| Multiple Linear Regression - Estimated Regression Equation |
| BEL20[t] = + 2720.12444444444 + 1182.90555555556`X `[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) | 2720.12444444444 | 117.919421 | 23.0677 | 0 | 0 |
| `X ` | 1182.90555555556 | 159.002514 | 7.4395 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.698781719572059 |
| R-squared | 0.488295891608084 |
| Adjusted R-squared | 0.479473406980637 |
| F-TEST (value) | 55.3467545966576 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 58 |
| p-value | 5.34898125792438e-10 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 612.727282529774 |
| Sum Squared Residuals | 21775213.9198667 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2756.76 | 2720.12444444445 | 36.6355555555497 |
| 2 | 2849.27 | 2720.12444444445 | 129.145555555554 |
| 3 | 2921.44 | 2720.12444444444 | 201.315555555556 |
| 4 | 2981.85 | 2720.12444444444 | 261.725555555556 |
| 5 | 3080.58 | 2720.12444444444 | 360.455555555556 |
| 6 | 3106.22 | 2720.12444444444 | 386.095555555556 |
| 7 | 3119.31 | 2720.12444444444 | 399.185555555556 |
| 8 | 3061.26 | 2720.12444444444 | 341.135555555556 |
| 9 | 3097.31 | 2720.12444444444 | 377.185555555556 |
| 10 | 3161.69 | 2720.12444444444 | 441.565555555556 |
| 11 | 3257.16 | 2720.12444444444 | 537.035555555556 |
| 12 | 3277.01 | 2720.12444444444 | 556.885555555556 |
| 13 | 3295.32 | 2720.12444444444 | 575.195555555556 |
| 14 | 3363.99 | 2720.12444444444 | 643.865555555556 |
| 15 | 3494.17 | 2720.12444444444 | 774.045555555556 |
| 16 | 3667.03 | 3903.03 | -236 |
| 17 | 3813.06 | 3903.03 | -89.9700000000001 |
| 18 | 3917.96 | 3903.03 | 14.9300000000000 |
| 19 | 3895.51 | 3903.03 | -7.51999999999984 |
| 20 | 3801.06 | 3903.03 | -101.970000000000 |
| 21 | 3570.12 | 2720.12444444444 | 849.995555555556 |
| 22 | 3701.61 | 3903.03 | -201.42 |
| 23 | 3862.27 | 3903.03 | -40.7600000000001 |
| 24 | 3970.1 | 3903.03 | 67.0699999999999 |
| 25 | 4138.52 | 3903.03 | 235.490000000000 |
| 26 | 4199.75 | 3903.03 | 296.72 |
| 27 | 4290.89 | 3903.03 | 387.86 |
| 28 | 4443.91 | 3903.03 | 540.88 |
| 29 | 4502.64 | 3903.03 | 599.61 |
| 30 | 4356.98 | 3903.03 | 453.95 |
| 31 | 4591.27 | 3903.03 | 688.24 |
| 32 | 4696.96 | 3903.03 | 793.93 |
| 33 | 4621.4 | 3903.03 | 718.37 |
| 34 | 4562.84 | 3903.03 | 659.81 |
| 35 | 4202.52 | 3903.03 | 299.490000000000 |
| 36 | 4296.49 | 3903.03 | 393.46 |
| 37 | 4435.23 | 3903.03 | 532.199999999999 |
| 38 | 4105.18 | 3903.03 | 202.150000000000 |
| 39 | 4116.68 | 3903.03 | 213.650000000000 |
| 40 | 3844.49 | 3903.03 | -58.5400000000003 |
| 41 | 3720.98 | 3903.03 | -182.05 |
| 42 | 3674.4 | 3903.03 | -228.63 |
| 43 | 3857.62 | 3903.03 | -45.4100000000002 |
| 44 | 3801.06 | 3903.03 | -101.970000000000 |
| 45 | 3504.37 | 3903.03 | -398.66 |
| 46 | 3032.6 | 3903.03 | -870.43 |
| 47 | 3047.03 | 2720.12444444444 | 326.905555555556 |
| 48 | 2962.34 | 3903.03 | -940.69 |
| 49 | 2197.82 | 3903.03 | -1705.21 |
| 50 | 2014.45 | 3903.03 | -1888.58 |
| 51 | 1862.83 | 2720.12444444444 | -857.294444444444 |
| 52 | 1905.41 | 2720.12444444444 | -814.714444444444 |
| 53 | 1810.99 | 2720.12444444444 | -909.134444444444 |
| 54 | 1670.07 | 2720.12444444444 | -1050.05444444444 |
| 55 | 1864.44 | 2720.12444444444 | -855.684444444444 |
| 56 | 2052.02 | 2720.12444444444 | -668.104444444444 |
| 57 | 2029.6 | 2720.12444444444 | -690.524444444444 |
| 58 | 2070.83 | 2720.12444444444 | -649.294444444444 |
| 59 | 2293.41 | 2720.12444444444 | -426.714444444444 |
| 60 | 2443.27 | 2720.12444444444 | -276.854444444444 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.015112383261817 | 0.030224766523634 | 0.984887616738183 |
| 6 | 0.00590128975371784 | 0.0118025795074357 | 0.994098710246282 |
