| Multiple Linear Regression - Estimated Regression Equation |
| SKIA[t] = + 84.3431696197983 -49.4381863504682x[t] + 2.03101643765592M1[t] -9.72842470770787M2[t] -24.4076067602814M3[t] -8.39016414129262M4[t] -12.4353195723707M5[t] -7.76618928916308M6[t] + 1.90294099404455M7[t] -12.8565001513193M8[t] -13.4597718020038M9[t] -12.8826746400687M10[t] -7.5452752032116M11[t] -0.0977017117790545t + 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) | 84.3431696197983 | 9.078669 | 9.2903 | 0 | 0 |
| x | -49.4381863504682 | 5.503078 | -8.9837 | 0 | 0 |
| M1 | 2.03101643765592 | 11.027033 | 0.1842 | 0.854433 | 0.427216 |
| M2 | -9.72842470770787 | 11.013738 | -0.8833 | 0.380281 | 0.19014 |
| M3 | -24.4076067602814 | 10.913126 | -2.2365 | 0.028701 | 0.014351 |
| M4 | -8.39016414129262 | 10.990601 | -0.7634 | 0.447948 | 0.223974 |
| M5 | -12.4353195723707 | 10.980767 | -1.1325 | 0.261537 | 0.130769 |
| M6 | -7.76618928916308 | 10.972092 | -0.7078 | 0.481554 | 0.240777 |
| M7 | 1.90294099404455 | 10.964581 | 0.1736 | 0.862748 | 0.431374 |
| M8 | -12.8565001513193 | 10.958234 | -1.1732 | 0.244921 | 0.122461 |
| M9 | -13.4597718020038 | 11.292727 | -1.1919 | 0.23757 | 0.118785 |
| M10 | -12.8826746400687 | 11.457683 | -1.1244 | 0.264929 | 0.132464 |
| M11 | -7.5452752032116 | 11.633276 | -0.6486 | 0.518851 | 0.259426 |
| t | -0.0977017117790545 | 0.113246 | -0.8627 | 0.391406 | 0.195703 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.8285933081517 |
| R-squared | 0.686566870313778 |
| Adjusted R-squared | 0.624830041739219 |
| F-TEST (value) | 11.1208639343146 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 66 |
| p-value | 4.18853840500333e-12 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 19.5507225404839 |
| Sum Squared Residuals | 25227.2296224290 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 37 | 36.838297995207 | 0.161702004792961 |
| 2 | 30 | 24.9811551380641 | 5.01884486193589 |
| 3 | 47 | 59.6424577241797 | -12.6424577241797 |
| 4 | 35 | 26.1240122809213 | 8.87598771907875 |
| 5 | 30 | 21.9811551380641 | 8.01884486193588 |
| 6 | 43 | 75.9907700599609 | -32.9907700599609 |
| 7 | 82 | 85.5621986313895 | -3.5621986313895 |
| 8 | 40 | 70.7050557742466 | -30.7050557742466 |
| 9 | 47 | 70.004082411783 | -23.004082411783 |
| 10 | 19 | 21.0452915114709 | -2.04529151147085 |
| 11 | 52 | 75.7231755870171 | -23.7231755870171 |
| 12 | 136 | 83.1707490784497 | 52.8292509215503 |
| 13 | 80 | 85.1040638043265 | -5.10406380432654 |
| 14 | 42 | 73.2469209471837 | -31.2469209471837 |
| 15 | 54 | 58.4700371828311 | -4.47003718283109 |
| 16 | 66 | 74.3897780900408 | -8.38977809004084 |
| 17 | 81 | 70.2469209471837 | 10.7530790528163 |
| 18 | 63 | 74.8183495186123 | -11.8183495186123 |
| 19 | 137 | 84.3897780900408 | 52.6102219099592 |
| 20 | 72 | 69.532635232898 | 2.46736476710202 |
| 21 | 107 | 68.8316618704343 | 38.1683381295657 |
| 22 | 58 | 69.3110573205904 | -11.3110573205904 |
| 23 | 36 | 25.1125686952002 | 10.8874313047998 |
| 24 | 52 | 81.998328537101 | -29.998328537101 |
| 25 | 79 | 83.9316432629779 | -4.93164326297789 |
| 26 | 77 | 72.074500405835 | 4.92549959416496 |
