| Multiple Linear Regression - Estimated Regression Equation |
| y[t] = + 81.0978124999999 -5.16078124999995x[t] + 16.3589279513888M1[t] + 15.9374317956349M2[t] + 24.1445070684524M3[t] + 15.8372966269841M4[t] + 12.5300861855159M5[t] + 21.3800186011905M6[t] + 6.18709387400795M7[t] -11.3772594246032M8[t] + 26.3012444196429M9[t] + 27.6858494543651M10[t] + 22.1929247271826M11[t] + 0.0929247271825398t + 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) | 81.0978124999999 | 2.446634 | 33.1467 | 0 | 0 |
| x | -5.16078124999995 | 2.000773 | -2.5794 | 0.012098 | 0.006049 |
| M1 | 16.3589279513888 | 2.801308 | 5.8397 | 0 | 0 |
| M2 | 15.9374317956349 | 2.799488 | 5.693 | 0 | 0 |
| M3 | 24.1445070684524 | 2.798001 | 8.6292 | 0 | 0 |
| M4 | 15.8372966269841 | 2.796846 | 5.6626 | 0 | 0 |
| M5 | 12.5300861855159 | 2.796024 | 4.4814 | 3e-05 | 1.5e-05 |
| M6 | 21.3800186011905 | 2.795535 | 7.6479 | 0 | 0 |
| M7 | 6.18709387400795 | 2.79538 | 2.2133 | 0.030285 | 0.015142 |
| M8 | -11.3772594246032 | 2.795558 | -4.0698 | 0.000127 | 6.3e-05 |
| M9 | 26.3012444196429 | 2.79607 | 9.4065 | 0 | 0 |
| M10 | 27.6858494543651 | 2.901285 | 9.5426 | 0 | 0 |
| M11 | 22.1929247271826 | 2.900803 | 7.6506 | 0 | 0 |
| t | 0.0929247271825398 | 0.030537 | 3.043 | 0.003344 | 0.001672 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.924878815061786 |
| R-squared | 0.855400822550093 |
| Adjusted R-squared | 0.827344265731454 |
| F-TEST (value) | 30.4884461796049 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 67 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 5.02406007724201 |
| Sum Squared Residuals | 1691.15903720238 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 101.5 | 97.5496651785718 | 3.95033482142816 |
| 2 | 99.2 | 97.22109375 | 1.97890625 |
| 3 | 107.8 | 105.52109375 | 2.27890625000002 |
| 4 | 92.3 | 97.3068080357142 | -5.00680803571423 |
| 5 | 99.2 | 94.0925223214286 | 5.10747767857144 |
| 6 | 101.6 | 103.035379464286 | -1.43537946428569 |
| 7 | 87 | 87.9353794642857 | -0.935379464285681 |
| 8 | 71.4 | 70.4639508928571 | 0.936049107142891 |
| 9 | 104.7 | 108.235379464286 | -3.5353794642857 |
| 10 | 115.1 | 109.712909226190 | 5.38709077380959 |
| 11 | 102.5 | 104.312909226190 | -1.81290922619042 |
| 12 | 75.3 | 82.2129092261904 | -6.91290922619044 |
| 13 | 96.7 | 93.5039806547618 | 3.19601934523818 |
| 14 | 94.6 | 93.1754092261905 | 1.42459077380952 |
| 15 | 98.6 | 101.475409226190 | -2.87540922619048 |
| 16 | 99.5 | 93.2611235119048 | 6.23887648809523 |
| 17 | 92 | 90.046837797619 | 1.95316220238095 |
| 18 | 93.6 | 98.9896949404762 | -5.38969494047620 |
| 19 | 89.3 | 83.8896949404762 | 5.41030505952381 |
| 20 | 66.9 | 66.4182663690476 | 0.481733630952386 |
| 21 | 108.8 | 104.189694940476 | 4.61030505952381 |
| 22 | 113.2 | 105.667224702381 | 7.53277529761904 |
| 23 | 105.5 | 100.267224702381 | 5.23277529761904 |
| 24 | 77.8 | 78.167224702381 | -0.367224702380958 |
| 25 | 102.1 | 94.6190773809523 | 7.48092261904768 |
| 26 | 97 | 94.290505952381 | 2.70949404761905 |
| 27 | 95.5 | 102.590505952381 | -7.09050595238095 |
