| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.21788686486356 + 0.484134343472141X[t] + 1.47743594518220Y1[t] -1.00247950308246Y2[t] + 0.142867662547923Y3[t] + 0.160203862531591Y4[t] -0.889739069238092M1[t] -1.03979564822641M2[t] -0.877831720066912M3[t] -0.372343703812319M4[t] -1.29197609960059M5[t] + 0.190290825479914M6[t] + 3.04103217720423M7[t] -2.16551128616970M8[t] + 0.636778689366172M9[t] + 0.306992689379753M10[t] -0.656329660215681M11[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) | 1.21788686486356 | 1.070239 | 1.138 | 0.262081 | 0.13104 |
| X | 0.484134343472141 | 0.249159 | 1.9431 | 0.059251 | 0.029625 |
| Y1 | 1.47743594518220 | 0.178676 | 8.2688 | 0 | 0 |
| Y2 | -1.00247950308246 | 0.298226 | -3.3615 | 0.001746 | 0.000873 |
| Y3 | 0.142867662547923 | 0.294579 | 0.485 | 0.630397 | 0.315198 |
| Y4 | 0.160203862531591 | 0.151234 | 1.0593 | 0.295975 | 0.147988 |
| M1 | -0.889739069238092 | 0.416499 | -2.1362 | 0.038992 | 0.019496 |
| M2 | -1.03979564822641 | 0.43316 | -2.4005 | 0.021243 | 0.010621 |
| M3 | -0.877831720066912 | 0.435959 | -2.0136 | 0.050993 | 0.025496 |
| M4 | -0.372343703812319 | 0.439712 | -0.8468 | 0.402279 | 0.201139 |
| M5 | -1.29197609960059 | 0.430019 | -3.0045 | 0.004631 | 0.002316 |
| M6 | 0.190290825479914 | 0.42282 | 0.4501 | 0.655165 | 0.327582 |
| M7 | 3.04103217720423 | 0.481829 | 6.3114 | 0 | 0 |
| M8 | -2.16551128616970 | 0.791093 | -2.7374 | 0.009281 | 0.00464 |
| M9 | 0.636778689366172 | 0.790135 | 0.8059 | 0.425181 | 0.212591 |
| M10 | 0.306992689379753 | 0.689957 | 0.4449 | 0.658819 | 0.32941 |
| M11 | -0.656329660215681 | 0.439887 | -1.492 | 0.143734 | 0.071867 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.980441846539918 |
| R-squared | 0.961266214446603 |
| Adjusted R-squared | 0.945375430629825 |
| F-TEST (value) | 60.4920578827372 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 39 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.5710872110191 |
| Sum Squared Residuals | 12.7194835009934 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 20.7 | 21.0064147224696 | -0.306414722469565 |
| 2 | 20.4 | 20.1243698633882 | 0.275630136611821 |
| 3 | 20.3 | 20.0722367797552 | 0.227763220244780 |
| 4 | 20.4 | 20.3876214480738 | 0.0123785519261583 |
| 5 | 19.8 | 19.5769979808287 | 0.223002019171304 |
| 6 | 19.5 | 19.8165537260885 | -0.316553726088509 |
| 7 | 23.1 | 23.0174721134981 | 0.0825278865018796 |
| 8 | 23.5 | 23.3607416924293 | 0.139258307570727 |
| 9 | 23.5 | 23.0545106530051 | 0.44548934699493 |
| 10 | 22.9 | 22.8384087125459 | 0.0615912874540699 |
| 11 | 21.9 | 21.6225057659741 | 0.277494234025931 |
| 12 | 21.5 | 21.5637955965641 | -0.0637955965640818 |
| 13 | 20.5 | 21.0966679235012 | -0.59666792350124 |
| 14 | 20.2 | 19.6795906548440 | 0.520409345155962 |
| 15 | 19.4 | 20.1834523749806 | -0.783452374980565 |
| 16 | 19.2 | 19.6007862784536 | -0.400786278453571 |
| 17 | 18.8 | 18.8393458317572 | -0.0393458317572162 |
| 18 | 18.8 | 19.4782983845002 | -0.678298384500229 |
| 19 | 22.6 | 22.3796411775338 | 0.220358822466189 |
| 20 | 23.3 | 22.5529261652851 | 0.74707383471487 |
| 21 | 23 | 22.5643310800698 | 0.435668919930205 |
