| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 284296.210684253 -731.579789057658X[t] + 2422.53918567349M1[t] + 871.362765106428M2[t] -3027.19042759867M3[t] -7372.77181586589M4[t] -10622.6551434852M5[t] -13130.8052342349M6[t] + 9825.14397187436M7[t] + 12604.1610808612M8[t] + 10987.1165759170M9[t] + 3088.28404218847M10[t] -2764.34787343459M11[t] + 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) | 284296.210684253 | 9679.166192 | 29.372 | 0 | 0 |
| X | -731.579789057658 | 257.065011 | -2.8459 | 0.006177 | 0.003088 |
| M1 | 2422.53918567349 | 9739.338985 | 0.2487 | 0.804474 | 0.402237 |
| M2 | 871.362765106428 | 9738.415413 | 0.0895 | 0.929022 | 0.464511 |
| M3 | -3027.19042759867 | 9742.033806 | -0.3107 | 0.757156 | 0.378578 |
| M4 | -7372.77181586589 | 9792.719622 | -0.7529 | 0.454674 | 0.227337 |
| M5 | -10622.6551434852 | 9740.424541 | -1.0906 | 0.280131 | 0.140065 |
| M6 | -13130.8052342349 | 9751.925699 | -1.3465 | 0.183572 | 0.091786 |
| M7 | 9825.14397187436 | 9737.736815 | 1.009 | 0.317326 | 0.158663 |
| M8 | 12604.1610808612 | 9738.175081 | 1.2943 | 0.200872 | 0.100436 |
| M9 | 10987.1165759170 | 9742.162874 | 1.1278 | 0.264217 | 0.132109 |
| M10 | 3088.28404218847 | 10170.801336 | 0.3036 | 0.762526 | 0.381263 |
| M11 | -2764.34787343459 | 10171.840845 | -0.2718 | 0.786802 | 0.393401 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.544664723571685 |
| R-squared | 0.296659661103420 |
| Adjusted R-squared | 0.145943874197011 |
| F-TEST (value) | 1.96833833530417 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 56 |
| p-value | 0.0450649302679921 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 16081.2434620038 |
| Sum Squared Residuals | 14481957911.9175 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 267413 | 271062.942384094 | -3649.94238409385 |
| 2 | 267366 | 265853.867018237 | 1512.13298176276 |
| 3 | 264777 | 261955.313825532 | 2821.68617446786 |
| 4 | 258863 | 255414.993070092 | 3448.00692990804 |
| 5 | 254844 | 248507.210797184 | 6336.78920281566 |
| 6 | 254868 | 253314.858597011 | 1553.14140298873 |
| 7 | 277267 | 274807.648225005 | 2459.35177499484 |
| 8 | 285351 | 278318.245123050 | 7032.75487695027 |
| 9 | 286602 | 272311.721883760 | 14290.2781162404 |
| 10 | 283042 | 267339.208506262 | 15702.7914937384 |
| 11 | 276687 | 261486.576590639 | 15200.4234093614 |
| 12 | 277915 | 262787.764885958 | 15127.2351140422 |
| 13 | 277128 | 263015.564704458 | 14112.4352955416 |
| 14 | 277103 | 265853.867018237 | 11249.1329817628 |
| 15 | 275037 | 264881.632981763 | 10155.3670182372 |
| 16 | 270150 | 262730.790960669 | 7419.20903933147 |
| 17 | 267140 | 258017.748054934 | 9122.25194506612 |
| 18 | 264993 | 254046.438386069 | 10946.5616139311 |
| 19 | 287259 | 277002.387592178 | 10256.6124078219 |
| 20 | 291186 | 278318.245123050 | 12867.7548769503 |
| 21 | 292300 | 274506.461250933 | 17793.5387490675 |
| 22 | 288186 | 267339.208506262 | 20846.7914937384 |
| 23 | 281477 | 265876.055324984 | 15600.9446750155 |
| 24 | 282656 | 271566.72235465 | 11089.2776453503 |
| 25 | 280190 | 268868.203016920 | 11321.7969830804 |
| 26 | 280408 | 265853.867018237 | 14554.1329817628 |
| 27 | 276836 | 264881.632981763 | 11954.3670182372 |
| 28 | 275216 | 266388.689905957 | 8827.31009404318 |
| 29 | 274352 | 260212.487422107 | 14139.5125778932 |
| 30 | 271311 | 252583.278807954 | 18727.7211920464 |
| 31 | 289802 | 272612.908857832 | 17189.0911421678 |
| 32 | 290726 | 277586.665333992 | 13139.3346660080 |
| 33 | 292300 | 275969.620829048 | 16330.3791709522 |
| 34 | 278506 | 272460.267029665 | 6045.73297033477 |
| 35 | 269826 | 262218.156379696 | 7607.84362030378 |
| 36 | 265861 | 262787.764885958 | 3073.23511404216 |
| 37 | 269034 | 262283.984915401 | 6750.0150845993 |
| 38 | 264176 | 261464.388283891 | 2711.61171610871 |
| 39 | 255198 | 255371.095724013 | -173.095724013213 |
| 40 | 253353 | 251757.094124804 | 1595.90587519633 |
| 41 | 246057 | 247044.051219069 | -987.051219069012 |
| 42 | 235372 | 247462.22028455 | -12090.22028455 |
| 43 | 258556 | 268955.009912544 | -10399.0099125439 |
| 44 | 260993 | 273928.766388704 | -12935.7663887037 |
| 45 | 254663 | 275238.04103999 | -20575.0410399902 |
