| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -54.694704417963 + 1.38126912837142X[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) | -54.694704417963 | 7.547577 | -7.2467 | 0 | 0 |
| X | 1.38126912837142 | 0.043034 | 32.0971 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.972986203223003 |
| R-squared | 0.946702151662315 |
| Adjusted R-squared | 0.9457832232427 |
| F-TEST (value) | 1030.22404297680 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 58 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 14.7658230603976 |
| Sum Squared Residuals | 12645.7127777562 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 108.2 | 95.172996010336 | 13.0270039896641 |
| 2 | 108.8 | 100.421818698147 | 8.37818130185281 |
| 3 | 110.2 | 106.361275950144 | 3.83872404985563 |
| 4 | 109.5 | 104.841879908936 | 4.65812009106418 |
| 5 | 109.5 | 111.195717899444 | -1.69571789944433 |
| 6 | 116 | 128.875962742598 | -12.8759627425985 |
| 7 | 111.2 | 122.245870926416 | -11.0458709264157 |
| 8 | 112.1 | 123.903393880461 | -11.8033938804614 |
| 9 | 114 | 128.32345509125 | -14.3234550912499 |
| 10 | 119.1 | 126.251551398693 | -7.1515513986928 |
| 11 | 114.1 | 117.825809715627 | -3.72580971562716 |
| 12 | 115.1 | 112.162606289304 | 2.93739371069566 |
| 13 | 115.4 | 113.82012924335 | 1.57987075664997 |
| 14 | 110.8 | 113.958256156187 | -3.15825615618717 |
| 15 | 116 | 121.278982536556 | -5.2789825365557 |
| 16 | 119.2 | 132.052881737853 | -12.8528817378527 |
| 17 | 126.5 | 134.953546907433 | -8.45354690743275 |
| 18 | 127.8 | 131.776627912178 | -3.97662791217847 |
| 19 | 131.3 | 133.15789704055 | -1.85789704054988 |
| 20 | 140.3 | 136.472942948641 | 3.82705705135871 |
| 21 | 137.3 | 131.362247173667 | 5.93775282633298 |
| 22 | 143 | 136.472942948641 | 6.5270570513587 |
| 23 | 134.5 | 130.25723187097 | 4.24276812903008 |
| 24 | 139.9 | 129.842851132458 | 10.0571488675415 |
| 25 | 159.3 | 140.340496508081 | 18.9595034919188 |
| 26 | 170.4 | 154.981949268818 | 15.4180507311817 |
| 27 | 175 | 159.954518130955 | 15.0454818690446 |
| 28 | 175.8 | 161.612041085001 | 14.1879589149989 |
| 29 | 180.9 | 168.518386726858 | 12.3816132731418 |
| 30 | 180.3 | 167.275244511324 | 13.0247554886761 |
| 31 | 169.6 | 160.783279607978 | 8.81672039202175 |
| 32 | 172.3 | 165.617721557278 | 6.6822784427218 |
| 33 | 184.8 | 178.325397538295 | 6.47460246170478 |
| 34 | 177.7 | 179.982920492341 | -2.28292049234097 |
| 35 | 184.6 | 179.982920492341 | 4.61707950765903 |
| 36 | 211.4 | 202.083226546284 | 9.31677345371636 |
| 37 | 215.3 | 208.851445275304 | 6.44855472469642 |
| 38 | 215.9 | 215.757790917161 | 0.14220908283931 |
| 39 | 244.7 | 237.996223883941 | 6.70377611605949 |
| 40 | 259.3 | 258.991514635186 | 0.308485364813961 |
| 41 | 289 | 292.418227541774 | -3.41822754177437 |
| 42 | 310.9 | 299.87708083498 | 11.0229191650200 |
| 43 | 321 | 293.246989018797 | 27.7530109812028 |
| 44 | 315.1 | 292.280100628937 | 22.8198993710628 |
| 45 | 333.2 | 318.662340980831 | 14.5376590191687 |
| 46 | 314.1 | 314.38040668288 | -0.280406682879869 |
| 47 | 284.7 | 280.953693776292 | 3.74630622370839 |
| 48 | 273.9 | 262.859068194626 | 11.0409318053739 |
| 49 | 216 | 203.878876413166 | 12.1211235868335 |
| 50 | 196.4 | 191.447454257824 | 4.9525457421763 |
| 51 | 190.9 | 187.303646872709 | 3.59635312729055 |
| 52 | 206.4 | 211.061475880698 | -4.66147588069786 |
| 53 | 196.3 | 203.602622587492 | -7.30262258749218 |
| 54 | 199.5 | 199.458815202378 | 0.0411847976220543 |
| 55 | 198.9 | 213.409633398929 | -14.5096333989292 |
| 56 | 214.4 | 239.101239186638 | -24.7012391866376 |
| 57 | 214.2 | 245.731331002820 | -31.5313310028204 |
| 58 | 187.6 | 222.249755820506 | -34.6497558205063 |
| 59 | 180.6 | 229.708609113712 | -49.108609113712 |
| 60 | 172.2 | 216.724679307021 | -44.5246793070207 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 5.32633432902799e-05 | 0.000106526686580560 | 0.99994673665671 |
