| Multiple Linear Regression - Estimated Regression Equation |
| y[t] = + 5030.67222222222 -605.844444444444`x `[t] -119.711111111111M1[t] -248.711111111112M2[t] + 331.538888888888M3[t] -77.0000000000006M4[t] + 111.000000000000M5[t] + 540M6[t] -473.5M7[t] -212.000000000000M8[t] -124.000000000000M9[t] + 168.750000000000M10[t] -487M11[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) | 5030.67222222222 | 244.423345 | 20.5818 | 0 | 0 |
| `x ` | -605.844444444444 | 139.670483 | -4.3377 | 0.000116 | 5.8e-05 |
| M1 | -119.711111111111 | 333.092872 | -0.3594 | 0.721461 | 0.36073 |
| M2 | -248.711111111112 | 333.092872 | -0.7467 | 0.460248 | 0.230124 |
| M3 | 331.538888888888 | 333.092872 | 0.9953 | 0.326405 | 0.163203 |
| M4 | -77.0000000000006 | 331.257636 | -0.2324 | 0.817544 | 0.408772 |
| M5 | 111.000000000000 | 331.257636 | 0.3351 | 0.73956 | 0.36978 |
| M6 | 540 | 331.257636 | 1.6302 | 0.112038 | 0.056019 |
| M7 | -473.5 | 331.257636 | -1.4294 | 0.161755 | 0.080877 |
| M8 | -212.000000000000 | 331.257636 | -0.64 | 0.52635 | 0.263175 |
| M9 | -124.000000000000 | 331.257636 | -0.3743 | 0.710416 | 0.355208 |
| M10 | 168.750000000000 | 331.257636 | 0.5094 | 0.613653 | 0.306827 |
| M11 | -487 | 331.257636 | -1.4702 | 0.150453 | 0.075226 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.725546782479452 |
| R-squared | 0.526418133566285 |
| Adjusted R-squared | 0.364047207931868 |
| F-TEST (value) | 3.24207139615335 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 35 |
| p-value | 0.00325497607145486 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 468.469040836449 |
| Sum Squared Residuals | 7681213.47777778 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 4143 | 4910.96111111111 | -767.96111111111 |
| 2 | 4429 | 4781.96111111111 | -352.961111111112 |
| 3 | 5219 | 5362.21111111111 | -143.211111111111 |
| 4 | 4929 | 4953.67222222222 | -24.6722222222219 |
| 5 | 5761 | 5141.67222222222 | 619.327777777778 |
| 6 | 5592 | 5570.67222222222 | 21.3277777777779 |
| 7 | 4163 | 4557.17222222222 | -394.172222222223 |
| 8 | 4962 | 4818.67222222222 | 143.327777777778 |
| 9 | 5208 | 4906.67222222222 | 301.327777777777 |
| 10 | 4755 | 5199.42222222222 | -444.422222222223 |
| 11 | 4491 | 4543.67222222222 | -52.6722222222223 |
| 12 | 5732 | 5030.67222222222 | 701.327777777777 |
| 13 | 5731 | 4910.96111111111 | 820.038888888889 |
| 14 | 5040 | 4781.96111111111 | 258.038888888889 |
| 15 | 6102 | 5362.21111111111 | 739.788888888889 |
| 16 | 4904 | 4953.67222222222 | -49.6722222222222 |
| 17 | 5369 | 5141.67222222222 | 227.327777777778 |
| 18 | 5578 | 5570.67222222222 | 7.32777777777756 |
| 19 | 4619 | 4557.17222222222 | 61.8277777777777 |
| 20 | 4731 | 4818.67222222222 | -87.6722222222223 |
| 21 | 5011 | 4906.67222222222 | 104.327777777778 |
| 22 | 5299 | 5199.42222222222 | 99.5777777777775 |
| 23 | 4146 | 4543.67222222222 | -397.672222222222 |
| 24 | 4625 | 5030.67222222222 | -405.672222222223 |
| 25 | 4736 | 4910.96111111111 | -174.961111111112 |
| 26 | 4219 | 4781.96111111111 | -562.961111111111 |
| 27 | 5116 | 5362.21111111111 | -246.211111111111 |
| 28 | 4205 | 4347.82777777778 | -142.827777777778 |
| 29 | 4121 | 4535.82777777778 | -414.827777777778 |
| 30 | 5103 | 4964.82777777778 | 138.172222222222 |
| 31 | 4300 | 3951.32777777778 | 348.672222222222 |
| 32 | 4578 | 4212.82777777778 | 365.172222222222 |
| 33 | 3809 | 4300.82777777778 | -491.827777777778 |
| 34 | 5526 | 4593.57777777778 | 932.422222222222 |
| 35 | 4248 | 3937.82777777778 | 310.172222222222 |
| 36 | 3830 | 4424.82777777778 | -594.827777777778 |
| 37 | 4428 | 4305.11666666667 | 122.883333333333 |
| 38 | 4834 | 4176.11666666667 | 657.883333333334 |
| 39 | 4406 | 4756.36666666667 | -350.366666666666 |
| 40 | 4565 | 4347.82777777778 | 217.172222222222 |
| 41 | 4104 | 4535.82777777778 | -431.827777777778 |
| 42 | 4798 | 4964.82777777778 | -166.827777777778 |
| 43 | 3935 | 3951.32777777778 | -16.3277777777776 |
| 44 | 3792 | 4212.82777777778 | -420.827777777778 |
| 45 | 4387 | 4300.82777777778 | 86.1722222222223 |
| 46 | 4006 | 4593.57777777778 | -587.577777777778 |
| 47 | 4078 | 3937.82777777778 | 140.172222222222 |
| 48 | 4724 | 4424.82777777778 | 299.172222222222 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.955126940217542 | 0.0897461195649153 | 0.0448730597824576 |
| 17 | 0.93861966467949 | 0.122760670641021 | 0.0613803353205103 |
| 18 | 0.88328067726988 | 0.23343864546024 | 0.11671932273012 |
| 19 | 0.823076516663566 | 0.353846966672869 | 0.176923483336434 |
| 20 | 0.733447610981983 | 0.533104778036035 | 0.266552389018017 |
| 21 | 0.67500821554878 | 0.649983568902439 | 0.324991784451219 |
| 22 | 0.614057394337103 | 0.771885211325794 | 0.385942605662897 |
| 23 | 0.512317316755411 | 0.975365366489178 | 0.487682683244589 |
| 24 | 0.546373389673638 | 0.907253220652725 | 0.453626610326362 |
| 25 | 0.433140767757026 | 0.866281535514052 | 0.566859232242974 |
| 26 | 0.460318549798184 | 0.920637099596369 | 0.539681450201816 |
| 27 | 0.373526399106525 | 0.747052798213049 | 0.626473600893475 |
| 28 | 0.272804497640682 | 0.545608995281365 | 0.727195502359318 |
| 29 | 0.194861497264691 | 0.389722994529383 | 0.805138502735309 |
| 30 | 0.133223522595867 | 0.266447045191734 | 0.866776477404133 |
| 31 | 0.094224497575638 | 0.188448995151276 | 0.905775502424362 |
| 32 | 0.0724027906984204 | 0.144805581396841 | 0.92759720930158 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 1 | 0.0588235294117647 | OK |
