| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 208567.107938821 -921.004563567302X[t] -11949.1975185385M1[t] -8082.79076424465M2[t] -3965.65512368413M3[t] -343.269483123576M4[t] -13602.4626075061M5[t] -7617.86920888109M6[t] -4314.85008049639M7[t] -468.345557023851M8[t] -12413.4718215697M9[t] -8127.28954572532M10[t] -3619.37471336142M11[t] + 2261.93056733788t + 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) | 208567.107938821 | 16132.48965 | 12.9284 | 0 | 0 |
| X | -921.004563567302 | 150.601916 | -6.1155 | 0 | 0 |
| M1 | -11949.1975185385 | 2732.774495 | -4.3726 | 3.8e-05 | 1.9e-05 |
| M2 | -8082.79076424465 | 2722.398061 | -2.969 | 0.003995 | 0.001998 |
| M3 | -3965.65512368413 | 2722.493331 | -1.4566 | 0.149339 | 0.074669 |
| M4 | -343.269483123576 | 2723.995504 | -0.126 | 0.900051 | 0.450026 |
| M5 | -13602.4626075061 | 2737.786077 | -4.9684 | 4e-06 | 2e-06 |
| M6 | -7617.86920888109 | 2723.022221 | -2.7976 | 0.00652 | 0.00326 |
| M7 | -4314.85008049639 | 2815.653101 | -1.5325 | 0.129564 | 0.064782 |
| M8 | -468.345557023851 | 2813.448906 | -0.1665 | 0.868232 | 0.434116 |
| M9 | -12413.4718215697 | 2814.539857 | -4.4105 | 3.3e-05 | 1.7e-05 |
| M10 | -8127.28954572532 | 2812.493631 | -2.8897 | 0.005023 | 0.002511 |
| M11 | -3619.37471336142 | 2810.379633 | -1.2879 | 0.201702 | 0.100851 |
| t | 2261.93056733788 | 181.715335 | 12.4477 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.987784594200056 |
| R-squared | 0.97571840453897 |
| Adjusted R-squared | 0.971564973736425 |
| F-TEST (value) | 234.918661445175 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 76 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 5257.57399585094 |
| Sum Squared Residuals | 2100798408.46045 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 106370 | 106503.083261820 | -133.083261819800 |
| 2 | 109375 | 111157.813281744 | -1782.81328174364 |
| 3 | 116476 | 117352.678576929 | -876.678576928715 |
| 4 | 123297 | 122223.889764903 | 1073.11023509688 |
| 5 | 114813 | 110766.124926075 | 4046.87507392511 |
| 6 | 117925 | 116710.137483119 | 1214.86251688052 |
| 7 | 126466 | 120893.580333491 | 5572.41966650889 |
| 8 | 131235 | 124975.805384453 | 6259.19461554652 |
| 9 | 120546 | 113634.801472824 | 6911.19852717565 |
| 10 | 123791 | 117235.699712591 | 6555.30028740875 |
| 11 | 129813 | 122992.440092369 | 6820.559907631 |
| 12 | 133463 | 126755.434876864 | 6707.56512313648 |
| 13 | 122987 | 115134.058342172 | 7852.94165782846 |
| 14 | 125418 | 116104.770107826 | 9313.22989217358 |
| 15 | 130199 | 120549.726732233 | 9649.2732677665 |
| 16 | 133016 | 124592.033812997 | 8423.96618700268 |
| 17 | 121454 | 112950.068061456 | 8503.9319385444 |
| 18 | 122044 | 118617.77924943 | 3426.22075056998 |
| 19 | 128313 | 123630.126207012 | 4682.87379298777 |
| 20 | 131556 | 128541.255365185 | 3014.74463481485 |
| 21 | 120027 | 118213.35647348 | 1813.64352651992 |
| 22 | 123001 | 122090.556082317 | 910.443917682825 |
| 23 | 130111 | 128952.501938376 | 1158.49806162433 |
| 24 | 132524 | 134281.204480935 | -1757.20448093461 |
| 25 | 123742 | 125422.841636945 | -1680.84163694455 |
| 26 | 124931 | 129524.968918728 | -4593.96891872821 |
| 27 | 133646 | 135535.633301200 | -1889.63330119970 |
| 28 | 136557 | 140959.447227314 | -4402.44722731448 |
| 29 | 127509 | 129777.983757556 | -2268.98375755644 |
| 30 | 128945 | 135721.996314601 | -6776.99631460102 |
| 31 | 137191 | 141194.845553967 | -4003.8455539669 |
| 32 | 139716 | 146474.376537567 | -6758.37653756674 |
| 33 | 129083 | 135593.874907721 | -6510.87490772127 |
| 34 | 131604 | 139655.275429272 | -8051.27542927183 |