| 27 | 54 | 57.2976166414824 | -3.29761664148243 |
| 28 | 84 | 73.2173575486922 | 10.7826424513078 |
| 29 | 48 | 69.074500405835 | -21.0745004058350 |
| 30 | 96 | 73.6459289772636 | 22.3540710227364 |
| 31 | 83 | 83.2173575486922 | -0.217357548692188 |
| 32 | 66 | 68.3602146915493 | -2.36021469154933 |
| 33 | 61 | 67.6592413290857 | -6.6592413290857 |
| 34 | 53 | 68.1386367792418 | -15.1386367792418 |
| 35 | 30 | 23.9401481538516 | 6.05985184614842 |
| 36 | 74 | 80.8259079957524 | -6.82590799575236 |
| 37 | 69 | 82.7592227216292 | -13.7592227216292 |
| 38 | 59 | 70.9020798644864 | -11.9020798644864 |
| 39 | 42 | 56.1251961001338 | -14.1251961001338 |
| 40 | 65 | 72.0449370073435 | -7.04493700734353 |
| 41 | 70 | 67.9020798644864 | 2.09792013551361 |
| 42 | 100 | 72.473508435915 | 27.5264915640850 |
| 43 | 63 | 82.0449370073435 | -19.0449370073435 |
| 44 | 105 | 67.1877941502007 | 37.8122058497993 |
| 45 | 82 | 66.486820787737 | 15.5131792122630 |
| 46 | 81 | 66.9662162378931 | 14.0337837621069 |
| 47 | 75 | 72.2059139629712 | 2.79408603702883 |
| 48 | 102 | 79.6534874544037 | 22.3465125455963 |
| 49 | 121 | 81.5868021802806 | 39.4131978197194 |
| 50 | 98 | 69.7296593231378 | 28.2703406768623 |
| 51 | 76 | 54.9527755587851 | 21.0472244412149 |
| 52 | 77 | 70.8725164659949 | 6.12748353400512 |
| 53 | 63 | 66.7296593231377 | -3.72965932313773 |
| 54 | 37 | 21.8629015440981 | 15.1370984559019 |
| 55 | 35 | 31.4343301155266 | 3.56566988447336 |
| 56 | 23 | 16.5771872583838 | 6.42281274161622 |
| 57 | 40 | 65.3144002463884 | -25.3144002463884 |
| 58 | 29 | 16.3556093460762 | 12.6443906539238 |
| 59 | 37 | 21.5953070711543 | 15.4046929288457 |
| 60 | 51 | 78.481066913055 | -27.4810669130551 |
| 61 | 20 | 30.9761952884637 | -10.9761952884637 |
| 62 | 28 | 19.1190524313208 | 8.88094756867917 |
| 63 | 13 | 4.34216866696824 | 8.65783133303176 |
| 64 | 22 | 20.261909574178 | 1.73809042582202 |
| 65 | 25 | 16.1190524313208 | 8.88094756867917 |
| 66 | 13 | 20.6904810027494 | -7.69048100274941 |
| 67 | 16 | 30.261909574178 | -14.2619095741780 |
| 68 | 13 | 15.4047667170351 | -2.40476671703513 |
| 69 | 16 | 14.7037933545715 | 1.29620664542850 |
| 70 | 17 | 15.1831888047276 | 1.81681119527242 |
| 71 | 9 | 20.4228865298056 | -11.4228865298056 |
| 72 | 17 | 27.8704600212382 | -10.8704600212382 |
| 73 | 25 | 29.8037747471150 | -4.80377474711503 |
| 74 | 14 | 17.9466318899722 | -3.94663188997218 |
| 75 | 8 | 3.16974812561958 | 4.83025187438042 |
| 76 | 7 | 19.0894890328293 | -12.0894890328293 |
| 77 | 10 | 14.9466318899722 | -4.94663188997219 |
| 78 | 7 | 19.5180604614008 | -12.5180604614008 |
| 79 | 10 | 29.0894890328293 | -19.0894890328293 |
| 80 | 3 | 14.2323461756865 | -11.2323461756865 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.280087347241597 | 0.560174694483195 | 0.719912652758403 |
| 18 | 0.175859644637170 | 0.351719289274340 | 0.82414035536283 |
| 19 | 0.438629546025162 | 0.877259092050325 | 0.561370453974838 |
| 20 | 0.312535142142585 | 0.625070284285169 | 0.687464857857415 |
| 21 | 0.438161196413922 | 0.876322392827844 | 0.561838803586078 |
