| Multiple Linear Regression - Estimated Regression Equation |
| Q1_2[t] = + 0.683448246864695 + 0.198926748843929Q1_3[t] -0.0928214103551924Q1_5[t] + 0.0904997968487101Q1_7[t] -0.075972113093604Q1_8[t] + 0.116383027938451Q1_12[t] + 0.580006004424285Q1_16[t] -0.00989775749926517Q1_22[t] + 0.124131261356080Q1_2v[t] -0.261297359223972Q1_3v[t] + 0.227200441858429Q1_5v[t] -0.128064165925015Q1_7v[t] + 0.308882429796853Q1_8v[t] -0.158991872319213Q1_12v[t] + 0.0889780949233021Q1_16v[t] -0.102927253819690Q1_22v[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) | 0.683448246864695 | 0.926271 | 0.7378 | 0.462638 | 0.231319 |
| Q1_3 | 0.198926748843929 | 0.106626 | 1.8657 | 0.065539 | 0.032769 |
| Q1_5 | -0.0928214103551924 | 0.14066 | -0.6599 | 0.511102 | 0.255551 |
| Q1_7 | 0.0904997968487101 | 0.086763 | 1.0431 | 0.299875 | 0.149938 |
| Q1_8 | -0.075972113093604 | 0.111699 | -0.6802 | 0.498257 | 0.249129 |
| Q1_12 | 0.116383027938451 | 0.125318 | 0.9287 | 0.355672 | 0.177836 |
| Q1_16 | 0.580006004424285 | 0.101982 | 5.6873 | 0 | 0 |
| Q1_22 | -0.00989775749926517 | 0.11257 | -0.0879 | 0.930143 | 0.465071 |
| Q1_2v | 0.124131261356080 | 0.112668 | 1.1017 | 0.273681 | 0.136841 |
| Q1_3v | -0.261297359223972 | 0.107925 | -2.4211 | 0.017601 | 0.008801 |
| Q1_5v | 0.227200441858429 | 0.239237 | 0.9497 | 0.344964 | 0.172482 |
| Q1_7v | -0.128064165925015 | 0.129997 | -0.9851 | 0.327356 | 0.163678 |
| Q1_8v | 0.308882429796853 | 0.161301 | 1.9149 | 0.058862 | 0.029431 |
| Q1_12v | -0.158991872319213 | 0.142698 | -1.1142 | 0.268339 | 0.13417 |
| Q1_16v | 0.0889780949233021 | 0.161312 | 0.5516 | 0.582676 | 0.291338 |
| Q1_22v | -0.102927253819690 | 0.153545 | -0.6703 | 0.504459 | 0.252229 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.673124912686542 |
| R-squared | 0.453097148079265 |
| Adjusted R-squared | 0.356584880093253 |
| F-TEST (value) | 4.69471039831883 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 85 |
| p-value | 1.81266670795655e-06 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.90392117898313 |
| Sum Squared Residuals | 69.4512473142114 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 7 | 6.55870471035365 | 0.441295289646353 |
| 2 | 5 | 5.20280688402397 | -0.202806884023974 |
| 3 | 6 | 4.61977537252105 | 1.38022462747895 |
| 4 | 5 | 5.0896922847082 | -0.0896922847081988 |
| 5 | 6 | 5.92346305685277 | 0.0765369431472323 |
| 6 | 6 | 5.11406065603278 | 0.885939343967223 |
| 7 | 6 | 5.63695894060445 | 0.363041059395548 |
| 8 | 6 | 5.33338489687718 | 0.66661510312282 |
| 9 | 4 | 3.92190972661016 | 0.07809027338984 |
| 10 | 6 | 5.50236374909422 | 0.497636250905775 |
| 11 | 6 | 6.11138431853196 | -0.111384318531962 |
| 12 | 3 | 3.50548105551907 | -0.505481055519066 |
| 13 | 5 | 5.59298873631076 | -0.592988736310762 |
| 14 | 5 | 5.24413792494949 | -0.244137924949490 |
| 15 | 2 | 3.09630144067017 | -1.09630144067017 |
| 16 | 3 | 5.22552251065442 | -2.22552251065442 |