| 35 | 139413 | 146056.719003547 | -6643.71900354668 |
| 36 | 143125 | 151753.823371533 | -8628.82337153254 |
| 37 | 133948 | 141329.752769478 | -7381.75276947805 |
| 38 | 137116 | 145708.181420332 | -8592.18142033193 |
| 39 | 144864 | 151810.946259160 | -6946.94625916016 |
| 40 | 149277 | 156866.358359848 | -7589.35835984802 |
| 41 | 138796 | 145040.191695593 | -6244.19169559285 |
| 42 | 143258 | 151444.706534421 | -8186.7065344211 |
| 43 | 150034 | 155628.149384793 | -5594.14938479273 |
| 44 | 154708 | 160539.278542966 | -5831.27854296567 |
| 45 | 144888 | 150395.580563974 | -5507.58056397406 |
| 46 | 148762 | 154180.679716454 | -5418.67971645442 |
| 47 | 156500 | 160490.022834373 | -3990.02283437255 |
| 48 | 161088 | 165726.624920575 | -4638.62492057473 |
| 49 | 152772 | 156684.061163871 | -3912.06116387121 |
| 50 | 158011 | 161154.590271082 | -3143.59027108181 |
| 51 | 163318 | 167441.556022623 | -4123.5560226235 |
| 52 | 169969 | 172220.666754241 | -2251.66675424115 |
| 53 | 162269 | 160578.701002699 | 1690.29899730054 |
| 54 | 165765 | 165970.110821604 | -205.110821603674 |
| 55 | 170600 | 171258.759148256 | -658.759148256062 |
| 56 | 174681 | 176354.089219142 | -1673.08921914246 |
| 57 | 166364 | 166855.094434648 | -491.094434647949 |
| 58 | 170240 | 171469.097694339 | -1229.09769433888 |
| 59 | 176150 | 178146.842637684 | -1996.84263768394 |
| 60 | 182056 | 184212.348831097 | -2156.34883109670 |
| 61 | 172218 | 174432.981423539 | -2214.98142353933 |
| 62 | 177856 | 178627.209161680 | -771.20916167975 |
| 63 | 182253 | 184453.672631438 | -2200.67263143779 |
| 64 | 188090 | 188864.381537629 | -774.381537628538 |
| 65 | 176863 | 176946.114417017 | -83.1144170166443 |
| 66 | 183273 | 183258.528799488 | 14.4712005118637 |
| 67 | 187969 | 188362.976213427 | -393.976213427077 |
| 68 | 194650 | 193458.306284313 | 1191.69371568653 |
| 69 | 183036 | 182946.206479895 | 89.7935201050704 |
| 70 | 189516 | 187191.807914159 | 2324.19208584106 |
| 71 | 193805 | 192948.548293937 | 856.45170606331 |
| 72 | 200499 | 197172.045360215 | 3326.95463978512 |
| 73 | 188142 | 187024.276127231 | 1117.72387276941 |
| 74 | 193732 | 191126.403409014 | 2605.59659098575 |
| 75 | 197126 | 196860.766422416 | 265.233577584431 |
| 76 | 205140 | 201731.97761039 | 3408.02238961003 |
| 77 | 191751 | 190274.212771562 | 1476.78722843826 |
| 78 | 196700 | 195389.321221396 | 1310.67877860426 |
| 79 | 199784 | 199388.563159054 | 395.436840946102 |
| 80 | 207360 | 203562.888666373 | 3797.11133362698 |
| 81 | 196101 | 192406.085667457 | 3694.91433254264 |
| 82 | 200824 | 195914.883450868 | 4909.11654913249 |
| 83 | 205743 | 201947.925199715 | 3795.07480028453 |
| 84 | 212489 | 205342.518158783 | 7146.48184121697 |
| 85 | 200810 | 194457.945274945 | 6352.05472505507 |
| 86 | 203683 | 196718.063429594 | 6964.936570406 |
| 87 | 207286 | 201163.020054001 | 6122.97994599892 |
| 88 | 210910 | 208797.244932677 | 2112.75506732260 |
| 89 | 194915 | 202036.603368042 | -7121.60336804239 |
| 90 | 217920 | 208717.419575941 | 9202.58042405917 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.211206215985269 | 0.422412431970538 | 0.788793784014731 |
| 18 | 0.261014386253473 | 0.522028772506947 | 0.738985613746527 |
| 19 | 0.491143328333681 | 0.982286656667362 | 0.508856671666319 |
| 20 | 0.770710092712927 | 0.458579814574147 | 0.229289907287073 |
| 21 | 0.937407333735248 | 0.125185332529505 | 0.0625926662647524 |
| 22 | 0.980813494645118 | 0.0383730107097632 | 0.0191865053548816 |
| 23 | 0.99418939688302 | 0.0116212062339602 | 0.00581060311698009 |
