| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -3.41688587976048 + 1.20546558206975X[t] + 0.734699728850762M1[t] -0.399983124851524M2[t] -1.07941969149607M3[t] -1.30156881538096M4[t] + 0.918927117380584M5[t] -1.14382590744882M6[t] -1.12257083876042M7[t] -0.918252357196105M8[t] -0.795192302966259M9[t] -0.822570838760416M10[t] -0.501366395517438M11[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) | -3.41688587976048 | 0.530798 | -6.4373 | 0 | 0 |
| X | 1.20546558206975 | 0.028393 | 42.4567 | 0 | 0 |
| M1 | 0.734699728850762 | 0.301944 | 2.4332 | 0.018014 | 0.009007 |
| M2 | -0.399983124851524 | 0.303831 | -1.3165 | 0.193109 | 0.096554 |
| M3 | -1.07941969149607 | 0.309045 | -3.4928 | 0.000913 | 0.000456 |
| M4 | -1.30156881538096 | 0.307785 | -4.2288 | 8.3e-05 | 4.1e-05 |
| M5 | 0.918927117380584 | 0.305402 | 3.0089 | 0.003852 | 0.001926 |
| M6 | -1.14382590744882 | 0.302514 | -3.7811 | 0.000367 | 0.000183 |
| M7 | -1.12257083876042 | 0.308844 | -3.6348 | 0.000585 | 0.000293 |
| M8 | -0.918252357196105 | 0.30294 | -3.0311 | 0.003615 | 0.001807 |
| M9 | -0.795192302966259 | 0.303063 | -2.6238 | 0.01105 | 0.005525 |
| M10 | -0.822570838760416 | 0.308844 | -2.6634 | 0.009957 | 0.004978 |
| M11 | -0.501366395517438 | 0.301944 | -1.6605 | 0.102128 | 0.051064 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.985670635867928 |
| R-squared | 0.971546602412285 |
| Adjusted R-squared | 0.96575947069953 |
| F-TEST (value) | 167.880506377776 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 59 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.522837820203883 |
| Sum Squared Residuals | 16.1282037878973 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 18 | 17.0874493950342 | 0.912550604965844 |
| 2 | 19.6 | 17.6404183562295 | 1.95958164377053 |
| 3 | 23.3 | 22.3855769088988 | 0.914423091101224 |
| 4 | 23.7 | 22.7661605760488 | 0.93383942395124 |
| 5 | 20.3 | 19.5620613894964 | 0.73793861050355 |
| 6 | 22.8 | 22.441717251153 | 0.358282748847004 |
| 7 | 24.3 | 24.271170692946 | 0.0288293070539764 |
| 8 | 21.5 | 21.341278661129 | 0.158721338871001 |
| 9 | 23.5 | 23.5136302048774 | -0.0136302048774122 |
| 10 | 22.2 | 21.5575067377717 | 0.642493262228339 |
| 11 | 20.9 | 21.6376180646007 | -0.737618064600691 |
| 12 | 22.2 | 21.7773447854972 | 0.422655214502796 |
| 13 | 19.5 | 18.8956477681387 | 0.604352231861272 |
| 14 | 21.1 | 21.1362685442317 | -0.0362685442317284 |
| 15 | 22 | 22.2650303506918 | -0.2650303506918 |
| 16 | 19.2 | 19.1497638298395 | 0.0502361701604758 |
| 17 | 17.8 | 18.8387820402546 | -1.03878204025460 |
| 18 | 19.2 | 19.0664136213577 | 0.133586378642285 |
| 19 | 19.9 | 20.5342273885298 | -0.634227388529817 |
| 20 | 19.6 | 19.5330802880244 | 0.066919711975621 |
| 21 | 18.1 | 18.2095816437705 | -0.109581643770531 |
| 22 | 20.4 | 21.0753205049438 | -0.675320504943764 |
| 23 | 18.1 | 18.5034075512194 | -0.403407551219352 |
