| Multiple Linear Regression - Estimated Regression Equation |
| S&P500[t] = + 1050.30650339918 + 0.0886434819321215Gold[t] + 98.9169823147264M1[t] + 83.611958587221M2[t] + 69.76921869153M3[t] + 62.9584613505614M4[t] + 78.6478279445748M5[t] + 89.1124244764496M6[t] + 58.7730879173032M7[t] + 46.2655331371204M8[t] + 54.173103801218M9[t] + 44.0432918683740M10[t] + 13.6299886258529M11[t] + 3.66758313090918t + 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) | 1050.30650339918 | 116.953732 | 8.9805 | 0 | 0 |
| Gold | 0.0886434819321215 | 0.330092 | 0.2685 | 0.789483 | 0.394741 |
| M1 | 98.9169823147264 | 87.450659 | 1.1311 | 0.263868 | 0.131934 |
| M2 | 83.611958587221 | 88.010283 | 0.95 | 0.347065 | 0.173532 |
| M3 | 69.76921869153 | 88.589149 | 0.7876 | 0.434994 | 0.217497 |
| M4 | 62.9584613505614 | 86.892063 | 0.7246 | 0.472392 | 0.236196 |
| M5 | 78.6478279445748 | 86.507707 | 0.9091 | 0.368014 | 0.184007 |
| M6 | 89.1124244764496 | 85.941572 | 1.0369 | 0.305205 | 0.152602 |
| M7 | 58.7730879173032 | 85.883988 | 0.6843 | 0.4972 | 0.2486 |
| M8 | 46.2655331371204 | 85.571244 | 0.5407 | 0.591346 | 0.295673 |
| M9 | 54.173103801218 | 85.480751 | 0.6337 | 0.529385 | 0.264693 |
| M10 | 44.0432918683740 | 85.415983 | 0.5156 | 0.60858 | 0.30429 |
| M11 | 13.6299886258529 | 85.572301 | 0.1593 | 0.874145 | 0.437073 |
| t | 3.66758313090918 | 3.374967 | 1.0867 | 0.28283 | 0.141415 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.555452976967711 |
| R-squared | 0.308528009622292 |
| Adjusted R-squared | 0.113112012341636 |
| F-TEST (value) | 1.57882677936128 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 46 |
| p-value | 0.126606643347300 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 134.947330579272 |
| Sum Squared Residuals | 837695.973401681 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1111.92 | 1189.78891819906 | -77.8689181990577 |
| 2 | 1131.13 | 1176.56475927588 | -45.4347592758774 |
| 3 | 1144.94 | 1166.53586425628 | -21.5958642562836 |
| 4 | 1113.89 | 1165.80822492887 | -51.9182249288745 |
| 5 | 1107.3 | 1181.97400930424 | -74.674009304241 |
| 6 | 1120.68 | 1196.63361768452 | -75.9536176845209 |
| 7 | 1140.84 | 1169.74911989965 | -28.9091198996467 |
| 8 | 1101.72 | 1160.61662476000 | -58.8966247599971 |
| 9 | 1104.24 | 1173.62337078821 | -69.3833707882077 |
| 10 | 1114.58 | 1168.08746637246 | -53.5074663724635 |
| 11 | 1130.2 | 1142.31682456210 | -12.1168245621048 |
| 12 | 1173.78 | 1134.45970176305 | 39.320298236951 |
| 13 | 1211.92 | 1234.81931581219 | -22.8993158121882 |
| 14 | 1181.27 | 1222.57466736436 | -41.3046673643571 |
| 15 | 1203.6 | 1213.51198629782 | -9.91198629782346 |
| 16 | 1180.59 | 1209.81035815159 | -29.2203581515917 |
| 17 | 1156.85 | 1229.23379048796 | -72.3837904879634 |
| 18 | 1191.5 | 1242.2534944525 | -50.7534944524991 |
| 19 | 1191.33 | 1217.11084108759 | -25.7808410875911 |
| 20 | 1234.18 | 1208.18665813048 | 25.9933418695182 |
| 21 | 1220.33 | 1220.46652760685 | -0.136527606849205 |
| 22 | 1228.81 | 1216.35335107612 | 12.4566489238846 |
| 23 | 1207.01 | 1189.02258398375 | 17.9874160162484 |
| 24 | 1249.48 | 1182.62807863658 | 66.8519213634244 |
| 25 | 1248.29 | 1287.89410941066 | -39.604109410658 |
| 26 | 1280.08 | 1279.64728199797 | 0.432718002034516 |
| 27 | 1280.66 | 1269.11755130545 | 11.5424486945450 |
| 28 | 1302.88 | 1267.99101630935 | 34.8889836906487 |
| 29 | 1310.61 | 1293.90758369725 | 16.7024163027489 |
| 30 | 1270.05 | 1304.84859801048 | -34.7985980104785 |
| 31 | 1270.06 | 1277.99512544428 | -7.93512544428057 |
| 32 | 1278.53 | 1270.42275558664 | 8.10724441336372 |
| 33 | 1303.8 | 1280.56188497434 | 23.2381150256572 |
