| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 136.045070422535 -39.2704225352113X[t] -20.6778672032194M1[t] -25.3492957746479M2[t] -0.277867203219396M3[t] -48.6921529175051M4[t] -50.5492957746479M5[t] -5.36173708920191M6[t] -9.94507042253522M7[t] -11.0166666666667M8[t] -27.5833333333334M9[t] -21.5M10[t] -16.3M11[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) | 136.045070422535 | 4.826988 | 28.1843 | 0 | 0 |
| X | -39.2704225352113 | 4.027376 | -9.7509 | 0 | 0 |
| M1 | -20.6778672032194 | 6.514871 | -3.1739 | 0.002312 | 0.001156 |
| M2 | -25.3492957746479 | 6.514871 | -3.891 | 0.00024 | 0.00012 |
| M3 | -0.277867203219396 | 6.514871 | -0.0427 | 0.966112 | 0.483056 |
| M4 | -48.6921529175051 | 6.514871 | -7.474 | 0 | 0 |
| M5 | -50.5492957746479 | 6.514871 | -7.7591 | 0 | 0 |
| M6 | -5.36173708920191 | 6.793312 | -0.7893 | 0.43287 | 0.216435 |
| M7 | -9.94507042253522 | 6.793312 | -1.464 | 0.148102 | 0.074051 |
| M8 | -11.0166666666667 | 6.760069 | -1.6297 | 0.108084 | 0.054042 |
| M9 | -27.5833333333334 | 6.760069 | -4.0803 | 0.000127 | 6.4e-05 |
| M10 | -21.5 | 6.760069 | -3.1804 | 0.002268 | 0.001134 |
| M11 | -16.3 | 6.760069 | -2.4112 | 0.01878 | 0.00939 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.894877704308231 |
| R-squared | 0.80080610566797 |
| Adjusted R-squared | 0.763457250480714 |
| F-TEST (value) | 21.4412490464024 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 64 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 11.7087829747050 |
| Sum Squared Residuals | 8774.1183199195 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 105.7 | 115.367203219316 | -9.66720321931598 |
| 2 | 105.7 | 110.695774647887 | -4.99577464788738 |
| 3 | 111.1 | 135.767203219316 | -24.6672032193159 |
| 4 | 82.4 | 87.3529175050302 | -4.95291750503018 |
| 5 | 60 | 85.4957746478872 | -25.4957746478872 |
| 6 | 107.3 | 130.683333333333 | -23.3833333333333 |
| 7 | 99.3 | 126.1 | -26.7999999999999 |
| 8 | 113.5 | 125.028403755869 | -11.5284037558685 |
| 9 | 108.9 | 108.461737089202 | 0.438262910798133 |
| 10 | 100.2 | 114.545070422535 | -14.3450704225352 |
| 11 | 103.9 | 119.745070422535 | -15.8450704225352 |
| 12 | 138.7 | 136.045070422535 | 2.65492957746474 |
| 13 | 120.2 | 115.367203219316 | 4.83279678068412 |
| 14 | 100.2 | 110.695774647887 | -10.4957746478873 |
| 15 | 143.2 | 135.767203219316 | 7.4327967806841 |
| 16 | 70.9 | 87.3529175050302 | -16.4529175050302 |
| 17 | 85.2 | 85.4957746478873 | -0.295774647887331 |
| 18 | 133 | 130.683333333333 | 2.31666666666667 |
| 19 | 136.6 | 126.1 | 10.5000000000000 |
| 20 | 117.9 | 125.028403755869 | -7.12840375586854 |
| 21 | 106.3 | 108.461737089202 | -2.16173708920188 |
| 22 | 122.3 | 114.545070422535 | 7.7549295774648 |
| 23 | 125.5 | 119.745070422535 | 5.75492957746479 |
| 24 | 148.4 | 136.045070422535 | 12.3549295774648 |
| 25 | 126.3 | 115.367203219316 | 10.9327967806841 |
| 26 | 99.6 | 110.695774647887 | -11.0957746478873 |
| 27 | 140.4 | 135.767203219316 | 4.63279678068412 |
