| Multiple Linear Regression - Estimated Regression Equation |
| HFCE[t] = + 207810.550167275 -916.412977675751RPI[t] -12387.1281946683Q1[t] -7662.91380445677Q2[t] -3693.15077859989Q3[t] + 2256.38373280118t + 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) | 207810.550167275 | 15140.955004 | 13.7251 | 0 | 0 |
| RPI | -916.412977675751 | 142.774914 | -6.4186 | 0 | 0 |
| Q1 | -12387.1281946683 | 1503.800975 | -8.2372 | 0 | 0 |
| Q2 | -7662.91380445677 | 1498.259582 | -5.1145 | 2e-06 | 1e-06 |
| Q3 | -3693.15077859989 | 1513.506414 | -2.4401 | 0.016785 | 0.008392 |
| t | 2256.38373280118 | 172.293592 | 13.0962 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.98769504249566 |
| R-squared | 0.975541496970502 |
| Adjusted R-squared | 0.974085633694937 |
| F-TEST (value) | 670.07768747493 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 84 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 5019.13495884401 |
| Sum Squared Residuals | 2116104121.74756 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 106370 | 105763.584044531 | 606.415955469496 |
| 2 | 109375 | 111277.921403262 | -1902.92140326173 |
| 3 | 116476 | 117320.785566385 | -844.785566384756 |
| 4 | 123297 | 122262.265802343 | 1034.73419765748 |
| 5 | 114813 | 111673.314851638 | 3139.68514836246 |
| 6 | 117925 | 116362.880530461 | 1562.11946953911 |
| 7 | 126466 | 121214.407822605 | 5251.59217739472 |
| 8 | 131235 | 125147.833783120 | 6087.16621688032 |
| 9 | 120546 | 113367.545961436 | 7178.45403856375 |
| 10 | 123791 | 117415.622555887 | 6375.37744411349 |
| 11 | 129813 | 122633.715039101 | 7179.28496089875 |
| 12 | 133463 | 126475.499701848 | 6987.5002981519 |
| 13 | 122987 | 114420.287986862 | 8566.71201313807 |
| 14 | 125418 | 116268.973434890 | 9149.02656510961 |
| 15 | 130199 | 120570.652940429 | 9628.34705957062 |
| 16 | 133016 | 124687.361496479 | 8328.63850352105 |
| 17 | 121454 | 113915.127950239 | 7538.87204976118 |
| 18 | 122044 | 118329.769735759 | 3714.23026424060 |
| 19 | 128313 | 124006.068707812 | 4306.93129218798 |
| 20 | 131556 | 128764.266348235 | 2791.7336517654 |
| 21 | 120027 | 117992.032801995 | 2034.96719800550 |
| 22 | 123001 | 122315.033289747 | 685.966710252511 |
| 23 | 130111 | 128632.821346173 | 1478.17865382688 |
| 24 | 132524 | 134032.508070969 | -1508.50807096875 |
| 25 | 123742 | 124726.535289010 | -984.535289009851 |
| 26 | 124931 | 129691.024861136 | -4760.02486113585 |
| 27 | 133646 | 135550.606428724 | -1904.60642872361 |
| 28 | 136557 | 141041.934451287 | -4484.93445128681 |
| 29 | 127509 | 130727.907393885 | -3218.90739388459 |
| 30 | 128945 | 135417.473072708 | -6472.47307270788 |
| 31 | 137191 | 141551.978533598 | -4360.97853359837 |
| 32 | 139716 | 146676.741365091 | -6960.74136509126 |
| 33 | 129083 | 135354.660032246 | -6271.6600322457 |
| 34 | 131604 | 139860.943115534 | -8256.94311553384 |
| 35 | 139413 | 145720.524683122 | -6307.5246831216 |
| 36 | 143125 | 151486.776598988 | -8361.77659898753 |
| 37 | 133948 | 140622.901754980 | -6674.90175497984 |
| 38 | 137116 | 145862.315220409 | -8746.31522040857 |
| 39 | 144864 | 151813.538085764 | -6949.53808576393 |
| 40 | 149277 | 156938.300917257 | -7661.30091725682 |
| 41 | 138796 | 145982.784775482 | -7186.78477548156 |
| 42 | 143258 | 151130.556943143 | -7872.55694314272 |
| 43 | 150034 | 155982.084235287 | -5948.08423528716 |
| 44 | 154708 | 160740.281875710 | -6032.28187570976 |
| 45 | 144888 | 150151.330925005 | -5263.33092500481 |
| 46 | 148762 | 154382.690114990 | -5620.69011499023 |
| 47 | 156500 | 160150.630384810 | -3650.63038481041 |
| 48 | 161088 | 165458.675811838 | -4370.67581183844 |
| 49 | 152772 | 155969.420434344 | -3197.4204343444 |
