| Multiple Linear Regression - Estimated Regression Equation |
| HFCE[t] = + 73767.229794668 -441.574474829804RPI[t] + 0.0134539688684464`HFCE-1`[t] + 0.670282928478978`HFCE-2`[t] -0.112605495888278`HFCE-3`[t] + 0.269398473310232`HFCE-4`[t] -11927.4055660515Q1[t] -10325.7832993243Q2[t] + 473.109328445136Q3[t] + 720.105157172006t + 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) | 73767.229794668 | 12600.382939 | 5.8544 | 0 | 0 |
| RPI | -441.574474829804 | 84.869548 | -5.203 | 2e-06 | 1e-06 |
| `HFCE-1` | 0.0134539688684464 | 0.17706 | 0.076 | 0.93963 | 0.469815 |
| `HFCE-2` | 0.670282928478978 | 0.213132 | 3.1449 | 0.002371 | 0.001186 |
| `HFCE-3` | -0.112605495888278 | 0.204417 | -0.5509 | 0.583344 | 0.291672 |
| `HFCE-4` | 0.269398473310232 | 0.190312 | 1.4156 | 0.160989 | 0.080494 |
| Q1 | -11927.4055660515 | 2951.295999 | -4.0414 | 0.000126 | 6.3e-05 |
| Q2 | -10325.7832993243 | 5126.094707 | -2.0144 | 0.047511 | 0.023755 |
| Q3 | 473.109328445136 | 3355.910076 | 0.141 | 0.88826 | 0.44413 |
| t | 720.105157172006 | 129.288081 | 5.5698 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.998054720351583 |
| R-squared | 0.996113224816076 |
| Adjusted R-squared | 0.995652948807453 |
| F-TEST (value) | 2164.16499264645 |
| F-TEST (DF numerator) | 9 |
| F-TEST (DF denominator) | 76 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 2000.54464928762 |
| Sum Squared Residuals | 304165595.928294 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 114813 | 112839.054216257 | 1973.94578374277 |
| 2 | 117925 | 118524.632622351 | -599.632622351276 |
| 3 | 126466 | 124881.373552473 | 1584.62644752682 |
| 4 | 131235 | 129150.648371672 | 2084.35162832833 |
| 5 | 120546 | 120301.557427003 | 244.442572997204 |
| 6 | 123791 | 124139.620852688 | -348.620852687663 |
| 7 | 129813 | 129815.807372434 | -2.80737243414336 |
| 8 | 133463 | 133791.671277259 | -328.671277258834 |
| 9 | 122987 | 122497.610137536 | 489.389862463521 |
| 10 | 125418 | 124848.197163124 | 569.802836876374 |
| 11 | 130199 | 129662.018736778 | 536.981263222051 |
| 12 | 133016 | 132882.606442646 | 133.393557354398 |
| 13 | 121454 | 121512.764045843 | -58.7640458432724 |
| 14 | 122044 | 124447.255974463 | -2403.25597446259 |
| 15 | 128313 | 128930.220116044 | -617.220116043573 |
| 16 | 131556 | 131143.819228906 | 412.180771094216 |
| 17 | 120027 | 120691.829196334 | -664.829196333544 |
| 18 | 123001 | 123204.628618729 | -203.628618728678 |
| 19 | 130111 | 128403.78347815 | 1707.21652185008 |
| 20 | 132524 | 132646.801780971 | -122.801780971092 |
| 21 | 123742 | 123194.310704238 | 547.689295761865 |
| 22 | 124931 | 126044.380219188 | -1113.38021918774 |
| 23 | 133646 | 133160.026388937 | 485.973611063157 |
| 24 | 136557 | 135739.412701887 | 817.58729811272 |
| 25 | 127509 | 127824.732295891 | -315.732295890568 |
| 26 | 128945 | 130210.943515295 | -1265.94351529532 |
| 27 | 137191 | 137660.396911539 | -469.396911539018 |
| 28 | 139716 | 140386.516908107 | -670.516908107316 |
| 29 | 129083 | 131567.075102973 | -2484.07510297302 |
| 30 | 131604 | 133704.271076842 | -2100.27107684168 |
| 31 | 139413 | 139890.56908265 | -477.569082649891 |
| 32 | 143125 | 143721.660704888 | -596.660704888409 |
| 33 | 133948 | 134296.888815235 | -348.888815235051 |
| 34 | 137116 | 137944.065128989 | -828.065128989324 |
| 35 | 144864 | 144907.767387548 | -43.7673875478447 |
| 36 | 149277 | 149018.431625836 | 258.568374163670 |
| 37 | 138796 | 139837.434683540 | -1041.43468353954 |
| 38 | 143258 | 144073.947654751 | -815.94765475105 |
| 39 | 150034 | 149555.751281003 | 478.248718996623 |