| 7 | 0.00212353367393449 | 0.00424706734786898 | 0.997876466326066 |
| 8 | 0.000521128559119572 | 0.00104225711823914 | 0.99947887144088 |
| 9 | 0.000141515345220278 | 0.000283030690440557 | 0.99985848465478 |
| 10 | 5.45789666814969e-05 | 0.000109157933362994 | 0.999945421033319 |
| 11 | 4.20319915274221e-05 | 8.40639830548442e-05 | 0.999957968008473 |
| 12 | 3.04345377919909e-05 | 6.08690755839819e-05 | 0.999969565462208 |
| 13 | 2.20629909457666e-05 | 4.41259818915332e-05 | 0.999977937009054 |
| 14 | 2.48869943199087e-05 | 4.97739886398174e-05 | 0.99997511300568 |
| 15 | 7.26098074549911e-05 | 0.000145219614909982 | 0.999927390192545 |
| 16 | 2.31345345559012e-05 | 4.62690691118024e-05 | 0.999976865465444 |
| 17 | 7.89136399188183e-06 | 1.57827279837637e-05 | 0.999992108636008 |
| 18 | 2.97432351437847e-06 | 5.94864702875694e-06 | 0.999997025676486 |
| 19 | 9.19531411981856e-07 | 1.83906282396371e-06 | 0.999999080468588 |
| 20 | 2.53853684531911e-07 | 5.07707369063822e-07 | 0.999999746146315 |
| 21 | 2.17907719214675e-06 | 4.3581543842935e-06 | 0.999997820922808 |
| 22 | 7.91171535306e-07 | 1.582343070612e-06 | 0.999999208828465 |
| 23 | 2.48674706096777e-07 | 4.97349412193553e-07 | 0.999999751325294 |
| 24 | 9.54046205115575e-08 | 1.90809241023115e-07 | 0.99999990459538 |
| 25 | 7.65008222643054e-08 | 1.53001644528611e-07 | 0.999999923499178 |
| 26 | 7.17649392667494e-08 | 1.43529878533499e-07 | 0.99999992823506 |
| 27 | 9.74850494793784e-08 | 1.94970098958757e-07 | 0.99999990251495 |
| 28 | 3.02854743550892e-07 | 6.05709487101783e-07 | 0.999999697145256 |
| 29 | 9.01709593689803e-07 | 1.80341918737961e-06 | 0.999999098290406 |
| 30 | 8.20336953933259e-07 | 1.64067390786652e-06 | 0.999999179663046 |
| 31 | 2.76284414407483e-06 | 5.52568828814966e-06 | 0.999997237155856 |
| 32 | 1.47215074206362e-05 | 2.94430148412723e-05 | 0.99998527849258 |
| 33 | 4.05991844540572e-05 | 8.11983689081144e-05 | 0.999959400815546 |
| 34 | 8.60504464406485e-05 | 0.000172100892881297 | 0.99991394955356 |
| 35 | 6.26542040377899e-05 | 0.000125308408075580 | 0.999937345795962 |
| 36 | 6.38902692225927e-05 | 0.000127780538445185 | 0.999936109730777 |
| 37 | 0.000139162893052007 | 0.000278325786104014 | 0.999860837106948 |
| 38 | 0.000148588601577723 | 0.000297177203155445 | 0.999851411398422 |
| 39 | 0.000209876440663146 | 0.000419752881326293 | 0.999790123559337 |
| 40 | 0.000278738147785383 | 0.000557476295570766 | 0.999721261852215 |
| 41 | 0.000428396861451111 | 0.000856793722902222 | 0.999571603138549 |
| 42 | 0.000731656083440803 | 0.00146331216688161 | 0.99926834391656 |
| 43 | 0.00200998125965109 | 0.00401996251930218 | 0.997990018740349 |
| 44 | 0.0101698964243120 | 0.0203397928486240 | 0.989830103575688 |
| 45 | 0.0534962086919083 | 0.106992417383817 | 0.946503791308092 |
| 46 | 0.179598061625135 | 0.359196123250271 | 0.820401938374865 |
| 47 | 0.634758832645377 | 0.730482334709245 | 0.365241167354623 |
| 48 | 0.952742874152915 | 0.0945142516941693 | 0.0472571258470846 |
| 49 | 0.980213802883078 | 0.0395723942338438 | 0.0197861971169219 |
| 50 | 0.98539201814405 | 0.0292159637119003 | 0.0146079818559502 |
| 51 | 0.978724218291408 | 0.0425515634171836 | 0.0212757817085918 |
| 52 | 0.96329127775015 | 0.0734174444996996 | 0.0367087222498498 |
| 53 | 0.946770295631935 | 0.106459408736129 | 0.0532297043680646 |
| 54 | 0.962926081916654 | 0.0741478361666921 | 0.0370739180833461 |
| 55 | 0.948846713080378 | 0.102306573839243 | 0.0511532869196215 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 37 | 0.725490196078431 | NOK |
| 5% type I error level | 43 | 0.843137254901961 | NOK |
| 10% type I error level | 46 | 0.901960784313726 | NOK |