| 50 | 158011 | 161300.475197541 | -3289.47519754071 |
| 51 | 163318 | 167434.980658431 | -4116.9806584312 |
| 52 | 169969 | 172284.819596621 | -2315.81959662135 |
| 53 | 162269 | 161512.586050381 | 756.413949618739 |
| 54 | 165765 | 165652.303942599 | 112.696057400897 |
| 55 | 170600 | 171603.526807954 | -1003.52680795443 |
| 56 | 174681 | 176545.007043912 | -1864.00704391218 |
| 57 | 166364 | 166597.545177580 | -233.545177580242 |
| 58 | 170240 | 171653.676047474 | -1413.67604747384 |
| 59 | 176150 | 177788.181508364 | -1638.18150836433 |
| 60 | 182056 | 183920.998615301 | -1864.99861530054 |
| 61 | 172218 | 173698.612855666 | -1480.61285566590 |
| 62 | 177856 | 178754.743725559 | -898.74372555949 |
| 63 | 182253 | 184431.042697612 | -2178.04269761211 |
| 64 | 188090 | 188914.316444732 | -824.316444731976 |
| 65 | 176863 | 177867.159005189 | -1004.15900518914 |
| 66 | 183273 | 182923.289875083 | 349.710124917284 |
| 67 | 187969 | 188691.230144903 | -722.230144902905 |
| 68 | 194650 | 193632.710380861 | 1017.28961913935 |
| 69 | 183036 | 182677.194239085 | 358.805760914604 |
| 70 | 189516 | 187366.759917909 | 2149.24008209132 |
| 71 | 193805 | 192584.852401123 | 1220.14759887658 |
| 72 | 200499 | 196884.843552708 | 3614.15644729185 |
| 73 | 188142 | 186295.892602003 | 1846.10739799680 |
| 74 | 193732 | 191260.382174129 | 2471.6178258708 |
| 75 | 197126 | 196845.039848414 | 280.960151585752 |
| 76 | 205140 | 201786.520084372 | 3353.47991562801 |
| 77 | 191751 | 191197.569133667 | 553.430866332951 |
| 78 | 196700 | 195062.363132582 | 1637.63686741785 |
| 79 | 199784 | 199730.607829191 | 53.3921708085906 |
| 80 | 207360 | 203755.675087473 | 3604.32491252657 |
| 81 | 196101 | 192158.669861325 | 3942.33013867486 |
| 82 | 200824 | 196115.105158008 | 4708.89484199219 |
| 83 | 205743 | 201608.121534525 | 4134.87846547471 |
| 84 | 212489 | 205083.341006202 | 7405.6589937982 |
| 85 | 200810 | 193761.259673356 | 7048.74032664374 |
| 86 | 203683 | 196892.923290131 | 6790.07670986924 |
| 87 | 207286 | 201194.602795670 | 6091.39720433025 |
| 88 | 210910 | 208885.321964655 | 2024.67803534524 |
| 89 | 194915 | 202970.077200096 | -8055.07720009614 |
| 90 | 217920 | 208392.77326106 | 9527.22673893995 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.0133604220550558 | 0.0267208441101116 | 0.986639577944944 |
| 10 | 0.00258489005530117 | 0.00516978011060233 | 0.997415109944699 |
| 11 | 0.00107740855493654 | 0.00215481710987308 | 0.998922591445063 |
| 12 | 0.00107590494660891 | 0.00215180989321783 | 0.998924095053391 |
| 13 | 0.000753547309656478 | 0.00150709461931296 | 0.999246452690344 |
| 14 | 0.000406935468693978 | 0.000813870937387956 | 0.999593064531306 |
| 15 | 0.000200740005016254 | 0.000401480010032508 | 0.999799259994984 |
| 16 | 0.000282888439568416 | 0.000565776879136832 | 0.999717111560432 |
| 17 | 0.00376915584763046 | 0.00753831169526092 | 0.99623084415237 |
| 18 | 0.0468723965891504 | 0.0937447931783007 | 0.95312760341085 |
| 19 | 0.188796242868056 | 0.377592485736112 | 0.811203757131944 |
| 20 | 0.486944526160188 | 0.973889052320376 | 0.513055473839812 |
| 21 | 0.782389426643155 | 0.435221146713689 | 0.217610573356845 |
| 22 | 0.877325863503558 | 0.245348272992885 | 0.122674136496442 |
| 23 | 0.944084890838707 | 0.111830218322586 | 0.0559151091612931 |
| 24 | 0.975849267294388 | 0.0483014654112234 | 0.0241507327056117 |
| 25 | 0.985113945156926 | 0.0297721096861472 | 0.0148860548430736 |
| 26 | 0.983781281676798 | 0.0324374366464043 | 0.0162187183232021 |
| 27 | 0.98707745758639 | 0.0258450848272185 | 0.0129225424136092 |
| 28 | 0.98457887750454 | 0.0308422449909189 | 0.0154211224954594 |
| 29 | 0.986755718647863 | 0.0264885627042738 | 0.0132442813521369 |
