| Multiple Linear Regression - Estimated Regression Equation |
| Months[t] = + 97.326923076923 -15.4317765567765M1[t] -25.2454212454212M2[t] -31.0590659340659M3[t] -21.8727106227106M4[t] -25.400641025641M5[t] -20.7857142857143M6[t] -5.24130036630036M7[t] -20.7930402930403M8[t] -14.5114468864469M9[t] -29.8965201465201M10[t] -29.6149267399267M11[t] -0.61492673992674t + 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) | 97.326923076923 | 13.478596 | 7.2209 | 0 | 0 |
| M1 | -15.4317765567765 | 16.320848 | -0.9455 | 0.347892 | 0.173946 |
| M2 | -25.2454212454212 | 16.314823 | -1.5474 | 0.126624 | 0.063312 |
| M3 | -31.0590659340659 | 16.310136 | -1.9043 | 0.061301 | 0.030651 |
| M4 | -21.8727106227106 | 16.306787 | -1.3413 | 0.184483 | 0.092241 |
| M5 | -25.400641025641 | 16.304777 | -1.5579 | 0.124121 | 0.062061 |
| M6 | -20.7857142857143 | 16.304107 | -1.2749 | 0.206892 | 0.103446 |
| M7 | -5.24130036630036 | 16.935704 | -0.3095 | 0.757945 | 0.378972 |
| M8 | -20.7930402930403 | 16.929898 | -1.2282 | 0.223806 | 0.111903 |
| M9 | -14.5114468864469 | 16.925381 | -0.8574 | 0.394386 | 0.197193 |
| M10 | -29.8965201465201 | 16.922154 | -1.7667 | 0.081972 | 0.040986 |
| M11 | -29.6149267399267 | 16.920217 | -1.7503 | 0.084791 | 0.042395 |
| t | -0.61492673992674 | 0.147804 | -4.1604 | 9.5e-05 | 4.8e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.527695037155309 |
| R-squared | 0.278462052238343 |
| Adjusted R-squared | 0.145255046497730 |
| F-TEST (value) | 2.09044599936866 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 65 |
| p-value | 0.029703790756373 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 29.3055581217501 |
| Sum Squared Residuals | 55823.0228937729 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 37 | 81.2802197802198 | -44.2802197802198 |
| 2 | 30 | 70.8516483516483 | -40.8516483516483 |
| 3 | 47 | 64.423076923077 | -17.4230769230769 |
| 4 | 35 | 72.9945054945055 | -37.9945054945055 |
| 5 | 30 | 68.8516483516484 | -38.8516483516484 |
| 6 | 43 | 72.8516483516484 | -29.8516483516483 |
| 7 | 82 | 87.7811355311355 | -5.78113553113554 |
| 8 | 40 | 71.6144688644688 | -31.6144688644688 |
| 9 | 47 | 77.2811355311355 | -30.2811355311355 |
| 10 | 19 | 61.2811355311356 | -42.2811355311356 |
| 11 | 52 | 60.9478021978022 | -8.94780219780221 |
| 12 | 136 | 89.9478021978022 | 46.0521978021978 |
| 13 | 80 | 73.901098901099 | 6.09890109890107 |
| 14 | 42 | 63.4725274725275 | -21.4725274725275 |
| 15 | 54 | 57.043956043956 | -3.04395604395604 |
| 16 | 66 | 65.6153846153846 | 0.384615384615373 |
| 17 | 81 | 61.4725274725275 | 19.5274725274725 |
| 18 | 63 | 65.4725274725275 | -2.47252747252747 |
| 19 | 137 | 80.4020146520146 | 56.5979853479854 |
| 20 | 72 | 64.235347985348 | 7.76465201465201 |
| 21 | 107 | 69.9020146520147 | 37.0979853479853 |
| 22 | 58 | 53.9020146520146 | 4.09798534798536 |
| 23 | 36 | 53.5686813186813 | -17.5686813186813 |
| 24 | 52 | 82.5686813186813 | -30.5686813186813 |
| 25 | 79 | 66.521978021978 | 12.4780219780219 |
| 26 | 77 | 56.0934065934066 | 20.9065934065934 |
