| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 3.1325199786894 + 0.448188598827917X[t] -0.196529035695261M1[t] -0.199326052210974M2[t] -0.129014384656366M3[t] + 0.0461667554608419M4[t] + 0.305492807671817M5[t] + 0.434456579648375M6[t] + 0.444094299413959M7[t] + 0.420623335109216M8[t] + 0.326116142781033M9[t] + 0.117152370804475M10[t] + 0.129637719765584M11[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) | 3.1325199786894 | 0.778925 | 4.0216 | 0.000208 | 0.000104 |
| X | 0.448188598827917 | 0.081127 | 5.5245 | 1e-06 | 1e-06 |
| M1 | -0.196529035695261 | 0.345024 | -0.5696 | 0.571655 | 0.285827 |
| M2 | -0.199326052210974 | 0.344688 | -0.5783 | 0.565836 | 0.282918 |
| M3 | -0.129014384656366 | 0.347362 | -0.3714 | 0.712 | 0.356 |
| M4 | 0.0461667554608419 | 0.346394 | 0.1333 | 0.894543 | 0.447271 |
| M5 | 0.305492807671817 | 0.345127 | 0.8852 | 0.380576 | 0.190288 |
| M6 | 0.434456579648375 | 0.345237 | 1.2584 | 0.214452 | 0.107226 |
| M7 | 0.444094299413959 | 0.346759 | 1.2807 | 0.206583 | 0.103291 |
| M8 | 0.420623335109216 | 0.349854 | 1.2023 | 0.235277 | 0.117638 |
| M9 | 0.326116142781033 | 0.354563 | 0.9198 | 0.36239 | 0.181195 |
| M10 | 0.117152370804475 | 0.354181 | 0.3308 | 0.742288 | 0.371144 |
| M11 | 0.129637719765584 | 0.34476 | 0.376 | 0.708592 | 0.354296 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.6765523075421 |
| R-squared | 0.45772302484054 |
| Adjusted R-squared | 0.319269329055146 |
| F-TEST (value) | 3.30596465658829 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 47 |
| p-value | 0.00159533698611725 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.544509777370832 |
| Sum Squared Residuals | 13.9350721896644 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 8.1 | 7.82124667021845 | 0.278753329781554 |
| 2 | 7.7 | 7.41507991475759 | 0.284920085242410 |
| 3 | 7.5 | 7.12684070324987 | 0.373159296750134 |
| 4 | 7.6 | 7.30202184336707 | 0.297978156632925 |
| 5 | 7.8 | 7.69580447522642 | 0.104195524773575 |
| 6 | 7.8 | 7.86958710708577 | -0.0695871070857745 |
| 7 | 7.8 | 7.83440596696857 | -0.0344059669685666 |
| 8 | 7.5 | 7.63165956313266 | -0.131659563132658 |
| 9 | 7.5 | 7.44751465103889 | 0.0524853489611086 |
| 10 | 7.1 | 7.28336973894512 | -0.183369738945125 |
| 11 | 7.5 | 7.78886254661694 | -0.288862546616941 |
| 12 | 7.5 | 7.74886254661694 | -0.248862546616941 |
| 13 | 7.6 | 7.50751465103889 | 0.0924853489611116 |
| 14 | 7.7 | 7.23580447522643 | 0.464195524773575 |
| 15 | 7.7 | 7.12684070324987 | 0.573159296750134 |
| 16 | 7.9 | 7.34684070324987 | 0.553159296750134 |
| 17 | 8.1 | 7.65098561534363 | 0.449014384656367 |
| 18 | 8.2 | 7.77994938732019 | 0.420050612679808 |
| 19 | 8.2 | 7.69994938732019 | 0.500050612679808 |
| 20 | 8.2 | 7.58684070324987 | 0.613159296750133 |
| 21 | 7.9 | 7.49233351092168 | 0.407666489078317 |
| 22 | 7.3 | 7.28336973894513 | 0.0166302610548752 |
| 23 | 6.9 | 7.65440596696857 | -0.754405966968567 |
| 24 | 6.6 | 7.61440596696857 | -1.01440596696857 |
| 25 | 6.7 | 7.32823921150772 | -0.628239211507722 |
| 26 | 6.9 | 7.10134789557805 | -0.20134789557805 |
| 27 | 7 | 7.03720298348428 | -0.0372029834842833 |
| 28 | 7.1 | 7.2123841236015 | -0.112384123601492 |
| 29 | 7.2 | 7.51652903569526 | -0.316529035695258 |
| 30 | 7.1 | 7.64549280767182 | -0.545492807671816 |
| 31 | 6.9 | 7.6551305274374 | -0.7551305274374 |
| 32 | 7 | 7.67647842301545 | -0.676478423015449 |
| 33 | 6.8 | 7.4026957911561 | -0.6026957911561 |
| 34 | 6.4 | 6.96963771976558 | -0.569637719765583 |
| 35 | 6.7 | 7.02694192860948 | -0.326941928609484 |
