| Multiple Linear Regression - Estimated Regression Equation |
| Dow [t] = + 5080.60794199417 + 1.82721379285696Bel20[t] -154.281007233768M1[t] -100.885510061914M2[t] -2.12146594401014M3[t] -263.807037356975M4[t] -379.610319780344M5[t] -487.750308038608M6[t] -428.770878933044M7[t] -177.896813632340M8[t] -105.478380888990M9[t] -69.6836007931012M10[t] + 21.5842920134465M11[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) | 5080.60794199417 | 408.727323 | 12.4303 | 0 | 0 |
| Bel20 | 1.82721379285696 | 0.091467 | 19.9767 | 0 | 0 |
| M1 | -154.281007233768 | 376.627695 | -0.4096 | 0.683933 | 0.341966 |
| M2 | -100.885510061914 | 376.697779 | -0.2678 | 0.790013 | 0.395007 |
| M3 | -2.12146594401014 | 376.651466 | -0.0056 | 0.99553 | 0.497765 |
| M4 | -263.807037356975 | 376.625732 | -0.7004 | 0.4871 | 0.24355 |
| M5 | -379.610319780344 | 376.620886 | -1.0079 | 0.318646 | 0.159323 |
| M6 | -487.750308038608 | 376.642898 | -1.295 | 0.201648 | 0.100824 |
| M7 | -428.770878933044 | 376.684482 | -1.1383 | 0.260774 | 0.130387 |
| M8 | -177.896813632340 | 376.71598 | -0.4722 | 0.638948 | 0.319474 |
| M9 | -105.478380888990 | 376.62779 | -0.2801 | 0.78066 | 0.39033 |
| M10 | -69.6836007931012 | 376.698919 | -0.185 | 0.854037 | 0.427018 |
| M11 | 21.5842920134465 | 376.657238 | 0.0573 | 0.954545 | 0.477273 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.946364785215958 |
| R-squared | 0.895606306696847 |
| Adjusted R-squared | 0.868952597768382 |
| F-TEST (value) | 33.6015640112431 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 47 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 595.489598070232 |
| Sum Squared Residuals | 16666569.4862628 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10001.6 | 9963.51683035672 | 38.0831696432784 |
| 2 | 10411.75 | 10185.9478755058 | 225.802124494193 |
| 3 | 10673.38 | 10416.5819390542 | 256.798060945796 |
| 4 | 10539.51 | 10265.2783528677 | 274.231647132273 |
| 5 | 10723.78 | 10329.8758882131 | 393.904111786874 |
| 6 | 10682.06 | 10268.5856616037 | 413.474338396285 |
| 7 | 10283.19 | 10351.4833192578 | -68.2933192577764 |
| 8 | 10377.18 | 10496.2876238831 | -119.107623883133 |
| 9 | 10486.64 | 10634.5771138590 | -147.937113858977 |
| 10 | 10545.38 | 10788.007917939 | -242.627917938998 |
| 11 | 10554.27 | 11053.7199115496 | -499.449911549598 |
| 12 | 10532.54 | 11068.4058133244 | -535.865813324363 |
| 13 | 10324.31 | 10947.5810906378 | -623.271090637807 |
| 14 | 10695.25 | 11126.4513589651 | -431.201358965147 |
| 15 | 10827.81 | 11463.0820946372 | -635.272094637172 |
| 16 | 10872.48 | 11517.2486994575 | -644.768699457461 |
| 17 | 10971.19 | 11668.273447205 | -697.083447204993 |
| 18 | 11145.65 | 11751.8081858174 | -606.158185817426 |
| 19 | 11234.68 | 11769.7666652733 | -535.08666527335 |
| 20 | 11333.88 | 11848.0603878387 | -514.180387838715 |
| 21 | 10997.97 | 11498.5020672597 | -500.532067259678 |
| 22 | 11036.89 | 11774.5571889783 | -737.667188978329 |
| 23 | 11257.35 | 12159.3852497453 | -902.035249745275 |
| 24 | 11533.59 | 12334.8294210156 | -801.239421015595 |
| 25 | 11963.12 | 12488.2877607748 | -525.167760774797 |
| 26 | 12185.15 | 12653.5635584833 | -468.413558483282 |
| 27 | 12377.62 | 12918.8598676822 | -541.23986768217 |
| 28 | 12512.89 | 12936.7745508522 | -423.884550852178 |
| 29 | 12631.48 | 12928.2835344833 | -296.803534483299 |
| 30 | 12268.53 | 12553.9915851575 | -285.461585157487 |
| 31 | 12754.8 | 13041.0689337915 | -286.268933791512 |
| 32 | 13407.75 | 13485.0612248593 | -77.311224859266 |
| 33 | 13480.21 | 13419.4153834143 | 60.7946165856559 |
| 34 | 13673.28 | 13348.2085238005 | 325.071476199471 |
| 35 | 13239.71 | 12781.0947427649 | 458.615257235142 |