| 46 | 250643 | 267339.208506262 | -16696.2085062616 |
| 47 | 243422 | 259291.837223466 | -15869.8372234656 |
| 48 | 247105 | 260593.025518785 | -13488.0255187849 |
| 49 | 248541 | 263015.564704458 | -14474.5647044583 |
| 50 | 245039 | 265122.287229180 | -20083.2872291796 |
| 51 | 237080 | 258297.414880244 | -21217.4148802438 |
| 52 | 237085 | 255414.993070092 | -18329.9930700920 |
| 53 | 225554 | 253628.269320588 | -28074.2693205879 |
| 54 | 226839 | 252583.278807954 | -25744.2788079536 |
| 55 | 247934 | 274807.648225005 | -26873.6482250052 |
| 56 | 248333 | 279781.404701165 | -31448.404701165 |
| 57 | 246969 | 281822.259141509 | -34853.2591415091 |
| 58 | 245098 | 270997.10745155 | -25899.1074515499 |
| 59 | 246263 | 268802.374481215 | -22539.3744812151 |
| 60 | 255765 | 271566.72235465 | -15801.7223546497 |
| 61 | 264319 | 278378.740274669 | -14059.7402746692 |
| 62 | 268347 | 278290.723432217 | -9943.7234322174 |
| 63 | 273046 | 276586.909606685 | -3540.90960668529 |
| 64 | 273963 | 276923.438868387 | -2960.43886838708 |
| 65 | 267430 | 267967.233186118 | -537.233186118014 |
| 66 | 271993 | 265385.925116463 | 6607.07488353739 |
| 67 | 292710 | 285342.397187435 | 7367.60281256456 |
| 68 | 295881 | 284536.67333004 | 11344.3266699602 |
| 69 | 293299 | 286284.895854761 | 7014.10414523919 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.118224212245494 | 0.236448424490988 | 0.881775787754506 |
| 17 | 0.0549234048119934 | 0.109846809623987 | 0.945076595188007 |
| 18 | 0.0294786596751302 | 0.0589573193502604 | 0.97052134032487 |
| 19 | 0.0144941280975493 | 0.0289882561950986 | 0.98550587190245 |
| 20 | 0.00628762596977568 | 0.0125752519395514 | 0.993712374030224 |
| 21 | 0.00270969245523458 | 0.00541938491046915 | 0.997290307544765 |
| 22 | 0.00139502983406424 | 0.00279005966812847 | 0.998604970165936 |
| 23 | 0.000553327570660461 | 0.00110665514132092 | 0.99944667242934 |
| 24 | 0.000202094877113869 | 0.000404189754227738 | 0.999797905122886 |
| 25 | 0.000102946012597557 | 0.000205892025195115 | 0.999897053987402 |
| 26 | 7.5301022346048e-05 | 0.000150602044692096 | 0.999924698977654 |
| 27 | 3.79703356015315e-05 | 7.5940671203063e-05 | 0.999962029664399 |
| 28 | 1.48953887144259e-05 | 2.97907774288518e-05 | 0.999985104611286 |
| 29 | 8.8401208702266e-06 | 1.76802417404532e-05 | 0.99999115987913 |
| 30 | 2.00818648204844e-05 | 4.01637296409687e-05 | 0.99997991813518 |
| 31 | 3.04426377056152e-05 | 6.08852754112304e-05 | 0.999969557362294 |
| 32 | 1.90051988191343e-05 | 3.80103976382685e-05 | 0.99998099480118 |
| 33 | 2.08031806036161e-05 | 4.16063612072321e-05 | 0.999979196819396 |
| 34 | 4.08259290902648e-05 | 8.16518581805296e-05 | 0.99995917407091 |
| 35 | 5.57416449967083e-05 | 0.000111483289993417 | 0.999944258355003 |
| 36 | 6.83363907838866e-05 | 0.000136672781567773 | 0.999931663609216 |
| 37 | 6.0402449525086e-05 | 0.000120804899050172 | 0.999939597550475 |
| 38 | 6.99575465209093e-05 | 0.000139915093041819 | 0.99993004245348 |
| 39 | 7.72882511476298e-05 | 0.000154576502295260 | 0.999922711748852 |
| 40 | 8.35434253109684e-05 | 0.000167086850621937 | 0.999916456574689 |
| 41 | 0.000204174427723525 | 0.000408348855447051 | 0.999795825572277 |
| 42 | 0.0008548517611612 | 0.0017097035223224 | 0.99914514823884 |
| 43 | 0.00160808927911828 | 0.00321617855823657 | 0.998391910720882 |
| 44 | 0.00337404544143199 | 0.00674809088286398 | 0.996625954558568 |
| 45 | 0.0266709865084713 | 0.0533419730169426 | 0.973329013491529 |
| 46 | 0.0497882923625857 | 0.0995765847251714 | 0.950211707637414 |
| 47 | 0.0703496912295551 | 0.140699382459110 | 0.929650308770445 |
| 48 | 0.0700947750120264 | 0.140189550024053 | 0.929905224987974 |
| 49 | 0.0842590229833847 | 0.168518045966769 | 0.915740977016615 |
| 50 | 0.087679490148068 | 0.175358980296136 | 0.912320509851932 |
| 51 | 0.0812485455750862 | 0.162497091150172 | 0.918751454424914 |
| 52 | 0.200853957317887 | 0.401707914635773 | 0.799146042682113 |
| 53 | 0.237352828469072 | 0.474705656938144 | 0.762647171530928 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 24 | 0.631578947368421 | NOK |
| 5% type I error level | 26 | 0.68421052631579 | NOK |
| 10% type I error level | 29 | 0.763157894736842 | NOK |