| 17 | 6 | 5.46113266977966 | 0.538867330220338 |
| 18 | 6 | 6.15542426851204 | -0.155424268512041 |
| 19 | 5 | 4.95268302267897 | 0.0473169773210339 |
| 20 | 7 | 5.5970783587263 | 1.40292164127370 |
| 21 | 5 | 5.2682410732817 | -0.268241073281701 |
| 22 | 5 | 5.2148943607927 | -0.214894360792697 |
| 23 | 5 | 5.16219315114779 | -0.162193151147789 |
| 24 | 5 | 6.32908536327162 | -1.32908536327162 |
| 25 | 5 | 5.69927039284263 | -0.699270392842633 |
| 26 | 6 | 5.48158007619131 | 0.518419923808686 |
| 27 | 5 | 5.02987609146532 | -0.0298760914653231 |
| 28 | 5 | 4.19536747379987 | 0.804632526200128 |
| 29 | 6 | 5.21382354606428 | 0.786176453935721 |
| 30 | 4 | 4.1546369894868 | -0.154636989486803 |
| 31 | 4 | 4.94180722238501 | -0.941807222385013 |
| 32 | 6 | 4.92733997743747 | 1.07266002256253 |
| 33 | 3 | 3.03556652955895 | -0.0355665295589454 |
| 34 | 6 | 4.95800170959353 | 1.04199829040647 |
| 35 | 5 | 4.29215877075394 | 0.707841229246058 |
| 36 | 6 | 6.12563144103092 | -0.125631441030924 |
| 37 | 7 | 5.2964813163199 | 1.70351868368010 |
| 38 | 4 | 4.59423748477401 | -0.594237484774013 |
| 39 | 5 | 4.48943873521316 | 0.510561264786845 |
| 40 | 4 | 4.89315052491175 | -0.893150524911754 |
| 41 | 5 | 4.85834639432 | 0.141653605679998 |
| 42 | 3 | 4.85705273681687 | -1.85705273681687 |
| 43 | 5 | 5.01173793183049 | -0.0117379318304941 |
| 44 | 6 | 5.97838556912085 | 0.021614430879145 |
| 45 | 6 | 5.91535766611832 | 0.0846423338816765 |
| 46 | 4 | 4.14414985171917 | -0.144149851719168 |
| 47 | 4 | 4.29273383980916 | -0.292733839809155 |
| 48 | 6 | 5.08470430685183 | 0.915295693148168 |
| 49 | 6 | 5.8460116407808 | 0.153988359219196 |
| 50 | 5 | 5.0012968806686 | -0.00129688066859569 |
| 51 | 6 | 6.00876467935651 | -0.00876467935650707 |
| 52 | 4 | 3.74678879265409 | 0.253211207345913 |
| 53 | 4 | 4.73897302711348 | -0.738973027113485 |
| 54 | 5 | 5.13605548000944 | -0.136055480009441 |
| 55 | 3 | 4.07988695643614 | -1.07988695643614 |
| 56 | 6 | 6.0055067618141 | -0.0055067618141013 |
| 57 | 6 | 5.67351456808306 | 0.326485431916937 |
| 58 | 4 | 4.20304535869686 | -0.203045358696862 |
| 59 | 5 | 4.72093031884291 | 0.279069681157086 |
| 60 | 5 | 4.77450000649779 | 0.225499993502207 |
| 61 | 4 | 5.18469068820968 | -1.18469068820968 |
| 62 | 6 | 5.09415628144966 | 0.905843718550336 |
| 63 | 5 | 5.79742881096996 | -0.797428810969963 |
| 64 | 4 | 4.85526770443865 | -0.855267704438649 |
| 65 | 6 | 4.66986410316892 | 1.33013589683108 |
| 66 | 5 | 5.92044923057021 | -0.920449230570208 |
| 67 | 6 | 5.40838594159228 | 0.591614058407717 |
| 68 | 5 | 6.19194862111634 | -1.19194862111634 |
| 69 | 6 | 5.52939889578658 | 0.470601104213425 |
| 70 | 5 | 4.70079537516183 | 0.299204624838168 |
| 71 | 4 | 4.05848111772794 | -0.0584811177279371 |
| 72 | 6 | 5.61194261669205 | 0.388057383307947 |
| 73 | 5 | 3.4976327233146 | 1.5023672766854 |
| 74 | 5 | 5.18323680512411 | -0.183236805124113 |
| 75 | 3 | 3.96240861283944 | -0.96240861283944 |
