| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 6.66044393743112 + 0.145004737137222X[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) | 6.66044393743112 | 0.185533 | 35.899 | 0 | 0 |
| X | 0.145004737137222 | 0.01964 | 7.383 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.661656111589323 |
| R-squared | 0.437788810003502 |
| Adjusted R-squared | 0.429757221574981 |
| F-TEST (value) | 54.5083720237515 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 70 |
| p-value | 2.49030684962293e-10 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.526392140220193 |
| Sum Squared Residuals | 19.3962079699917 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 8.3 | 8.11049130880333 | 0.189508691196674 |
| 2 | 8.2 | 7.67547709739168 | 0.524522902608324 |
| 3 | 8 | 7.38546762311723 | 0.61453237688277 |
| 4 | 7.9 | 7.96548657166612 | -0.0654865716661187 |
| 5 | 7.6 | 8.11049130880334 | -0.510491308803342 |
| 6 | 7.6 | 7.96548657166612 | -0.365486571666119 |
| 7 | 8.3 | 7.8204818345289 | 0.479518165471104 |
| 8 | 8.4 | 7.67547709739167 | 0.724522902608326 |
| 9 | 8.4 | 8.11049130880334 | 0.289508691196659 |
| 10 | 8.4 | 7.96548657166612 | 0.434513428333881 |
| 11 | 8.4 | 8.25549604594056 | 0.144503954059437 |
| 12 | 8.6 | 8.40050078307779 | 0.199499216922214 |
| 13 | 8.9 | 8.40050078307779 | 0.499499216922214 |
| 14 | 8.8 | 8.40050078307779 | 0.399499216922215 |
| 15 | 8.3 | 8.40050078307779 | -0.100500783077785 |
| 16 | 7.5 | 8.40050078307779 | -0.900500783077786 |
| 17 | 7.2 | 8.25549604594056 | -1.05549604594056 |
| 18 | 7.4 | 8.40050078307779 | -1.00050078307779 |
| 19 | 8.8 | 8.25549604594056 | 0.544503954059437 |
| 20 | 9.3 | 8.40050078307779 | 0.899499216922215 |
| 21 | 9.3 | 8.25549604594056 | 1.04450395405944 |
| 22 | 8.7 | 8.54550552021501 | 0.154494479784991 |
| 23 | 8.2 | 8.11049130880334 | 0.0895086911966579 |
| 24 | 8.3 | 8.25549604594056 | 0.044503954059437 |
| 25 | 8.5 | 8.40050078307779 | 0.099499216922214 |
| 26 | 8.6 | 8.40050078307779 | 0.199499216922214 |
| 27 | 8.5 | 8.25549604594056 | 0.244503954059436 |
| 28 | 8.2 | 7.96548657166612 | 0.23451342833388 |
| 29 | 8.1 | 7.8204818345289 | 0.279518165471103 |
| 30 | 7.9 | 7.96548657166612 | -0.0654865716661187 |
| 31 | 8.6 | 7.96548657166612 | 0.634513428333881 |
| 32 | 8.7 | 7.8204818345289 | 0.879518165471103 |
| 33 | 8.7 | 7.53047236025445 | 1.16952763974555 |
| 34 | 8.5 | 8.11049130880334 | 0.389508691196659 |
| 35 | 8.4 | 8.11049130880334 | 0.289508691196659 |
| 36 | 8.5 | 8.25549604594056 | 0.244503954059436 |
| 37 | 8.7 | 8.40050078307779 | 0.299499216922213 |
| 38 | 8.7 | 8.40050078307779 | 0.299499216922213 |
| 39 | 8.6 | 8.25549604594056 | 0.344503954059436 |
| 40 | 8.5 | 8.25549604594056 | 0.244503954059436 |
| 41 | 8.3 | 7.96548657166612 | 0.334513428333882 |
| 42 | 8 | 8.25549604594056 | -0.255496045940564 |
| 43 | 8.2 | 8.25549604594056 | -0.0554960459405645 |
