| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -19851.0732190765 + 0.927997599540739X[t] + 3488.77411053802M1[t] + 5238.89859350010M2[t] + 5813.70309850114M3[t] + 6726.8417983221M4[t] + 5285.69400486605M5[t] -899.207493524473M6[t] -7657.43328196939M7[t] -13975.7005108038M8[t] -7847.9064228879M9[t] -4738.03673981474M10[t] -1569.55783649424M11[t] + 455.91333933419t + 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) | -19851.0732190765 | 24988.342126 | -0.7944 | 0.430498 | 0.215249 |
| X | 0.927997599540739 | 0.076411 | 12.1448 | 0 | 0 |
| M1 | 3488.77411053802 | 4731.157147 | 0.7374 | 0.464129 | 0.232064 |
| M2 | 5238.89859350010 | 4742.258034 | 1.1047 | 0.274268 | 0.137134 |
| M3 | 5813.70309850114 | 4778.274174 | 1.2167 | 0.229111 | 0.114555 |
| M4 | 6726.8417983221 | 4817.976952 | 1.3962 | 0.168476 | 0.084238 |
| M5 | 5285.69400486605 | 4888.685793 | 1.0812 | 0.284499 | 0.14225 |
| M6 | -899.207493524473 | 4797.847171 | -0.1874 | 0.852048 | 0.426024 |
| M7 | -7657.43328196939 | 4937.908632 | -1.5507 | 0.126914 | 0.063457 |
| M8 | -13975.7005108038 | 5248.174096 | -2.663 | 0.010235 | 0.005117 |
| M9 | -7847.9064228879 | 5087.925466 | -1.5425 | 0.128913 | 0.064456 |
| M10 | -4738.03673981474 | 4961.929918 | -0.9549 | 0.343975 | 0.171987 |
| M11 | -1569.55783649424 | 4926.611899 | -0.3186 | 0.751291 | 0.375646 |
| t | 455.91333933419 | 85.376267 | 5.34 | 2e-06 | 1e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.911439378287059 |
| R-squared | 0.830721740292301 |
| Adjusted R-squared | 0.789200657722488 |
| F-TEST (value) | 20.0072273861245 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 53 |
| p-value | 6.66133814775094e-16 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 7787.83778390367 |
| Sum Squared Residuals | 3214472119.46507 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 267413 | 257771.242306554 | 9641.75769344596 |
| 2 | 267366 | 258655.811547104 | 8710.18845289556 |
| 3 | 264777 | 256964.712431987 | 7812.28756801327 |
| 4 | 258863 | 252933.746439414 | 5929.25356058568 |
| 5 | 254844 | 249240.614989833 | 5603.38501016744 |
| 6 | 254868 | 249113.020341604 | 5754.97965839585 |
| 7 | 277267 | 269174.191697846 | 8092.80830215374 |
| 8 | 285351 | 271802.087846544 | 13548.9121534557 |
| 9 | 286602 | 278941.665835919 | 7660.33416408076 |
| 10 | 283042 | 284614.931406884 | -1572.93140688361 |
| 11 | 276687 | 278215.093579299 | -1528.09357929924 |
| 12 | 277915 | 280295.316613501 | -2380.31661350057 |
| 13 | 277128 | 280711.757189919 | -3583.75718991889 |
| 14 | 277103 | 281561.990519286 | -4458.99051928617 |
| 15 | 275037 | 279915.435288946 | -4878.43528894634 |
| 16 | 270150 | 275307.254789460 | -5157.2547894596 |
| 17 | 267140 | 271877.674658147 | -4737.67465814742 |
| 18 | 264993 | 269599.909571783 | -4606.90957178310 |
| 19 | 287259 | 290618.774450751 | -3359.77445075127 |
| 20 | 291186 | 288674.426426512 | 2511.57357348796 |
| 21 | 292300 | 293619.290092973 | -1319.29009297319 |
| 22 | 288186 | 286048.173923292 | 2137.82607670787 |
| 23 | 281477 | 280388.878180141 | 1088.12181985873 |
| 24 | 282656 | 282932.172016513 | -276.172016513435 |
| 25 | 280190 | 285701.086507767 | -5511.08650776752 |
| 26 | 280408 | 284609.020861296 | -4201.02086129601 |
| 27 | 276836 | 279421.226791109 | -2585.22679110875 |
| 28 | 275216 | 277102.416369689 | -1886.41636968901 |
| 29 | 274352 | 275591.935274227 | -1239.93527422708 |
| 30 | 271311 | 272839.963414497 | -1528.96341449744 |
| 31 | 289802 | 292645.935430866 | -2843.93543086586 |
| 32 | 290726 | 291718.672775723 | -992.672775723291 |
| 33 | 292300 | 291373.022127203 | 926.977872797318 |
| 34 | 278506 | 277773.633550905 | 732.366449095013 |
| 35 | 269826 | 269145.673486823 | 680.326513176694 |
| 36 | 265861 | 266992.37147192 | -1131.37147191979 |
| 37 | 269034 | 271056.770612133 | -2022.77061213275 |
| 38 | 264176 | 266893.032911181 | -2717.03291118140 |
| 39 | 255198 | 260311.386446484 | -5113.38644648395 |
| 40 | 253353 | 258052.895869034 | -4699.89586903435 |
| 41 | 246057 | 250028.799622396 | -3971.79962239598 |
