| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.10312509344711 + 0.104087521816943X[t] + 1.38413536249161Y1[t] -0.67705851157981Y2[t] + 0.0212423842191513M1[t] + 0.112739859643006M2[t] + 0.35310377017092M3[t] + 0.271985478125367M4[t] + 0.0747982571942579M5[t] + 0.0628831265365121M6[t] + 0.123428674625584M7[t] + 0.142214073231639M8[t] + 0.148011045842880M9[t] + 0.540049045509759M10[t] -0.265589260227732M11[t] -0.00122112624684944t + 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) | 1.10312509344711 | 0.61133 | 1.8045 | 0.076841 | 0.038421 |
| X | 0.104087521816943 | 0.056235 | 1.8509 | 0.069754 | 0.034877 |
| Y1 | 1.38413536249161 | 0.107835 | 12.8356 | 0 | 0 |
| Y2 | -0.67705851157981 | 0.103939 | -6.514 | 0 | 0 |
| M1 | 0.0212423842191513 | 0.137612 | 0.1544 | 0.877909 | 0.438954 |
| M2 | 0.112739859643006 | 0.14153 | 0.7966 | 0.429248 | 0.214624 |
| M3 | 0.35310377017092 | 0.138677 | 2.5462 | 0.013832 | 0.006916 |
| M4 | 0.271985478125367 | 0.13833 | 1.9662 | 0.054522 | 0.027261 |
| M5 | 0.0747982571942579 | 0.141903 | 0.5271 | 0.600317 | 0.300159 |
| M6 | 0.0628831265365121 | 0.143958 | 0.4368 | 0.664018 | 0.332009 |
| M7 | 0.123428674625584 | 0.149545 | 0.8254 | 0.412867 | 0.206433 |
| M8 | 0.142214073231639 | 0.152619 | 0.9318 | 0.355653 | 0.177826 |
| M9 | 0.148011045842880 | 0.146823 | 1.0081 | 0.317991 | 0.158996 |
| M10 | 0.540049045509759 | 0.144237 | 3.7442 | 0.000447 | 0.000224 |
| M11 | -0.265589260227732 | 0.148222 | -1.7918 | 0.078869 | 0.039435 |
| t | -0.00122112624684944 | 0.002247 | -0.5434 | 0.589166 | 0.294583 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.955139201380093 |
| R-squared | 0.912290894013003 |
| Adjusted R-squared | 0.88746756212989 |
| F-TEST (value) | 36.7513474141497 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 53 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.221380152278365 |
| Sum Squared Residuals | 2.59748610660797 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 7.9 | 7.51183271804123 | 0.388167281958774 |
| 2 | 7.9 | 7.93923507262606 | -0.039235072626056 |
| 3 | 8.1 | 8.00648655997826 | 0.0935134400217406 |
| 4 | 8.2 | 8.26342672727434 | -0.0634267272743444 |
| 5 | 8 | 8.05761146184789 | -0.0576114618478894 |
| 6 | 7.5 | 7.64789852037852 | -0.147898520378522 |
| 7 | 6.8 | 7.04647944147396 | -0.246479441473960 |
| 8 | 6.5 | 6.40245195933386 | 0.0975480406661404 |
| 9 | 6.6 | 6.51777191596511 | 0.0822280840348927 |
| 10 | 7.6 | 7.44788617056043 | 0.152113829439569 |
| 11 | 8 | 8.03031751518158 | -0.0303175151815784 |
| 12 | 8.1 | 8.1504637782159 | -0.0504637782159069 |
| 13 | 7.7 | 7.9443963981702 | -0.244396398170196 |
| 14 | 7.5 | 7.33004273373902 | 0.169957266260976 |
| 15 | 7.6 | 7.56318185015369 | 0.0368181498463102 |
| 16 | 7.8 | 7.7858939269715 | 0.0141060730285068 |
| 17 | 7.8 | 7.80701555331557 | -0.00701555331556997 |
| 18 | 7.8 | 7.64805884191332 | 0.151941158086682 |
| 19 | 7.5 | 7.66574825502876 | -0.165748255028764 |
| 20 | 7.5 | 7.2472544142771 | 0.252745585722902 |
| 21 | 7.1 | 7.46535656629713 | -0.365356566297127 |
| 22 | 7.5 | 7.41701556871915 | 0.0829844312808508 |
| 23 | 7.5 | 7.45545119072677 | 0.0445488092732339 |
| 24 | 7.6 | 7.43858716789403 | 0.16141283210597 |
| 25 | 7.7 | 7.53456944902533 | 0.165430550974674 |
| 26 | 7.7 | 7.65391847456674 | 0.0460815254332645 |
| 27 | 7.9 | 7.83576415987151 | 0.0642358401284878 |
| 28 | 8.1 | 8.04066056625913 | 0.0593394337408725 |
| 29 | 8.2 | 7.98366758926353 | 0.216332410736472 |
| 30 | 8.2 | 7.95271566192874 | 0.247284338071257 |
| 31 | 8.2 | 7.9235167282496 | 0.276483271750404 |
| 32 | 7.9 | 7.9410810006088 | -0.0410810006088001 |
| 33 | 7.3 | 7.53041623822571 | -0.230416238225711 |
| 34 | 6.9 | 7.37713946507827 | -0.477139465078271 |
| 35 | 6.6 | 6.44367849940856 | 0.156321500591436 |
| 36 | 6.7 | 6.5428119249105 | 0.157188075089503 |
| 37 | 6.9 | 6.85232051169743 | 0.0476794883025676 |
| 38 | 7 | 7.1204918256697 | -0.120491825669696 |
