| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 129.806666666667 -4.99103174603175M1[t] -6.33730158730159M2[t] -6.91690476190476M3[t] -3.69650793650794M4[t] -2.87611111111111M5[t] -1.30571428571429M6[t] + 0.314682539682539M7[t] -0.964920634920632M8[t] -1.44452380952381M9[t] -0.840793650793654M10[t] + 1.17960317460317M11[t] -0.920396825396825t + 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) | 129.806666666667 | 6.944222 | 18.6928 | 0 | 0 |
| M1 | -4.99103174603175 | 8.502817 | -0.587 | 0.559453 | 0.279726 |
| M2 | -6.33730158730159 | 8.494061 | -0.7461 | 0.458578 | 0.229289 |
| M3 | -6.91690476190476 | 8.48613 | -0.8151 | 0.418303 | 0.209151 |
| M4 | -3.69650793650794 | 8.479028 | -0.436 | 0.664458 | 0.332229 |
| M5 | -2.87611111111111 | 8.472757 | -0.3395 | 0.735473 | 0.367737 |
| M6 | -1.30571428571429 | 8.467318 | -0.1542 | 0.877973 | 0.438987 |
| M7 | 0.314682539682539 | 8.462713 | 0.0372 | 0.970463 | 0.485232 |
| M8 | -0.964920634920632 | 8.458944 | -0.1141 | 0.909569 | 0.454784 |
| M9 | -1.44452380952381 | 8.456011 | -0.1708 | 0.864943 | 0.432472 |
| M10 | -0.840793650793654 | 8.453915 | -0.0995 | 0.921113 | 0.460557 |
| M11 | 1.17960317460317 | 8.452658 | 0.1396 | 0.889488 | 0.444744 |
| t | -0.920396825396825 | 0.084186 | -10.9329 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.81915668734884 |
| R-squared | 0.671017678428325 |
| Adjusted R-squared | 0.604106019803578 |
| F-TEST (value) | 10.0284119721424 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 59 |
| p-value | 2.5357738131504e-10 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 14.6397064190342 |
| Sum Squared Residuals | 12644.9392380952 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 112.8 | 123.895238095238 | -11.0952380952381 |
| 2 | 116.7 | 121.628571428571 | -4.92857142857143 |
| 3 | 119.4 | 120.128571428571 | -0.728571428571423 |
| 4 | 129.8 | 122.428571428571 | 7.37142857142859 |
| 5 | 131.9 | 122.328571428571 | 9.57142857142857 |
| 6 | 129.8 | 122.978571428571 | 6.82142857142858 |
| 7 | 131.6 | 123.678571428571 | 7.92142857142857 |
| 8 | 134.3 | 121.478571428571 | 12.8214285714286 |
| 9 | 136.7 | 120.078571428571 | 16.6214285714286 |
| 10 | 134.7 | 119.761904761905 | 14.9380952380952 |
| 11 | 138.1 | 120.861904761905 | 17.2380952380952 |
| 12 | 132.4 | 118.761904761905 | 13.6380952380952 |
| 13 | 125 | 112.850476190476 | 12.1495238095238 |
| 14 | 117.7 | 110.58380952381 | 7.11619047619049 |
| 15 | 112 | 109.08380952381 | 2.91619047619047 |
| 16 | 106.3 | 111.38380952381 | -5.08380952380953 |
| 17 | 100.5 | 111.28380952381 | -10.7838095238095 |
| 18 | 95.6 | 111.93380952381 | -16.3338095238095 |
| 19 | 89.5 | 112.63380952381 | -23.1338095238095 |
| 20 | 87.7 | 110.43380952381 | -22.7338095238095 |
| 21 | 88.2 | 109.03380952381 | -20.8338095238095 |
| 22 | 88.7 | 108.717142857143 | -20.0171428571429 |
