| Multiple Linear Regression - Estimated Regression Equation |
| Dow[t] = + 14.2051609637165 -0.00154349887564725Jones[t] -0.14136410517928V3[t] -0.00107111846532049Gold[t] + 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) | 14.2051609637165 | 1.071252 | 13.2603 | 0 | 0 |
| Jones | -0.00154349887564725 | 0.000816 | -1.8914 | 0.063656 | 0.031828 |
| V3 | -0.14136410517928 | 0.051276 | -2.7569 | 0.007825 | 0.003912 |
| Gold | -0.00107111846532049 | 0.000685 | -1.5646 | 0.123212 | 0.061606 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.4219251705199 |
| R-squared | 0.178020849518247 |
| Adjusted R-squared | 0.134758788966575 |
| F-TEST (value) | 4.1149415272447 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 57 |
| p-value | 0.0103519664612729 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.55254061021451 |
| Sum Squared Residuals | 137.391793742819 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10 | 11.5228416181378 | -1.52284161813778 |
| 2 | 10 | 11.1784384462643 | -1.17843844626433 |
| 3 | 10 | 11.1432192020815 | -1.14321920208153 |
| 4 | 10 | 11.6624739367321 | -1.66247393673211 |
| 5 | 10 | 11.4574178433521 | -1.45741784335207 |
| 6 | 10 | 11.5209226956413 | -1.52092269564129 |
| 7 | 10 | 11.437755400943 | -1.43775540094302 |
| 8 | 10 | 11.3115662570799 | -1.31156625707986 |
| 9 | 10 | 10.7956227149383 | -0.795622714938269 |
| 10 | 10 | 11.39339758211 | -1.39339758211001 |
| 11 | 10 | 11.2611053306672 | -1.26110533066716 |
| 12 | 10 | 10.2199555982961 | -0.219955598296057 |
| 13 | 10 | 10.2967031470475 | -0.296703147047504 |
| 14 | 10 | 9.72982152695334 | 0.270178473046665 |
| 15 | 11 | 11.0522419196946 | -0.0522419196945913 |
| 16 | 11 | 11.5757513723845 | -0.575751372384504 |
| 17 | 11 | 11.2180761892871 | -0.218076189287107 |
| 18 | 10 | 10.3643859109238 | -0.364385910923752 |
| 19 | 11 | 11.8328396840594 | -0.832839684059352 |
| 20 | 11 | 10.7888115579756 | 0.211188442024424 |
| 21 | 11 | 11.1143605912218 | -0.114360591221759 |
| 22 | 11 | 9.71764183817744 | 1.28235816182256 |
| 23 | 12 | 11.1048358036735 | 0.89516419632648 |
| 24 | 12 | 11.1751522086826 | 0.82484779131738 |
| 25 | 12 | 10.672876656276 | 1.327123343724 |
| 26 | 12 | 10.5958973849227 | 1.40410261507725 |
| 27 | 12 | 10.6762256971323 | 1.32377430286768 |
| 28 | 12 | 10.5951410719397 | 1.40485892806035 |
| 29 | 13 | 10.4516997174768 | 2.54830028252318 |
| 30 | 13 | 10.5797883251792 | 2.42021167482079 |
| 31 | 13 | 10.4092480946311 | 2.59075190536887 |
| 32 | 13 | 10.983133358732 | 2.01686664126801 |
| 33 | 13 | 10.6133915050779 | 2.38660849492209 |
| 34 | 13 | 10.3765707181351 | 2.62342928186489 |
| 35 | 13 | 10.7468777193283 | 2.25312228067166 |
| 36 | 13 | 10.3758301815828 | 2.6241698184172 |
| 37 | 12 | 10.2666346750106 | 1.73336532498941 |
| 38 | 12 | 10.5717475040081 | 1.42825249599187 |
| 39 | 12 | 10.9629445038658 | 1.03705549613422 |
| 40 | 12 | 10.021566220026 | 1.97843377997398 |
| 41 | 12 | 9.93418186079723 | 2.06581813920277 |
| 42 | 12 | 11.1543296692662 | 0.845670330733797 |
| 43 | 11 | 10.830990710952 | 0.169009289048046 |
| 44 | 11 | 10.7567766834793 | 0.243223316520656 |
| 45 | 11 | 10.9671745000058 | 0.0328254999941904 |
| 46 | 9 | 10.5489426229724 | -1.54894262297239 |
| 47 | 8 | 10.3618176305436 | -2.36181763054365 |
| 48 | 8 | 9.90376977247137 | -1.90376977247137 |
| 49 | 8 | 9.87731627938344 | -1.87731627938344 |
| 50 | 7 | 9.25068508409292 | -2.25068508409292 |
| 51 | 7 | 9.72806496751837 | -2.72806496751837 |
| 52 | 7 | 8.83328821967357 | -1.83328821967357 |
| 53 | 8 | 9.62763317204259 | -1.62763317204259 |
| 54 | 8 | 9.48896087413876 | -1.48896087413876 |
| 55 | 8 | 9.77708302201263 | -1.77708302201263 |
| 56 | 9 | 10.1580614478632 | -1.1580614478632 |