| 28 | 80.3 | 87.3529175050302 | -7.05291750503019 |
| 29 | 92.6 | 85.4957746478873 | 7.10422535211266 |
| 30 | 138.5 | 130.683333333333 | 7.81666666666667 |
| 31 | 110.9 | 126.1 | -15.2 |
| 32 | 119.6 | 125.028403755869 | -5.42840375586855 |
| 33 | 105 | 108.461737089202 | -3.46173708920187 |
| 34 | 109 | 114.545070422535 | -5.54507042253521 |
| 35 | 129.4 | 119.745070422535 | 9.6549295774648 |
| 36 | 148.6 | 136.045070422535 | 12.5549295774648 |
| 37 | 101.4 | 115.367203219316 | -13.9672032193159 |
| 38 | 134.8 | 110.695774647887 | 24.1042253521127 |
| 39 | 143.7 | 135.767203219316 | 7.9327967806841 |
| 40 | 81.6 | 87.3529175050302 | -5.75291750503019 |
| 41 | 90.3 | 85.4957746478873 | 4.80422535211267 |
| 42 | 141.5 | 130.683333333333 | 10.8166666666667 |
| 43 | 140.7 | 126.1 | 14.6000000000000 |
| 44 | 140.2 | 125.028403755869 | 15.1715962441314 |
| 45 | 100.2 | 108.461737089202 | -8.26173708920187 |
| 46 | 125.7 | 114.545070422535 | 11.1549295774648 |
| 47 | 119.6 | 119.745070422535 | -0.145070422535225 |
| 48 | 134.7 | 136.045070422535 | -1.34507042253524 |
| 49 | 109 | 115.367203219316 | -6.36720321931588 |
| 50 | 116.3 | 110.695774647887 | 5.60422535211269 |
| 51 | 146.9 | 135.767203219316 | 11.1327967806841 |
| 52 | 97.4 | 87.3529175050302 | 10.0470824949698 |
| 53 | 89.4 | 85.4957746478873 | 3.90422535211267 |
| 54 | 132.1 | 130.683333333333 | 1.41666666666666 |
| 55 | 139.8 | 126.1 | 13.7 |
| 56 | 129 | 125.028403755869 | 3.97159624413146 |
| 57 | 112.5 | 108.461737089202 | 4.03826291079813 |
| 58 | 121.9 | 114.545070422535 | 7.3549295774648 |
| 59 | 121.7 | 119.745070422535 | 1.95492957746479 |
| 60 | 123.1 | 136.045070422535 | -12.9450704225352 |
| 61 | 131.6 | 115.367203219316 | 16.2327967806841 |
| 62 | 119.3 | 110.695774647887 | 8.60422535211269 |
| 63 | 132.5 | 135.767203219316 | -3.26720321931589 |
| 64 | 98.3 | 87.3529175050302 | 10.9470824949698 |
| 65 | 85.1 | 85.4957746478873 | -0.39577464788734 |
| 66 | 131.7 | 130.683333333333 | 1.01666666666666 |
| 67 | 129.3 | 126.1 | 3.20000000000001 |
| 68 | 90.7 | 85.7579812206573 | 4.94201877934273 |
| 69 | 78.6 | 69.1913145539906 | 9.40868544600938 |
| 70 | 68.9 | 75.2746478873239 | -6.37464788732393 |
| 71 | 79.1 | 80.474647887324 | -1.37464788732396 |
| 72 | 83.5 | 96.774647887324 | -13.2746478873240 |
| 73 | 74.1 | 76.0967806841046 | -1.99678068410461 |
| 74 | 59.7 | 71.425352112676 | -11.7253521126760 |
| 75 | 93.3 | 96.4967806841046 | -3.19678068410462 |
| 76 | 61.3 | 48.0824949698189 | 13.2175050301811 |
| 77 | 56.6 | 46.2253521126761 | 10.3746478873239 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.938027844487452 | 0.123944311025096 | 0.0619721555125482 |
| 17 | 0.963983124841072 | 0.0720337503178552 | 0.0360168751589276 |
| 18 | 0.977166447338137 | 0.045667105323727 | 0.0228335526618635 |
| 19 | 0.994930442740934 | 0.0101391145181310 | 0.00506955725906551 |
| 20 | 0.99130757538901 | 0.0173848492219802 | 0.00869242461099011 |
