917750092 | 100.082249907925 |
| 41 | 144888 | 144524.162187966 | 363.837812033706 |
| 42 | 148762 | 149007.070663782 | -245.070663782258 |
| 43 | 156500 | 154977.845808218 | 1522.15419178214 |
| 44 | 161088 | 160024.299834532 | 1063.70016546766 |
| 45 | 152772 | 151218.238088927 | 1553.76191107349 |
| 46 | 158011 | 156054.251810869 | 1956.74818913052 |
| 47 | 163318 | 163353.609051836 | -35.6090518361932 |
| 48 | 169969 | 169020.861880621 | 948.138119378625 |
| 49 | 162269 | 158380.017682861 | 3888.98231713871 |
| 50 | 165765 | 164229.088551916 | 1535.91144808422 |
| 51 | 170600 | 171314.414753673 | -714.414753673445 |
| 52 | 174681 | 176363.194866438 | -1682.19486643813 |
| 53 | 166364 | 165953.678145304 | 410.321854695638 |
| 54 | 170240 | 170257.312052448 | -17.3120524476215 |
| 55 | 176150 | 176942.543681398 | -792.543681398274 |
| 56 | 182056 | 182263.624360908 | -207.624360907873 |
| 57 | 172218 | 172268.476741380 | -50.4767413797112 |
| 58 | 177856 | 177802.855461865 | 53.1445381350352 |
| 59 | 182253 | 183534.972381959 | -1281.97238195882 |
| 60 | 188090 | 189555.087147190 | -1465.08714719031 |
| 61 | 176863 | 177886.057827069 | -1023.05782706950 |
| 62 | 183273 | 183749.306539341 | -476.306539341452 |
| 63 | 187969 | 188330.38305437 | -361.383054369768 |
| 64 | 194650 | 195044.059264597 | -394.059264596803 |
| 65 | 183036 | 183314.271786935 | -278.271786935468 |
| 66 | 189516 | 189695.513425381 | -179.513425381408 |
| 67 | 193805 | 193830.031668451 | -25.0316684512737 |
| 68 | 200499 | 200456.109367181 | 42.8906328194848 |
| 69 | 188142 | 188565.166524664 | -423.166524664422 |
| 70 | 193732 | 195102.291424166 | -1370.29142416612 |
| 71 | 197126 | 198859.620847824 | -1733.62084782451 |
| 72 | 205140 | 205237.498606936 | -97.4986069363634 |
| 73 | 191751 | 192625.348664677 | -874.348664677184 |
| 74 | 196700 | 199274.90619809 | -2574.90619809002 |
| 75 | 199784 | 201749.560589 | -1965.56058899985 |
| 76 | 207360 | 207559.340089389 | -199.340089388571 |
| 77 | 196101 | 194046.396843587 | 2054.60315641288 |
| 78 | 200824 | 200328.683967844 | 495.316032155527 |
| 79 | 205743 | 204479.215042721 | 1263.78495727856 |
| 80 | 212489 | 209788.175754026 | 2700.82424597419 |
| 81 | 200810 | 198015.006306630 | 2794.99369337044 |
| 82 | 203683 | 203327.633776398 | 355.3662236015 |
| 83 | 207286 | 207025.320561614 | 260.679438385779 |
| 84 | 210910 | 213030.403525761 | -2120.40352576076 |
| 85 | 194915 | 202952.502783364 | -8037.50278336425 |
| 86 | 217920 | 207013.588227776 | 10906.4117722243 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.113073177669745 | 0.226146355339490 | 0.886926822330255 |
| 12 | 0.0579507703149179 | 0.115901540629836 | 0.942049229685082 |
| 13 | 0.0223412149828266 | 0.0446824299656531 | 0.977658785017173 |
| 14 | 0.00811049374063787 | 0.0162209874812757 | 0.991889506259362 |
| 15 | 0.00477605397739956 | 0.00955210795479913 | 0.9952239460226 |
| 16 | 0.00460524344286830 | 0.00921048688573661 | 0.995394756557132 |
| 17 | 0.00176711583955673 | 0.00353423167911345 | 0.998232884160443 |
| 18 | 0.00153682717133702 | 0.00307365434267403 | 0.998463172828663 |
| 19 | 0.00240144017456847 | 0.00480288034913693 | 0.997598559825432 |
| 20 | 0.00116305764280964 | 0.00232611528561928 | 0.99883694235719 |
| 21 | 0.000516912283490055 | 0.00103382456698011 | 0.99948308771651 |
| 22 | 0.000196616444311713 | 0.000393232888623426 | 0.999803383555688 |
| 23 | 9.3338518393699e-05 | 0.000186677036787398 | 0.999906661481606 |
| 24 | 3.85954730223443e-05 | 7.71909460446885e-05 | 0.999961404526978 |
| 25 | 1.51403647196483e-05 | 3.02807294392967e-05 | 0.99998485963528 |
| 26 | 5.60047744306368e-06 | 1.12009548861274e-05 | 0.999994399522557 |
