| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -8.2638347760359 -293.374157093177X[t] + 1.02469638380372Y1[t] -0.211002410605720Y2[t] + 0.316813468663976Y3[t] -0.0490383619885906Y4[t] -99.3752633320272M1[t] -2.92769282470823M2[t] -229.805644167399M3[t] + 73.407137286512M4[t] -312.343953515152M5[t] -434.547944602932M6[t] -401.501954448354M7[t] -270.918868937814M8[t] + 2.58702742390048M9[t] -299.756615294635M10[t] -158.836682680342M11[t] -20.2906549503601t + 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) | -8.2638347760359 | 458.159706 | -0.018 | 0.985695 | 0.492847 |
| X | -293.374157093177 | 402.161209 | -0.7295 | 0.469749 | 0.234874 |
| Y1 | 1.02469638380372 | 0.151917 | 6.7451 | 0 | 0 |
| Y2 | -0.211002410605720 | 0.218097 | -0.9675 | 0.338846 | 0.169423 |
| Y3 | 0.316813468663976 | 0.251223 | 1.2611 | 0.214238 | 0.107119 |
| Y4 | -0.0490383619885906 | 0.196424 | -0.2497 | 0.804071 | 0.402036 |
| M1 | -99.3752633320272 | 319.651277 | -0.3109 | 0.757425 | 0.378712 |
| M2 | -2.92769282470823 | 323.522995 | -0.009 | 0.992823 | 0.496411 |
| M3 | -229.805644167399 | 316.481369 | -0.7261 | 0.471788 | 0.235894 |
| M4 | 73.407137286512 | 316.18102 | 0.2322 | 0.817535 | 0.408768 |
| M5 | -312.343953515152 | 313.758726 | -0.9955 | 0.325199 | 0.162599 |
| M6 | -434.547944602932 | 318.304515 | -1.3652 | 0.17946 | 0.08973 |
| M7 | -401.501954448354 | 308.731621 | -1.3005 | 0.200525 | 0.100262 |
| M8 | -270.918868937814 | 309.463729 | -0.8754 | 0.38631 | 0.193155 |
| M9 | 2.58702742390048 | 306.975332 | 0.0084 | 0.993316 | 0.496658 |
| M10 | -299.756615294635 | 296.032723 | -1.0126 | 0.317059 | 0.15853 |
| M11 | -158.836682680342 | 293.554017 | -0.5411 | 0.59131 | 0.295655 |
| t | -20.2906549503601 | 16.467423 | -1.2322 | 0.224739 | 0.11237 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.987348952648184 |
| R-squared | 0.974857954295467 |
| Adjusted R-squared | 0.964681411986489 |
| F-TEST (value) | 95.7946151744927 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 42 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 449.915088892889 |
| Sum Squared Residuals | 8501790.66296685 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 6802.96 | 6700.75768514592 | 102.202314854076 |
| 2 | 7132.68 | 7274.53056299462 | -141.85056299462 |
| 3 | 7073.29 | 7276.99511397056 | -203.70511397056 |
| 4 | 7264.5 | 7570.83267050452 | -306.332670504523 |
| 5 | 7105.33 | 7455.48765278204 | -350.157652782038 |
| 6 | 7218.71 | 7074.56183178311 | 144.148168216890 |
| 7 | 7225.72 | 7300.57278834085 | -74.8527883408454 |
| 8 | 7354.25 | 7334.32106223393 | 19.9289377660697 |
| 9 | 7745.46 | 7761.48715011208 | -16.0271501120761 |
| 10 | 8070.26 | 7809.26507784895 | 260.994922151053 |
| 11 | 8366.33 | 8220.5457641291 | 145.784235870896 |
| 12 | 8667.51 | 8711.57776365675 | -44.0677636567545 |
| 13 | 8854.34 | 8921.77513556884 | -67.4351355688379 |
| 14 | 9218.1 | 9203.69767417906 | 14.4023258209366 |
| 15 | 9332.9 | 9370.75013674324 | -37.8501367432404 |
| 16 | 9358.31 | 9738.97405771229 | -380.664057712288 |
| 17 | 9248.66 | 9440.82900052606 | -192.169000526059 |
| 18 | 9401.2 | 9199.146816396 | 202.053183603996 |
| 19 | 9652.04 | 9393.76637859102 | 258.273621408980 |
| 20 | 9957.38 | 9692.9226807336 | 264.457319266406 |
| 21 | 10110.63 | 10259.7946542013 | -149.164654201287 |
| 22 | 10169.26 | 10101.7567800379 | 67.503219962108 |
| 23 | 10343.78 | 10334.5629290596 | 9.21707094044965 |
| 24 | 10750.21 | 10673.1461889803 | 77.0638110196967 |
| 25 | 11337.5 | 10944.1831259614 | 393.316874038635 |