| 39 | 7.1 | 7.36263644388396 | -0.262636443883958 |
| 40 | 7.2 | 7.36141346286443 | -0.16141346286443 |
| 41 | 7.1 | 7.23371280077765 | -0.133712800777653 |
| 42 | 6.9 | 7.01445715646591 | -0.114457156465914 |
| 43 | 7 | 6.87506910914949 | 0.124930890850509 |
| 44 | 6.8 | 7.12482361134704 | -0.324823611347042 |
| 45 | 6.4 | 6.73282277314666 | -0.332822773146659 |
| 46 | 6.7 | 6.7158059560677 | -0.0158059560677022 |
| 47 | 6.6 | 6.56378428091769 | 0.0362157190823141 |
| 48 | 6.4 | 6.44498631644869 | -0.0449863164486863 |
| 49 | 6.3 | 6.27670385744404 | 0.0232961425559623 |
| 50 | 6.2 | 6.36397837268784 | -0.163978372687843 |
| 51 | 6.5 | 6.54282222405942 | -0.0428222240594221 |
| 52 | 6.8 | 6.93302051349079 | -0.133020513490789 |
| 53 | 6.8 | 6.91550896504129 | -0.115508965041287 |
| 54 | 6.4 | 6.64721139375428 | -0.247211393754277 |
| 55 | 6.1 | 6.12165541405477 | -0.0216554140547755 |
| 56 | 5.8 | 5.96357622575334 | -0.163576225753338 |
| 57 | 6.1 | 5.79766402557097 | 0.302335974429033 |
| 58 | 7.2 | 6.94215283957445 | 0.257847160425553 |
| 59 | 7.3 | 7.5067685137654 | -0.206768513765406 |
| 60 | 6.9 | 7.12315081253088 | -0.22315081253088 |
| 61 | 6.1 | 6.48017706562178 | -0.380177065621782 |
| 62 | 5.8 | 5.69233352071065 | 0.107666479289354 |
| 63 | 6.2 | 6.08910876205316 | 0.110891237946842 |
| 64 | 7.1 | 6.81558480313982 | 0.284415196860185 |
| 65 | 7.7 | 7.60248362975407 | 0.0975163702459272 |
| 66 | 7.9 | 7.78965842555923 | 0.110341574440774 |
| 67 | 7.7 | 7.66753105204341 | 0.0324689479565864 |
| 68 | 7.4 | 7.22081278867986 | 0.179187211320137 |
| 69 | 7.5 | 6.95596848079443 | 0.544031519205571 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.202899351740548 | 0.405798703481097 | 0.797100648259452 |
| 20 | 0.576239056456999 | 0.847521887086002 | 0.423760943543001 |
| 21 | 0.460977090563427 | 0.921954181126854 | 0.539022909436573 |
| 22 | 0.391999439979005 | 0.783998879958011 | 0.608000560020995 |
| 23 | 0.277031587419743 | 0.554063174839485 | 0.722968412580257 |
| 24 | 0.190832853924902 | 0.381665707849803 | 0.809167146075098 |
| 25 | 0.132296210452335 | 0.264592420904669 | 0.867703789547665 |
| 26 | 0.0865137338034053 | 0.173027467606811 | 0.913486266196595 |
| 27 | 0.0531462432634167 | 0.106292486526833 | 0.946853756736583 |
| 28 | 0.0315110228985738 | 0.0630220457971476 | 0.968488977101426 |
| 29 | 0.032849346011344 | 0.065698692022688 | 0.967150653988656 |
| 30 | 0.0439709367977439 | 0.0879418735954878 | 0.956029063202256 |
| 31 | 0.191132604181237 | 0.382265208362474 | 0.808867395818763 |
| 32 | 0.225796422560088 | 0.451592845120176 | 0.774203577439912 |
| 33 | 0.160573794275787 | 0.321147588551574 | 0.839426205724213 |
| 34 | 0.38449939485368 | 0.76899878970736 | 0.61550060514632 |
| 35 | 0.324587537162582 | 0.649175074325163 | 0.675412462837418 |
| 36 | 0.321397837265785 | 0.64279567453157 | 0.678602162734215 |
| 37 | 0.443750385441205 | 0.88750077088241 | 0.556249614558795 |
| 38 | 0.482047619154762 | 0.964095238309523 | 0.517952380845238 |
| 39 | 0.491668280847826 | 0.98333656169565 | 0.508331719152174 |
| 40 | 0.417141671452322 | 0.834283342904645 | 0.582858328547678 |
| 41 | 0.343566164124738 | 0.687132328249476 | 0.656433835875262 |
| 42 | 0.27385840173725 | 0.5477168034745 | 0.72614159826275 |
| 43 | 0.334955275969812 | 0.669910551939623 | 0.665044724030188 |
| 44 | 0.337794932280802 | 0.675589864561604 | 0.662205067719198 |
| 45 | 0.413076891786667 | 0.826153783573334 | 0.586923108213333 |
| 46 | 0.613451871872878 | 0.773096256254243 | 0.386548128127122 |
| 47 | 0.485704198468398 | 0.971408396936796 | 0.514295801531602 |
| 48 | 0.654498430443604 | 0.691003139112791 | 0.345501569556396 |
| 49 | 0.994394810455065 | 0.0112103790898699 | 0.00560518954493494 |
| 50 | 0.9956530471557 | 0.00869390568859886 | 0.00434695284429943 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 1 | 0.03125 | NOK |
| 5% type I error level | 2 | 0.0625 | NOK |
| 10% type I error level | 5 | 0.15625 | NOK |
