| Multiple Linear Regression - Estimated Regression Equation |
| S&P500[t] = + 966.129982902622 + 0.43035784722686Gold[t] + 79.2882926988925M1[t] + 60.6832961939366M2[t] + 44.0736579306548M3[t] + 45.6598105362746M4[t] + 63.6943256675065M5[t] + 78.8140598459922M6[t] + 48.70465990289M7[t] + 40.1346426021993M8[t] + 56.910689036992M9[t] + 40.5558293597744M10[t] + 19.6090020272143M11[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) | 966.129982902622 | 87.792906 | 11.0046 | 0 | 0 |
| Gold | 0.43035784722686 | 0.100599 | 4.278 | 9.2e-05 | 4.6e-05 |
| M1 | 79.2882926988925 | 85.72947 | 0.9249 | 0.35976 | 0.17988 |
| M2 | 60.6832961939366 | 85.608012 | 0.7089 | 0.481919 | 0.240959 |
| M3 | 44.0736579306548 | 85.539391 | 0.5152 | 0.608798 | 0.304399 |
| M4 | 45.6598105362746 | 85.58575 | 0.5335 | 0.596203 | 0.298102 |
| M5 | 63.6943256675065 | 85.570508 | 0.7443 | 0.460371 | 0.230185 |
| M6 | 78.8140598459922 | 85.581723 | 0.9209 | 0.361794 | 0.180897 |
| M7 | 48.70465990289 | 85.546944 | 0.5693 | 0.571842 | 0.285921 |
| M8 | 40.1346426021993 | 85.549242 | 0.4691 | 0.641138 | 0.320569 |
| M9 | 56.910689036992 | 85.607917 | 0.6648 | 0.509438 | 0.254719 |
| M10 | 40.5558293597744 | 85.519799 | 0.4742 | 0.637534 | 0.318767 |
| M11 | 19.6090020272143 | 85.559441 | 0.2292 | 0.819719 | 0.409859 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.539236875404102 |
| R-squared | 0.290776407795579 |
| Adjusted R-squared | 0.109698043828493 |
| F-TEST (value) | 1.60580425747845 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 47 |
| p-value | 0.122579274521098 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 135.206812857309 |
| Sum Squared Residuals | 859201.465422471 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1111.92 | 1224.55472950969 | -112.634729509693 |
| 2 | 1131.13 | 1198.24632753938 | -67.1163275393772 |
| 3 | 1144.94 | 1182.34677972402 | -37.4067797240199 |
| 4 | 1113.89 | 1195.66018366657 | -81.7701836665715 |
| 5 | 1107.3 | 1198.20181629764 | -90.9018162976366 |
| 6 | 1120.68 | 1215.88217966712 | -95.2021796671222 |
| 7 | 1140.84 | 1184.73992089068 | -43.8999208906755 |
| 8 | 1101.72 | 1174.74972269414 | -73.0297226941361 |
| 9 | 1104.24 | 1198.47604836164 | -94.2360483616427 |
| 10 | 1114.58 | 1186.61842818795 | -72.0384281879458 |
| 11 | 1130.2 | 1170.40553717488 | -40.2055371748809 |
| 12 | 1173.78 | 1161.01753401930 | 12.7624659806953 |
| 13 | 1211.92 | 1229.50384475280 | -17.5838447528029 |
| 14 | 1181.27 | 1207.95089699434 | -26.6808969943431 |
| 15 | 1203.6 | 1196.74224971376 | 6.85775028624147 |
| 16 | 1180.59 | 1195.61714788185 | -15.027147881849 |
| 17 | 1156.85 | 1213.9744313985 | -57.1244313985011 |
| 18 | 1191.5 | 1223.69317459429 | -32.1931745942897 |
| 19 | 1191.33 | 1201.00744751585 | -9.67744751585082 |
| 20 | 1234.18 | 1192.02859026029 | 42.1514097397056 |
| 21 | 1220.33 | 1212.22598158054 | 8.1040184194591 |
| 22 | 1228.81 | 1207.27560485483 | 21.5343951451650 |
| 23 | 1207.01 | 1183.48841573058 | 23.5215842694224 |
| 24 | 1249.48 | 1181.20131705424 | 68.2786829457556 |
| 25 | 1248.29 | 1273.50793463175 | -25.2179346317495 |
| 26 | 1280.08 | 1271.36412578322 | 8.715874216779 |
| 27 | 1280.66 | 1253.03305613103 | 27.6269438689684 |
| 28 | 1302.88 | 1264.40984976106 | 38.4701502389376 |
| 29 | 1310.61 | 1314.29084558708 | -3.68084558708223 |
| 30 | 1270.05 | 1313.9176972654 | -43.8676972654009 |
| 31 | 1270.06 | 1282.92606373548 | -12.8660637354836 |
| 32 | 1278.53 | 1280.51016365014 | -1.98016365013698 |
| 33 | 1303.8 | 1290.31441295985 | 13.4855870401454 |
| 34 | 1335.83 | 1265.15873530685 | 70.6712646931523 |
| 35 | 1377.76 | 1250.02173891185 | 127.73826108815 |