| 44 | 8.1 | 8.25549604594056 | -0.155496045940564 |
| 45 | 8.1 | 7.96548657166612 | 0.134513428333881 |
| 46 | 8 | 8.40050078307779 | -0.400500783077786 |
| 47 | 7.9 | 8.40050078307779 | -0.500500783077786 |
| 48 | 7.9 | 8.11049130880334 | -0.210491308803341 |
| 49 | 8 | 8.40050078307779 | -0.400500783077786 |
| 50 | 8 | 8.25549604594056 | -0.255496045940564 |
| 51 | 7.9 | 8.11049130880334 | -0.210491308803341 |
| 52 | 8 | 8.25549604594056 | -0.255496045940564 |
| 53 | 7.7 | 8.25549604594056 | -0.555496045940564 |
| 54 | 7.2 | 8.11049130880334 | -0.910491308803341 |
| 55 | 7.5 | 7.96548657166612 | -0.465486571666119 |
| 56 | 7.3 | 7.8204818345289 | -0.520481834528897 |
| 57 | 7 | 7.96548657166612 | -0.965486571666119 |
| 58 | 7 | 7.8204818345289 | -0.820481834528897 |
| 59 | 7 | 7.38546762311723 | -0.38546762311723 |
| 60 | 7.2 | 7.53047236025445 | -0.330472360254452 |
| 61 | 7.3 | 7.24046288598001 | 0.0595371140199923 |
| 62 | 7.1 | 7.67547709739167 | -0.575477097391675 |
| 63 | 6.8 | 7.24046288598001 | -0.440462885980008 |
| 64 | 6.4 | 7.24046288598001 | -0.840462885980007 |
| 65 | 6.1 | 7.24046288598001 | -1.14046288598001 |
| 66 | 6.5 | 6.66044393743112 | -0.160443937431118 |
| 67 | 7.7 | 6.95045341170556 | 0.749546588294437 |
| 68 | 7.9 | 7.24046288598001 | 0.659537114019993 |
| 69 | 7.5 | 7.53047236025445 | -0.0304723602544521 |
| 70 | 6.9 | 6.80544867456834 | 0.09455132543166 |
| 71 | 6.6 | 6.95045341170556 | -0.350453411705563 |
| 72 | 6.9 | 6.80544867456834 | 0.09455132543166 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.201634931661317 | 0.403269863322634 | 0.798365068338683 |
| 6 | 0.158680686646084 | 0.317361373292168 | 0.841319313353916 |
| 7 | 0.123378916740595 | 0.246757833481191 | 0.876621083259405 |
| 8 | 0.100275141591751 | 0.200550283183502 | 0.899724858408249 |
| 9 | 0.100018571552418 | 0.200037143104836 | 0.899981428447582 |
| 10 | 0.0794261745575863 | 0.158852349115173 | 0.920573825442414 |
| 11 | 0.0583718492516754 | 0.116743698503351 | 0.941628150748325 |
| 12 | 0.0499758852399392 | 0.0999517704798785 | 0.95002411476006 |
| 13 | 0.0650402193122202 | 0.130080438624440 | 0.93495978068778 |
| 14 | 0.0523920457599798 | 0.104784091519960 | 0.94760795424002 |
| 15 | 0.0337859294207408 | 0.0675718588414816 | 0.96621407057926 |
| 16 | 0.127123665630304 | 0.254247331260609 | 0.872876334369696 |
| 17 | 0.354887190760272 | 0.709774381520544 | 0.645112809239728 |
| 18 | 0.49254786714204 | 0.98509573428408 | 0.50745213285796 |
| 19 | 0.527498302243903 | 0.945003395512193 | 0.472501697756097 |
| 20 | 0.723851034925295 | 0.55229793014941 | 0.276148965074705 |
| 21 | 0.866935713272604 | 0.266128573454791 | 0.133064286727396 |
| 22 | 0.831601228539993 | 0.336797542920013 | 0.168398771460007 |
| 23 | 0.782815682817092 | 0.434368634365815 | 0.217184317182908 |
| 24 | 0.725836239374492 | 0.548327521251015 | 0.274163760625508 |
| 25 | 0.665731572908055 | 0.66853685418389 | 0.334268427091945 |
