| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 103.640526315790 + 7.77683217477653X[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) | 103.640526315790 | 0.983599 | 105.3687 | 0 | 0 |
| X | 7.77683217477653 | 1.146427 | 6.7835 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.629791177928378 |
| R-squared | 0.396636927796414 |
| Adjusted R-squared | 0.388017455336363 |
| F-TEST (value) | 46.0163808904445 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 70 |
| p-value | 3.09137426768302e-09 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4.28740968238986 |
| Sum Squared Residuals | 1286.73172492552 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 103.52 | 103.640526315789 | -0.120526315788941 |
| 2 | 103.5 | 103.640526315789 | -0.140526315789487 |
| 3 | 103.52 | 103.640526315790 | -0.120526315789508 |
| 4 | 103.53 | 103.640526315790 | -0.110526315789503 |
| 5 | 103.53 | 103.640526315790 | -0.110526315789503 |
| 6 | 103.53 | 103.640526315790 | -0.110526315789503 |
| 7 | 103.52 | 103.640526315790 | -0.120526315789508 |
| 8 | 103.54 | 103.640526315790 | -0.100526315789498 |
| 9 | 103.59 | 103.640526315790 | -0.0505263157895004 |
| 10 | 103.59 | 103.640526315790 | -0.0505263157895004 |
| 11 | 103.59 | 103.640526315790 | -0.0505263157895004 |
| 12 | 103.59 | 103.640526315790 | -0.0505263157895004 |
| 13 | 103.63 | 103.640526315790 | -0.0105263157895084 |
| 14 | 103.74 | 103.640526315790 | 0.099473684210491 |
| 15 | 103.7 | 103.640526315790 | 0.059473684210499 |
| 16 | 103.72 | 103.640526315790 | 0.079473684210495 |
| 17 | 103.81 | 103.640526315790 | 0.169473684210498 |
| 18 | 103.8 | 103.640526315790 | 0.159473684210493 |
| 19 | 104.22 | 103.640526315790 | 0.579473684210495 |
| 20 | 106.91 | 111.417358490566 | -4.50735849056604 |
| 21 | 107.06 | 111.417358490566 | -4.35735849056604 |
| 22 | 107.17 | 111.417358490566 | -4.24735849056604 |
| 23 | 107.25 | 111.417358490566 | -4.16735849056604 |
| 24 | 107.28 | 111.417358490566 | -4.13735849056604 |
| 25 | 107.24 | 111.417358490566 | -4.17735849056604 |
| 26 | 107.23 | 111.417358490566 | -4.18735849056603 |
| 27 | 107.34 | 111.417358490566 | -4.07735849056603 |
| 28 | 107.34 | 111.417358490566 | -4.07735849056603 |
| 29 | 107.3 | 111.417358490566 | -4.11735849056604 |
| 30 | 107.24 | 111.417358490566 | -4.17735849056604 |
| 31 | 107.3 | 111.417358490566 | -4.11735849056604 |
| 32 | 107.32 | 111.417358490566 | -4.09735849056604 |
| 33 | 107.28 | 111.417358490566 | -4.13735849056604 |
| 34 | 107.33 | 111.417358490566 | -4.08735849056604 |
| 35 | 107.33 | 111.417358490566 | -4.08735849056604 |
| 36 | 107.33 | 111.417358490566 | -4.08735849056604 |
| 37 | 107.28 | 111.417358490566 | -4.13735849056604 |
| 38 | 107.28 | 111.417358490566 | -4.13735849056604 |
| 39 | 107.29 | 111.417358490566 | -4.12735849056603 |
| 40 | 107.29 | 111.417358490566 | -4.12735849056603 |
| 41 | 107.23 | 111.417358490566 | -4.18735849056603 |