| 23 | 91.4 | 109.817142857143 | -18.4171428571429 |
| 24 | 95.7 | 107.717142857143 | -12.0171428571429 |
| 25 | 96.8 | 101.805714285714 | -5.00571428571429 |
| 26 | 93.8 | 99.5390476190476 | -5.73904761904763 |
| 27 | 91 | 98.0390476190476 | -7.03904761904763 |
| 28 | 86.8 | 100.339047619048 | -13.5390476190476 |
| 29 | 91.5 | 100.239047619048 | -8.73904761904762 |
| 30 | 89.3 | 100.889047619048 | -11.5890476190476 |
| 31 | 97.9 | 101.589047619048 | -3.68904761904761 |
| 32 | 95.7 | 99.3890476190476 | -3.68904761904762 |
| 33 | 86.9 | 97.9890476190476 | -11.0890476190476 |
| 34 | 82 | 97.6723809523809 | -15.6723809523809 |
| 35 | 83.2 | 98.772380952381 | -15.5723809523809 |
| 36 | 85.7 | 96.6723809523809 | -10.9723809523809 |
| 37 | 77.8 | 90.7609523809524 | -12.9609523809524 |
| 38 | 79.4 | 88.4942857142857 | -9.09428571428571 |
| 39 | 83.4 | 86.9942857142857 | -3.59428571428571 |
| 40 | 102.8 | 89.2942857142857 | 13.5057142857143 |
| 41 | 108.7 | 89.1942857142857 | 19.5057142857143 |
| 42 | 120.3 | 89.8442857142857 | 30.4557142857143 |
| 43 | 121.9 | 90.5442857142857 | 31.3557142857143 |
| 44 | 112.7 | 88.3442857142857 | 24.3557142857143 |
| 45 | 113.1 | 86.9442857142857 | 26.1557142857143 |
| 46 | 115.7 | 86.627619047619 | 29.072380952381 |
| 47 | 113.5 | 87.727619047619 | 25.772380952381 |
| 48 | 103.1 | 85.627619047619 | 17.4723809523809 |
| 49 | 95.9 | 79.7161904761905 | 16.1838095238095 |
| 50 | 88.5 | 77.4495238095238 | 11.0504761904762 |
| 51 | 86.2 | 75.9495238095238 | 10.2504761904762 |
| 52 | 83.8 | 78.2495238095238 | 5.5504761904762 |
| 53 | 76.4 | 78.1495238095238 | -1.7495238095238 |
| 54 | 76 | 78.7995238095238 | -2.79952380952381 |
| 55 | 75.7 | 79.4995238095238 | -3.7995238095238 |
| 56 | 71.5 | 77.2995238095238 | -5.79952380952381 |
| 57 | 69.7 | 75.8995238095238 | -6.1995238095238 |
| 58 | 72.1 | 75.5828571428571 | -3.48285714285714 |
| 59 | 72.6 | 76.6828571428571 | -4.08285714285715 |
| 60 | 70.2 | 74.5828571428571 | -4.38285714285714 |
| 61 | 69.4 | 68.6714285714286 | 0.728571428571433 |
| 62 | 68 | 66.4047619047619 | 1.59523809523809 |
| 63 | 63.1 | 64.9047619047619 | -1.80476190476191 |
| 64 | 59.4 | 67.2047619047619 | -7.80476190476191 |
| 65 | 59.3 | 67.1047619047619 | -7.80476190476191 |
| 66 | 61.2 | 67.7547619047619 | -6.55476190476189 |
| 67 | 59.8 | 68.4547619047619 | -8.65476190476191 |
| 68 | 61.3 | 66.2547619047619 | -4.95476190476193 |
| 69 | 60.2 | 64.8547619047619 | -4.65476190476191 |
| 70 | 59.7 | 64.5380952380952 | -4.83809523809524 |
| 71 | 60.7 | 65.6380952380952 | -4.93809523809524 |
| 72 | 59.8 | 63.5380952380952 | -3.73809523809524 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.318873622070317 | 0.637747244140633 | 0.681126377929683 |
| 17 | 0.395346616235721 | 0.790693232471443 | 0.604653383764279 |
| 18 | 0.413465768883137 | 0.826931537766274 | 0.586534231116863 |
