| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 227.039845124434 -97.252462831136X[t] + 0.945504547175353Y1[t] -0.78610162790592t + 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) | 227.039845124434 | 132.04536 | 1.7194 | 0.090227 | 0.045114 |
| X | -97.252462831136 | 139.774326 | -0.6958 | 0.489008 | 0.244504 |
| Y1 | 0.945504547175353 | 0.048001 | 19.6977 | 0 | 0 |
| t | -0.78610162790592 | 2.146013 | -0.3663 | 0.715307 | 0.357653 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.981200998591577 |
| R-squared | 0.962755399637109 |
| Adjusted R-squared | 0.961062463256977 |
| F-TEST (value) | 568.689651268741 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 66 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 167.074407875857 |
| Sum Squared Residuals | 1842314.61262650 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2440.25 | 2448.60545135936 | -8.35545135936304 |
| 2 | 2408.64 | 2532.73511311328 | -124.095113113279 |
| 3 | 2472.81 | 2502.06161274916 | -29.2516127491589 |
| 4 | 2407.6 | 2561.94853791350 | -154.348537913496 |
| 5 | 2454.62 | 2499.50608476428 | -44.8860847642851 |
| 6 | 2448.05 | 2543.17760694456 | -95.127606944564 |
| 7 | 2497.84 | 2536.17954044172 | -38.3395404417162 |
| 8 | 2645.64 | 2582.47011021767 | 63.1698897823285 |
| 9 | 2756.76 | 2721.42958066228 | 35.3304193377178 |
| 10 | 2849.27 | 2825.7079443165 | 23.5620556834978 |
| 11 | 2921.44 | 2912.39046834779 | 9.04953165221215 |
| 12 | 2981.85 | 2979.84142988953 | 2.00857011047251 |
| 13 | 3080.58 | 3036.17325795648 | 44.4067420435156 |
| 14 | 3106.22 | 3128.7368202712 | -22.5168202712014 |
| 15 | 3119.31 | 3152.19345523287 | -32.8834552328712 |
| 16 | 3061.26 | 3163.78400812749 | -102.524008127491 |
| 17 | 3097.31 | 3108.11136753606 | -10.8013675360559 |
| 18 | 3161.69 | 3141.41070483382 | 20.2792951661789 |
| 19 | 3257.16 | 3201.49618595306 | 55.6638140469353 |
| 20 | 3277.01 | 3290.97740344399 | -13.9674034439893 |
| 21 | 3295.32 | 3308.95956707751 | -13.6395670775145 |
| 22 | 3363.99 | 3325.48565370839 | 38.5043462916103 |
| 23 | 3494.17 | 3389.62734933501 | 104.542650664985 |
| 24 | 3667.03 | 3511.92702965840 | 155.102970341604 |
| 25 | 3813.06 | 3674.58084405522 | 138.479155944778 |
| 26 | 3917.96 | 3811.86677145133 | 106.093228548667 |
| 27 | 3895.51 | 3910.26409682212 | -14.7540968221217 |
| 28 | 3801.06 | 3888.25141811013 | -87.1914181101295 |
| 29 | 3570.12 | 3798.16241200151 | -228.042412001511 |
| 30 | 3701.61 | 3579.02149024893 | 122.588509751071 |
| 31 | 3862.27 | 3702.55978152911 | 159.710218470889 |
| 32 | 3970.1 | 3853.6784404504 | 116.421559549603 |
| 33 | 4138.52 | 3954.84609414441 | 183.673905855591 |
| 34 | 4199.75 | 4113.30186835178 | 86.4481316482232 |
| 35 | 4290.89 | 4170.40901014742 | 120.480989852583 |
| 36 | 4443.91 | 4255.79619294907 | 188.113807050926 |
| 37 | 4502.64 | 4399.69119712994 | 102.948802870061 |
| 38 | 4356.98 | 4454.43457755764 | -97.4545775576433 |
| 39 | 4591.27 | 4315.92628358817 | 275.343716411826 |
