| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -0.113771342246555 + 0.91769036315211X[t] -0.0925798631239247M1[t] -0.0284991943610653M2[t] -0.163362011632986M3[t] -0.0494389995279161M4[t] + 0.0508763137876616M5[t] -0.0463800316507418M6[t] -0.206029905255629M7[t] -0.177600337053634M8[t] -0.271640057957075M9[t] + 0.055004922621967M10[t] -0.0387321832417344M11[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) | -0.113771342246555 | 0.716703 | -0.1587 | 0.874443 | 0.437221 |
| X | 0.91769036315211 | 0.15556 | 5.8993 | 0 | 0 |
| M1 | -0.0925798631239247 | 0.759731 | -0.1219 | 0.903447 | 0.451724 |
| M2 | -0.0284991943610653 | 0.760091 | -0.0375 | 0.970224 | 0.485112 |
| M3 | -0.163362011632986 | 0.760078 | -0.2149 | 0.830604 | 0.415302 |
| M4 | -0.0494389995279161 | 0.760354 | -0.065 | 0.948389 | 0.474194 |
| M5 | 0.0508763137876616 | 0.760698 | 0.0669 | 0.946915 | 0.473457 |
| M6 | -0.0463800316507418 | 0.760384 | -0.061 | 0.95158 | 0.47579 |
| M7 | -0.206029905255629 | 0.759872 | -0.2711 | 0.787282 | 0.393641 |
| M8 | -0.177600337053634 | 0.759614 | -0.2338 | 0.81599 | 0.407995 |
| M9 | -0.271640057957075 | 0.759552 | -0.3576 | 0.721963 | 0.360982 |
| M10 | 0.055004922621967 | 0.793272 | 0.0693 | 0.944967 | 0.472483 |
| M11 | -0.0387321832417344 | 0.792953 | -0.0488 | 0.961216 | 0.480608 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.626562034371423 |
| R-squared | 0.392579982915657 |
| Adjusted R-squared | 0.262418550683297 |
| F-TEST (value) | 3.01610066962722 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 56 |
| p-value | 0.00255174287534687 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.25367055569551 |
| Sum Squared Residuals | 88.0146322842021 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.4 | 1.62902952093374 | -0.229029520933737 |
| 2 | 1.2 | 1.69311018969660 | -0.493110189696596 |
| 3 | 1 | 1.55824737242468 | -0.558247372424678 |
| 4 | 1.7 | 1.67217038452975 | 0.0278296154702518 |
| 5 | 2.4 | 1.77248569784533 | 0.627514302154674 |
| 6 | 2 | 1.67522935240692 | 0.324770647593079 |
| 7 | 2.1 | 1.51557947880203 | 0.584420521197966 |
| 8 | 2 | 1.54400904700403 | 0.455990952995969 |
| 9 | 1.8 | 1.44996932610059 | 0.350030673899411 |
| 10 | 2.7 | 1.77661430667963 | 0.92338569332037 |
| 11 | 2.3 | 1.68287720081593 | 0.617122799184071 |
| 12 | 1.9 | 1.72160938405766 | 0.178390615942336 |
| 13 | 2 | 1.62902952093374 | 0.370970479066261 |
| 14 | 2.3 | 1.6931101896966 | 0.606889810303401 |
| 15 | 2.8 | 1.55824737242468 | 1.24175262757532 |
| 16 | 2.4 | 1.67217038452975 | 0.727829615470252 |
| 17 | 2.3 | 1.77248569784533 | 0.527514302154674 |
| 18 | 2.7 | 1.67522935240692 | 1.02477064759308 |
| 19 | 2.7 | 1.51557947880203 | 1.18442052119797 |
| 20 | 2.9 | 1.54400904700403 | 1.35599095299597 |
| 21 | 3 | 1.44996932610059 | 1.55003067389941 |
| 22 | 2.2 | 1.77661430667963 | 0.423385693320369 |
| 23 | 2.3 | 1.68287720081593 | 0.61712279918407 |
| 24 | 2.8 | 1.91432436031961 | 0.885675639680393 |
| 25 | 2.8 | 1.85845211172177 | 0.941547888278233 |
| 26 | 2.8 | 1.92253278048463 | 0.877467219515374 |
| 27 | 2.2 | 1.97120803584313 | 0.228791964156873 |
| 28 | 2.6 | 2.1310155661058 | 0.468984433894197 |
| 29 | 2.8 | 2.23133087942138 | 0.56866912057862 |
| 30 | 2.5 | 2.26255118482427 | 0.237448815175728 |
| 31 | 2.4 | 2.20384725116612 | 0.196152748833883 |
| 32 | 2.3 | 2.39746108473549 | -0.097461084735493 |
| 33 | 1.9 | 2.3676596892527 | -0.467659689252699 |
| 34 | 1.7 | 2.8503120315676 | -1.1503120315676 |
| 35 | 2 | 2.82999015475607 | -0.829990154756067 |
| 36 | 2.1 | 2.99719898883910 | -0.897198988839096 |
| 37 | 1.7 | 3.00556506566190 | -1.30556506566190 |
| 38 | 1.8 | 3.06964573442476 | -1.26964573442476 |
| 39 | 1.8 | 3.07243647162566 | -1.27243647162566 |
| 40 | 1.8 | 3.27812852004594 | -1.47812852004594 |
| 41 | 1.3 | 3.37844383336152 | -2.07844383336152 |
| 42 | 1.3 | 3.41884104239593 | -2.11884104239593 |
| 43 | 1.3 | 3.35096020510625 | -2.05096020510625 |
| 44 | 1.2 | 3.37938977330825 | -2.17938977330825 |
| 45 | 1.4 | 3.28535005240481 | -1.88535005240481 |
| 46 | 2.2 | 3.61199503298385 | -1.41199503298385 |