| 19 | 0.485333293874861 | 0.970666587749722 | 0.514666706125139 |
| 20 | 0.549394950839641 | 0.901210098320719 | 0.450605049160359 |
| 21 | 0.583210639158538 | 0.833578721682923 | 0.416789360841462 |
| 22 | 0.573654259337667 | 0.852691481324666 | 0.426345740662333 |
| 23 | 0.554314421788755 | 0.89137115642249 | 0.445685578211245 |
| 24 | 0.472782998609391 | 0.945565997218782 | 0.527217001390609 |
| 25 | 0.459084844945297 | 0.918169689890595 | 0.540915155054703 |
| 26 | 0.411964265071544 | 0.823928530143088 | 0.588035734928456 |
| 27 | 0.352923822145329 | 0.705847644290657 | 0.647076177854671 |
| 28 | 0.299044986775281 | 0.598089973550561 | 0.700955013224719 |
| 29 | 0.253580483229293 | 0.507160966458585 | 0.746419516770707 |
| 30 | 0.234835290895179 | 0.469670581790358 | 0.765164709104821 |
| 31 | 0.238214882225075 | 0.47642976445015 | 0.761785117774925 |
| 32 | 0.219526432311116 | 0.439052864622231 | 0.780473567688884 |
| 33 | 0.205579422784574 | 0.411158845569147 | 0.794420577215426 |
| 34 | 0.244275063710492 | 0.488550127420983 | 0.755724936289508 |
| 35 | 0.331244058197795 | 0.662488116395589 | 0.668755941802205 |
| 36 | 0.431278808954744 | 0.862557617909488 | 0.568721191045256 |
| 37 | 0.644046883127688 | 0.711906233744623 | 0.355953116872312 |
| 38 | 0.847751914964477 | 0.304496170071047 | 0.152248085035523 |
| 39 | 0.957438698571071 | 0.0851226028578572 | 0.0425613014289286 |
| 40 | 0.97491897118879 | 0.0501620576224192 | 0.0250810288112096 |
| 41 | 0.982518044191135 | 0.0349639116177292 | 0.0174819558088646 |
| 42 | 0.995175742606012 | 0.00964851478797616 | 0.00482425739398808 |
| 43 | 0.998784689850785 | 0.00243062029842981 | 0.0012153101492149 |
| 44 | 0.998946809249652 | 0.00210638150069593 | 0.00105319075034797 |
| 45 | 0.999359600139012 | 0.00128079972197686 | 0.000640399860988428 |
| 46 | 0.999848424762154 | 0.000303150475692109 | 0.000151575237846055 |
| 47 | 0.999981712436681 | 3.65751266386637e-05 | 1.82875633193318e-05 |
| 48 | 0.999992044014577 | 1.59119708459586e-05 | 7.95598542297929e-06 |
| 49 | 0.999993376036124 | 1.32479277512967e-05 | 6.62396387564833e-06 |
| 50 | 0.999979717542638 | 4.05649147239065e-05 | 2.02824573619532e-05 |
| 51 | 0.999974274456637 | 5.1451086726094e-05 | 2.5725543363047e-05 |
| 52 | 0.999997203404371 | 5.59319125879757e-06 | 2.79659562939879e-06 |
| 53 | 0.999994203231254 | 1.15935374918616e-05 | 5.79676874593078e-06 |
| 54 | 0.99996988694874 | 6.02261025191907e-05 | 3.01130512595953e-05 |
| 55 | 0.999984461576694 | 3.10768466112475e-05 | 1.55384233056237e-05 |
| 56 | 0.99973238866906 | 0.000535222661879657 | 0.000267611330939829 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 15 | 0.365853658536585 | NOK |
| 5% type I error level | 16 | 0.390243902439024 | NOK |
| 10% type I error level | 18 | 0.439024390243902 | NOK |