| 42 | 107.24 | 111.417358490566 | -4.17735849056604 |
| 43 | 107.24 | 111.417358490566 | -4.17735849056604 |
| 44 | 107.2 | 111.417358490566 | -4.21735849056603 |
| 45 | 107.23 | 111.417358490566 | -4.18735849056603 |
| 46 | 107.2 | 111.417358490566 | -4.21735849056603 |
| 47 | 107.21 | 111.417358490566 | -4.20735849056604 |
| 48 | 107.24 | 111.417358490566 | -4.17735849056604 |
| 49 | 107.21 | 111.417358490566 | -4.20735849056604 |
| 50 | 113.89 | 111.417358490566 | 2.47264150943396 |
| 51 | 114.05 | 111.417358490566 | 2.63264150943396 |
| 52 | 114.05 | 111.417358490566 | 2.63264150943396 |
| 53 | 114.05 | 111.417358490566 | 2.63264150943396 |
| 54 | 114.05 | 111.417358490566 | 2.63264150943396 |
| 55 | 115.12 | 111.417358490566 | 3.70264150943397 |
| 56 | 115.68 | 111.417358490566 | 4.26264150943397 |
| 57 | 116.05 | 111.417358490566 | 4.63264150943396 |
| 58 | 116.18 | 111.417358490566 | 4.76264150943397 |
| 59 | 116.35 | 111.417358490566 | 4.93264150943396 |
| 60 | 116.44 | 111.417358490566 | 5.02264150943396 |
| 61 | 117 | 111.417358490566 | 5.58264150943396 |
| 62 | 117.61 | 111.417358490566 | 6.19264150943396 |
| 63 | 118.17 | 111.417358490566 | 6.75264150943396 |
| 64 | 118.33 | 111.417358490566 | 6.91264150943396 |
| 65 | 118.33 | 111.417358490566 | 6.91264150943396 |
| 66 | 118.42 | 111.417358490566 | 7.00264150943396 |
| 67 | 118.5 | 111.417358490566 | 7.08264150943396 |
| 68 | 118.67 | 111.417358490566 | 7.25264150943396 |
| 69 | 119.09 | 111.417358490566 | 7.67264150943397 |
| 70 | 119.14 | 111.417358490566 | 7.72264150943396 |
| 71 | 119.23 | 111.417358490566 | 7.81264150943397 |
| 72 | 119.33 | 111.417358490566 | 7.91264150943396 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 4.48941822190818e-08 | 8.97883644381637e-08 | 0.999999955105818 |
| 6 | 1.48936788031150e-10 | 2.97873576062301e-10 | 0.999999999851063 |
| 7 | 3.68370850672314e-13 | 7.36741701344627e-13 | 0.999999999999632 |
| 8 | 2.46720343835644e-15 | 4.93440687671288e-15 | 0.999999999999998 |
| 9 | 1.65570516334699e-15 | 3.31141032669399e-15 | 0.999999999999998 |
| 10 | 6.14831937223353e-17 | 1.22966387444671e-16 | 1 |
| 11 | 1.32168788705674e-18 | 2.64337577411347e-18 | 1 |
| 12 | 2.21773586180352e-20 | 4.43547172360704e-20 | 1 |
| 13 | 1.51734534586769e-21 | 3.03469069173538e-21 | 1 |
| 14 | 4.79506582668233e-21 | 9.59013165336467e-21 | 1 |
| 15 | 3.79285067676758e-22 | 7.58570135353516e-22 | 1 |
| 16 | 3.12960649708841e-23 | 6.25921299417682e-23 | 1 |
| 17 | 1.24035444243874e-23 | 2.48070888487748e-23 | 1 |
| 18 | 1.67278439035596e-24 | 3.34556878071192e-24 | 1 |
| 19 | 3.93552234610264e-22 | 7.87104469220529e-22 | 1 |
| 20 | 1.51178590861411e-23 | 3.02357181722822e-23 | 1 |
| 21 | 6.93285959542567e-25 | 1.38657191908513e-24 | 1 |
| 22 | 3.90331210525806e-26 | 7.80662421051611e-26 | 1 |
| 23 | 2.56502675287941e-27 | 5.13005350575881e-27 | 1 |