| 40 | 154708 | 154679.740477500 | 28.2595224995953 |
| 41 | 144888 | 144530.362683653 | 357.63731634734 |
| 42 | 148762 | 148967.192264256 | -205.19226425627 |
| 43 | 156500 | 155034.471096884 | 1465.52890311603 |
| 44 | 161088 | 160038.102103136 | 1049.89789686351 |
| 45 | 152772 | 151306.553237399 | 1465.44676260102 |
| 46 | 158011 | 155969.129835776 | 2041.87016422364 |
| 47 | 163318 | 163508.354054245 | -190.354054244632 |
| 48 | 169969 | 168980.900487616 | 988.099512383786 |
| 49 | 162269 | 158280.913897731 | 3988.08610226872 |
| 50 | 165765 | 164401.997881678 | 1363.00211832212 |
| 51 | 170600 | 171355.138394751 | -755.138394750844 |
| 52 | 174681 | 176183.592922932 | -1502.59292293248 |
| 53 | 166364 | 165892.293957053 | 471.706042947255 |
| 54 | 170240 | 170307.612445926 | -67.6124459258823 |
| 55 | 176150 | 177102.855840294 | -952.855840293737 |
| 56 | 182056 | 182151.651229665 | -95.6512296654724 |
| 57 | 172218 | 172263.978616167 | -45.9786161666594 |
| 58 | 177856 | 177863.420474643 | -7.42047464301231 |
| 59 | 182253 | 183526.180519338 | -1273.18051933804 |
| 60 | 188090 | 189603.749692135 | -1513.74969213537 |
| 61 | 176863 | 177695.427694989 | -832.427694989112 |
| 62 | 183273 | 183874.984693894 | -601.984693893728 |
| 63 | 187969 | 188261.435551479 | -292.435551478773 |
| 64 | 194650 | 195219.093658299 | -569.093658298867 |
| 65 | 183036 | 183105.572931722 | -69.572931722097 |
| 66 | 189516 | 189843.318824504 | -327.318824503875 |
| 67 | 193805 | 193691.878386681 | 113.121613319474 |
| 68 | 200499 | 200652.829039166 | -153.829039166426 |
| 69 | 188142 | 188331.168258343 | -189.168258342689 |
| 70 | 193732 | 195264.792202733 | -1532.79220273261 |
| 71 | 197126 | 198668.878256605 | -1542.87825660458 |
| 72 | 205140 | 205417.505996586 | -277.505996585815 |
| 73 | 191751 | 192413.757059351 | -662.757059350805 |
| 74 | 196700 | 199549.397881239 | -2849.39788123889 |
| 75 | 199784 | 201421.802595861 | -1637.80259586087 |
| 76 | 207360 | 207766.848630034 | -406.848630034271 |
| 77 | 196101 | 193857.848122702 | 2243.15187729816 |
| 78 | 200824 | 200634.942705422 | 189.057294577589 |
| 79 | 205743 | 204295.23416856 | 1447.76583143992 |
| 80 | 212489 | 209890.693371321 | 2598.30662867898 |
| 81 | 200810 | 197932.235176257 | 2877.7648237428 |
| 82 | 203683 | 203482.412094146 | 200.587905854467 |
| 83 | 207286 | 206850.056827748 | 435.943172251792 |
| 84 | 210910 | 213042.723349435 | -2132.72334943486 |
| 85 | 194915 | 202860.631739784 | -7945.63173978427 |
| 86 | 217920 | 207013.855869365 | 10906.1441306354 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 13 | 0.0305171520858574 | 0.0610343041717148 | 0.969482847914143 |
| 14 | 0.00732516862210036 | 0.0146503372442007 | 0.9926748313779 |
| 15 | 0.0103530625475485 | 0.0207061250950970 | 0.989646937452451 |
| 16 | 0.0039317189757869 | 0.0078634379515738 | 0.996068281024213 |
| 17 | 0.00126719315037428 | 0.00253438630074856 | 0.998732806849626 |
| 18 | 0.000467388481958151 | 0.000934776963916302 | 0.999532611518042 |
| 19 | 0.000221245378027514 | 0.000442490756055028 | 0.999778754621973 |
| 20 | 0.000139424518874187 | 0.000278849037748375 | 0.999860575481126 |
| 21 | 7.12040120366285e-05 | 0.000142408024073257 | 0.999928795987963 |
| 22 | 0.000127302778497150 | 0.000254605556994299 | 0.999872697221503 |
| 23 | 0.000204194467820281 | 0.000408388935640562 | 0.99979580553218 |
| 24 | 8.97737506206766e-05 | 0.000179547501241353 | 0.99991022624938 |
| 25 | 3.58912272030788e-05 | 7.17824544061576e-05 | 0.999964108772797 |
| 26 | 1.72735113587092e-05 | 3.45470227174184e-05 | 0.999982726488641 |
