| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 7.70546056652312 -0.309228385849713X[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) | 7.70546056652312 | 0.324173 | 23.7696 | 0 | 0 |
| X | -0.309228385849713 | 0.155277 | -1.9915 | 0.051066 | 0.025533 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.250968372521009 |
| R-squared | 0.0629851240058438 |
| Adjusted R-squared | 0.0471035159381463 |
| F-TEST (value) | 3.96591602924345 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 59 |
| p-value | 0.0510662732824697 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.74579163111317 |
| Sum Squared Residuals | 32.8161042652681 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 5.4 | 6.8705439247289 | -1.47054392472889 |
| 2 | 5.4 | 6.93238960189883 | -1.53238960189883 |
| 3 | 5.6 | 7.02515811765375 | -1.42515811765375 |
| 4 | 5.7 | 6.80869824755895 | -1.10869824755895 |
| 5 | 5.8 | 6.746852570389 | -0.946852570389005 |
| 6 | 5.8 | 6.77777540897398 | -0.977775408973976 |
| 7 | 5.8 | 6.83962108614392 | -1.03962108614392 |
| 8 | 5.9 | 6.93238960189883 | -1.03238960189883 |
| 9 | 6.1 | 7.11792663340866 | -1.01792663340866 |
| 10 | 6.4 | 7.11792663340866 | -0.717926633408661 |
| 11 | 6.4 | 7.14884947199363 | -0.748849471993632 |
| 12 | 6.3 | 7.08700379482369 | -0.78700379482369 |
| 13 | 6.2 | 6.90146676331386 | -0.701466763313861 |
| 14 | 6.2 | 6.93238960189883 | -0.732389601898833 |
| 15 | 6.3 | 6.93238960189883 | -0.632389601898833 |
| 16 | 6.4 | 7.21069514916358 | -0.810695149163575 |
| 17 | 6.5 | 7.27254082633352 | -0.772540826333518 |
| 18 | 6.6 | 7.45807785784335 | -0.858077857843347 |
| 19 | 6.6 | 7.36530934208843 | -0.765309342088433 |
| 20 | 6.6 | 7.30346366491849 | -0.70346366491849 |
| 21 | 6.8 | 7.33438650350346 | -0.534386503503461 |
| 22 | 7 | 7.30346366491849 | -0.303463664918490 |
| 23 | 7.2 | 7.36530934208843 | -0.165309342088432 |
| 24 | 7.3 | 7.30346366491849 | -0.00346366491848968 |
| 25 | 7.5 | 7.33438650350346 | 0.165613496496539 |
| 26 | 7.6 | 7.21069514916358 | 0.389304850836424 |
| 27 | 7.6 | 7.1797723105786 | 0.420227689421396 |
| 28 | 7.7 | 7.24161798774855 | 0.458382012251453 |
| 29 | 7.7 | 7.42715501925838 | 0.272844980741625 |
| 30 | 7.7 | 7.24161798774855 | 0.458382012251453 |
| 31 | 7.7 | 7.27254082633352 | 0.427459173666482 |
| 32 | 7.6 | 7.21069514916358 | 0.389304850836424 |
| 33 | 7.7 | 7.1797723105786 | 0.520227689421396 |
| 34 | 7.9 | 7.27254082633352 | 0.627459173666482 |
| 35 | 7.9 | 7.14884947199363 | 0.751150528006368 |
| 36 | 7.9 | 7.1797723105786 | 0.720227689421396 |
| 37 | 7.8 | 7.27254082633352 | 0.527459173666482 |
| 38 | 7.6 | 7.33438650350346 | 0.265613496496539 |
| 39 | 7.4 | 7.39623218067340 | 0.0037678193265967 |
| 40 | 7 | 7.1797723105786 | -0.179772310578604 |
| 41 | 7 | 6.96331244048380 | 0.0366875595161955 |
| 42 | 7.2 | 7.08700379482369 | 0.112996205176310 |
| 43 | 7.5 | 7.05608095623872 | 0.443919043761281 |
| 44 | 7.8 | 7.08700379482369 | 0.71299620517631 |
| 45 | 7.8 | 7.14884947199363 | 0.651150528006367 |
| 46 | 7.7 | 6.87054392472889 | 0.82945607527111 |
| 47 | 7.6 | 6.99423527906878 | 0.605764720931224 |
| 48 | 7.6 | 7.11792663340866 | 0.482073366591338 |
| 49 | 7.5 | 7.08700379482369 | 0.41299620517631 |
| 50 | 7.5 | 6.99423527906878 | 0.505764720931224 |
| 51 | 7.6 | 6.83962108614392 | 0.760378913856081 |
| 52 | 7.6 | 6.96331244048380 | 0.636687559516195 |
| 53 | 7.9 | 6.99423527906878 | 0.905764720931225 |
| 54 | 7.6 | 6.87054392472889 | 0.72945607527111 |
| 55 | 7.5 | 6.87054392472889 | 0.62945607527111 |
| 56 | 7.5 | 6.80869824755895 | 0.691301752441053 |
| 57 | 7.6 | 6.77777540897398 | 0.822224591026024 |
| 58 | 7.7 | 7.02515811765375 | 0.674841882346253 |
| 59 | 7.8 | 6.99423527906878 | 0.805764720931224 |
| 60 | 7.9 | 6.83962108614392 | 1.06037891385608 |