| 47 | 2.9 | 3.51825792712015 | -0.618257927120149 |
| 48 | 3.1 | 3.55699011036188 | -0.456990110361884 |
| 49 | 3.5 | 3.46441024723796 | 0.035589752762041 |
| 50 | 3.6 | 3.52849091600082 | 0.0715090839991817 |
| 51 | 4.4 | 3.3936280987289 | 1.00637190127110 |
| 52 | 4.1 | 3.50755111083397 | 0.592448889166032 |
| 53 | 5.1 | 3.60786642414955 | 1.49213357585045 |
| 54 | 5.8 | 3.51061007871114 | 2.28938992128886 |
| 55 | 5.9 | 3.51614447047363 | 2.38385552952637 |
| 56 | 5.4 | 3.60881236409628 | 1.79118763590372 |
| 57 | 5.5 | 3.51477264319284 | 1.98522735680716 |
| 58 | 4.8 | 3.58446432208929 | 1.21553567791071 |
| 59 | 3.2 | 2.98599751649193 | 0.214002483508075 |
| 60 | 2.7 | 2.40987715642175 | 0.290122843578254 |
| 61 | 2.1 | 1.91351353351089 | 0.186486466489107 |
| 62 | 1.9 | 1.6931101896966 | 0.206889810303402 |
| 63 | 0.6 | 1.24623264895296 | -0.64623264895296 |
| 64 | 0.7 | 1.03896403395479 | -0.338964033954792 |
| 65 | -0.2 | 0.937387467376906 | -1.13738746737691 |
| 66 | -1 | 0.757538989254811 | -1.75753898925481 |
| 67 | -1.7 | 0.597889115649925 | -2.29788911564992 |
| 68 | -0.7 | 0.62631868385192 | -1.32631868385192 |
| 69 | -1 | 0.532278962948479 | -1.53227896294848 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.271617070596562 | 0.543234141193124 | 0.728382929403438 |
| 17 | 0.138541768660063 | 0.277083537320127 | 0.861458231339937 |
| 18 | 0.078927784053455 | 0.15785556810691 | 0.921072215946545 |
| 19 | 0.043541970063468 | 0.087083940126936 | 0.956458029936532 |
| 20 | 0.0296119228130647 | 0.0592238456261295 | 0.970388077186935 |
| 21 | 0.0274416082811100 | 0.0548832165622201 | 0.97255839171889 |
| 22 | 0.0146319290352657 | 0.0292638580705314 | 0.985368070964734 |
| 23 | 0.00698982869017801 | 0.0139796573803560 | 0.993010171309822 |
| 24 | 0.00330579546680039 | 0.00661159093360077 | 0.9966942045332 |
| 25 | 0.00154173812244075 | 0.00308347624488151 | 0.99845826187756 |
| 26 | 0.000691848191199495 | 0.00138369638239899 | 0.9993081518088 |
| 27 | 0.000682503046308733 | 0.00136500609261747 | 0.999317496953691 |
| 28 | 0.00033323214137309 | 0.00066646428274618 | 0.999666767858627 |
| 29 | 0.000160596463132366 | 0.000321192926264733 | 0.999839403536868 |
| 30 | 9.2026202691436e-05 | 0.000184052405382872 | 0.999907973797309 |
| 31 | 5.37366783881139e-05 | 0.000107473356776228 | 0.999946263321612 |
| 32 | 2.97596600300527e-05 | 5.95193200601055e-05 | 0.99997024033997 |
| 33 | 1.81012770883963e-05 | 3.62025541767927e-05 | 0.999981898722912 |
| 34 | 1.15872292575225e-05 | 2.31744585150451e-05 | 0.999988412770742 |
| 35 | 4.21209320490344e-06 | 8.42418640980689e-06 | 0.999995787906795 |
| 36 | 1.50500642268526e-06 | 3.01001284537052e-06 | 0.999998494993577 |
| 37 | 6.54242088049186e-07 | 1.30848417609837e-06 | 0.999999345757912 |
| 38 | 2.80614837912025e-07 | 5.6122967582405e-07 | 0.999999719385162 |
| 39 | 1.29979638438219e-07 | 2.59959276876439e-07 | 0.999999870020362 |
| 40 | 7.60870347538039e-08 | 1.52174069507608e-07 | 0.999999923912965 |
| 41 | 1.96674797758102e-07 | 3.93349595516204e-07 | 0.999999803325202 |
| 42 | 6.42757174953938e-07 | 1.28551434990788e-06 | 0.999999357242825 |
| 43 | 2.16452600486395e-06 | 4.32905200972791e-06 | 0.999997835473995 |
| 44 | 2.65473640077253e-05 | 5.30947280154506e-05 | 0.999973452635992 |
| 45 | 0.000449890900587829 | 0.000899781801175658 | 0.999550109099412 |
| 46 | 0.00254254723900535 | 0.00508509447801069 | 0.997457452760995 |
| 47 | 0.0050037942149748 | 0.0100075884299496 | 0.994996205785025 |
| 48 | 0.0164291107207545 | 0.0328582214415089 | 0.983570889279246 |
| 49 | 0.0680893785913216 | 0.136178757182643 | 0.931910621408678 |
| 50 | 0.276385333526188 | 0.552770667052376 | 0.723614666473812 |
| 51 | 0.36007785048039 | 0.72015570096078 | 0.63992214951961 |
| 52 | 0.761874145322949 | 0.476251709354102 | 0.238125854677051 |
| 53 | 0.7756739101057 | 0.448652179788599 | 0.224326089894299 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 23 | 0.605263157894737 | NOK |
| 5% type I error level | 27 | 0.710526315789474 | NOK |
| 10% type I error level | 30 | 0.789473684210526 | NOK |
