| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.72689738135436 + 0.0180325925060919X[t] + 0.563065517828795M1[t] + 0.604580838282066M2[t] + 0.559211418219497M3[t] + 0.588103923918503M4[t] + 0.419685140811662M5[t] + 0.349102446604088M6[t] + 0.262651070991155M7[t] + 0.172953828727124M8[t] + 0.0885022159716228M9[t] + 0.0892638773611261M10[t] + 0.0662548720061118M11[t] + 0.0109433460576948t + 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) | 1.72689738135436 | 1.140728 | 1.5139 | 0.136904 | 0.068452 |
| X | 0.0180325925060919 | 0.020237 | 0.8911 | 0.377519 | 0.18876 |
| M1 | 0.563065517828795 | 0.945477 | 0.5955 | 0.554404 | 0.277202 |
| M2 | 0.604580838282066 | 0.946487 | 0.6388 | 0.526145 | 0.263073 |
| M3 | 0.559211418219497 | 0.943146 | 0.5929 | 0.556138 | 0.278069 |
| M4 | 0.588103923918503 | 0.9432 | 0.6235 | 0.536023 | 0.268011 |
| M5 | 0.419685140811662 | 0.941771 | 0.4456 | 0.657952 | 0.328976 |
| M6 | 0.349102446604088 | 0.940309 | 0.3713 | 0.712146 | 0.356073 |
| M7 | 0.262651070991155 | 0.937969 | 0.28 | 0.780717 | 0.390358 |
| M8 | 0.172953828727124 | 0.936351 | 0.1847 | 0.854268 | 0.427134 |
| M9 | 0.0885022159716228 | 0.935871 | 0.0946 | 0.92507 | 0.462535 |
| M10 | 0.0892638773611261 | 0.935356 | 0.0954 | 0.924385 | 0.462193 |
| M11 | 0.0662548720061118 | 0.935156 | 0.0708 | 0.943825 | 0.471913 |
| t | 0.0109433460576948 | 0.013621 | 0.8034 | 0.425863 | 0.212931 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.193509298948104 |
| R-squared | 0.0374458487793868 |
| Adjusted R-squared | -0.234580324391656 |
| F-TEST (value) | 0.137655315820812 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 46 |
| p-value | 0.999798347790672 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.47849940054841 |
| Sum Squared Residuals | 100.554181961413 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2.6 | 2.85090031667666 | -0.250900316676658 |
| 2 | 2.4 | 2.86909705742605 | -0.469097057426048 |
| 3 | 2.5 | 2.8599166129297 | -0.359916612929702 |
| 4 | 2.7 | 2.86729379817544 | -0.167293798175439 |
| 5 | 3.2 | 2.69899880562264 | 0.501001194377364 |
| 6 | 2.8 | 2.59067145770631 | 0.209328542293690 |
| 7 | 2.8 | 2.49532757639437 | 0.30467242360563 |
| 8 | 3 | 2.42558997644108 | 0.57441002355892 |
| 9 | 3.1 | 2.33945889498901 | 0.76054110501099 |
| 10 | 3.1 | 2.36198345793986 | 0.738016542060138 |
| 11 | 3 | 2.4202449094163 | 0.5797550905837 |
| 12 | 2.4 | 2.40099856848007 | -0.000998568480067793 |
| 13 | 2.7 | 2.99304002487265 | -0.293040024872649 |
| 14 | 3 | 3.06172802463910 | -0.0617280246390973 |
| 15 | 2.7 | 3.03451498763666 | -0.334514987636661 |
| 16 | 2.7 | 3.10320298740311 | -0.403202987403108 |
| 17 | 2 | 2.96556340211066 | -0.965563402110662 |
| 18 | 2.4 | 2.94198923897297 | -0.541989238972968 |
| 19 | 2.6 | 2.87008772791895 | -0.270087727918947 |
| 20 | 2.4 | 2.80575990571749 | -0.405759905717485 |
| 21 | 2.3 | 2.75749726852821 | -0.457497268528208 |
| 22 | 2.4 | 2.74756316496809 | -0.347563164968095 |
| 23 | 2.5 | 2.71746491316468 | -0.217464913164683 |
| 24 | 2.6 | 2.68739901672480 | -0.0873990167247952 |
| 25 | 2.6 | 3.23976876960397 | -0.639768769603974 |
| 26 | 2.6 | 3.31386654712225 | -0.71386654712225 |
| 27 | 2.7 | 3.2650143991125 | -0.565014399112503 |
| 28 | 2.8 | 3.28140788061128 | -0.481407880611284 |
| 29 | 2.6 | 3.10409659180544 | -0.504096591805436 |
| 30 | 2.6 | 3.08232568791835 | -0.482325687918351 |
| 31 | 2 | 3.02485025086920 | -1.02485025086920 |
| 32 | 2 | 2.97675176192322 | -0.976751761923225 |
| 33 | 2.1 | 2.8798011249675 | -0.779801124967498 |