| 40 | 4696.96 | 4536.66244231798 | 160.297557682017 |
| 41 | 4621.4 | 4635.80671628104 | -14.4067162810398 |
| 42 | 4562.84 | 4563.57829106856 | -0.738291068563195 |
| 43 | 4202.52 | 4507.42344315807 | -304.903443158069 |
| 44 | 4296.49 | 4165.95314309194 | 130.536856908060 |
| 45 | 4435.23 | 4254.0161037621 | 181.213896237898 |
| 46 | 4105.18 | 4384.40930300930 | -279.229303009304 |
| 47 | 4116.68 | 4071.55942558617 | 45.1205744138270 |
| 48 | 3844.49 | 4081.64662625078 | -237.156626250784 |
| 49 | 3720.98 | 3823.50364192722 | -102.523641927218 |
| 50 | 3674.4 | 3705.93827367768 | -31.5382736776845 |
| 51 | 3857.62 | 3661.11057024235 | 196.509429757649 |
| 52 | 3801.06 | 3833.55981174791 | -32.499811747913 |
| 53 | 3504.37 | 3779.29597293177 | -274.925972931769 |
| 54 | 3032.6 | 3497.98812720241 | -465.388127202408 |
| 55 | 3047.03 | 3051.14134535359 | -4.11134535358478 |
| 56 | 2962.34 | 2966.74641151028 | -4.4064115102838 |
| 57 | 2197.82 | 2885.8855297821 | -688.065529782097 |
| 58 | 2014.45 | 2162.24229174769 | -147.79229174769 |
| 59 | 1862.83 | 1988.07902130424 | -125.249021304240 |
| 60 | 1905.41 | 1843.93552023361 | 61.4744797663938 |
| 61 | 1810.99 | 1883.40900222443 | -72.419002224427 |
| 62 | 1670.07 | 1793.34836125222 | -123.278361252224 |
| 63 | 1864.44 | 1659.32175883637 | 205.118241163633 |
| 64 | 2052.02 | 1842.31337604294 | 209.706623957065 |
| 65 | 2029.6 | 2018.88501737418 | 10.714982625818 |
| 66 | 2070.83 | 1996.90070379860 | 73.9292962013954 |
| 67 | 2293.41 | 2035.09775465074 | 258.312245349261 |
| 68 | 2443.27 | 2244.76205513312 | 198.507944866877 |
| 69 | 2513.17 | 2385.66926494492 | 127.500735055085 |
| 70 | 2466.92 | 2450.97393116457 | 15.9460688354334 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.00436997205751246 | 0.00873994411502492 | 0.995630027942488 |
| 8 | 0.0447049107775033 | 0.0894098215550066 | 0.955295089222497 |
| 9 | 0.0358279626223361 | 0.0716559252446722 | 0.964172037377664 |
| 10 | 0.0138310404379099 | 0.0276620808758197 | 0.98616895956209 |
| 11 | 0.00484381497398504 | 0.00968762994797008 | 0.995156185026015 |
| 12 | 0.00162683951957476 | 0.00325367903914951 | 0.998373160480425 |
| 13 | 0.000519198981312534 | 0.00103839796262507 | 0.999480801018688 |
| 14 | 0.000209695223304542 | 0.000419390446609084 | 0.999790304776695 |
| 15 | 9.19898580263282e-05 | 0.000183979716052656 | 0.999908010141974 |
| 16 | 0.000153439033691687 | 0.000306878067383375 | 0.999846560966308 |
| 17 | 5.64214273901768e-05 | 0.000112842854780354 | 0.99994357857261 |
| 18 | 1.77480496866038e-05 | 3.54960993732076e-05 | 0.999982251950313 |
| 19 | 5.86728816088942e-06 | 1.17345763217788e-05 | 0.99999413271184 |
| 20 | 2.15687405336657e-06 | 4.31374810673314e-06 | 0.999997843125947 |
| 21 | 8.13616181000394e-07 | 1.62723236200079e-06 | 0.999999186383819 |
| 22 | 2.34280832501783e-07 | 4.68561665003566e-07 | 0.999999765719167 |
| 23 | 1.20123152761869e-07 | 2.40246305523739e-07 | 0.999999879876847 |