| 24 | 18.6 | 19.3664136213577 | -0.766413621357711 |
| 25 | 17.6 | 18.1723684188969 | -0.572368418896882 |
| 26 | 19.4 | 20.2924426367829 | -0.892442636782911 |
| 27 | 19.3 | 19.4924595119314 | -0.192459511931384 |
| 28 | 18.6 | 18.7881241552186 | -0.188124155218597 |
| 29 | 16.9 | 17.03058366715 | -0.130583667149985 |
| 30 | 16.4 | 16.6554824572182 | -0.255482457218225 |
| 31 | 19 | 19.3287618064601 | -0.328761806460069 |
| 32 | 18.7 | 19.0508940551965 | -0.35089405519648 |
| 33 | 17.1 | 16.5219298288729 | 0.578070171127115 |
| 34 | 21.5 | 21.1958670631507 | 0.304132936849261 |
| 35 | 17.8 | 17.5390350855636 | 0.260964914436444 |
| 36 | 18.1 | 17.6787618064601 | 0.421238193539931 |
| 37 | 19 | 19.0161943263457 | -0.0161943263457042 |
| 38 | 18.9 | 19.2075236129201 | -0.307523612920141 |
| 39 | 16.8 | 16.8404352313779 | -0.0404352313779446 |
| 40 | 18.1 | 18.4264844805977 | -0.326484480597673 |
| 41 | 15.7 | 15.7045715268733 | -0.00457152687326499 |
| 42 | 15.1 | 15.0883772005276 | 0.0116227994724468 |
| 43 | 18.3 | 17.8822031079764 | 0.417796892023625 |
| 44 | 16.5 | 16.3988697746430 | 0.101130225356960 |
| 45 | 16.9 | 17.2452091781147 | -0.345209178114737 |
| 46 | 18.4 | 18.7849358990112 | -0.384935899011249 |
| 47 | 16.4 | 16.0924763870799 | 0.307523612920135 |
| 48 | 15.7 | 15.8705634333555 | -0.170563433355452 |
| 49 | 16.9 | 17.4490890696550 | -0.549089069655036 |
| 50 | 16.6 | 17.1582321234016 | -0.558232123401568 |
| 51 | 16.7 | 17.0815283477919 | -0.381528347791894 |
| 52 | 16.6 | 16.7388326657000 | -0.138832665700031 |
| 53 | 14.4 | 14.2580128283896 | 0.141987171610430 |
| 54 | 14.5 | 14.6061909676997 | -0.106190967699654 |
| 55 | 17.5 | 17.0383772005275 | 0.461622799472449 |
| 56 | 14.3 | 14.2290317269175 | 0.0709682730825013 |
| 57 | 15.4 | 15.5575573632171 | -0.157557363217089 |
| 58 | 17.2 | 17.3383772005275 | -0.138377200527550 |
| 59 | 14.6 | 14.5253711303892 | 0.074628869610807 |
| 60 | 14.2 | 14.1829116184578 | 0.0170883815421924 |
| 61 | 14.9 | 15.2792510219295 | -0.379251021929493 |
| 62 | 14.1 | 14.2651147264342 | -0.165114726434182 |
| 63 | 15.6 | 15.6349696493082 | -0.0349696493082004 |
| 64 | 14.6 | 14.9306342925954 | -0.330634292595414 |
| 65 | 11.9 | 11.6059885478361 | 0.294011452163872 |
| 66 | 13.5 | 13.6418185020439 | -0.141818502043857 |
| 67 | 14.2 | 14.1452598035602 | 0.0547401964398365 |
| 68 | 13.7 | 13.7468454940896 | -0.0468454940896024 |
| 69 | 14.4 | 14.3520917811473 | 0.0479082188526546 |
| 70 | 15.3 | 15.0479925945950 | 0.252007405404966 |
| 71 | 14.3 | 13.8020917811473 | 0.497908218852657 |
| 72 | 14.5 | 14.4240047348718 | 0.0759952651282423 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.999943081156998 | 0.000113837686004742 | 5.69188430023711e-05 |
| 17 | 0.99999951865373 | 9.62692539743804e-07 | 4.81346269871902e-07 |
| 18 | 0.999999223567387 | 1.55286522666963e-06 | 7.76432613334816e-07 |