| 22 | 21.4 | 21.7293026307475 | -0.32930263074753 |
| 23 | 19.9 | 19.4600220955361 | 0.43997790446389 |
| 24 | 18.8 | 19.6218608822654 | -0.821860882265362 |
| 25 | 18.6 | 18.3824255434616 | 0.217574456538409 |
| 26 | 18.4 | 18.5205681206079 | -0.120568120607895 |
| 27 | 18.6 | 18.0932536690529 | 0.506746330947098 |
| 28 | 19.9 | 18.9383404280133 | 0.961659571986684 |
| 29 | 19.2 | 19.5814376866351 | -0.381437686635085 |
| 30 | 18.4 | 18.5291551186953 | -0.129155118695265 |
| 31 | 21.1 | 21.2626924032918 | -0.162692403291790 |
| 32 | 20.5 | 20.9070538175361 | -0.40705381753609 |
| 33 | 19.1 | 19.7929238651351 | -0.692923865135126 |
| 34 | 18.1 | 18.20538140825 | -0.105381408250001 |
| 35 | 17 | 17.4665108147471 | -0.46651081474713 |
| 36 | 17.1 | 17.3492436963004 | -0.249243696300431 |
| 37 | 17.4 | 17.4880629079208 | -0.0880629079207592 |
| 38 | 16.8 | 17.3636308708445 | -0.563630870844548 |
| 39 | 15.3 | 15.9827981610512 | -0.682798161051174 |
| 40 | 14.3 | 14.7872603433578 | -0.487260343357824 |
| 41 | 13.4 | 13.7110115152001 | -0.311011515200116 |
| 42 | 15.3 | 14.7008820843999 | 0.59911791560011 |
| 43 | 22.1 | 21.4103576062187 | 0.68964239378135 |
| 44 | 23.7 | 24.1052961897495 | -0.405296189749542 |
| 45 | 22.2 | 22.38823440179 | -0.188234401790009 |
| 46 | 19.5 | 19.1269072484565 | 0.373092751543461 |
| 47 | 16.6 | 16.8509613237427 | -0.250961323742691 |
| 48 | 17.3 | 16.1650998248701 | 1.13490017512987 |
| 49 | 19.8 | 19.0264289026468 | 0.773571097353156 |
| 50 | 21.2 | 21.3118404903153 | -0.111840490315340 |
| 51 | 21.5 | 20.7682590151601 | 0.731740984839863 |
| 52 | 20.6 | 20.6859915021014 | -0.0859915021014472 |
| 53 | 19.1 | 18.5912069855789 | 0.508793014421113 |
| 54 | 19.6 | 19.0751106863161 | 0.524889313683893 |
| 55 | 23.5 | 24.3298366994576 | -0.829836699457628 |
| 56 | 24 | 24.0739821350000 | -0.0739821349999634 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.0980677490405858 | 0.196135498081172 | 0.901932250959414 |
| 21 | 0.077831759910241 | 0.155663519820482 | 0.922168240089759 |
| 22 | 0.110664936338311 | 0.221329872676621 | 0.88933506366169 |
| 23 | 0.0612881930852984 | 0.122576386170597 | 0.938711806914702 |
| 24 | 0.0627886477706587 | 0.125577295541317 | 0.937211352229341 |
| 25 | 0.0632106496471335 | 0.126421299294267 | 0.936789350352867 |
| 26 | 0.0316840630378131 | 0.0633681260756263 | 0.968315936962187 |
| 27 | 0.0169137220273416 | 0.0338274440546831 | 0.983086277972658 |
| 28 | 0.125101809083701 | 0.250203618167403 | 0.874898190916299 |
| 29 | 0.152959612823328 | 0.305919225646656 | 0.847040387176672 |
| 30 | 0.110221160697594 | 0.220442321395187 | 0.889778839302406 |
| 31 | 0.0733131176384588 | 0.146626235276918 | 0.926686882361541 |
| 32 | 0.0656672326977005 | 0.131334465395401 | 0.9343327673023 |
| 33 | 0.0525241960963519 | 0.105048392192704 | 0.947475803903648 |
| 34 | 0.0398562634174893 | 0.0797125268349786 | 0.96014373658251 |
| 35 | 0.0468459147210362 | 0.0936918294420724 | 0.953154085278964 |
| 36 | 0.588280239357918 | 0.823439521284165 | 0.411719760642082 |
| 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 | 1 | 0.0588235294117647 | NOK |
| 10% type I error level | 4 | 0.235294117647059 | NOK |