| 34 | 1335.83 | 1272.28689696690 | 63.543103033104 |
| 35 | 1377.76 | 1246.73786386137 | 131.022136138632 |
| 36 | 1400.63 | 1239.84695501537 | 160.783044984628 |
| 37 | 1418.03 | 1341.63372912362 | 76.3962708763815 |
| 38 | 1437.9 | 1331.80904773253 | 106.090952267466 |
| 39 | 1406.8 | 1322.53805448346 | 84.26194551654 |
| 40 | 1420.83 | 1318.31786196793 | 102.512138032075 |
| 41 | 1482.37 | 1339.03548914051 | 143.334510859494 |
| 42 | 1530.63 | 1352.53830008157 | 178.091699918428 |
| 43 | 1504.66 | 1324.82498574063 | 179.835014259368 |
| 44 | 1455.18 | 1316.96009239261 | 138.219907607388 |
| 45 | 1473.96 | 1329.08926794969 | 144.870732050306 |
| 46 | 1527.29 | 1328.87640462397 | 198.413595376026 |
| 47 | 1545.79 | 1306.36341077462 | 239.426589225379 |
| 48 | 1479.63 | 1295.86914438808 | 183.760855611915 |
| 49 | 1467.97 | 1403.99392745448 | 63.9760725455222 |
| 50 | 1378.6 | 1398.38424362927 | -19.784243629266 |
| 51 | 1330.45 | 1394.74654365698 | -64.296543656978 |
| 52 | 1326.41 | 1382.67253864226 | -56.2625386422572 |
| 53 | 1385.97 | 1398.94912737004 | -12.9791273700387 |
| 54 | 1399.62 | 1416.20598977093 | -16.5859897709299 |
| 55 | 1276.69 | 1393.89992782785 | -117.209927827850 |
| 56 | 1269.42 | 1382.84386913027 | -113.423869130273 |
| 57 | 1287.83 | 1386.41894868091 | -98.588948680906 |
| 58 | 1164.17 | 1385.07588096055 | -220.905880960551 |
| 59 | 968.67 | 1344.98931681815 | -376.319316818155 |
| 60 | 888.61 | 1339.32612019692 | -450.716120196919 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00109057808360239 | 0.00218115616720479 | 0.998909421916398 |
| 18 | 8.58923399562958e-05 | 0.000171784679912592 | 0.999914107660044 |
| 19 | 5.97652863613641e-06 | 1.19530572722728e-05 | 0.999994023471364 |
| 20 | 4.56392914525523e-05 | 9.12785829051046e-05 | 0.999954360708547 |
| 21 | 1.37742626097482e-05 | 2.75485252194964e-05 | 0.99998622573739 |
| 22 | 2.71535982390933e-06 | 5.43071964781867e-06 | 0.999997284640176 |
| 23 | 3.79780465551594e-07 | 7.59560931103189e-07 | 0.999999620219534 |
| 24 | 5.12840642033831e-08 | 1.02568128406766e-07 | 0.999999948715936 |
| 25 | 1.79996093388865e-08 | 3.59992186777730e-08 | 0.99999998200039 |
| 26 | 3.22284136241513e-09 | 6.44568272483025e-09 | 0.999999996777159 |
| 27 | 4.33797053489750e-10 | 8.67594106979499e-10 | 0.999999999566203 |
| 28 | 1.69046912483306e-10 | 3.38093824966611e-10 | 0.999999999830953 |
| 29 | 6.98148417753035e-11 | 1.39629683550607e-10 | 0.999999999930185 |
| 30 | 6.16275344994378e-11 | 1.23255068998876e-10 | 0.999999999938372 |
| 31 | 4.95074615942361e-11 | 9.90149231884722e-11 | 0.999999999950492 |
| 32 | 4.30476165160437e-11 | 8.60952330320873e-11 | 0.999999999956952 |
| 33 | 1.76344787162719e-10 | 3.52689574325437e-10 | 0.999999999823655 |
| 34 | 9.5845089065071e-10 | 1.91690178130142e-09 | 0.99999999904155 |
| 35 | 1.11894447430857e-07 | 2.23788894861714e-07 | 0.999999888105553 |
| 36 | 7.8688147410268e-06 | 1.57376294820536e-05 | 0.99999213118526 |
| 37 | 0.000353611435955858 | 0.000707222871911715 | 0.999646388564044 |
| 38 | 0.000457079719638151 | 0.000914159439276301 | 0.999542920280362 |
| 39 | 0.000194709091825589 | 0.000389418183651179 | 0.999805290908174 |
| 40 | 0.000157233481145535 | 0.00031446696229107 | 0.999842766518855 |
| 41 | 0.00859291468352392 | 0.0171858293670478 | 0.991407085316476 |
| 42 | 0.0525098795499005 | 0.105019759099801 | 0.9474901204501 |
| 43 | 0.112209664759354 | 0.224419329518708 | 0.887790335240646 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 24 | 0.888888888888889 | NOK |
| 5% type I error level | 25 | 0.925925925925926 | NOK |
| 10% type I error level | 25 | 0.925925925925926 | NOK |