| 22 | 0.341355188243008 | 0.682710376486016 | 0.658644811756992 |
| 23 | 0.484738180328861 | 0.969476360657722 | 0.515261819671139 |
| 24 | 0.994052584186999 | 0.0118948316260027 | 0.00594741581300134 |
| 25 | 0.990142124828936 | 0.0197157503421288 | 0.0098578751710644 |
| 26 | 0.98373622530073 | 0.0325275493985388 | 0.0162637746992694 |
| 27 | 0.977185108978373 | 0.0456297820432533 | 0.0228148910216266 |
| 28 | 0.96388072421979 | 0.0722385515604191 | 0.0361192757802095 |
| 29 | 0.97701664799726 | 0.0459667040054818 | 0.0229833520027409 |
| 30 | 0.97445117781485 | 0.0510976443703008 | 0.0255488221851504 |
| 31 | 0.979437358546625 | 0.0411252829067491 | 0.0205626414533746 |
| 32 | 0.971604242405477 | 0.0567915151890461 | 0.0283957575945230 |
| 33 | 0.966995373970574 | 0.0660092520588528 | 0.0330046260294264 |
| 34 | 0.970064247310346 | 0.0598715053793087 | 0.0299357526896543 |
| 35 | 0.955823743869291 | 0.0883525122614172 | 0.0441762561307086 |
| 36 | 0.950415429386932 | 0.099169141226136 | 0.049584570613068 |
| 37 | 0.959789181374796 | 0.0804216372504078 | 0.0402108186252039 |
| 38 | 0.973576638909642 | 0.0528467221807151 | 0.0264233610903576 |
| 39 | 0.991282375096389 | 0.0174352498072228 | 0.0087176249036114 |
| 40 | 0.992707629069357 | 0.0145847418612857 | 0.00729237093064286 |
| 41 | 0.991875749692263 | 0.0162485006154732 | 0.0081242503077366 |
| 42 | 0.991086108144828 | 0.0178277837103443 | 0.00891389185517214 |
| 43 | 0.997305457809802 | 0.00538908438039582 | 0.00269454219019791 |
| 44 | 0.99860795612255 | 0.00278408775489920 | 0.00139204387744960 |
| 45 | 0.997746713280786 | 0.00450657343842864 | 0.00225328671921432 |
| 46 | 0.996328621093035 | 0.0073427578139306 | 0.0036713789069653 |
| 47 | 0.99429055988521 | 0.0114188802295798 | 0.0057094401147899 |
| 48 | 0.996056898054173 | 0.00788620389165412 | 0.00394310194582706 |
| 49 | 0.999865654267627 | 0.000268691464746629 | 0.000134345732373315 |
| 50 | 0.999971155829371 | 5.76883412570502e-05 | 2.88441706285251e-05 |
| 51 | 0.999982267406255 | 3.54651874895263e-05 | 1.77325937447631e-05 |
| 52 | 0.999996049361645 | 7.90127671075527e-06 | 3.95063835537764e-06 |
| 53 | 0.999992065256448 | 1.58694871039703e-05 | 7.93474355198514e-06 |
| 54 | 0.99998767506137 | 2.46498772618967e-05 | 1.23249386309483e-05 |
| 55 | 0.999971663594703 | 5.66728105947067e-05 | 2.83364052973534e-05 |
| 56 | 0.999898663767641 | 0.000202672464717532 | 0.000101336232358766 |
| 57 | 0.999796308643023 | 0.000407382713954126 | 0.000203691356977063 |
| 58 | 0.999263564584962 | 0.00147287083007523 | 0.000736435415037614 |
| 59 | 0.999765409037025 | 0.000469181925950827 | 0.000234590962975413 |
| 60 | 0.999144090012886 | 0.00171181997422746 | 0.000855909987113732 |
| 61 | 0.99966196452916 | 0.000676070941679413 | 0.000338035470839707 |
| 62 | 0.998355686158384 | 0.00328862768323270 | 0.00164431384161635 |
| 63 | 0.99290038655636 | 0.0141992268872799 | 0.00709961344363993 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 19 | 0.404255319148936 | NOK |
| 5% type I error level | 31 | 0.659574468085106 | NOK |
| 10% type I error level | 40 | 0.851063829787234 | NOK |