| 24 | 1.78601221051951e-07 | 3.57202442103902e-07 | 0.99999982139878 |
| 25 | 1.23915243810773e-07 | 2.47830487621545e-07 | 0.999999876084756 |
| 26 | 4.06655233399634e-08 | 8.13310466799267e-08 | 0.999999959334477 |
| 27 | 2.69797558612951e-08 | 5.39595117225902e-08 | 0.999999973020244 |
| 28 | 7.93435862365834e-08 | 1.58687172473167e-07 | 0.999999920656414 |
| 29 | 1.55058372478887e-05 | 3.10116744957774e-05 | 0.999984494162752 |
| 30 | 6.80578369277434e-06 | 1.36115673855487e-05 | 0.999993194216307 |
| 31 | 3.46386010073290e-06 | 6.92772020146579e-06 | 0.9999965361399 |
| 32 | 1.43172668297632e-06 | 2.86345336595265e-06 | 0.999998568273317 |
| 33 | 1.01785187752707e-06 | 2.03570375505413e-06 | 0.999998982148123 |
| 34 | 3.868120218297e-07 | 7.736240436594e-07 | 0.999999613187978 |
| 35 | 1.65294207754987e-07 | 3.30588415509975e-07 | 0.999999834705792 |
| 36 | 1.49933500641581e-07 | 2.99867001283162e-07 | 0.9999998500665 |
| 37 | 6.61412462175626e-08 | 1.32282492435125e-07 | 0.999999933858754 |
| 38 | 1.15583504528919e-07 | 2.31167009057838e-07 | 0.999999884416495 |
| 39 | 4.73207841751131e-07 | 9.46415683502262e-07 | 0.999999526792158 |
| 40 | 5.82163448665894e-07 | 1.16432689733179e-06 | 0.99999941783655 |
| 41 | 4.82113099288891e-07 | 9.64226198577783e-07 | 0.9999995178869 |
| 42 | 5.25044569782968e-07 | 1.05008913956594e-06 | 0.99999947495543 |
| 43 | 6.83806499226659e-05 | 0.000136761299845332 | 0.999931619350077 |
| 44 | 8.9659646447785e-05 | 0.00017931929289557 | 0.999910340353552 |
| 45 | 0.000326969066855951 | 0.000653938133711903 | 0.999673030933144 |
| 46 | 0.00252570917956236 | 0.00505141835912471 | 0.997474290820438 |
| 47 | 0.00369272286360572 | 0.00738544572721144 | 0.996307277136394 |
| 48 | 0.00556596651534672 | 0.0111319330306934 | 0.994434033484653 |
| 49 | 0.00379507509201423 | 0.00759015018402846 | 0.996204924907986 |
| 50 | 0.00286056826299607 | 0.00572113652599215 | 0.997139431737004 |
| 51 | 0.0221055396926093 | 0.0442110793852186 | 0.97789446030739 |
| 52 | 0.0439194317478808 | 0.0878388634957616 | 0.95608056825212 |
| 53 | 0.0491552518244991 | 0.0983105036489983 | 0.950844748175501 |
| 54 | 0.112118092355505 | 0.22423618471101 | 0.887881907644495 |
| 55 | 0.0884559440984547 | 0.176911888196909 | 0.911544055901545 |
| 56 | 0.826876001136514 | 0.346247997726973 | 0.173123998863486 |
| 57 | 0.87716690765118 | 0.245666184697639 | 0.122833092348819 |
| 58 | 0.853048796579507 | 0.293902406840987 | 0.146951203420493 |
| 59 | 0.791992454995627 | 0.416015090008746 | 0.208007545004373 |
| 60 | 0.88098527087576 | 0.238029458248482 | 0.119014729124241 |
| 61 | 0.894300419425571 | 0.211399161148857 | 0.105699580574428 |
| 62 | 0.836337679623903 | 0.327324640752193 | 0.163662320376097 |
| 63 | 0.725621684569723 | 0.548756630860554 | 0.274378315430277 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 40 | 0.701754385964912 | NOK |
| 5% type I error level | 43 | 0.75438596491228 | NOK |
| 10% type I error level | 47 | 0.824561403508772 | NOK |