| 57 | 9 | 10.0593770085059 | -1.05937700850592 |
| 58 | 9 | 9.04348676730697 | -0.0434867673069741 |
| 59 | 10 | 10.1010306940404 | -0.101030694040371 |
| 60 | 10 | 9.0969255461351 | 0.9030744538649 |
| 61 | 10 | 9.72519175714909 | 0.274808242850911 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 1.41382209077369e-47 | 2.82764418154737e-47 | 1 |
| 8 | 2.22659144582217e-61 | 4.45318289164435e-61 | 1 |
| 9 | 4.93314500673616e-77 | 9.86629001347232e-77 | 1 |
| 10 | 5.66198029594408e-102 | 1.13239605918882e-101 | 1 |
| 11 | 1.19037096171431e-105 | 2.38074192342861e-105 | 1 |
| 12 | 1.26660952010995e-118 | 2.53321904021991e-118 | 1 |
| 13 | 6.06683433924116e-141 | 1.21336686784823e-140 | 1 |
| 14 | 3.31227919255892e-150 | 6.62455838511783e-150 | 1 |
| 15 | 7.40820176696058e-09 | 1.48164035339212e-08 | 0.999999992591798 |
| 16 | 1.97720657558033e-09 | 3.95441315116066e-09 | 0.999999998022793 |
| 17 | 2.70268707058971e-10 | 5.40537414117942e-10 | 0.999999999729731 |
| 18 | 5.08448881362586e-11 | 1.01689776272517e-10 | 0.999999999949155 |
| 19 | 1.02816233812777e-11 | 2.05632467625554e-11 | 0.999999999989718 |
| 20 | 2.67268167287277e-12 | 5.34536334574554e-12 | 0.999999999997327 |
| 21 | 1.72340288625157e-11 | 3.44680577250315e-11 | 0.999999999982766 |
| 22 | 9.35565521918338e-10 | 1.87113104383668e-09 | 0.999999999064434 |
| 23 | 2.21215201601196e-08 | 4.42430403202392e-08 | 0.99999997787848 |
| 24 | 4.02692850699666e-07 | 8.05385701399332e-07 | 0.999999597307149 |
| 25 | 1.59644354953499e-06 | 3.19288709906998e-06 | 0.99999840355645 |
| 26 | 2.79515269926128e-06 | 5.59030539852257e-06 | 0.999997204847301 |
| 27 | 1.53083450220884e-06 | 3.06166900441767e-06 | 0.999998469165498 |
| 28 | 2.61354376816657e-06 | 5.22708753633314e-06 | 0.999997386456232 |
| 29 | 1.5360239896164e-05 | 3.0720479792328e-05 | 0.999984639760104 |
| 30 | 5.72731993649195e-05 | 0.000114546398729839 | 0.999942726800635 |
| 31 | 0.000210718796704644 | 0.000421437593409289 | 0.999789281203295 |
| 32 | 0.000228733868468442 | 0.000457467736936885 | 0.999771266131532 |
| 33 | 0.000303404423789334 | 0.000606808847578668 | 0.999696595576211 |
| 34 | 0.000517208695682344 | 0.00103441739136469 | 0.999482791304318 |
| 35 | 0.000443286811086936 | 0.000886573622173873 | 0.999556713188913 |
| 36 | 0.00089683914250658 | 0.00179367828501316 | 0.999103160857493 |
| 37 | 0.00147105310493537 | 0.00294210620987073 | 0.998528946895065 |
| 38 | 0.00181336302921177 | 0.00362672605842355 | 0.998186636970788 |
| 39 | 0.00172876557900933 | 0.00345753115801867 | 0.998271234420991 |
| 40 | 0.00531238318983375 | 0.0106247663796675 | 0.994687616810166 |
| 41 | 0.0543311139702093 | 0.108662227940419 | 0.945668886029791 |
| 42 | 0.0676431568689689 | 0.135286313737938 | 0.932356843131031 |
| 43 | 0.0861308943085813 | 0.172261788617163 | 0.913869105691419 |
| 44 | 0.151610353926528 | 0.303220707853057 | 0.848389646073472 |
| 45 | 0.408899893547321 | 0.817799787094643 | 0.591100106452679 |
| 46 | 0.675576076289163 | 0.648847847421673 | 0.324423923710837 |
| 47 | 0.780943498476198 | 0.438113003047603 | 0.219056501523802 |
| 48 | 0.841663439323421 | 0.316673121353157 | 0.158336560676579 |
| 49 | 0.851601624783991 | 0.296796750432017 | 0.148398375216008 |
| 50 | 0.963597816881568 | 0.0728043662368639 | 0.036402183118432 |
| 51 | 0.995659783409844 | 0.00868043318031253 | 0.00434021659015627 |
| 52 | 0.996057930057626 | 0.00788413988474753 | 0.00394206994237376 |
| 53 | 0.991292203557585 | 0.0174155928848291 | 0.00870779644241454 |
| 54 | 0.985840160767824 | 0.0283196784643525 | 0.0141598392321763 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 35 | 0.729166666666667 | NOK |
| 5% type I error level | 38 | 0.791666666666667 | NOK |
| 10% type I error level | 39 | 0.8125 | NOK |