| 24 | 0.997586513246027 | 0.00482697350794683 | 0.00241348675397342 |
| 25 | 0.997371015430165 | 0.00525796913966987 | 0.00262898456983494 |
| 26 | 0.995784305096446 | 0.00843138980710884 | 0.00421569490355442 |
| 27 | 0.996447837044364 | 0.00710432591127247 | 0.00355216295563623 |
| 28 | 0.995253664870073 | 0.00949267025985409 | 0.00474633512992704 |
| 29 | 0.997464778069645 | 0.00507044386070992 | 0.00253522193035496 |
| 30 | 0.9954695031813 | 0.00906099363739892 | 0.00453049681869946 |
| 31 | 0.994871283163326 | 0.0102574336733486 | 0.00512871683667431 |
| 32 | 0.991494230999957 | 0.0170115380000860 | 0.00850576900004298 |
| 33 | 0.986260677957435 | 0.0274786440851295 | 0.0137393220425647 |
| 34 | 0.979064584296247 | 0.0418708314075065 | 0.0209354157037532 |
| 35 | 0.967906554934248 | 0.0641868901315044 | 0.0320934450657522 |
| 36 | 0.958243792759204 | 0.083512414481591 | 0.0417562072407955 |
| 37 | 0.951711425125311 | 0.0965771497493778 | 0.0482885748746889 |
| 38 | 0.95486724596435 | 0.0902655080713021 | 0.0451327540356511 |
| 39 | 0.948638493008892 | 0.102723013982215 | 0.0513615069911076 |
| 40 | 0.942046454467135 | 0.115907091065730 | 0.0579535455328648 |
| 41 | 0.925890233430573 | 0.148219533138855 | 0.0741097665694274 |
| 42 | 0.94710931422156 | 0.105781371556878 | 0.0528906857784389 |
| 43 | 0.936378482024093 | 0.127243035951813 | 0.0636215179759065 |
| 44 | 0.9357729797013 | 0.128454040597399 | 0.0642270202986997 |
| 45 | 0.937039656324475 | 0.125920687351049 | 0.0629603436755247 |
| 46 | 0.949150474807711 | 0.101699050384577 | 0.0508495251922886 |
| 47 | 0.949449759433212 | 0.101100481133577 | 0.0505502405667884 |
| 48 | 0.966008804038021 | 0.0679823919239577 | 0.0339911959619789 |
| 49 | 0.975737971285994 | 0.0485240574280111 | 0.0242620287140056 |
| 50 | 0.98600654091514 | 0.0279869181697210 | 0.0139934590848605 |
| 51 | 0.985886386853033 | 0.028227226293933 | 0.0141136131469665 |
| 52 | 0.986720966333837 | 0.0265580673323266 | 0.0132790336661633 |
| 53 | 0.996965878211644 | 0.00606824357671248 | 0.00303412178835624 |
| 54 | 0.997432846607075 | 0.00513430678585079 | 0.00256715339292539 |
| 55 | 0.996815108740522 | 0.006369782518956 | 0.003184891259478 |
| 56 | 0.995605207188998 | 0.00878958562200451 | 0.00439479281100225 |
| 57 | 0.993946412046476 | 0.0121071759070481 | 0.00605358795352404 |
| 58 | 0.991930276846118 | 0.0161394463077644 | 0.00806972315388218 |
| 59 | 0.987503161516327 | 0.0249936769673457 | 0.0124968384836728 |
| 60 | 0.98738564485686 | 0.0252287102862821 | 0.0126143551431411 |
| 61 | 0.98327942536772 | 0.0334411492645586 | 0.0167205746322793 |
| 62 | 0.977658332888707 | 0.0446833342225855 | 0.0223416671112928 |
| 63 | 0.966046111064364 | 0.0679077778712726 | 0.0339538889356363 |
| 64 | 0.947795942752344 | 0.104408114495312 | 0.0522040572476562 |
| 65 | 0.94851762683861 | 0.102964746322781 | 0.0514823731613903 |
| 66 | 0.934219970627858 | 0.131560058744284 | 0.0657800293721418 |
| 67 | 0.893716893260073 | 0.212566213479854 | 0.106283106739927 |
| 68 | 0.839877595372661 | 0.320244809254678 | 0.160122404627339 |
| 69 | 0.765102352424426 | 0.469795295151148 | 0.234897647575574 |
| 70 | 0.671839603637274 | 0.656320792725453 | 0.328160396362726 |
| 71 | 0.549230760608345 | 0.90153847878331 | 0.450769239391655 |
| 72 | 0.430518651947018 | 0.861037303894036 | 0.569481348052982 |
| 73 | 0.308003549494393 | 0.616007098988787 | 0.691996450505607 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 11 | 0.192982456140351 | NOK |
| 5% type I error level | 27 | 0.473684210526316 | NOK |
| 10% type I error level | 33 | 0.578947368421053 | NOK |
