| Multiple Linear Regression - Estimated Regression Equation |
| x[t] = + 29406.7468837864 + 1.28058662621852y[t] + 0.0213665756704032y1[t] -0.109951546684521y2[t] + 0.189129502860375y3[t] -0.583466893077811y4[t] + 645.041944741420M1[t] -7862.50086321254M2[t] -27771.3308989242M3[t] -36054.2742253516M4[t] -28597.9078937059M5[t] -24167.9784519473M6[t] -1856.21403375339M7[t] + 3394.51888208249M8[t] + 1692.51508426616M9[t] + 874.021498903283M10[t] -2481.97169085193M11[t] + 347.710441098343t + 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) | 29406.7468837864 | 15680.061815 | 1.8754 | 0.06586 | 0.03293 |
| y | 1.28058662621852 | 0.240176 | 5.3319 | 2e-06 | 1e-06 |
| y1 | 0.0213665756704032 | 0.354919 | 0.0602 | 0.952206 | 0.476103 |
| y2 | -0.109951546684521 | 0.357412 | -0.3076 | 0.759483 | 0.379742 |
| y3 | 0.189129502860375 | 0.360595 | 0.5245 | 0.60197 | 0.300985 |
| y4 | -0.583466893077811 | 0.236417 | -2.468 | 0.016614 | 0.008307 |
| M1 | 645.041944741420 | 3894.791103 | 0.1656 | 0.869045 | 0.434522 |
| M2 | -7862.50086321254 | 4442.824227 | -1.7697 | 0.082125 | 0.041062 |
| M3 | -27771.3308989242 | 9119.007139 | -3.0454 | 0.003515 | 0.001757 |
| M4 | -36054.2742253516 | 9351.733966 | -3.8554 | 0.000296 | 0.000148 |
| M5 | -28597.9078937059 | 8984.909714 | -3.1829 | 0.002362 | 0.001181 |
| M6 | -24167.9784519473 | 8377.212555 | -2.885 | 0.005517 | 0.002759 |
| M7 | -1856.21403375339 | 4557.770143 | -0.4073 | 0.68534 | 0.34267 |
| M8 | 3394.51888208249 | 4770.991306 | 0.7115 | 0.479682 | 0.239841 |
| M9 | 1692.51508426616 | 5147.300768 | 0.3288 | 0.7435 | 0.37175 |
| M10 | 874.021498903283 | 4915.03157 | 0.1778 | 0.85949 | 0.429745 |
| M11 | -2481.97169085193 | 3988.729095 | -0.6222 | 0.536261 | 0.268131 |
| t | 347.710441098343 | 49.249558 | 7.0602 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.93604685848075 |
| R-squared | 0.87618372127168 |
| Adjusted R-squared | 0.839256059194813 |
| F-TEST (value) | 23.727029332316 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 57 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 6717.02322907089 |
| Sum Squared Residuals | 2571748860.41304 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 236089 | 237104.715982948 | -1015.71598294806 |
| 2 | 236997 | 235889.846554026 | 1107.15344597378 |
| 3 | 264579 | 263804.184677969 | 774.81532203129 |
| 4 | 270349 | 261103.674183552 | 9245.32581644765 |
| 5 | 269645 | 267092.11822842 | 2552.88177157981 |
| 6 | 267037 | 262175.00567702 | 4861.9943229800 |
| 7 | 258113 | 253545.003725884 | 4567.99627411648 |
| 8 | 262813 | 260662.874751582 | 2150.12524841765 |
| 9 | 267413 | 262857.213251797 | 4555.78674820312 |
| 10 | 267366 | 264372.678011467 | 2993.32198853329 |
| 11 | 264777 | 263139.613896336 | 1637.38610366372 |
| 12 | 258863 | 257565.905481654 | 1297.09451834614 |
| 13 | 254844 | 253037.099197745 | 1806.90080225508 |
| 14 | 254868 | 253460.488112949 | 1407.51188705142 |