| 6 | 3.67566274439432e-05 | 7.35132548878864e-05 | 0.999963243372556 |
| 7 | 1.26819185214159e-05 | 2.53638370428317e-05 | 0.999987318081479 |
| 8 | 1.29560165374478e-06 | 2.59120330748957e-06 | 0.999998704398346 |
| 9 | 9.9033352498121e-08 | 1.98066704996242e-07 | 0.999999900966647 |
| 10 | 1.37164895890241e-06 | 2.74329791780481e-06 | 0.99999862835104 |
| 11 | 2.17683158923165e-07 | 4.35366317846331e-07 | 0.99999978231684 |
| 12 | 1.06374520001497e-07 | 2.12749040002995e-07 | 0.99999989362548 |
| 13 | 3.68644907866256e-08 | 7.37289815732512e-08 | 0.99999996313551 |
| 14 | 6.22716377146135e-09 | 1.24543275429227e-08 | 0.999999993772836 |
| 15 | 1.22441854958749e-09 | 2.44883709917498e-09 | 0.999999998775581 |
| 16 | 3.01303856864222e-10 | 6.02607713728445e-10 | 0.999999999698696 |
| 17 | 3.25135899330630e-09 | 6.50271798661261e-09 | 0.99999999674864 |
| 18 | 1.64477215476875e-08 | 3.2895443095375e-08 | 0.999999983552278 |
| 19 | 8.66746283068959e-08 | 1.73349256613792e-07 | 0.999999913325372 |
| 20 | 2.38028094233192e-06 | 4.76056188466385e-06 | 0.999997619719058 |
| 21 | 7.54636980244194e-06 | 1.50927396048839e-05 | 0.999992453630198 |
| 22 | 2.07946122459713e-05 | 4.15892244919427e-05 | 0.999979205387754 |
| 23 | 1.53563995989539e-05 | 3.07127991979079e-05 | 0.9999846436004 |
| 24 | 2.64764940408655e-05 | 5.29529880817309e-05 | 0.999973523505959 |
| 25 | 0.000304314973414154 | 0.000608629946828309 | 0.999695685026586 |
| 26 | 0.000617057557212414 | 0.00123411511442483 | 0.999382942442788 |
| 27 | 0.000680099842254827 | 0.00136019968450965 | 0.999319900157745 |
| 28 | 0.000558254465916214 | 0.00111650893183243 | 0.999441745534084 |
| 29 | 0.00036364230617476 | 0.00072728461234952 | 0.999636357693825 |
| 30 | 0.00025171437271054 | 0.00050342874542108 | 0.99974828562729 |
| 31 | 0.000151820693609304 | 0.000303641387218608 | 0.99984817930639 |
| 32 | 8.99472904022848e-05 | 0.000179894580804570 | 0.999910052709598 |
| 33 | 5.59921379925886e-05 | 0.000111984275985177 | 0.999944007862007 |
| 34 | 4.56150396589783e-05 | 9.12300793179565e-05 | 0.999954384960341 |
| 35 | 2.86814370405655e-05 | 5.7362874081131e-05 | 0.99997131856296 |
| 36 | 2.00398841299929e-05 | 4.00797682599859e-05 | 0.99997996011587 |
| 37 | 1.34093529289311e-05 | 2.68187058578621e-05 | 0.999986590647071 |
| 38 | 9.67818202034328e-06 | 1.93563640406866e-05 | 0.99999032181798 |
| 39 | 5.39636822420693e-06 | 1.07927364484139e-05 | 0.999994603631776 |
| 40 | 3.26235697250277e-06 | 6.52471394500555e-06 | 0.999996737643027 |
| 41 | 2.51278327933808e-06 | 5.02556655867617e-06 | 0.99999748721672 |
| 42 | 1.06542646860194e-06 | 2.13085293720389e-06 | 0.999998934573531 |
| 43 | 4.70746855102879e-06 | 9.41493710205758e-06 | 0.999995292531449 |
| 44 | 8.70510066233932e-06 | 1.74102013246786e-05 | 0.999991294899338 |
| 45 | 7.74823863091375e-06 | 1.54964772618275e-05 | 0.99999225176137 |
| 46 | 8.71832825284645e-06 | 1.74366565056929e-05 | 0.999991281671747 |
| 47 | 2.3531303258829e-05 | 4.7062606517658e-05 | 0.99997646869674 |
| 48 | 0.0159111644243968 | 0.0318223288487936 | 0.984088835575603 |
| 49 | 0.0364476221556426 | 0.0728952443112853 | 0.963552377844357 |
| 50 | 0.0230244179202818 | 0.0460488358405637 | 0.976975582079718 |
| 51 | 0.0125201093680853 | 0.0250402187361707 | 0.987479890631915 |
| 52 | 0.0147054716377828 | 0.0294109432755656 | 0.985294528362217 |
| 53 | 0.0115253657324846 | 0.0230507314649691 | 0.988474634267515 |
| 54 | 0.0435133073637958 | 0.0870266147275917 | 0.956486692636204 |
| 55 | 0.396994320950279 | 0.793988641900559 | 0.603005679049720 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 43 | 0.843137254901961 | NOK |
| 5% type I error level | 48 | 0.941176470588235 | NOK |
| 10% type I error level | 50 | 0.980392156862745 | NOK |
