| Multiple Linear Regression - Estimated Regression Equation |
| Yt[t] = + 2260.17634798638 + 0.0339916897977066`Yt-1`[t] + 0.0350118995045006`Yt-2`[t] + 0.112475389948690`Yt-3`[t] -0.0118409575464806`Yt-4`[t] + 0.316083003027644`Yt-5`[t] + 0.280257052615370`Yt-6`[t] -179.026837499078M1[t] + 129.398081382818M2[t] -238.937569078416M3[t] + 585.739880957248M4[t] + 356.881038974051M5[t] -33.0550838310855M6[t] + 33.6060774247583M7[t] -732.859928093812M8[t] -442.640351857356M9[t] -299.092191974959M10[t] -930.99474257794M11[t] + 5.03344278382259t + 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) | 2260.17634798638 | 1654.976206 | 1.3657 | 0.17815 | 0.089075 |
| `Yt-1` | 0.0339916897977066 | 0.142601 | 0.2384 | 0.812569 | 0.406285 |
| `Yt-2` | 0.0350118995045006 | 0.138265 | 0.2532 | 0.801134 | 0.400567 |
| `Yt-3` | 0.112475389948690 | 0.141274 | 0.7961 | 0.429709 | 0.214854 |
| `Yt-4` | -0.0118409575464806 | 0.141917 | -0.0834 | 0.933838 | 0.466919 |
| `Yt-5` | 0.316083003027644 | 0.138898 | 2.2757 | 0.027186 | 0.013593 |
| `Yt-6` | 0.280257052615370 | 0.146375 | 1.9147 | 0.061267 | 0.030633 |
| M1 | -179.026837499078 | 259.767839 | -0.6892 | 0.493896 | 0.246948 |
| M2 | 129.398081382818 | 243.254589 | 0.5319 | 0.59712 | 0.29856 |
| M3 | -238.937569078416 | 204.957972 | -1.1658 | 0.249231 | 0.124616 |
| M4 | 585.739880957248 | 240.233465 | 2.4382 | 0.018356 | 0.009178 |
| M5 | 356.881038974051 | 288.871255 | 1.2354 | 0.222443 | 0.111221 |
| M6 | -33.0550838310855 | 227.53212 | -0.1453 | 0.885077 | 0.442538 |
| M7 | 33.6060774247583 | 226.529303 | 0.1484 | 0.882662 | 0.441331 |
| M8 | -732.859928093812 | 247.114973 | -2.9657 | 0.00462 | 0.00231 |
| M9 | -442.640351857356 | 212.508568 | -2.0829 | 0.042392 | 0.021196 |
| M10 | -299.092191974959 | 234.463331 | -1.2756 | 0.207976 | 0.103988 |
| M11 | -930.99474257794 | 233.06605 | -3.9946 | 0.000213 | 0.000106 |
| t | 5.03344278382259 | 2.594575 | 1.94 | 0.058032 | 0.029016 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.89795489295522 |
| R-squared | 0.806322989782221 |
| Adjusted R-squared | 0.736599266103821 |
| F-TEST (value) | 11.5645428448626 |
| F-TEST (DF numerator) | 18 |
| F-TEST (DF denominator) | 50 |
| p-value | 4.02222699591448e-12 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 257.046161709542 |
| Sum Squared Residuals | 3303636.46248041 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9563 | 9294.73089451873 | 268.269105481266 |
| 2 | 9998 | 9332.17665696794 | 665.823343032063 |
| 3 | 9437 | 9329.27829841387 | 107.721701586131 |
| 4 | 10038 | 9942.00555477032 | 95.9944452296808 |
| 5 | 9918 | 9807.50536365309 | 110.494636346913 |
| 6 | 9252 | 9638.82844584766 | -386.828445847658 |
| 7 | 9737 | 9848.3365645619 | -111.336564561893 |
| 8 | 9035 | 9004.04783721894 | 30.9521627810651 |
| 9 | 9133 | 9251.67344476305 | -118.673444763048 |
| 10 | 9487 | 9571.94904968687 | -84.949049686874 |
| 11 | 8700 | 8631.70145172327 | 68.2985482767347 |
| 12 | 9627 | 9539.356389478 | 87.6436105220008 |
| 13 | 8947 | 9322.0092028905 | -375.009202890506 |
| 14 | 9283 | 9386.3350988341 | -103.335098834101 |
| 15 | 8829 | 9263.58810156527 | -434.588101565267 |
| 16 | 9947 | 9852.6246058825 | 94.3753941175035 |
| 17 | 9628 | 9769.19673905461 | -141.196739054611 |
| 18 | 9318 | 9402.41347057719 | -84.4134705771869 |
| 19 | 9605 | 9499.1542287652 | 105.845771234796 |
| 20 | 8640 | 8638.17043852962 | 1.82956147038141 |
| 21 | 9214 | 9105.72388212366 | 108.276117876336 |
| 22 | 9567 | 9488.47827232477 | 78.5217276752286 |
| 23 | 8547 | 8594.38022448059 | -47.3802244805876 |
| 24 | 9185 | 9587.91962019485 | -402.91962019485 |
| 25 | 9470 | 9208.22156527508 | 261.778434724916 |
| 26 | 9123 | 9345.78398261948 | -222.783982619484 |
| 27 | 9278 | 9336.9469736957 | -58.9469736957062 |
| 28 | 10170 | 9960.80448101153 | 209.195518988473 |
| 29 | 9434 | 9646.12164258592 | -212.121642585921 |
| 30 | 9655 | 9557.86184637367 | 97.1381536263302 |
