| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -1.86988843332436 + 1.09005922831809X[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) | -1.86988843332436 | 0.704185 | -2.6554 | 0.009801 | 0.0049 |
| X | 1.09005922831809 | 0.038656 | 28.1987 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.958692162093623 |
| R-squared | 0.919090661659746 |
| Adjusted R-squared | 0.917934813969171 |
| F-TEST (value) | 795.16589352917 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 70 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.809424302599723 |
| Sum Squared Residuals | 45.8617391147334 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 18 | 16.0070829110923 | 1.9929170889077 |
| 2 | 19.6 | 17.5331658307376 | 2.06683416926241 |
| 3 | 23.3 | 22.4384323581690 | 0.861567641831023 |
| 4 | 23.7 | 22.9834619723280 | 0.716538027671978 |
| 5 | 20.3 | 18.0781954448966 | 2.22180455510337 |
| 6 | 22.8 | 22.5474382810008 | 0.252561718999217 |
| 7 | 24.3 | 24.1825271234779 | 0.117472876522087 |
| 8 | 21.5 | 21.3483731298509 | 0.151626870149109 |
| 9 | 23.5 | 23.2014738179916 | 0.298526182008362 |
| 10 | 22.2 | 21.4573790526827 | 0.742620947317302 |
| 11 | 20.9 | 21.2393672070191 | -0.339367207019082 |
| 12 | 22.2 | 20.9123494385237 | 1.28765056147635 |
| 13 | 19.5 | 17.6421717535694 | 1.85782824643061 |
| 14 | 21.1 | 20.6943375928600 | 0.405662407139965 |
| 15 | 22 | 22.3294264353372 | -0.329426435337167 |
| 16 | 19.2 | 19.7132842873738 | -0.513284287373761 |
| 17 | 17.8 | 17.4241599079058 | 0.375840092094224 |
| 18 | 19.2 | 19.4952724417101 | -0.295272441710145 |
| 19 | 19.9 | 20.8033435156918 | -0.903343515691849 |
| 20 | 19.6 | 19.7132842873738 | -0.113284287373759 |
| 21 | 18.1 | 18.4052132133921 | -0.305213213392056 |
| 22 | 20.4 | 21.0213553613555 | -0.621355361355466 |
| 23 | 18.1 | 18.4052132133921 | -0.305213213392056 |
| 24 | 18.6 | 18.7322309818875 | -0.132230981887479 |
| 25 | 17.6 | 16.9881362165785 | 0.611863783421458 |
| 26 | 19.4 | 19.9312961330374 | -0.531296133037379 |
| 27 | 19.3 | 19.8222902102056 | -0.522290210205566 |
| 28 | 18.6 | 19.3862665188783 | -0.786266518878332 |
| 29 | 16.9 | 15.7890710654286 | 1.11092893457135 |
| 30 | 16.4 | 17.3151539850740 | -0.915153985073972 |
| 31 | 19 | 19.7132842873738 | -0.713284287373761 |
| 32 | 18.7 | 19.2772605960465 | -0.577260596046524 |
| 33 | 17.1 | 16.8791302937467 | 0.220869706253268 |
| 34 | 21.5 | 21.1303612841873 | 0.369638715812726 |
| 35 | 17.8 | 17.5331658307376 | 0.266834169262414 |
| 36 | 18.1 | 17.2061480622422 | 0.893851937757841 |
| 37 | 19 | 17.7511776764012 | 1.24882232359880 |
| 38 | 18.9 | 18.9502428275511 | -0.050242827551102 |
| 39 | 16.8 | 17.4241599079058 | -0.624159907905776 |
| 40 | 18.1 | 19.0592487503829 | -0.959248750382905 |
| 41 | 15.7 | 14.5900059142788 | 1.10999408572125 |
| 42 | 15.1 | 15.8980769882605 | -0.798076988260457 |
| 43 | 18.3 | 18.4052132133921 | -0.105213213392056 |
| 44 | 16.5 | 16.8791302937467 | -0.379130293746733 |