| 28 | 99.3 | 94.3762202380952 | 4.92377976190475 |
| 29 | 86.4 | 91.1619345238095 | -4.76193452380952 |
| 30 | 92.4 | 100.104791666667 | -7.70479166666666 |
| 31 | 85.7 | 85.0047916666667 | 0.695208333333334 |
| 32 | 61.9 | 67.5333630952381 | -5.6333630952381 |
| 33 | 104.9 | 105.304791666667 | -0.404791666666663 |
| 34 | 107.9 | 106.782321428571 | 1.11767857142857 |
| 35 | 95.6 | 101.382321428571 | -5.78232142857144 |
| 36 | 79.8 | 79.2823214285714 | 0.517678571428565 |
| 37 | 94.8 | 95.7341741071428 | -0.934174107142794 |
| 38 | 93.7 | 95.4056026785714 | -1.70560267857143 |
| 39 | 108.1 | 103.705602678571 | 4.39439732142857 |
| 40 | 96.9 | 95.4913169642857 | 1.40868303571428 |
| 41 | 88.8 | 92.27703125 | -3.47703125000001 |
| 42 | 106.7 | 101.219888392857 | 5.48011160714286 |
| 43 | 86.8 | 86.1198883928571 | 0.680111607142851 |
| 44 | 69.8 | 68.6484598214286 | 1.15154017857142 |
| 45 | 110.9 | 106.419888392857 | 4.48011160714286 |
| 46 | 105.4 | 107.897418154762 | -2.49741815476191 |
| 47 | 99.2 | 102.497418154762 | -3.29741815476191 |
| 48 | 84.4 | 80.3974181547619 | 4.00258184523809 |
| 49 | 87.2 | 96.8492708333333 | -9.64927083333327 |
| 50 | 91.9 | 96.520699404762 | -4.6206994047619 |
| 51 | 97.9 | 104.820699404762 | -6.9206994047619 |
| 52 | 94.5 | 96.6064136904762 | -2.1064136904762 |
| 53 | 85 | 93.3921279761905 | -8.39212797619048 |
| 54 | 100.3 | 102.334985119048 | -2.03498511904762 |
| 55 | 78.7 | 87.2349851190476 | -8.53498511904762 |
| 56 | 65.8 | 69.763556547619 | -3.96355654761906 |
| 57 | 104.8 | 107.534985119048 | -2.73498511904763 |
| 58 | 96 | 109.012514880952 | -13.0125148809524 |
| 59 | 103.3 | 103.612514880952 | -0.312514880952395 |
| 60 | 82.9 | 81.5125148809524 | 1.38748511904762 |
| 61 | 91.4 | 97.9643675595238 | -6.56436755952374 |
| 62 | 94.5 | 97.6357961309524 | -3.13579613095239 |
| 63 | 109.3 | 105.935796130952 | 3.36420386904761 |
| 64 | 92.1 | 97.7215104166667 | -5.62151041666668 |
| 65 | 99.3 | 94.507224702381 | 4.79277529761904 |
| 66 | 109.6 | 103.450081845238 | 6.1499181547619 |
| 67 | 87.5 | 88.3500818452381 | -0.850081845238102 |
| 68 | 73.1 | 70.8786532738095 | 2.22134672619046 |
| 69 | 110.7 | 108.650081845238 | 2.0499181547619 |
| 70 | 111.6 | 110.127611607143 | 1.47238839285712 |
| 71 | 110.7 | 104.727611607143 | 5.97238839285714 |
| 72 | 84 | 82.627611607143 | 1.37238839285713 |
| 73 | 101.6 | 99.0794642857142 | 2.52053571428577 |
| 74 | 102.1 | 98.7508928571429 | 3.34910714285713 |
| 75 | 113.9 | 107.050892857143 | 6.84910714285714 |
| 76 | 99 | 98.8366071428571 | 0.163392857142846 |
| 77 | 100.4 | 95.6223214285714 | 4.77767857142857 |
| 78 | 109.5 | 104.565178571429 | 4.93482142857142 |
| 79 | 93 | 89.4651785714286 | 3.53482142857142 |
| 80 | 76.8 | 71.99375 | 4.80624999999999 |
| 81 | 105.3 | 109.765178571429 | -4.46517857142858 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.584933565008126 | 0.830132869983748 | 0.415066434991874 |
| 18 | 0.466688979110695 | 0.93337795822139 | 0.533311020889305 |
| 19 | 0.432626591611028 | 0.865253183222057 | 0.567373408388972 |