| 31 | 9429 | 9679.98501318263 | -250.985013182632 |
| 32 | 8739 | 8777.00760542215 | -38.0076054221516 |
| 33 | 9552 | 9399.8515569829 | 152.148443017093 |
| 34 | 9687 | 9541.22610375494 | 145.773896245056 |
| 35 | 9019 | 8736.06373864074 | 282.93626135926 |
| 36 | 9672 | 9744.22688432985 | -72.2268843298488 |
| 37 | 9206 | 9293.16422736113 | -87.1642273611266 |
| 38 | 9069 | 9600.51125735992 | -531.511257359922 |
| 39 | 9788 | 9568.1130214737 | 219.886978526302 |
| 40 | 10312 | 10184.0128881123 | 127.987111887712 |
| 41 | 10105 | 10012.4719377343 | 92.5280622656796 |
| 42 | 9863 | 9757.08440576917 | 105.915594230830 |
| 43 | 9656 | 9689.825855604 | -33.8258556040046 |
| 44 | 9295 | 9072.26552889588 | 222.734471104122 |
| 45 | 9946 | 9690.36443296323 | 255.635567036772 |
| 46 | 9701 | 9909.44394991723 | -208.443949917230 |
| 47 | 9049 | 9124.38179049164 | -75.381790491636 |
| 48 | 10190 | 9973.91415489793 | 216.085845102073 |
| 49 | 9706 | 9608.49341188037 | 97.5065881196283 |
| 50 | 9765 | 9979.61269234782 | -214.612692347824 |
| 51 | 9893 | 9842.4319647709 | 50.568035229107 |
| 52 | 9994 | 10335.8617787948 | -341.861778794763 |
| 53 | 10433 | 10310.2412430103 | 122.758756989678 |
| 54 | 10073 | 10124.2844736471 | -51.284473647103 |
| 55 | 10112 | 10091.9611487737 | 20.038851226269 |
| 56 | 9266 | 9424.4245280866 | -158.424528086599 |
| 57 | 9820 | 9714.39400691482 | 105.605993085180 |
| 58 | 10097 | 10027.9026243162 | 69.0973756838189 |
| 59 | 9115 | 9343.47279466377 | -228.472794663771 |
| 60 | 10411 | 10239.5829510994 | 171.417048900625 |
| 61 | 9678 | 9843.38069807418 | -165.380698074178 |
| 62 | 10408 | 10001.5803118707 | 406.419688129268 |
| 63 | 10153 | 10037.6416400806 | 115.358359919433 |
| 64 | 10368 | 10553.6906914286 | -185.690691428607 |
| 65 | 10581 | 10553.4630739617 | 27.5369260382616 |
| 66 | 10597 | 10277.5273577852 | 319.472642214787 |
| 67 | 10680 | 10409.7371891125 | 270.262810887464 |
| 68 | 9738 | 9797.08406184682 | -59.0840618468182 |
| 69 | 9556 | 10058.9926762523 | -502.992676252334 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 22 | 0.75685797105104 | 0.486284057897921 | 0.243142028948960 |
| 23 | 0.618942493574355 | 0.76211501285129 | 0.381057506425645 |
| 24 | 0.508026964785722 | 0.983946070428556 | 0.491973035214278 |
| 25 | 0.867705574184534 | 0.264588851630932 | 0.132294425815466 |
| 26 | 0.807016959499262 | 0.385966081001475 | 0.192983040500738 |
| 27 | 0.806941582230303 | 0.386116835539395 | 0.193058417769697 |
| 28 | 0.91105565350603 | 0.177888692987941 | 0.0889443464939705 |
| 29 | 0.894254536195609 | 0.211490927608783 | 0.105745463804391 |
| 30 | 0.888994745453796 | 0.222010509092407 | 0.111005254546204 |
| 31 | 0.831288966286405 | 0.337422067427189 | 0.168711033713594 |
| 32 | 0.817237631024834 | 0.365524737950332 | 0.182762368975166 |
| 33 | 0.78144497563237 | 0.437110048735259 | 0.218555024367630 |
| 34 | 0.785304710259179 | 0.429390579481643 | 0.214695289740821 |
| 35 | 0.732540612827977 | 0.534918774344045 | 0.267459387172023 |
| 36 | 0.64844062497472 | 0.70311875005056 | 0.35155937502528 |
| 37 | 0.558827483234743 | 0.882345033530514 | 0.441172516765257 |
| 38 | 0.798004511415968 | 0.403990977168064 | 0.201995488584032 |
| 39 | 0.83483510135885 | 0.330329797282299 | 0.165164898641149 |
| 40 | 0.809625956220406 | 0.380748087559188 | 0.190374043779594 |
| 41 | 0.727589447761097 | 0.544821104477805 | 0.272410552238903 |
| 42 | 0.662638609254431 | 0.674722781491137 | 0.337361390745569 |
| 43 | 0.543458829954104 | 0.913082340091792 | 0.456541170045896 |
| 44 | 0.479817645922714 | 0.959635291845427 | 0.520182354077286 |
| 45 | 0.698446612386112 | 0.603106775227777 | 0.301553387613888 |
| 46 | 0.564038921651281 | 0.871922156697438 | 0.435961078348719 |
| 47 | 0.702770487101842 | 0.594459025796316 | 0.297229512898158 |
| 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 | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