| 27 | 54 | 49.6648351648352 | 4.33516483516485 |
| 28 | 84 | 58.2362637362638 | 25.7637362637363 |
| 29 | 48 | 54.0934065934066 | -6.0934065934066 |
| 30 | 96 | 58.0934065934066 | 37.9065934065934 |
| 31 | 83 | 73.0228937728938 | 9.97710622710622 |
| 32 | 66 | 56.8562271062271 | 9.14377289377289 |
| 33 | 61 | 62.5228937728938 | -1.52289377289377 |
| 34 | 53 | 46.5228937728938 | 6.47710622710624 |
| 35 | 30 | 46.1895604395604 | -16.1895604395604 |
| 36 | 74 | 75.1895604395604 | -1.18956043956043 |
| 37 | 69 | 59.1428571428572 | 9.85714285714283 |
| 38 | 59 | 48.7142857142857 | 10.2857142857143 |
| 39 | 42 | 42.2857142857143 | -0.285714285714273 |
| 40 | 65 | 50.8571428571429 | 14.1428571428571 |
| 41 | 70 | 46.7142857142857 | 23.2857142857143 |
| 42 | 100 | 50.7142857142857 | 49.2857142857143 |
| 43 | 63 | 65.6437728937729 | -2.64377289377290 |
| 44 | 105 | 49.4771062271062 | 55.5228937728938 |
| 45 | 82 | 55.1437728937729 | 26.8562271062271 |
| 46 | 81 | 39.1437728937729 | 41.8562271062271 |
| 47 | 75 | 38.8104395604396 | 36.1895604395604 |
| 48 | 102 | 67.8104395604395 | 34.1895604395605 |
| 49 | 121 | 51.7637362637363 | 69.2362637362637 |
| 50 | 98 | 41.3351648351648 | 56.6648351648352 |
| 51 | 76 | 34.9065934065934 | 41.0934065934066 |
| 52 | 77 | 43.478021978022 | 33.521978021978 |
| 53 | 63 | 39.3351648351648 | 23.6648351648352 |
| 54 | 37 | 43.3351648351648 | -6.33516483516482 |
| 55 | 35 | 58.264652014652 | -23.264652014652 |
| 56 | 23 | 42.0979853479853 | -19.0979853479853 |
| 57 | 40 | 47.764652014652 | -7.764652014652 |
| 58 | 29 | 31.764652014652 | -2.76465201465201 |
| 59 | 37 | 31.4313186813187 | 5.56868131868132 |
| 60 | 51 | 60.4313186813187 | -9.43131868131866 |
| 61 | 20 | 44.3846153846154 | -24.3846153846154 |
| 62 | 28 | 33.9560439560439 | -5.95604395604393 |
| 63 | 13 | 27.5274725274725 | -14.5274725274725 |
| 64 | 22 | 36.0989010989011 | -14.0989010989011 |
| 65 | 25 | 31.9560439560440 | -6.95604395604396 |
| 66 | 13 | 35.9560439560439 | -22.9560439560439 |
| 67 | 16 | 50.8855311355311 | -34.8855311355311 |
| 68 | 13 | 34.7188644688645 | -21.7188644688645 |
| 69 | 16 | 40.3855311355311 | -24.3855311355311 |
| 70 | 17 | 24.3855311355311 | -7.38553113553113 |
| 71 | 25 | 24.0521978021978 | 0.947802197802195 |
| 72 | 14 | 53.0521978021978 | -39.0521978021978 |
| 73 | 8 | 37.0054945054945 | -29.0054945054945 |
| 74 | 7 | 26.5769230769231 | -19.5769230769231 |
| 75 | 10 | 20.1483516483516 | -10.1483516483516 |
| 76 | 7 | 28.7197802197802 | -21.7197802197802 |
| 77 | 10 | 24.5769230769231 | -14.5769230769231 |
| 78 | 3 | 28.5769230769231 | -25.5769230769231 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.124088818732798 | 0.248177637465597 | 0.875911181267202 |
| 17 | 0.118143548451484 | 0.236287096902968 | 0.881856451548516 |
| 18 | 0.0606599772583055 | 0.121319954516611 | 0.939340022741694 |
| 19 | 0.0703743384421939 | 0.140748676884388 | 0.929625661557806 |
| 20 | 0.0342212011222353 | 0.0684424022444706 | 0.965778798877765 |