| 36 | 6.6 | 6.76284762919552 | -0.162847629195525 |
| 37 | 6.4 | 6.3870431539691 | 0.0129568460309029 |
| 38 | 6.3 | 6.47388385721897 | -0.173883857218968 |
| 39 | 6.2 | 6.54419552477358 | -0.344195524773575 |
| 40 | 6.5 | 6.76419552477358 | -0.264195524773575 |
| 41 | 6.8 | 6.97870271710176 | -0.178702717101759 |
| 42 | 6.8 | 6.97320990942994 | -0.173209909429942 |
| 43 | 6.4 | 6.75875332978157 | -0.358753329781567 |
| 44 | 6.1 | 6.60082578582845 | -0.500825785828451 |
| 45 | 5.8 | 6.37186201385189 | -0.571862013851893 |
| 46 | 6.1 | 6.3421736814065 | -0.242173681406501 |
| 47 | 7.2 | 6.9373042088439 | 0.2626957911561 |
| 48 | 7.3 | 7.03176078849227 | 0.268239211507725 |
| 49 | 6.9 | 6.65595631326585 | 0.244043686734153 |
| 50 | 6.1 | 6.47388385721897 | -0.373883857218968 |
| 51 | 5.8 | 6.36492008524241 | -0.564920085242409 |
| 52 | 6.2 | 6.67455780500799 | -0.474557805007992 |
| 53 | 7.1 | 7.15797815663293 | -0.0579781566329257 |
| 54 | 7.7 | 7.33176078849228 | 0.368239211507725 |
| 55 | 7.9 | 7.25176078849228 | 0.648239211507725 |
| 56 | 7.7 | 7.00419552477357 | 0.695804475226425 |
| 57 | 7.4 | 6.68559403303143 | 0.714405966968567 |
| 58 | 7.5 | 6.52144912093767 | 0.978550879062333 |
| 59 | 8 | 6.89248534896111 | 1.10751465103889 |
| 60 | 8.1 | 6.94212306872669 | 1.15787693127331 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0260356253292302 | 0.0520712506584604 | 0.97396437467077 |
| 17 | 0.0177052556515251 | 0.0354105113030503 | 0.982294744348475 |
| 18 | 0.0195832449421587 | 0.0391664898843175 | 0.980416755057841 |
| 19 | 0.0185891664020576 | 0.0371783328041152 | 0.981410833597942 |
| 20 | 0.0357056445972754 | 0.0714112891945508 | 0.964294355402725 |
| 21 | 0.0269332443137380 | 0.0538664886274761 | 0.973066755686262 |
| 22 | 0.0135731993444336 | 0.0271463986888672 | 0.986426800655566 |
| 23 | 0.0133401153186102 | 0.0266802306372205 | 0.98665988468139 |
| 24 | 0.0300301079921946 | 0.0600602159843892 | 0.969969892007805 |
| 25 | 0.0313305910906898 | 0.0626611821813795 | 0.96866940890931 |
| 26 | 0.0194156002054765 | 0.0388312004109531 | 0.980584399794523 |
| 27 | 0.0150835011996666 | 0.0301670023993332 | 0.984916498800333 |
| 28 | 0.0106636471950221 | 0.0213272943900441 | 0.989336352804978 |
| 29 | 0.00644859414466569 | 0.0128971882893314 | 0.993551405855334 |
| 30 | 0.00465363711349979 | 0.00930727422699958 | 0.9953463628865 |
| 31 | 0.0086922297835737 | 0.0173844595671474 | 0.991307770216426 |
| 32 | 0.0279623899324669 | 0.0559247798649337 | 0.972037610067533 |
| 33 | 0.0517542429340556 | 0.103508485868111 | 0.948245757065944 |
| 34 | 0.211861924464144 | 0.423723848928288 | 0.788138075535856 |
| 35 | 0.618881821674431 | 0.762236356651138 | 0.381118178325569 |
| 36 | 0.649555474025257 | 0.700889051949486 | 0.350444525974743 |
| 37 | 0.583746010559743 | 0.832507978880514 | 0.416253989440257 |
| 38 | 0.487899793404532 | 0.975799586809064 | 0.512100206595468 |
| 39 | 0.412647576214355 | 0.825295152428709 | 0.587352423785645 |
| 40 | 0.313542094258642 | 0.627084188517284 | 0.686457905741358 |
| 41 | 0.227899764598937 | 0.455799529197874 | 0.772100235401063 |
| 42 | 0.160248327951017 | 0.320496655902034 | 0.839751672048983 |
| 43 | 0.107322358884908 | 0.214644717769816 | 0.892677641115092 |
| 44 | 0.0540735552047762 | 0.108147110409552 | 0.945926444795224 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 1 | 0.0344827586206897 | NOK |
| 5% type I error level | 11 | 0.379310344827586 | NOK |
| 10% type I error level | 17 | 0.586206896551724 | NOK |