| 42 | 235372 | 242730.567522516 | -7358.56752251627 |
| 43 | 258556 | 267531.022619613 | -8975.02261961294 |
| 44 | 260993 | 267971.628426193 | -6978.62842619341 |
| 45 | 254663 | 259146.863710669 | -4483.86371066908 |
| 46 | 250643 | 252906.496098729 | -2263.49609872944 |
| 47 | 243422 | 247248.128353178 | -3826.12835317812 |
| 48 | 247105 | 249950.109779072 | -2845.10977907175 |
| 49 | 248541 | 255034.37828118 | -6493.37828117998 |
| 50 | 245039 | 251803.278167767 | -6764.27816776707 |
| 51 | 237080 | 246356.572767308 | -9276.57276730794 |
| 52 | 237085 | 245513.278529158 | -8428.27852915797 |
| 53 | 225554 | 235846.626531332 | -10292.6265313325 |
| 54 | 226839 | 236556.08571789 | -9717.08571788981 |
| 55 | 247934 | 257819.013965537 | -9885.01396553719 |
| 56 | 248333 | 256422.184525027 | -8089.184525027 |
| 57 | 246969 | 249753.158233236 | -2784.15823323581 |
| 58 | 245098 | 244131.76502019 | 966.23497981016 |
| 59 | 246263 | 242677.226400558 | 3585.77359944193 |
| 60 | 255765 | 249132.030118994 | 6632.96988100556 |
| 61 | 264319 | 256349.765102447 | 7969.23489755317 |
| 62 | 268347 | 258915.865993365 | 9431.1340066351 |
| 63 | 273046 | 259004.666274166 | 14041.3337258337 |
| 64 | 273963 | 259720.408003245 | 14242.5919967552 |
| 65 | 267430 | 252791.348924064 | 14638.6510759355 |
| 66 | 271993 | 254536.453431709 | 17456.5465682908 |
| 67 | 292710 | 275739.061835386 | 16970.9381646135 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00726201907065687 | 0.0145240381413137 | 0.992737980929343 |
| 18 | 0.0055463371653911 | 0.0110926743307822 | 0.994453662834609 |
| 19 | 0.00175074949827093 | 0.00350149899654186 | 0.99824925050173 |
| 20 | 0.00706026674206305 | 0.0141205334841261 | 0.992939733257937 |
| 21 | 0.00250555708055028 | 0.00501111416110055 | 0.99749444291945 |
| 22 | 0.0175471017057880 | 0.0350942034115760 | 0.982452898294212 |
| 23 | 0.00842422176546652 | 0.0168484435309330 | 0.991575778234533 |
| 24 | 0.0034080255791513 | 0.0068160511583026 | 0.996591974420849 |
| 25 | 0.00435305364689601 | 0.00870610729379202 | 0.995646946353104 |
| 26 | 0.00225632652978714 | 0.00451265305957428 | 0.997743673470213 |
| 27 | 0.00104744799551491 | 0.00209489599102982 | 0.998952552004485 |
| 28 | 0.00148080876257197 | 0.00296161752514393 | 0.998519191237428 |
| 29 | 0.00742524834270035 | 0.0148504966854007 | 0.9925747516573 |
| 30 | 0.00600324064779367 | 0.0120064812955873 | 0.993996759352206 |
| 31 | 0.0041811848539413 | 0.0083623697078826 | 0.995818815146059 |
| 32 | 0.0387550303304036 | 0.0775100606608073 | 0.961244969669596 |
| 33 | 0.113675971696636 | 0.227351943393272 | 0.886324028303364 |
| 34 | 0.552578638305095 | 0.894842723389811 | 0.447421361694905 |
| 35 | 0.798966972629651 | 0.402066054740698 | 0.201033027370349 |
| 36 | 0.932690654049104 | 0.134618691901791 | 0.0673093459508957 |
| 37 | 0.94201608151558 | 0.115967836968841 | 0.0579839184844206 |
| 38 | 0.936026293682779 | 0.127947412634443 | 0.0639737063172214 |
| 39 | 0.954289155680746 | 0.091421688638508 | 0.045710844319254 |
| 40 | 0.94320897396948 | 0.11358205206104 | 0.05679102603052 |
| 41 | 0.949441181493093 | 0.101117637013814 | 0.050558818506907 |
| 42 | 0.999722883958528 | 0.000554232082943912 | 0.000277116041471956 |
| 43 | 0.999951528647924 | 9.69427041527627e-05 | 4.84713520763814e-05 |
| 44 | 0.99996365616824 | 7.26876635207699e-05 | 3.63438317603850e-05 |
| 45 | 0.99991809203713 | 0.000163815925739454 | 8.1907962869727e-05 |
| 46 | 0.999651688370477 | 0.000696623259046901 | 0.000348311629523451 |
| 47 | 0.998504597696979 | 0.00299080460604252 | 0.00149540230302126 |
| 48 | 0.997196532503452 | 0.00560693499309545 | 0.00280346749654773 |
| 49 | 0.996474419669294 | 0.00705116066141138 | 0.00352558033070569 |
| 50 | 0.987433637580712 | 0.0251327248385755 | 0.0125663624192877 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 16 | 0.470588235294118 | NOK |
| 5% type I error level | 24 | 0.705882352941177 | NOK |
| 10% type I error level | 26 | 0.764705882352941 | NOK |