| 20 | 0.304044838479112 | 0.608089676958223 | 0.695955161520888 |
| 21 | 0.314714198735596 | 0.629428397471192 | 0.685285801264404 |
| 22 | 0.262940899776432 | 0.525881799552864 | 0.737059100223568 |
| 23 | 0.247939549239335 | 0.49587909847867 | 0.752060450760665 |
| 24 | 0.199337746253199 | 0.398675492506398 | 0.800662253746801 |
| 25 | 0.193420874180443 | 0.386841748360886 | 0.806579125819557 |
| 26 | 0.155497744350837 | 0.310995488701674 | 0.844502255649163 |
| 27 | 0.218522391268997 | 0.437044782537995 | 0.781477608731003 |
| 28 | 0.231859487085595 | 0.46371897417119 | 0.768140512914405 |
| 29 | 0.284567745427051 | 0.569135490854102 | 0.715432254572949 |
| 30 | 0.279313251162901 | 0.558626502325803 | 0.720686748837099 |
| 31 | 0.224903134430864 | 0.449806268861728 | 0.775096865569136 |
| 32 | 0.205529655740551 | 0.411059311481103 | 0.794470344259449 |
| 33 | 0.155483119789080 | 0.310966239578159 | 0.84451688021092 |
| 34 | 0.155174949196330 | 0.310349898392661 | 0.84482505080367 |
| 35 | 0.146959856118107 | 0.293919712236214 | 0.853040143881893 |
| 36 | 0.154300989960944 | 0.308601979921887 | 0.845699010039056 |
| 37 | 0.131715025788507 | 0.263430051577014 | 0.868284974211493 |
| 38 | 0.0979965278485596 | 0.195993055697119 | 0.90200347215144 |
| 39 | 0.217726590875205 | 0.435453181750410 | 0.782273409124795 |
| 40 | 0.216576188821209 | 0.433152377642418 | 0.783423811178791 |
| 41 | 0.165364338666489 | 0.330728677332979 | 0.83463566133351 |
| 42 | 0.342911930323334 | 0.685823860646667 | 0.657088069676666 |
| 43 | 0.340815544169974 | 0.681631088339947 | 0.659184455830026 |
| 44 | 0.328764348448233 | 0.657528696896467 | 0.671235651551767 |
| 45 | 0.552933605313916 | 0.894132789372168 | 0.447066394686084 |
| 46 | 0.665676227791506 | 0.668647544416988 | 0.334323772208494 |
| 47 | 0.590664463287805 | 0.818671073424389 | 0.409335536712195 |
| 48 | 0.725267296223677 | 0.549465407552647 | 0.274732703776323 |
| 49 | 0.765725597331916 | 0.468548805336168 | 0.234274402668084 |
| 50 | 0.70878796570435 | 0.582424068591298 | 0.291212034295649 |
| 51 | 0.703680847613257 | 0.592638304773486 | 0.296319152386743 |
| 52 | 0.73731930471502 | 0.525361390569959 | 0.262680695284979 |
| 53 | 0.777987635375933 | 0.444024729248133 | 0.222012364624067 |
| 54 | 0.719500594005495 | 0.560998811989009 | 0.280499405994505 |
| 55 | 0.712323277451198 | 0.575353445097605 | 0.287676722548802 |
| 56 | 0.640420041274918 | 0.719159917450164 | 0.359579958725082 |
| 57 | 0.582511707241971 | 0.834976585516057 | 0.417488292758029 |
| 58 | 0.85175954132453 | 0.296480917350941 | 0.148240458675470 |
| 59 | 0.818176148912118 | 0.363647702175764 | 0.181823851087882 |
| 60 | 0.759205494604614 | 0.481589010790771 | 0.240794505395386 |
| 61 | 0.791866626494876 | 0.416266747010249 | 0.208133373505124 |
| 62 | 0.764858828388111 | 0.470282343223778 | 0.235141171611889 |
| 63 | 0.68755783097635 | 0.624884338047301 | 0.312442169023650 |
| 64 | 0.656569947866097 | 0.686860104267807 | 0.343430052133903 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