| 36 | 13557.69 | 12931.2137308662 | 626.476269133822 |
| 37 | 13901.28 | 13030.4403652534 | 870.839634746616 |
| 38 | 13200.58 | 12480.7639500928 | 719.8160499072 |
| 39 | 13406.97 | 12600.5409528286 | 806.42904717144 |
| 40 | 12538.12 | 11841.5060591379 | 696.613940862145 |
| 41 | 12419.57 | 11500.0236011587 | 919.546398841275 |
| 42 | 12193.88 | 11306.7719944292 | 887.108005570816 |
| 43 | 12656.63 | 11700.533534662 | 956.09646533800 |
| 44 | 12812.48 | 11848.0603878387 | 964.419612161286 |
| 45 | 12056.67 | 11378.3627603793 | 678.307239620669 |
| 46 | 11322.38 | 10552.1328894191 | 770.247110580907 |
| 47 | 11530.75 | 10669.7674772566 | 860.982522743434 |
| 48 | 11114.08 | 10493.4364491261 | 620.643550873937 |
| 49 | 9181.73 | 8942.2139529773 | 239.516047022709 |
| 50 | 8614.55 | 8660.55325695296 | -46.0032569529636 |
| 51 | 8595.56 | 8482.2751457979 | 113.284854202105 |
| 52 | 8396.2 | 8298.39233768478 | 97.8076623152214 |
| 53 | 7690.5 | 8010.06352893986 | -319.563528939856 |
| 54 | 7235.47 | 7644.43257299219 | -408.962572992188 |
| 55 | 7992.12 | 8058.56754701536 | -66.4475470153609 |
| 56 | 8398.37 | 8652.19037558017 | -253.820375580172 |
| 57 | 8593.01 | 8683.64267508767 | -90.6326750876692 |
| 58 | 8679.75 | 8794.77347986305 | -115.023479863052 |
| 59 | 9374.63 | 9292.7426186837 | 81.8873813162975 |
| 60 | 9634.97 | 9544.9845856678 | 89.9854143321996 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.000915297056985617 | 0.00183059411397123 | 0.999084702943014 |
| 17 | 0.000121279413678726 | 0.000242558827357451 | 0.999878720586321 |
| 18 | 1.97790705066177e-05 | 3.95581410132355e-05 | 0.999980220929493 |
| 19 | 0.000982521155222042 | 0.00196504231044408 | 0.999017478844778 |
| 20 | 0.00127346744925903 | 0.00254693489851806 | 0.998726532550741 |
| 21 | 0.000446022142584769 | 0.000892044285169539 | 0.999553977857415 |
| 22 | 0.000163117202090055 | 0.00032623440418011 | 0.99983688279791 |
| 23 | 0.000122305315913707 | 0.000244610631827415 | 0.999877694684086 |
| 24 | 0.000242107932808926 | 0.000484215865617852 | 0.999757892067191 |
| 25 | 0.00324902764204664 | 0.00649805528409329 | 0.996750972357953 |
| 26 | 0.00433259445653402 | 0.00866518891306804 | 0.995667405543466 |
| 27 | 0.00648096452236246 | 0.0129619290447249 | 0.993519035477638 |
| 28 | 0.0114435020521876 | 0.0228870041043751 | 0.988556497947812 |
| 29 | 0.0178006092837947 | 0.0356012185675894 | 0.982199390716205 |
| 30 | 0.0210866116318919 | 0.0421732232637838 | 0.978913388368108 |
| 31 | 0.0765743655196869 | 0.153148731039374 | 0.923425634480313 |
| 32 | 0.252744951453329 | 0.505489902906658 | 0.747255048546671 |
| 33 | 0.540496408433165 | 0.91900718313367 | 0.459503591566835 |
| 34 | 0.852960780583375 | 0.29407843883325 | 0.147039219416625 |
| 35 | 0.969920984139128 | 0.0601580317217447 | 0.0300790158608724 |
| 36 | 0.990246209632509 | 0.0195075807349824 | 0.00975379036749119 |
| 37 | 0.995404907217923 | 0.00919018556415319 | 0.00459509278207659 |
| 38 | 0.994522350856226 | 0.0109552982875484 | 0.0054776491437742 |
| 39 | 0.997566880638166 | 0.0048662387236673 | 0.00243311936183365 |
| 40 | 0.999494603774267 | 0.0010107924514659 | 0.00050539622573295 |
| 41 | 0.998407272111265 | 0.00318545577747081 | 0.00159272788873541 |
| 42 | 0.994704976677784 | 0.0105900466444314 | 0.00529502332221568 |
| 43 | 0.992194551708255 | 0.0156108965834900 | 0.00780544829174499 |
| 44 | 0.970538515341088 | 0.0589229693178248 | 0.0294614846589124 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 15 | 0.517241379310345 | NOK |
| 5% type I error level | 23 | 0.793103448275862 | NOK |
| 10% type I error level | 25 | 0.862068965517241 | NOK |