| 27 | 6.40407928285482e-06 | 1.28081585657096e-05 | 0.999993595920717 |
| 28 | 2.76212777338138e-06 | 5.52425554676275e-06 | 0.999997237872227 |
| 29 | 1.99996741565744e-06 | 3.99993483131488e-06 | 0.999998000032584 |
| 30 | 6.8434914807691e-07 | 1.36869829615382e-06 | 0.999999315650852 |
| 31 | 3.88086036132218e-07 | 7.76172072264436e-07 | 0.999999611913964 |
| 32 | 1.39539040085575e-07 | 2.79078080171151e-07 | 0.99999986046096 |
| 33 | 8.14889789967227e-08 | 1.62977957993445e-07 | 0.999999918511021 |
| 34 | 6.73928396325658e-08 | 1.34785679265132e-07 | 0.99999993260716 |
| 35 | 2.5478464957233e-08 | 5.0956929914466e-08 | 0.999999974521535 |
| 36 | 1.22514834096202e-08 | 2.45029668192404e-08 | 0.999999987748517 |
| 37 | 4.33732763848020e-09 | 8.67465527696041e-09 | 0.999999995662672 |
| 38 | 8.06331936646638e-09 | 1.61266387329328e-08 | 0.99999999193668 |
| 39 | 2.83936756510294e-09 | 5.67873513020588e-09 | 0.999999997160632 |
| 40 | 1.31809478193916e-09 | 2.63618956387831e-09 | 0.999999998681905 |
| 41 | 5.60446912367825e-10 | 1.12089382473565e-09 | 0.999999999439553 |
| 42 | 9.10468538416632e-10 | 1.82093707683326e-09 | 0.999999999089531 |
| 43 | 4.26005726385211e-10 | 8.52011452770423e-10 | 0.999999999573994 |
| 44 | 1.78772658407056e-10 | 3.57545316814113e-10 | 0.999999999821227 |
| 45 | 1.32181621919898e-10 | 2.64363243839797e-10 | 0.999999999867818 |
| 46 | 3.92912885768024e-10 | 7.85825771536048e-10 | 0.999999999607087 |
| 47 | 1.94104394184173e-09 | 3.88208788368345e-09 | 0.999999998058956 |
| 48 | 8.22246261121178e-10 | 1.64449252224236e-09 | 0.999999999177754 |
| 49 | 3.80872175639238e-09 | 7.61744351278476e-09 | 0.999999996191278 |
| 50 | 1.39889164001503e-09 | 2.79778328003006e-09 | 0.999999998601108 |
| 51 | 7.63274295594752e-09 | 1.52654859118950e-08 | 0.999999992367257 |
| 52 | 1.09370600915712e-08 | 2.18741201831425e-08 | 0.99999998906294 |
| 53 | 5.29512931113407e-09 | 1.05902586222681e-08 | 0.99999999470487 |
| 54 | 1.98658545888064e-09 | 3.97317091776128e-09 | 0.999999998013415 |
| 55 | 2.1348051419923e-09 | 4.2696102839846e-09 | 0.999999997865195 |
| 56 | 1.26466853567520e-09 | 2.52933707135040e-09 | 0.999999998735331 |
| 57 | 9.13036013538756e-10 | 1.82607202707751e-09 | 0.999999999086964 |
| 58 | 8.30567299684864e-10 | 1.66113459936973e-09 | 0.999999999169433 |
| 59 | 2.13362858721561e-09 | 4.26725717443122e-09 | 0.999999997866371 |
| 60 | 3.39786929324157e-09 | 6.79573858648314e-09 | 0.99999999660213 |
| 61 | 1.95948170464652e-09 | 3.91896340929303e-09 | 0.999999998040518 |
| 62 | 1.78157744706822e-09 | 3.56315489413645e-09 | 0.999999998218423 |
| 63 | 8.2182147429345e-10 | 1.6436429485869e-09 | 0.999999999178179 |
| 64 | 8.54556776645712e-10 | 1.70911355329142e-09 | 0.999999999145443 |
| 65 | 9.3364544849719e-10 | 1.86729089699438e-09 | 0.999999999066355 |
| 66 | 8.34068859069626e-09 | 1.66813771813925e-08 | 0.999999991659311 |
| 67 | 7.59749745876459e-09 | 1.51949949175292e-08 | 0.999999992402502 |
| 68 | 4.759787966876e-08 | 9.519575933752e-08 | 0.99999995240212 |
| 69 | 1.32789889669839e-05 | 2.65579779339678e-05 | 0.999986721011033 |
| 70 | 0.000198414591093837 | 0.000396829182187674 | 0.999801585408906 |
| 71 | 0.00253889960830893 | 0.00507779921661786 | 0.997461100391691 |
| 72 | 0.00199796468042651 | 0.00399592936085302 | 0.998002035319574 |
| 73 | 0.00158316704442400 | 0.00316633408884799 | 0.998416832955576 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 58 | 0.950819672131147 | NOK |
| 5% type I error level | 60 | 0.98360655737705 | NOK |
| 10% type I error level | 61 | 1 | NOK |