| 76 | 5 | 4.99253777823451 | 0.0074622217654881 |
| 77 | 4 | 4.65301480590733 | -0.653014805907328 |
| 78 | 5 | 4.65495648746336 | 0.345043512536640 |
| 79 | 5 | 3.28163075852555 | 1.71836924147445 |
| 80 | 7 | 6.19194862111634 | 0.808051378883662 |
| 81 | 7 | 5.22398687650346 | 1.77601312349654 |
| 82 | 5 | 4.20168452213125 | 0.798315477868746 |
| 83 | 4 | 3.98018739112785 | 0.0198126088721492 |
| 84 | 6 | 5.36733099341657 | 0.632669006583427 |
| 85 | 5 | 4.8934170267239 | 0.106582973276100 |
| 86 | 5 | 5.35597544608194 | -0.355975446081937 |
| 87 | 4 | 4.57286602021234 | -0.572866020212344 |
| 88 | 5 | 5.07529374484956 | -0.075293744849557 |
| 89 | 2 | 3.42809714193190 | -1.42809714193190 |
| 90 | 7 | 5.89647513474844 | 1.10352486525156 |
| 91 | 4 | 4.63935094582333 | -0.639350945823334 |
| 92 | 5 | 4.76839329766487 | 0.23160670233513 |
| 93 | 5 | 5.63782584778179 | -0.637825847781794 |
| 94 | 7 | 6.16476161345815 | 0.835238386541853 |
| 95 | 2 | 5.43194755917554 | -3.43194755917554 |
| 96 | 4 | 3.92583521406147 | 0.0741647859385272 |
| 97 | 6 | 5.76410663321951 | 0.23589336678049 |
| 98 | 5 | 5.32778390224284 | -0.327783902242838 |
| 99 | 5 | 4.54885114897462 | 0.451148851025376 |
| 100 | 4 | 4.71345469906492 | -0.713454699064917 |
| 101 | 4 | 4.41641927952197 | -0.416419279521968 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.528924560611165 | 0.94215087877767 | 0.471075439388835 |
| 20 | 0.425771933664231 | 0.851543867328462 | 0.574228066335769 |
| 21 | 0.461811903016353 | 0.923623806032706 | 0.538188096983647 |
| 22 | 0.370945247380006 | 0.741890494760013 | 0.629054752619994 |
| 23 | 0.265945077207121 | 0.531890154414241 | 0.73405492279288 |
| 24 | 0.280463611133787 | 0.560927222267574 | 0.719536388866213 |
| 25 | 0.228421122740208 | 0.456842245480416 | 0.771578877259792 |
| 26 | 0.161366673334423 | 0.322733346668846 | 0.838633326665577 |
| 27 | 0.114106068196947 | 0.228212136393895 | 0.885893931803053 |
| 28 | 0.163596451299720 | 0.327192902599439 | 0.83640354870028 |
| 29 | 0.144686678924467 | 0.289373357848934 | 0.855313321075533 |
| 30 | 0.140156346836836 | 0.280312693673671 | 0.859843653163164 |
| 31 | 0.324557983866481 | 0.649115967732961 | 0.675442016133519 |
| 32 | 0.284279883672147 | 0.568559767344293 | 0.715720116327853 |
| 33 | 0.21963082530862 | 0.43926165061724 | 0.78036917469138 |
| 34 | 0.250924036101114 | 0.501848072202228 | 0.749075963898886 |
| 35 | 0.217468980735126 | 0.434937961470251 | 0.782531019264874 |
| 36 | 0.165746389678256 | 0.331492779356511 | 0.834253610321744 |
| 37 | 0.267483022711206 | 0.534966045422412 | 0.732516977288794 |
| 38 | 0.55280168599752 | 0.89439662800496 | 0.44719831400248 |
| 39 | 0.526745507377447 | 0.946508985245107 | 0.473254492622553 |
| 40 | 0.52690102899124 | 0.94619794201752 | 0.47309897100876 |
| 41 | 0.45546418097561 | 0.91092836195122 | 0.54453581902439 |
| 42 | 0.578472470614584 | 0.843055058770833 | 0.421527529385416 |