| 21 | 0.983382180400485 | 0.0332356391990299 | 0.0166178195995150 |
| 22 | 0.98395952342713 | 0.0320809531457408 | 0.0160404765728704 |
| 23 | 0.983304470271292 | 0.0333910594574162 | 0.0166955297287081 |
| 24 | 0.979724223486962 | 0.0405515530260765 | 0.0202757765130383 |
| 25 | 0.977039471163037 | 0.0459210576739253 | 0.0229605288369627 |
| 26 | 0.975037985425793 | 0.0499240291484149 | 0.0249620145742075 |
| 27 | 0.967502391838595 | 0.06499521632281 | 0.032497608161405 |
| 28 | 0.961385241163356 | 0.0772295176732883 | 0.0386147588366441 |
| 29 | 0.962263817741625 | 0.0754723645167501 | 0.0377361822583751 |
| 30 | 0.959748453540396 | 0.0805030929192081 | 0.0402515464596041 |
| 31 | 0.975554155504746 | 0.0488916889905081 | 0.0244458444952540 |
| 32 | 0.972562839475185 | 0.0548743210496301 | 0.0274371605248151 |
| 33 | 0.95992812074445 | 0.080143758511099 | 0.0400718792555495 |
| 34 | 0.949297698250104 | 0.101404603499791 | 0.0507023017498956 |
| 35 | 0.943901330566287 | 0.112197338867426 | 0.0560986694337128 |
| 36 | 0.95863499458215 | 0.0827300108357021 | 0.0413650054178511 |
| 37 | 0.97450218477813 | 0.0509956304437394 | 0.0254978152218697 |
| 38 | 0.99678545470379 | 0.00642909059242165 | 0.00321454529621083 |
| 39 | 0.99543029690055 | 0.00913940619890028 | 0.00456970309945014 |
| 40 | 0.997562927254875 | 0.00487414549025082 | 0.00243707274512541 |
| 41 | 0.995980989647354 | 0.00803802070529133 | 0.00401901035264567 |
| 42 | 0.995702353939425 | 0.00859529212114998 | 0.00429764606057499 |
| 43 | 0.99606802783494 | 0.0078639443301192 | 0.0039319721650596 |
| 44 | 0.99641301605494 | 0.00717396789012188 | 0.00358698394506094 |
| 45 | 0.997834347903726 | 0.00433130419254821 | 0.00216565209627410 |
| 46 | 0.99736562147541 | 0.00526875704917866 | 0.00263437852458933 |
| 47 | 0.994865997292135 | 0.0102680054157307 | 0.00513400270786537 |
| 48 | 0.99384042122205 | 0.0123191575558994 | 0.00615957877794969 |
| 49 | 0.996024118426953 | 0.00795176314609357 | 0.00397588157304679 |
| 50 | 0.99303250933156 | 0.0139349813368817 | 0.00696749066844085 |
| 51 | 0.994352533110022 | 0.0112949337799565 | 0.00564746688997827 |
| 52 | 0.990973112712228 | 0.018053774575544 | 0.009026887287772 |
| 53 | 0.9828149392532 | 0.0343701214936017 | 0.0171850607468009 |
| 54 | 0.966574044731 | 0.0668519105380015 | 0.0334259552690007 |
| 55 | 0.960728901842932 | 0.078542196314136 | 0.039271098157068 |
| 56 | 0.932134242851356 | 0.135731514297289 | 0.0678657571486444 |
| 57 | 0.908967570020208 | 0.182064859959585 | 0.0910324299797923 |
| 58 | 0.870148956253278 | 0.259702087493444 | 0.129851043746722 |
| 59 | 0.775257049827581 | 0.449485900344838 | 0.224742950172419 |
| 60 | 0.667595007514385 | 0.66480998497123 | 0.332404992485615 |
| 61 | 0.650189773513047 | 0.699620452973906 | 0.349810226486953 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 10 | 0.217391304347826 | NOK |
| 5% type I error level | 26 | 0.565217391304348 | NOK |
| 10% type I error level | 37 | 0.804347826086957 | NOK |