| 26 | 0.610434143690936 | 0.779131712618129 | 0.389565856309064 |
| 27 | 0.554465045123061 | 0.891069909753877 | 0.445534954876939 |
| 28 | 0.493809414030442 | 0.987618828060883 | 0.506190585969558 |
| 29 | 0.437573228193504 | 0.875146456387008 | 0.562426771806496 |
| 30 | 0.38352280216428 | 0.76704560432856 | 0.61647719783572 |
| 31 | 0.397782321866463 | 0.795564643732925 | 0.602217678133537 |
| 32 | 0.490744827381155 | 0.98148965476231 | 0.509255172618845 |
| 33 | 0.702294077844172 | 0.595411844311656 | 0.297705922155828 |
| 34 | 0.691276605191057 | 0.617446789617885 | 0.308723394808943 |
| 35 | 0.665764939704677 | 0.668470120590645 | 0.334235060295323 |
| 36 | 0.639417883149273 | 0.721164233701455 | 0.360582116850727 |
| 37 | 0.63870386642472 | 0.72259226715056 | 0.36129613357528 |
| 38 | 0.647659279552814 | 0.704681440894372 | 0.352340720447186 |
| 39 | 0.672061869582135 | 0.65587626083573 | 0.327938130417865 |
| 40 | 0.682312990557057 | 0.635374018885886 | 0.317687009442943 |
| 41 | 0.712298243100874 | 0.575403513798252 | 0.287701756899126 |
| 42 | 0.676144482275835 | 0.64771103544833 | 0.323855517724165 |
| 43 | 0.649654165532517 | 0.700691668934966 | 0.350345834467483 |
| 44 | 0.616244601276595 | 0.76751079744681 | 0.383755398723405 |
| 45 | 0.626590229424199 | 0.746819541151603 | 0.373409770575801 |
| 46 | 0.58606269177445 | 0.8278746164511 | 0.41393730822555 |
| 47 | 0.546744741600744 | 0.906510516798511 | 0.453255258399256 |
| 48 | 0.517798934429409 | 0.964402131141182 | 0.482201065570591 |
| 49 | 0.476008378673189 | 0.952016757346378 | 0.523991621326811 |
| 50 | 0.453317430924227 | 0.906634861848453 | 0.546682569075773 |
| 51 | 0.443673750357212 | 0.887347500714424 | 0.556326249642788 |
| 52 | 0.457426313878433 | 0.914852627756866 | 0.542573686121567 |
| 53 | 0.447457284311792 | 0.894914568623584 | 0.552542715688208 |
| 54 | 0.477882628320142 | 0.955765256640283 | 0.522117371679858 |
| 55 | 0.459589790892676 | 0.919179581785353 | 0.540410209107324 |
| 56 | 0.439058752885508 | 0.878117505771016 | 0.560941247114492 |
| 57 | 0.460423949973459 | 0.920847899946919 | 0.539576050026541 |
| 58 | 0.457134691176783 | 0.914269382353566 | 0.542865308823217 |
| 59 | 0.400867044330790 | 0.801734088661581 | 0.59913295566921 |
| 60 | 0.327674745806351 | 0.655349491612702 | 0.672325254193649 |
| 61 | 0.264108729655594 | 0.528217459311188 | 0.735891270344406 |
| 62 | 0.206313250807009 | 0.412626501614019 | 0.79368674919299 |
| 63 | 0.156153685838297 | 0.312307371676595 | 0.843846314161703 |
| 64 | 0.197857373104450 | 0.395714746208901 | 0.80214262689555 |
| 65 | 0.646915582436826 | 0.706168835126348 | 0.353084417563174 |
| 66 | 0.538000476943639 | 0.923999046112722 | 0.461999523056361 |
| 67 | 0.624180258619905 | 0.75163948276019 | 0.375819741380095 |
| 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 | 0 | 0 | OK |
| 10% type I error level | 2 | 0.0317460317460317 | OK |