| 30 | 0.980169919975476 | 0.0396601600490475 | 0.0198300800245237 |
| 31 | 0.978572332461795 | 0.0428553350764093 | 0.0214276675382047 |
| 32 | 0.968758023500476 | 0.0624839529990472 | 0.0312419764995236 |
| 33 | 0.95786689854204 | 0.0842662029159206 | 0.0421331014579603 |
| 34 | 0.943282981050768 | 0.113434037898464 | 0.0567170189492318 |
| 35 | 0.924536042773884 | 0.150927914452232 | 0.0754639572261158 |
| 36 | 0.9041995991623 | 0.191600801675401 | 0.0958004008377004 |
| 37 | 0.883785164751393 | 0.232429670497214 | 0.116214835248607 |
| 38 | 0.885472091837342 | 0.229055816325316 | 0.114527908162658 |
| 39 | 0.86848857822009 | 0.26302284355982 | 0.13151142177991 |
| 40 | 0.865658568146349 | 0.268682863707302 | 0.134341431853651 |
| 41 | 0.852328612874887 | 0.295342774250226 | 0.147671387125113 |
| 42 | 0.890770336345988 | 0.218459327308025 | 0.109229663654012 |
| 43 | 0.88618244424751 | 0.227635111504981 | 0.113817555752490 |
| 44 | 0.898723248840586 | 0.202553502318828 | 0.101276751159414 |
| 45 | 0.902801431539164 | 0.194397136921672 | 0.0971985684608359 |
| 46 | 0.939205942379239 | 0.121588115241522 | 0.0607940576207611 |
| 47 | 0.945632665526299 | 0.108734668947402 | 0.0543673344737011 |
| 48 | 0.959703844454563 | 0.0805923110908738 | 0.0402961555454369 |
| 49 | 0.96766842015986 | 0.0646631596802807 | 0.0323315798401403 |
| 50 | 0.983110948950965 | 0.0337781020980708 | 0.0168890510490354 |
| 51 | 0.98397355275316 | 0.0320528944936781 | 0.0160264472468391 |
| 52 | 0.987861426590954 | 0.0242771468180915 | 0.0121385734090458 |
| 53 | 0.993574852376297 | 0.0128502952474059 | 0.00642514762370294 |
| 54 | 0.995551657913243 | 0.0088966841735144 | 0.0044483420867572 |
| 55 | 0.99483411637496 | 0.0103317672500815 | 0.00516588362504075 |
| 56 | 0.994620599382428 | 0.0107588012351437 | 0.00537940061757184 |
| 57 | 0.99385177049673 | 0.0122964590065392 | 0.00614822950326962 |
| 58 | 0.994213870117966 | 0.0115722597640684 | 0.00578612988203419 |
| 59 | 0.99198275370299 | 0.0160344925940212 | 0.0080172462970106 |
| 60 | 0.99068137959589 | 0.0186372408082188 | 0.00931862040410941 |
| 61 | 0.986191645385102 | 0.0276167092297954 | 0.0138083546148977 |
| 62 | 0.984810936432748 | 0.0303781271345039 | 0.0151890635672520 |
| 63 | 0.978466308160133 | 0.0430673836797343 | 0.0215336918398671 |
| 64 | 0.974201367551695 | 0.0515972648966101 | 0.0257986324483050 |
| 65 | 0.962729039579407 | 0.0745419208411854 | 0.0372709604205927 |
| 66 | 0.960634887671608 | 0.0787302246567842 | 0.0393651123283921 |
| 67 | 0.9447543777205 | 0.110491244558999 | 0.0552456222794994 |
| 68 | 0.928464043808275 | 0.143071912383451 | 0.0715359561917254 |
| 69 | 0.899112137580236 | 0.201775724839528 | 0.100887862419764 |
| 70 | 0.880062089339664 | 0.239875821320672 | 0.119937910660336 |
| 71 | 0.837340867627117 | 0.325318264745766 | 0.162659132372883 |
| 72 | 0.798752430984234 | 0.402495138031532 | 0.201247569015766 |
| 73 | 0.744109526034257 | 0.511780947931486 | 0.255890473965743 |
| 74 | 0.690172853696265 | 0.61965429260747 | 0.309827146303735 |
| 75 | 0.599847699673499 | 0.800304600653001 | 0.400152300326501 |
| 76 | 0.520758562522424 | 0.958482874955152 | 0.479241437477576 |
| 77 | 0.422470366305636 | 0.844940732611272 | 0.577529633694364 |
| 78 | 0.369946444425491 | 0.739892888850982 | 0.630053555574509 |
| 79 | 0.290864993224098 | 0.581729986448197 | 0.709135006775902 |
| 80 | 0.200078067964217 | 0.400156135928433 | 0.799921932035784 |
| 81 | 0.131274864127197 | 0.262549728254395 | 0.868725135872803 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 9 | 0.123287671232877 | NOK |
| 5% type I error level | 31 | 0.424657534246575 | NOK |
| 10% type I error level | 39 | 0.534246575342466 | NOK |