| 36 | 1400.63 | 1245.32463629105 | 155.305363708954 |
| 37 | 1418.03 | 1320.73970836490 | 97.2902916351026 |
| 38 | 1437.9 | 1310.93552983573 | 126.964470164269 |
| 39 | 1406.8 | 1298.71554161416 | 108.084458385837 |
| 40 | 1420.83 | 1295.07284637598 | 125.757153624024 |
| 41 | 1482.37 | 1319.71335446214 | 162.656645537859 |
| 42 | 1530.63 | 1331.77754792532 | 198.852452074685 |
| 43 | 1504.66 | 1296.61144327730 | 208.048556722702 |
| 44 | 1455.18 | 1292.77536229610 | 162.404637703898 |
| 45 | 1473.96 | 1312.24114527606 | 161.718854723937 |
| 46 | 1527.29 | 1326.22651382834 | 201.063486171661 |
| 47 | 1545.79 | 1325.82927370086 | 219.960726299138 |
| 48 | 1479.63 | 1303.63812459029 | 175.991875409714 |
| 49 | 1467.97 | 1409.82378274086 | 58.1462172591427 |
| 50 | 1378.6 | 1420.48311984733 | -41.8831198473281 |
| 51 | 1330.45 | 1435.61237281703 | -105.162372817027 |
| 52 | 1326.41 | 1393.83997231454 | -67.4299723145406 |
| 53 | 1385.97 | 1396.91955225464 | -10.9495522546392 |
| 54 | 1399.62 | 1427.20940054787 | -27.5894005478719 |
| 55 | 1276.69 | 1418.29512458069 | -141.605124580692 |
| 56 | 1269.42 | 1398.96616109933 | -129.54616109933 |
| 57 | 1287.83 | 1376.9024118219 | -89.0724118218989 |
| 58 | 1164.17 | 1385.40071782203 | -221.230717822032 |
| 59 | 968.67 | 1299.68503448183 | -331.01503448183 |
| 60 | 888.61 | 1300.94838804512 | -412.338388045118 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0261477322182245 | 0.052295464436449 | 0.973852267781776 |
| 17 | 0.00694502732620366 | 0.0138900546524073 | 0.993054972673796 |
| 18 | 0.00189743461728283 | 0.00379486923456566 | 0.998102565382717 |
| 19 | 0.000451033835614018 | 0.000902067671228036 | 0.999548966164386 |
| 20 | 0.000149900895380581 | 0.000299801790761163 | 0.99985009910462 |
| 21 | 4.44691646432391e-05 | 8.89383292864782e-05 | 0.999955530835357 |
| 22 | 8.66445843210221e-06 | 1.73289168642044e-05 | 0.999991335541568 |
| 23 | 1.57261827453181e-06 | 3.14523654906362e-06 | 0.999998427381726 |
| 24 | 3.68782019236857e-07 | 7.37564038473714e-07 | 0.99999963121798 |
| 25 | 2.70900057744506e-06 | 5.41800115489012e-06 | 0.999997290999423 |
| 26 | 2.20614485988824e-06 | 4.41228971977648e-06 | 0.99999779385514 |
| 27 | 8.47269116020372e-07 | 1.69453823204074e-06 | 0.999999152730884 |
| 28 | 2.01188439286955e-07 | 4.0237687857391e-07 | 0.99999979881156 |
| 29 | 8.94396251969942e-08 | 1.78879250393988e-07 | 0.999999910560375 |
| 30 | 8.03497798793192e-08 | 1.60699559758638e-07 | 0.99999991965022 |
| 31 | 4.45784081335017e-08 | 8.91568162670033e-08 | 0.999999955421592 |
| 32 | 1.9931616406731e-08 | 3.9863232813462e-08 | 0.999999980068384 |
| 33 | 5.21678241684605e-09 | 1.04335648336921e-08 | 0.999999994783218 |
| 34 | 2.10739001335331e-09 | 4.21478002670661e-09 | 0.99999999789261 |
| 35 | 1.55453700447082e-09 | 3.10907400894164e-09 | 0.999999998445463 |
| 36 | 7.45988643266476e-10 | 1.49197728653295e-09 | 0.999999999254011 |
| 37 | 6.6279610160492e-10 | 1.32559220320984e-09 | 0.999999999337204 |
| 38 | 3.61574508232931e-10 | 7.23149016465861e-10 | 0.999999999638425 |
| 39 | 8.63274522516247e-11 | 1.72654904503249e-10 | 0.999999999913673 |
| 40 | 3.29534367840143e-11 | 6.59068735680287e-11 | 0.999999999967047 |
| 41 | 6.50325314630043e-11 | 1.30065062926009e-10 | 0.999999999934967 |
| 42 | 2.23947639891672e-10 | 4.47895279783344e-10 | 0.999999999776052 |
| 43 | 2.05135208348553e-10 | 4.10270416697106e-10 | 0.999999999794865 |
| 44 | 4.29151088698244e-11 | 8.58302177396488e-11 | 0.999999999957085 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 27 | 0.93103448275862 | NOK |
| 5% type I error level | 28 | 0.96551724137931 | NOK |
| 10% type I error level | 29 | 1 | NOK |