| 45 | 16.9 | 17.5331658307376 | -0.633165830737588 |
| 46 | 18.4 | 18.9502428275511 | -0.550242827551102 |
| 47 | 16.4 | 16.2250947567559 | 0.174905243244115 |
| 48 | 15.7 | 15.5710592197650 | 0.128940780234969 |
| 49 | 16.9 | 16.3341006795877 | 0.565899320412309 |
| 50 | 16.6 | 17.0971421394104 | -0.497142139410349 |
| 51 | 16.7 | 17.6421717535694 | -0.942171753569394 |
| 52 | 16.6 | 17.5331658307376 | -0.933165830737586 |
| 53 | 14.4 | 13.2819348402970 | 1.11806515970295 |
| 54 | 14.5 | 15.4620532969332 | -0.962053296933222 |
| 55 | 17.5 | 17.6421717535694 | -0.142171753569393 |
| 56 | 14.3 | 14.9170236827742 | -0.617023682774178 |
| 57 | 15.4 | 16.0070829110923 | -0.607082911092263 |
| 58 | 17.2 | 17.6421717535694 | -0.442171753569394 |
| 59 | 14.6 | 14.8080177599424 | -0.208017759942370 |
| 60 | 14.2 | 14.0449763001197 | 0.155023699880291 |
| 61 | 14.9 | 14.3719940686151 | 0.528005931384865 |
| 62 | 14.1 | 14.4809999914469 | -0.380999991446944 |
| 63 | 15.6 | 16.3341006795877 | -0.73410067958769 |
| 64 | 14.6 | 15.8980769882605 | -1.29807698826046 |
| 65 | 11.9 | 10.8838045379973 | 1.01619546200274 |
| 66 | 13.5 | 14.5900059142788 | -1.09000591427875 |
| 67 | 14.2 | 15.0260296056060 | -0.826029605605987 |
| 68 | 13.7 | 14.4809999914469 | -0.780999991446944 |
| 69 | 14.4 | 14.9170236827742 | -0.517023682774178 |
| 70 | 15.3 | 15.5710592197650 | -0.271059219765029 |
| 71 | 14.3 | 14.1539822229515 | 0.146017777048484 |
| 72 | 14.5 | 14.2629881457833 | 0.237011854216673 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0879894781837294 | 0.175978956367459 | 0.91201052181627 |
| 6 | 0.109322579870755 | 0.218645159741510 | 0.890677420129245 |
| 7 | 0.0507323155755954 | 0.101464631151191 | 0.949267684424405 |
| 8 | 0.113619909266188 | 0.227239818532376 | 0.886380090733812 |
| 9 | 0.0620477901398665 | 0.124095580279733 | 0.937952209860134 |
| 10 | 0.0351613740771529 | 0.0703227481543059 | 0.964838625922847 |
| 11 | 0.179161988130851 | 0.358323976261702 | 0.82083801186915 |
| 12 | 0.186006978680771 | 0.372013957361541 | 0.81399302131923 |
| 13 | 0.209868177537428 | 0.419736355074855 | 0.790131822462573 |
| 14 | 0.216726225180914 | 0.433452450361828 | 0.783273774819086 |
| 15 | 0.258791453168791 | 0.517582906337581 | 0.741208546831209 |
| 16 | 0.647802691900097 | 0.704394616199807 | 0.352197308099903 |
| 17 | 0.763136528688076 | 0.473726942623848 | 0.236863471311924 |
| 18 | 0.837234631704201 | 0.325530736591597 | 0.162765368295799 |
| 19 | 0.91494819211673 | 0.17010361576654 | 0.08505180788327 |
| 20 | 0.914086116601828 | 0.171827766796344 | 0.0859138833981718 |
| 21 | 0.935069711949611 | 0.129860576100777 | 0.0649302880503887 |
| 22 | 0.936142795992415 | 0.127714408015170 | 0.0638572040075848 |
| 23 | 0.941778500336307 | 0.116442999327386 | 0.0582214996636932 |
| 24 | 0.934791671917591 | 0.130416656164817 | 0.0652083280824086 |
| 25 | 0.927093367780395 | 0.145813264439211 | 0.0729066322196055 |
| 26 | 0.923627841328919 | 0.152744317342163 | 0.0763721586710813 |