| 27 | 2.04870017605542e-06 | 4.09740035211084e-06 | 0.999997951299824 |
| 28 | 7.45712585792165e-07 | 1.49142517158433e-06 | 0.999999254287414 |
| 29 | 8.01848485735302e-07 | 1.60369697147060e-06 | 0.999999198151514 |
| 30 | 3.18796800462823e-07 | 6.37593600925646e-07 | 0.9999996812032 |
| 31 | 1.72074146108611e-07 | 3.44148292217223e-07 | 0.999999827925854 |
| 32 | 6.60889359225331e-08 | 1.32177871845066e-07 | 0.999999933911064 |
| 33 | 4.57107100686876e-08 | 9.14214201373752e-08 | 0.99999995428929 |
| 34 | 6.27642329314905e-08 | 1.25528465862981e-07 | 0.999999937235767 |
| 35 | 3.18502061387298e-08 | 6.37004122774595e-08 | 0.999999968149794 |
| 36 | 1.9861765013917e-08 | 3.9723530027834e-08 | 0.999999980138235 |
| 37 | 7.09973856037044e-09 | 1.41994771207409e-08 | 0.999999992900261 |
| 38 | 9.93207370174289e-09 | 1.98641474034858e-08 | 0.999999990067926 |
| 39 | 7.40515131545105e-09 | 1.48103026309021e-08 | 0.999999992594849 |
| 40 | 3.56815344651333e-09 | 7.13630689302666e-09 | 0.999999996431847 |
| 41 | 2.45221629833006e-09 | 4.90443259666012e-09 | 0.999999997547784 |
| 42 | 4.96853179751971e-09 | 9.93706359503941e-09 | 0.999999995031468 |
| 43 | 5.15119093568681e-09 | 1.03023818713736e-08 | 0.99999999484881 |
| 44 | 3.04504367912784e-09 | 6.09008735825569e-09 | 0.999999996954956 |
| 45 | 2.59364542844847e-09 | 5.18729085689694e-09 | 0.999999997406355 |
| 46 | 1.34114427967779e-08 | 2.68228855935559e-08 | 0.999999986588557 |
| 47 | 1.13039473784277e-08 | 2.26078947568555e-08 | 0.999999988696053 |
| 48 | 4.6087750046188e-09 | 9.2175500092376e-09 | 0.999999995391225 |
| 49 | 5.68675936267155e-08 | 1.13735187253431e-07 | 0.999999943132406 |
| 50 | 2.49836299052218e-08 | 4.99672598104436e-08 | 0.99999997501637 |
| 51 | 4.59745495067858e-08 | 9.19490990135716e-08 | 0.99999995402545 |
| 52 | 2.54943167700930e-07 | 5.09886335401859e-07 | 0.999999745056832 |
| 53 | 2.33447832053266e-07 | 4.66895664106532e-07 | 0.999999766552168 |
| 54 | 1.01321132888002e-07 | 2.02642265776003e-07 | 0.999999898678867 |
| 55 | 8.86884895039645e-08 | 1.77376979007929e-07 | 0.99999991131151 |
| 56 | 5.84407036040984e-08 | 1.16881407208197e-07 | 0.999999941559296 |
| 57 | 3.06795256232356e-08 | 6.13590512464713e-08 | 0.999999969320474 |
| 58 | 1.62051504315226e-08 | 3.24103008630452e-08 | 0.99999998379485 |
| 59 | 1.78734280458408e-08 | 3.57468560916816e-08 | 0.999999982126572 |
| 60 | 4.33518048156874e-08 | 8.67036096313748e-08 | 0.999999956648195 |
| 61 | 2.48333521653283e-08 | 4.96667043306565e-08 | 0.999999975166648 |
| 62 | 1.53608198601331e-08 | 3.07216397202663e-08 | 0.99999998463918 |
| 63 | 7.9240922743439e-09 | 1.58481845486878e-08 | 0.999999992075908 |
| 64 | 1.48050709172517e-08 | 2.96101418345035e-08 | 0.99999998519493 |
| 65 | 1.71390945758549e-08 | 3.42781891517098e-08 | 0.999999982860905 |
| 66 | 8.34203198647446e-08 | 1.66840639729489e-07 | 0.99999991657968 |
| 67 | 1.32883450006375e-07 | 2.65766900012749e-07 | 0.99999986711655 |
| 68 | 2.9665872629177e-07 | 5.9331745258354e-07 | 0.999999703341274 |
| 69 | 3.37298606721484e-07 | 6.74597213442968e-07 | 0.999999662701393 |
| 70 | 1.64924718326091e-07 | 3.29849436652182e-07 | 0.999999835075282 |
| 71 | 7.7409490203867e-08 | 1.54818980407734e-07 | 0.99999992259051 |
| 72 | 5.63556525324159e-08 | 1.12711305064832e-07 | 0.999999943644347 |
| 73 | 1.77201105772803e-08 | 3.54402211545605e-08 | 0.99999998227989 |
| 74 | 2.75984526279561e-08 | 5.51969052559121e-08 | 0.999999972401547 |
| 75 | 9.43391343773175e-09 | 1.88678268754635e-08 | 0.999999990566087 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 61 | 0.938461538461538 | NOK |
| 5% type I error level | 63 | 0.96923076923077 | NOK |
| 10% type I error level | 63 | 0.96923076923077 | NOK |