| 34 | 1.9 | 2.85183442890129 | -0.951834428901294 |
| 35 | 2 | 2.83435899185215 | -0.834358991852147 |
| 36 | 2.5 | 2.73576924388911 | -0.235769243889109 |
| 37 | 2.9 | 3.31158136702621 | -0.411581367026208 |
| 38 | 3.3 | 3.32256507077316 | -0.022565070773162 |
| 39 | 3.5 | 3.32059766327925 | 0.179402336720746 |
| 40 | 3.8 | 3.35682699653474 | 0.443173003465263 |
| 41 | 4.6 | 3.20476133723742 | 1.39523866276258 |
| 42 | 4.4 | 3.07479487831378 | 1.32520512168622 |
| 43 | 5.3 | 3.04256507077316 | 2.25743492922684 |
| 44 | 5.8 | 2.93135250805586 | 2.86864749194414 |
| 45 | 5.9 | 2.82177905634587 | 3.07822094365413 |
| 46 | 5.6 | 2.84250036004611 | 2.75749963995389 |
| 47 | 5.8 | 2.73666521971712 | 3.06333478028288 |
| 48 | 5.5 | 2.57496139798276 | 2.92503860201724 |
| 49 | 4.6 | 3.00470952182051 | 1.59529047817949 |
| 50 | 4.2 | 2.93274330003944 | 1.26725669996056 |
| 51 | 4 | 2.91995633704188 | 1.08004366295812 |
| 52 | 3.5 | 2.89126833727543 | 0.608731662724568 |
| 53 | 2.3 | 2.72657986322385 | -0.426579863223848 |
| 54 | 2.2 | 2.71021873708859 | -0.51021873708859 |
| 55 | 1.4 | 2.66716937404432 | -1.26716937404432 |
| 56 | 0.6 | 2.66054584786235 | -2.06054584786235 |
| 57 | 0 | 2.60146365516942 | -2.60146365516942 |
| 58 | 0.5 | 2.69611858814464 | -2.19611858814464 |
| 59 | 0.1 | 2.69126596584975 | -2.59126596584975 |
| 60 | 0.1 | 2.70087177292327 | -2.60087177292327 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0138075381305970 | 0.0276150762611940 | 0.986192461869403 |
| 18 | 0.00443858268568820 | 0.00887716537137641 | 0.995561417314312 |
| 19 | 0.00114220879465170 | 0.00228441758930339 | 0.998857791205348 |
| 20 | 0.000199888195492114 | 0.000399776390984229 | 0.999800111804508 |
| 21 | 3.25100474291404e-05 | 6.50200948582808e-05 | 0.99996748995257 |
| 22 | 4.86497989531882e-06 | 9.72995979063765e-06 | 0.999995135020105 |
| 23 | 7.27302783944554e-07 | 1.45460556788911e-06 | 0.999999272697216 |
| 24 | 1.83868799642384e-07 | 3.67737599284769e-07 | 0.9999998161312 |
| 25 | 2.51690393533294e-08 | 5.03380787066588e-08 | 0.99999997483096 |
| 26 | 3.35947602774986e-09 | 6.71895205549972e-09 | 0.999999996640524 |
| 27 | 4.40800755874597e-10 | 8.81601511749195e-10 | 0.9999999995592 |
| 28 | 5.28526746225048e-11 | 1.05705349245010e-10 | 0.999999999947147 |
| 29 | 7.15652035792799e-12 | 1.43130407158560e-11 | 0.999999999992844 |
| 30 | 8.21563564372013e-13 | 1.64312712874403e-12 | 0.999999999999178 |
| 31 | 7.26440141194268e-13 | 1.45288028238854e-12 | 0.999999999999274 |
| 32 | 3.55035417224154e-13 | 7.10070834448308e-13 | 0.999999999999645 |
| 33 | 1.52964399504690e-13 | 3.05928799009381e-13 | 0.999999999999847 |
| 34 | 5.12498726838839e-13 | 1.02499745367768e-12 | 0.999999999999488 |
| 35 | 2.91443539269332e-12 | 5.82887078538663e-12 | 0.999999999997086 |
| 36 | 3.54022438716447e-10 | 7.08044877432895e-10 | 0.999999999645978 |
| 37 | 8.40932300284752e-09 | 1.68186460056950e-08 | 0.999999991590677 |
| 38 | 1.12082152461754e-07 | 2.24164304923509e-07 | 0.999999887917848 |
| 39 | 1.35584549101814e-05 | 2.71169098203629e-05 | 0.99998644154509 |
| 40 | 0.00115705419455419 | 0.00231410838910839 | 0.998842945805446 |
| 41 | 0.0128869350971765 | 0.0257738701943531 | 0.987113064902823 |
| 42 | 0.346597511435971 | 0.693195022871942 | 0.653402488564029 |
| 43 | 0.836388118591422 | 0.327223762817157 | 0.163611881408578 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 23 | 0.851851851851852 | NOK |
| 5% type I error level | 25 | 0.925925925925926 | NOK |
| 10% type I error level | 25 | 0.925925925925926 | NOK |