| 27 | 0.917823817153975 | 0.164352365692051 | 0.0821761828460255 |
| 28 | 0.927074320846162 | 0.145851358307676 | 0.072925679153838 |
| 29 | 0.938074196454099 | 0.123851607091802 | 0.0619258035459011 |
| 30 | 0.961860062909505 | 0.0762798741809903 | 0.0381399370904952 |
| 31 | 0.958885947538335 | 0.08222810492333 | 0.041114052461665 |
| 32 | 0.952060793599196 | 0.0958784128016079 | 0.0479392064008039 |
| 33 | 0.938178530522884 | 0.123642938954233 | 0.0618214694771164 |
| 34 | 0.940763328584768 | 0.118473342830465 | 0.0592366714152323 |
| 35 | 0.929322965609145 | 0.141354068781711 | 0.0706770343908553 |
| 36 | 0.949602332518056 | 0.100795334963888 | 0.0503976674819442 |
| 37 | 0.988930612053154 | 0.0221387758936918 | 0.0110693879468459 |
| 38 | 0.98912437014858 | 0.0217512597028385 | 0.0108756298514193 |
| 39 | 0.987764728761765 | 0.0244705424764693 | 0.0122352712382347 |
| 40 | 0.986983514079233 | 0.0260329718415347 | 0.0130164859207673 |
| 41 | 0.993594616860872 | 0.0128107662782570 | 0.00640538313912848 |
| 42 | 0.994477182713451 | 0.0110456345730975 | 0.00552281728654873 |
| 43 | 0.99413994364589 | 0.0117201127082176 | 0.00586005635410881 |
| 44 | 0.991632094851948 | 0.0167358102961042 | 0.0083679051480521 |
| 45 | 0.988576368605601 | 0.0228472627887976 | 0.0114236313943988 |
| 46 | 0.985945947975429 | 0.0281081040491426 | 0.0140540520245713 |
| 47 | 0.984337761654986 | 0.031324476690027 | 0.0156622383450135 |
| 48 | 0.979674404216127 | 0.0406511915677471 | 0.0203255957838736 |
| 49 | 0.990958164441276 | 0.0180836711174485 | 0.00904183555872425 |
| 50 | 0.987691432315885 | 0.0246171353682301 | 0.0123085676841151 |
| 51 | 0.98343437183381 | 0.0331312563323805 | 0.0165656281661902 |
| 52 | 0.977240465842374 | 0.0455190683152526 | 0.0227595341576263 |
| 53 | 0.988704463770273 | 0.0225910724594544 | 0.0112955362297272 |
| 54 | 0.988648926975736 | 0.0227021460485277 | 0.0113510730242639 |
| 55 | 0.992900772490808 | 0.0141984550183835 | 0.00709922750919175 |
| 56 | 0.989015899324737 | 0.0219682013505260 | 0.0109841006752630 |
| 57 | 0.980930894004468 | 0.0381382119910647 | 0.0190691059955323 |
| 58 | 0.988418878361802 | 0.023162243276397 | 0.0115811216381985 |
| 59 | 0.978871432309137 | 0.0422571353817269 | 0.0211285676908635 |
| 60 | 0.964269053394728 | 0.0714618932105432 | 0.0357309466052716 |
| 61 | 0.978410894608649 | 0.0431782107827015 | 0.0215891053913508 |
| 62 | 0.95739077607793 | 0.0852184478441398 | 0.0426092239220699 |
| 63 | 0.937536716759945 | 0.124926566480111 | 0.0624632832400554 |
| 64 | 0.912413782777501 | 0.175172434444999 | 0.0875862172224993 |
| 65 | 0.842089988387512 | 0.315820023224976 | 0.157910011612488 |
| 66 | 0.878297309615333 | 0.243405380769335 | 0.121702690384667 |
| 67 | 0.820148913214373 | 0.359702173571254 | 0.179851086785627 |
| 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 | 24 | 0.380952380952381 | NOK |
| 10% type I error level | 30 | 0.476190476190476 | NOK |