| 21 | 0.0382791082701236 | 0.0765582165402473 | 0.961720891729876 |
| 22 | 0.0201507693646034 | 0.0403015387292069 | 0.979849230635397 |
| 23 | 0.0923538569282151 | 0.184707713856430 | 0.907646143071785 |
| 24 | 0.81358711976967 | 0.372825760460659 | 0.186412880230329 |
| 25 | 0.760216539242193 | 0.479566921515615 | 0.239783460757807 |
| 26 | 0.699336230547116 | 0.601327538905769 | 0.300663769452884 |
| 27 | 0.684732208613686 | 0.630535582772628 | 0.315267791386314 |
| 28 | 0.606959484905226 | 0.786081030189547 | 0.393040515094774 |
| 29 | 0.665785651755235 | 0.668428696489531 | 0.334214348244766 |
| 30 | 0.60592728347513 | 0.78814543304974 | 0.39407271652487 |
| 31 | 0.66444036909667 | 0.671119261806661 | 0.335559630903331 |
| 32 | 0.612707653169253 | 0.774584693661493 | 0.387292346830746 |
| 33 | 0.62801904400307 | 0.743961911993862 | 0.371980955996931 |
| 34 | 0.600694336861396 | 0.798611326277208 | 0.399305663138604 |
| 35 | 0.750354590563695 | 0.49929081887261 | 0.249645409436305 |
| 36 | 0.781438116060439 | 0.437123767879123 | 0.218561883939561 |
| 37 | 0.784140781319079 | 0.431718437361842 | 0.215859218680921 |
| 38 | 0.81503609274016 | 0.369927814519681 | 0.184963907259841 |
| 39 | 0.904047358751966 | 0.191905282496069 | 0.0959526412480345 |
| 40 | 0.920463010093181 | 0.159073979813637 | 0.0795369899068185 |
| 41 | 0.928033611913347 | 0.143932776173307 | 0.0719663880866534 |
| 42 | 0.910271596812216 | 0.179456806375568 | 0.0897284031877842 |
| 43 | 0.929097511807441 | 0.141804976385117 | 0.0709024881925586 |
| 44 | 0.95373367521101 | 0.0925326495779811 | 0.0462663247889906 |
| 45 | 0.929900485632031 | 0.140199028735938 | 0.070099514367969 |
| 46 | 0.909073746933862 | 0.181852506132277 | 0.0909262530661383 |
| 47 | 0.879096463708148 | 0.241807072583704 | 0.120903536291852 |
| 48 | 0.854936076154903 | 0.290127847690195 | 0.145063923845097 |
| 49 | 0.986376385790934 | 0.0272472284181319 | 0.0136236142090659 |
| 50 | 0.997895503195728 | 0.00420899360854454 | 0.00210449680427227 |
| 51 | 0.999329008596604 | 0.00134198280679120 | 0.000670991403395602 |
| 52 | 0.999964341767098 | 7.13164658047125e-05 | 3.56582329023562e-05 |
| 53 | 0.999989944580735 | 2.01108385299669e-05 | 1.00554192649835e-05 |
| 54 | 0.999982870328258 | 3.42593434831371e-05 | 1.71296717415685e-05 |
| 55 | 0.999970696014419 | 5.8607971162252e-05 | 2.9303985581126e-05 |
| 56 | 0.999934264767794 | 0.000131470464412422 | 6.57352322062111e-05 |
| 57 | 0.999839975081302 | 0.000320049837396833 | 0.000160024918698417 |
| 58 | 0.99941504867264 | 0.00116990265471896 | 0.00058495132735948 |
| 59 | 0.99785351408557 | 0.00429297182886008 | 0.00214648591443004 |
| 60 | 0.999709514147605 | 0.000580971704789711 | 0.000290485852394856 |
| 61 | 0.998352758995889 | 0.00329448200822256 | 0.00164724100411128 |
| 62 | 0.995998918025244 | 0.00800216394951295 | 0.00400108197475647 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 13 | 0.276595744680851 | NOK |
| 5% type I error level | 15 | 0.319148936170213 | NOK |
| 10% type I error level | 18 | 0.382978723404255 | NOK |