| 24 | 1.58403090376922e-28 | 3.16806180753845e-28 | 1 |
| 25 | 7.339093868117e-30 | 1.4678187736234e-29 | 1 |
| 26 | 3.19237540411187e-31 | 6.38475080822375e-31 | 1 |
| 27 | 2.12301415109164e-32 | 4.24602830218327e-32 | 1 |
| 28 | 1.29252148591915e-33 | 2.58504297183829e-33 | 1 |
| 29 | 6.3750245527402e-35 | 1.27500491054804e-34 | 1 |
| 30 | 2.78331940240981e-36 | 5.56663880481962e-36 | 1 |
| 31 | 1.39837264457149e-37 | 2.79674528914298e-37 | 1 |
| 32 | 7.62541544071102e-39 | 1.52508308814220e-38 | 1 |
| 33 | 3.81328475781301e-40 | 7.62656951562602e-40 | 1 |
| 34 | 2.29119597759008e-41 | 4.58239195518016e-41 | 1 |
| 35 | 1.43550210780219e-42 | 2.87100421560438e-42 | 1 |
| 36 | 9.52907316021083e-44 | 1.90581463204217e-43 | 1 |
| 37 | 6.1181707651741e-45 | 1.22363415303482e-44 | 1 |
| 38 | 4.37553446014350e-46 | 8.75106892028701e-46 | 1 |
| 39 | 3.61984423218559e-47 | 7.23968846437118e-47 | 1 |
| 40 | 3.53470727561178e-48 | 7.06941455122356e-48 | 1 |
| 41 | 4.32625188387039e-49 | 8.65250376774077e-49 | 1 |
| 42 | 6.88201314497856e-50 | 1.37640262899571e-49 | 1 |
| 43 | 1.57411786130581e-50 | 3.14823572261162e-50 | 1 |
| 44 | 6.51121154588855e-51 | 1.30224230917771e-50 | 1 |
| 45 | 4.95791005788827e-51 | 9.91582011577654e-51 | 1 |
| 46 | 1.16105013115708e-50 | 2.32210026231415e-50 | 1 |
| 47 | 1.41301114269706e-49 | 2.82602228539413e-49 | 1 |
| 48 | 3.6725639591611e-47 | 7.3451279183222e-47 | 1 |
| 49 | 3.84085774702536e-41 | 7.68171549405073e-41 | 1 |
| 50 | 3.24351135942703e-05 | 6.48702271885406e-05 | 0.999967564886406 |
| 51 | 0.0301719775185354 | 0.0603439550370709 | 0.969828022481465 |
| 52 | 0.280419067277532 | 0.560838134555063 | 0.719580932722468 |
| 53 | 0.670384262374515 | 0.65923147525097 | 0.329615737625485 |
| 54 | 0.922859034375704 | 0.154281931248593 | 0.0771409656242964 |
| 55 | 0.983097646777899 | 0.0338047064442021 | 0.0169023532221010 |
| 56 | 0.995663363850163 | 0.00867327229967389 | 0.00433663614983694 |
| 57 | 0.998611993818176 | 0.00277601236364849 | 0.00138800618182425 |
| 58 | 0.999551098232475 | 0.000897803535049933 | 0.000448901767524967 |
| 59 | 0.99986647423669 | 0.000267051526620119 | 0.000133525763310059 |
| 60 | 0.99997935439231 | 4.12912153780045e-05 | 2.06456076890022e-05 |
| 61 | 0.99999611817532 | 7.7636493584692e-06 | 3.8818246792346e-06 |
| 62 | 0.999997985028813 | 4.02994237350239e-06 | 2.01497118675119e-06 |
| 63 | 0.999995235425308 | 9.52914938448087e-06 | 4.76457469224044e-06 |
| 64 | 0.999983362338363 | 3.32753232733442e-05 | 1.66376616366721e-05 |
| 65 | 0.999945671904782 | 0.000108656190436553 | 5.43280952182767e-05 |
| 66 | 0.999805912848085 | 0.000388174303830706 | 0.000194087151915353 |
| 67 | 0.999390369102224 | 0.00121926179555277 | 0.000609630897776385 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 58 | 0.92063492063492 | NOK |
| 5% type I error level | 59 | 0.936507936507937 | NOK |
| 10% type I error level | 60 | 0.952380952380952 | NOK |