| 26 | 11786.96 | 11588.7914384078 | 198.168561592226 |
| 27 | 12083.04 | 11798.4675861894 | 284.572413810645 |
| 28 | 12007.74 | 12456.0753950873 | -448.335395087311 |
| 29 | 11745.93 | 12023.9956599162 | -278.065659916154 |
| 30 | 11051.51 | 11700.8750847756 | -649.365084775614 |
| 31 | 11445.9 | 11018.9279658516 | 426.972034148441 |
| 32 | 11924.88 | 11600.6223516197 | 324.257648380264 |
| 33 | 12247.63 | 12054.2665508692 | 193.363449130801 |
| 34 | 12690.91 | 12120.2883596795 | 570.621640320473 |
| 35 | 12910.7 | 12759.4510979690 | 151.248902031035 |
| 36 | 13202.12 | 13108.4451477079 | 93.6748522921336 |
| 37 | 13654.67 | 13365.6299728241 | 289.040027175923 |
| 38 | 13862.82 | 13891.9176215480 | -29.0976215480415 |
| 39 | 13523.93 | 13844.0980660807 | -320.168066080698 |
| 40 | 14211.17 | 13864.9238591026 | 346.246140897404 |
| 41 | 14510.35 | 14278.3534758705 | 231.996524129522 |
| 42 | 14289.23 | 14179.8459458306 | 109.384054169398 |
| 43 | 14111.82 | 14137.2382141421 | -25.4182141420642 |
| 44 | 13086.59 | 14173.4792419466 | -1086.88924194661 |
| 45 | 13351.54 | 13328.8538561257 | 22.6861438742812 |
| 46 | 13747.69 | 13448.6763518982 | 299.013648101837 |
| 47 | 12855.61 | 13603.2272366380 | -747.61723663798 |
| 48 | 12926.93 | 12878.2888377270 | 48.6411622730297 |
| 49 | 12121.95 | 12839.0740804998 | -717.124080499796 |
| 50 | 11731.65 | 11773.2727028705 | -41.6227028705009 |
| 51 | 11639.51 | 11362.3590970161 | 277.150902983853 |
| 52 | 12163.78 | 11374.6940175933 | 789.085982406717 |
| 53 | 12029.53 | 11441.1342109053 | 588.39578909473 |
| 54 | 11234.18 | 11040.4003212147 | 193.779678785330 |
| 55 | 9852.13 | 10437.1046530745 | -584.974653074511 |
| 56 | 9709.04 | 9230.79466346613 | 478.245336533875 |
| 57 | 9332.75 | 9383.60778869172 | -50.8577886917192 |
| 58 | 7108.6 | 8306.73343053547 | -1198.13343053547 |
| 59 | 6691.49 | 6250.1229722044 | 441.3670277956 |
| 60 | 6143.05 | 6318.3620619281 | -175.312061928106 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.0265552878003875 | 0.0531105756007750 | 0.973444712199612 |
| 22 | 0.00908618661348883 | 0.0181723732269777 | 0.990913813386511 |
| 23 | 0.00293207907877454 | 0.00586415815754908 | 0.997067920921225 |
| 24 | 0.000658798584190608 | 0.00131759716838122 | 0.99934120141581 |
| 25 | 0.000162236350742073 | 0.000324472701484146 | 0.999837763649258 |
| 26 | 3.60728114571536e-05 | 7.21456229143072e-05 | 0.999963927188543 |
| 27 | 5.74045473760715e-05 | 0.000114809094752143 | 0.999942595452624 |
| 28 | 2.44794183670405e-05 | 4.89588367340811e-05 | 0.999975520581633 |
| 29 | 1.13724702369786e-05 | 2.27449404739573e-05 | 0.999988627529763 |
| 30 | 0.000648321526902901 | 0.00129664305380580 | 0.999351678473097 |
| 31 | 0.000296090357475758 | 0.000592180714951517 | 0.999703909642524 |
| 32 | 0.000111666502299438 | 0.000223333004598877 | 0.9998883334977 |
| 33 | 6.97681770834204e-05 | 0.000139536354166841 | 0.999930231822917 |
| 34 | 2.29928147778418e-05 | 4.59856295556837e-05 | 0.999977007185222 |
| 35 | 5.75027431962601e-06 | 1.15005486392520e-05 | 0.99999424972568 |
| 36 | 1.3024290361657e-06 | 2.6048580723314e-06 | 0.999998697570964 |
| 37 | 7.3079956699905e-06 | 1.4615991339981e-05 | 0.99999269200433 |
| 38 | 6.57844337229648e-06 | 1.31568867445930e-05 | 0.999993421556628 |
| 39 | 5.19287966714735e-05 | 0.000103857593342947 | 0.999948071203329 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 17 | 0.894736842105263 | NOK |
| 5% type I error level | 18 | 0.947368421052632 | NOK |
| 10% type I error level | 19 | 1 | NOK |