| 15 | 277267 | 271340.125066802 | 5926.87493319829 |
| 16 | 285351 | 277907.628698652 | 7443.37130134816 |
| 17 | 286602 | 286394.788244815 | 207.211755185062 |
| 18 | 283042 | 294938.666114167 | -11896.6661141668 |
| 19 | 276687 | 288902.541610152 | -12215.5416101521 |
| 20 | 277915 | 288871.187832565 | -10956.1878325655 |
| 21 | 277128 | 283917.077790258 | -6789.07779025772 |
| 22 | 277103 | 278119.604519057 | -1016.60451905721 |
| 23 | 275037 | 278117.416586895 | -3080.41658689528 |
| 24 | 270150 | 272044.341981702 | -1894.34198170234 |
| 25 | 267140 | 271785.640216177 | -4645.64021617714 |
| 26 | 264993 | 269347.034379142 | -4354.03437914184 |
| 27 | 287259 | 288321.859174519 | -1062.85917451887 |
| 28 | 291186 | 289273.349725057 | 1912.65027494299 |
| 29 | 292300 | 293909.261129945 | -1609.26112994523 |
| 30 | 288186 | 286214.880427174 | 1971.11957282623 |
| 31 | 281477 | 279621.776796573 | 1855.22320342702 |
| 32 | 282656 | 284243.164855065 | -1587.16485506543 |
| 33 | 280190 | 281138.905434533 | -948.905434532673 |
| 34 | 280408 | 281138.627643475 | -730.627643474796 |
| 35 | 276836 | 275555.042773191 | 1280.95722680916 |
| 36 | 275216 | 272978.062419437 | 2237.93758056337 |
| 37 | 274352 | 273964.963617819 | 387.036382180673 |
| 38 | 271311 | 271144.391651899 | 166.608348101282 |
| 39 | 289802 | 290900.283755638 | -1098.28375563846 |
| 40 | 290726 | 292235.263361159 | -1509.26336115896 |
| 41 | 292300 | 288434.420137580 | 3865.57986241972 |
| 42 | 278506 | 272229.990289954 | 6276.0097100456 |
| 43 | 269826 | 262998.203698562 | 6827.79630143823 |
| 44 | 265861 | 260066.729402835 | 5794.27059716494 |
| 45 | 269034 | 261091.527177735 | 7942.47282226516 |
| 46 | 264176 | 260623.975829083 | 3552.02417091696 |
| 47 | 255198 | 253802.060298558 | 1395.93970144219 |
| 48 | 253353 | 254857.115830237 | -1504.11583023651 |
| 49 | 246057 | 245581.577112526 | 475.422887474289 |
| 50 | 235372 | 237977.495322387 | -2605.49532238681 |
| 51 | 258556 | 266181.240391493 | -7625.24039149274 |
| 52 | 260993 | 268692.026892898 | -7699.02689289788 |
| 53 | 254663 | 255799.007461843 | -1136.0074618429 |
| 54 | 250643 | 253268.633871999 | -2625.63387199911 |
| 55 | 243422 | 246447.3467803 | -3025.34678029991 |
| 56 | 247105 | 246824.252521854 | 280.747478146419 |
| 57 | 248541 | 255847.293933219 | -7306.29393321932 |
| 58 | 245039 | 252093.269465372 | -7054.26946537164 |
| 59 | 237080 | 245860.579538571 | -8780.5795385706 |
| 60 | 237085 | 245939.31423192 | -8854.31423191995 |
| 61 | 225554 | 233844.095506987 | -8290.09550698674 |
| 62 | 226839 | 236729.621921312 | -9890.62192131193 |
| 63 | 247934 | 260005.599671992 | -12071.5996719923 |
| 64 | 248333 | 257726.057138682 | -9393.05713868196 |
| 65 | 246969 | 250849.404797396 | -3880.40479739647 |
| 66 | 245098 | 243684.823619686 | 1413.17638031405 |
| 67 | 246263 | 244273.12738853 | 1989.87261147028 |
| 68 | 255765 | 251446.790636098 | 4318.20936390187 |