| 61 | 7.9 | 6.83962108614392 | 1.06037891385608 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0250964473554747 | 0.0501928947109494 | 0.974903552644525 |
| 6 | 0.00808807516244473 | 0.0161761503248895 | 0.991911924837555 |
| 7 | 0.00362281824282741 | 0.00724563648565482 | 0.996377181757173 |
| 8 | 0.00575133818551505 | 0.0115026763710301 | 0.994248661814485 |
| 9 | 0.0143788168960079 | 0.0287576337920157 | 0.985621183103992 |
| 10 | 0.0288702907906709 | 0.0577405815813417 | 0.97112970920933 |
| 11 | 0.0258361420904582 | 0.0516722841809165 | 0.974163857909542 |
| 12 | 0.0222763819609424 | 0.0445527639218847 | 0.977723618039058 |
| 13 | 0.0393816861219376 | 0.0787633722438753 | 0.960618313878062 |
| 14 | 0.0668008641661893 | 0.133601728332379 | 0.93319913583381 |
| 15 | 0.148875668308548 | 0.297751336617096 | 0.851124331691452 |
| 16 | 0.176396926584069 | 0.352793853168139 | 0.82360307341593 |
| 17 | 0.203264153808227 | 0.406528307616454 | 0.796735846191773 |
| 18 | 0.216057773958275 | 0.432115547916549 | 0.783942226041725 |
| 19 | 0.267248008247553 | 0.534496016495107 | 0.732751991752447 |
| 20 | 0.41092928092471 | 0.82185856184942 | 0.58907071907529 |
| 21 | 0.573923001319233 | 0.852153997361534 | 0.426076998680767 |
| 22 | 0.7728524432904 | 0.4542951134192 | 0.2271475567096 |
| 23 | 0.875509536159304 | 0.248980927681392 | 0.124490463840696 |
| 24 | 0.954212949923442 | 0.091574100153117 | 0.0457870500765585 |
| 25 | 0.982421326803677 | 0.0351573463926463 | 0.0175786731963232 |
| 26 | 0.99749170260408 | 0.00501659479183989 | 0.00250829739591994 |
| 27 | 0.999493670515697 | 0.00101265896860615 | 0.000506329484303077 |
| 28 | 0.999799622669284 | 0.000400754661432992 | 0.000200377330716496 |
| 29 | 0.999707960862645 | 0.000584078274710898 | 0.000292039137355449 |
| 30 | 0.999809315256334 | 0.000381369487332947 | 0.000190684743666474 |
| 31 | 0.999817234786196 | 0.000365530427608374 | 0.000182765213804187 |
| 32 | 0.999815782399926 | 0.000368435200148294 | 0.000184217600074147 |
| 33 | 0.999853065793984 | 0.000293868412032814 | 0.000146934206016407 |
| 34 | 0.999903303322528 | 0.000193393354943482 | 9.6696677471741e-05 |
| 35 | 0.999962288705724 | 7.54225885522416e-05 | 3.77112942761208e-05 |
| 36 | 0.999981516437207 | 3.69671255865273e-05 | 1.84835627932637e-05 |
| 37 | 0.999981627305686 | 3.6745388627857e-05 | 1.83726943139285e-05 |
| 38 | 0.99996396756905 | 7.20648618987994e-05 | 3.60324309493997e-05 |
| 39 | 0.999912832345487 | 0.000174335309026698 | 8.7167654513349e-05 |
| 40 | 0.999964467091453 | 7.10658170942894e-05 | 3.55329085471447e-05 |
| 41 | 0.999998647473245 | 2.70505351066890e-06 | 1.35252675533445e-06 |
| 42 | 0.99999983477046 | 3.30459081437200e-07 | 1.65229540718600e-07 |
| 43 | 0.999999776918393 | 4.46163214019253e-07 | 2.23081607009627e-07 |
| 44 | 0.99999962322536 | 7.53549279051757e-07 | 3.76774639525879e-07 |
| 45 | 0.99999929529489 | 1.40941022172089e-06 | 7.04705110860446e-07 |
| 46 | 0.999998721258512 | 2.55748297697487e-06 | 1.27874148848743e-06 |
| 47 | 0.999996178287939 | 7.64342412227562e-06 | 3.82171206113781e-06 |
| 48 | 0.99998634159904 | 2.7316801918806e-05 | 1.3658400959403e-05 |
| 49 | 0.999971626301324 | 5.67473973513371e-05 | 2.83736986756686e-05 |
| 50 | 0.999957617940749 | 8.47641185018995e-05 | 4.23820592509497e-05 |
| 51 | 0.999868815800677 | 0.000262368398646118 | 0.000131184199323059 |
| 52 | 0.999647590370066 | 0.000704819259868467 | 0.000352409629934233 |
| 53 | 0.999033139145377 | 0.00193372170924613 | 0.000966860854623063 |
| 54 | 0.996646245815013 | 0.00670750836997378 | 0.00335375418498689 |
| 55 | 0.992747936783641 | 0.0145041264327172 | 0.00725206321635859 |
| 56 | 0.98768159889554 | 0.0246368022089197 | 0.0123184011044599 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 30 | 0.576923076923077 | NOK |
| 5% type I error level | 37 | 0.711538461538462 | NOK |
| 10% type I error level | 42 | 0.807692307692308 | NOK |