| 43 | 0.508981178624633 | 0.982037642750734 | 0.491018821375367 |
| 44 | 0.445293357363088 | 0.890586714726175 | 0.554706642636912 |
| 45 | 0.392664833524062 | 0.785329667048125 | 0.607335166475938 |
| 46 | 0.333475855674066 | 0.666951711348132 | 0.666524144325934 |
| 47 | 0.276028579325721 | 0.552057158651442 | 0.723971420674279 |
| 48 | 0.274992305443309 | 0.549984610886618 | 0.725007694556691 |
| 49 | 0.22061892671951 | 0.44123785343902 | 0.77938107328049 |
| 50 | 0.187695933870764 | 0.375391867741528 | 0.812304066129236 |
| 51 | 0.147317073027014 | 0.294634146054029 | 0.852682926972986 |
| 52 | 0.124988026324315 | 0.249976052648629 | 0.875011973675685 |
| 53 | 0.111910626380483 | 0.223821252760965 | 0.888089373619517 |
| 54 | 0.083114825104717 | 0.166229650209434 | 0.916885174895283 |
| 55 | 0.115939185307801 | 0.231878370615602 | 0.884060814692199 |
| 56 | 0.0868206378146791 | 0.173641275629358 | 0.91317936218532 |
| 57 | 0.0625109961237968 | 0.125021992247594 | 0.937489003876203 |
| 58 | 0.0459391734501822 | 0.0918783469003644 | 0.954060826549818 |
| 59 | 0.0326205101680775 | 0.065241020336155 | 0.967379489831923 |
| 60 | 0.0217643755085743 | 0.0435287510171486 | 0.978235624491426 |
| 61 | 0.0194493629112935 | 0.0388987258225871 | 0.980550637088706 |
| 62 | 0.0149079517588295 | 0.0298159035176590 | 0.98509204824117 |
| 63 | 0.0113650613967455 | 0.0227301227934910 | 0.988634938603254 |
| 64 | 0.0114200635973934 | 0.0228401271947869 | 0.988579936402607 |
| 65 | 0.0157300331418038 | 0.0314600662836076 | 0.984269966858196 |
| 66 | 0.0138807142603025 | 0.0277614285206049 | 0.986119285739698 |
| 67 | 0.0102552269157575 | 0.0205104538315149 | 0.989744773084243 |
| 68 | 0.0105440772931698 | 0.0210881545863397 | 0.98945592270683 |
| 69 | 0.0071879609401197 | 0.0143759218802394 | 0.99281203905988 |
| 70 | 0.0044095161096923 | 0.0088190322193846 | 0.995590483890308 |
| 71 | 0.00249422795383619 | 0.00498845590767237 | 0.997505772046164 |
| 72 | 0.00153316485347292 | 0.00306632970694584 | 0.998466835146527 |
| 73 | 0.00353505491791912 | 0.00707010983583824 | 0.99646494508208 |
| 74 | 0.00194807135451326 | 0.00389614270902653 | 0.998051928645487 |
| 75 | 0.00141272042951811 | 0.00282544085903623 | 0.998587279570482 |
| 76 | 0.000684504761069371 | 0.00136900952213874 | 0.99931549523893 |
| 77 | 0.000424482530190974 | 0.000848965060381949 | 0.999575517469809 |
| 78 | 0.000200609305027282 | 0.000401218610054564 | 0.999799390694973 |
| 79 | 0.000702923025125764 | 0.00140584605025153 | 0.999297076974874 |
| 80 | 0.000373741810994602 | 0.000747483621989205 | 0.999626258189005 |
| 81 | 0.00100657544499765 | 0.00201315088999531 | 0.998993424555002 |
| 82 | 0.000588796151804718 | 0.00117759230360944 | 0.999411203848195 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 13 | 0.203125 | NOK |
| 5% type I error level | 23 | 0.359375 | NOK |
| 10% type I error level | 25 | 0.390625 | NOK |