| 19 | 0.999999404013188 | 1.19197362386398e-06 | 5.95986811931988e-07 |
| 20 | 0.99999852666596 | 2.94666808025999e-06 | 1.47333404013000e-06 |
| 21 | 0.999995316999454 | 9.36600109286098e-06 | 4.68300054643049e-06 |
| 22 | 0.999998855392727 | 2.28921454524931e-06 | 1.14460727262465e-06 |
| 23 | 0.999998807595469 | 2.3848090628943e-06 | 1.19240453144715e-06 |
| 24 | 0.999999836762293 | 3.26475414824186e-07 | 1.63237707412093e-07 |
| 25 | 0.999999942482399 | 1.15035201905097e-07 | 5.75176009525486e-08 |
| 26 | 0.999999997162399 | 5.67520310122625e-09 | 2.83760155061313e-09 |
| 27 | 0.999999991301039 | 1.73979217390166e-08 | 8.69896086950832e-09 |
| 28 | 0.999999978561583 | 4.28768334043395e-08 | 2.14384167021698e-08 |
| 29 | 0.99999994045989 | 1.19080220746376e-07 | 5.9540110373188e-08 |
| 30 | 0.999999833846073 | 3.32307854473301e-07 | 1.66153927236650e-07 |
| 31 | 0.999999902779703 | 1.94440594027424e-07 | 9.72202970137118e-08 |
| 32 | 0.999999875063428 | 2.49873143519910e-07 | 1.24936571759955e-07 |
| 33 | 0.999999987865384 | 2.42692319722496e-08 | 1.21346159861248e-08 |
| 34 | 0.999999987170623 | 2.56587533799543e-08 | 1.28293766899771e-08 |
| 35 | 0.999999970320703 | 5.93585949494231e-08 | 2.96792974747115e-08 |
| 36 | 0.999999987433061 | 2.51338776630236e-08 | 1.25669388315118e-08 |
| 37 | 0.999999996105242 | 7.78951557615589e-09 | 3.89475778807795e-09 |
| 38 | 0.999999991842276 | 1.63154479881632e-08 | 8.15772399408162e-09 |
| 39 | 0.99999997681598 | 4.6368038952554e-08 | 2.3184019476277e-08 |
| 40 | 0.999999922764627 | 1.54470746348536e-07 | 7.7235373174268e-08 |
| 41 | 0.99999971900605 | 5.61987899112769e-07 | 2.80993949556384e-07 |
| 42 | 0.999999210953666 | 1.57809266894906e-06 | 7.89046334474532e-07 |
| 43 | 0.999998894040755 | 2.21191849070622e-06 | 1.10595924535311e-06 |
| 44 | 0.999997718078146 | 4.56384370714652e-06 | 2.28192185357326e-06 |
| 45 | 0.9999932402951 | 1.35194098008716e-05 | 6.75970490043579e-06 |
| 46 | 0.999988720340174 | 2.25593196512221e-05 | 1.12796598256111e-05 |
| 47 | 0.999967940102444 | 6.41197951114319e-05 | 3.20598975557160e-05 |
| 48 | 0.999902085188597 | 0.000195829622805687 | 9.79148114028435e-05 |
| 49 | 0.99972088810802 | 0.000558223783961812 | 0.000279111891980906 |
| 50 | 0.999470031893128 | 0.00105993621374417 | 0.000529968106872087 |
| 51 | 0.999045411911242 | 0.00190917617751602 | 0.00095458808875801 |
| 52 | 0.997561718121414 | 0.00487656375717122 | 0.00243828187858561 |
| 53 | 0.992634396420818 | 0.0147312071583634 | 0.00736560357918168 |
| 54 | 0.978009444755588 | 0.0439811104888239 | 0.0219905552444119 |
| 55 | 0.995498962967695 | 0.00900207406461086 | 0.00450103703230543 |
| 56 | 0.98723992887832 | 0.0255201422433587 | 0.0127600711216793 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 38 | 0.926829268292683 | NOK |
| 5% type I error level | 41 | 1 | NOK |
| 10% type I error level | 41 | 1 | NOK |