| 69 | 264319 | 261772.982412459 | 2546.01758754143 |
| 70 | 268347 | 266090.844531547 | 2256.15546845338 |
| 71 | 273046 | 265499.286906449 | 7546.71309355081 |
| 72 | 273963 | 265245.260055051 | 8717.7399449493 |
| 73 | 267430 | 256147.908365798 | 11282.0916342019 |
| 74 | 271993 | 257824.122058286 | 14168.8779417141 |
| 75 | 292710 | 277553.707261587 | 15156.2927384128 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.349923334180428 | 0.699846668360856 | 0.650076665819572 |
| 22 | 0.236068188816044 | 0.472136377632088 | 0.763931811183956 |
| 23 | 0.146066008069133 | 0.292132016138267 | 0.853933991930867 |
| 24 | 0.0888411485817269 | 0.177682297163454 | 0.911158851418273 |
| 25 | 0.0468393897260121 | 0.0936787794520242 | 0.953160610273988 |
| 26 | 0.040349227105183 | 0.080698454210366 | 0.959650772894817 |
| 27 | 0.076931814653297 | 0.153863629306594 | 0.923068185346703 |
| 28 | 0.62229991790806 | 0.75540016418388 | 0.37770008209194 |
| 29 | 0.614616521829831 | 0.770766956340338 | 0.385383478170169 |
| 30 | 0.557365701738416 | 0.885268596523167 | 0.442634298261584 |
| 31 | 0.481415239664417 | 0.962830479328834 | 0.518584760335583 |
| 32 | 0.428173257176285 | 0.85634651435257 | 0.571826742823715 |
| 33 | 0.468055863311585 | 0.93611172662317 | 0.531944136688415 |
| 34 | 0.422758885386186 | 0.84551777077237 | 0.577241114613815 |
| 35 | 0.342899566926469 | 0.685799133852938 | 0.657100433073531 |
| 36 | 0.282885479409400 | 0.565770958818801 | 0.7171145205906 |
| 37 | 0.280160707268189 | 0.560321414536378 | 0.719839292731811 |
| 38 | 0.230935510149074 | 0.461871020298147 | 0.769064489850926 |
| 39 | 0.181631878896699 | 0.363263757793398 | 0.818368121103301 |
| 40 | 0.288822124894768 | 0.577644249789536 | 0.711177875105232 |
| 41 | 0.507700867280505 | 0.98459826543899 | 0.492299132719495 |
| 42 | 0.883400919792576 | 0.233198160414848 | 0.116599080207424 |
| 43 | 0.919966908746612 | 0.160066182506775 | 0.0800330912533877 |
| 44 | 0.941497416143007 | 0.117005167713986 | 0.0585025838569928 |
| 45 | 0.923465694703016 | 0.153068610593968 | 0.0765343052969842 |
| 46 | 0.903591044891752 | 0.192817910216497 | 0.0964089551082483 |
| 47 | 0.896735715935605 | 0.20652856812879 | 0.103264284064395 |
| 48 | 0.860256711977625 | 0.279486576044749 | 0.139743288022375 |
| 49 | 0.837617535098684 | 0.324764929802631 | 0.162382464901316 |
| 50 | 0.997539101643485 | 0.00492179671303087 | 0.00246089835651544 |
| 51 | 0.997322415555544 | 0.005355168888912 | 0.002677584444456 |
| 52 | 0.993880374768 | 0.0122392504639997 | 0.00611962523199985 |
| 53 | 0.979513271779469 | 0.0409734564410623 | 0.0204867282205311 |
| 54 | 0.942043055915325 | 0.115913888169350 | 0.0579569440846752 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 2 | 0.0588235294117647 | NOK |
| 5% type I error level | 4 | 0.117647058823529 | NOK |
| 10% type I error level | 6 | 0.176470588235294 | NOK |
