| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 85.3644295390171 -1.76326950435899X[t] + 5.27565729087253M1[t] + 4.40171315059118M2[t] + 16.4648034314210M3[t] + 9.49537782336185M4[t] + 9.24836954419162M5[t] + 15.0024448772436M6[t] + 2.10976788585115M7[t] -0.762959099985754M8[t] + 1.02460681417736M9[t] + 9.56288284167381M10[t] -9.89589302082977M11[t] + 0.366035712503561t + 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) | 85.3644295390171 | 5.818583 | 14.671 | 0 | 0 |
| X | -1.76326950435899 | 5.081565 | -0.347 | 0.729372 | 0.364686 |
| M1 | 5.27565729087253 | 6.744029 | 0.7823 | 0.436022 | 0.218011 |
| M2 | 4.40171315059118 | 6.734716 | 0.6536 | 0.514974 | 0.257487 |
| M3 | 16.4648034314210 | 6.726279 | 2.4478 | 0.016228 | 0.008114 |
| M4 | 9.49537782336185 | 6.718721 | 1.4133 | 0.160879 | 0.080439 |
| M5 | 9.24836954419162 | 6.712045 | 1.3779 | 0.171513 | 0.085756 |
| M6 | 15.0024448772436 | 6.706254 | 2.2371 | 0.027644 | 0.013822 |
| M7 | 2.10976788585115 | 6.70135 | 0.3148 | 0.753591 | 0.376795 |
| M8 | -0.762959099985754 | 6.697335 | -0.1139 | 0.909544 | 0.454772 |
| M9 | 1.02460681417736 | 6.694211 | 0.1531 | 0.87868 | 0.43934 |
| M10 | 9.56288284167381 | 6.691978 | 1.429 | 0.156317 | 0.078159 |
| M11 | -9.89589302082977 | 6.690638 | -1.4791 | 0.142466 | 0.071233 |
| t | 0.366035712503561 | 0.077314 | 4.7344 | 8e-06 | 4e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.685296660999714 |
| R-squared | 0.469631513577357 |
| Adjusted R-squared | 0.396282680348693 |
| F-TEST (value) | 6.40271280271481 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 94 |
| p-value | 1.59991639936408e-08 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 14.1920393586397 |
| Sum Squared Residuals | 18932.9142287749 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 100 | 91.0061225423931 | 8.99387745760688 |
| 2 | 108.1560276 | 90.4982141146154 | 17.6578134853846 |
| 3 | 114.0150276 | 102.927340107949 | 11.0876874920513 |
| 4 | 102.1880309 | 96.3239502123931 | 5.86408068760685 |
| 5 | 110.3672031 | 96.4429776457265 | 13.9242254542735 |
| 6 | 96.8602511 | 102.563088691282 | -5.70283759128207 |
| 7 | 94.1944583 | 90.0364474123932 | 4.15801088760679 |
| 8 | 99.51621961 | 87.5297561390598 | 11.9864634709402 |
| 9 | 94.06333487 | 89.6833577657265 | 4.37997710427351 |
| 10 | 97.5541476 | 98.5876695057265 | -1.03352190572648 |
| 11 | 78.15062422 | 79.4949293557265 | -1.34430513572649 |
| 12 | 81.2434643 | 89.7568580890599 | -8.51339378905987 |
| 13 | 92.36262465 | 95.398551092436 | -3.03592644243589 |
| 14 | 96.06324371 | 94.8906426646581 | 1.17260104534188 |
| 15 | 114.0523777 | 107.319768657991 | 6.73260904200854 |
| 16 | 110.6616666 | 100.716378762436 | 9.9452878375641 |
| 17 | 104.9171949 | 100.835406195769 | 4.08178870423077 |
| 18 | 90.00187193 | 106.955517241325 | -16.9536453113248 |
| 19 | 95.7008067 | 94.428875962436 | 1.27193073756411 |
| 20 | 86.02741157 | 91.9221846891026 | -5.89477311910256 |
| 21 | 84.85287668 | 94.0757863157692 | -9.22290963576923 |
| 22 | 100.04328 | 102.980098055769 | -2.93681805576923 |
| 23 | 80.91713823 | 83.8873579057692 | -2.97021967576922 |
| 24 | 74.06539709 | 94.1492866391026 | -20.0838895491026 |
| 25 | 77.30281369 | 99.7909796424786 | -22.4881659524786 |
| 26 | 97.23043249 | 99.2830712147009 | -2.05263872470086 |
| 27 | 90.75515676 | 111.712197208034 | -20.9570404480342 |
| 28 | 100.5614455 | 105.108807312479 | -4.54736181247863 |
| 29 | 92.01293267 | 105.227834745812 | -13.2149020758120 |
| 30 | 99.24012138 | 111.347945791368 | -12.1078244113675 |
| 31 | 105.8672755 | 98.8213045124786 | 7.04597098752138 |
| 32 | 90.9920463 | 96.3146132391453 | -5.3225669391453 |
| 33 | 93.30624423 | 98.468214865812 | -5.16197063581196 |
| 34 | 91.17419413 | 107.372526605812 | -16.1983324758120 |
| 35 | 77.33295039 | 88.279786455812 | -10.9468360658120 |
| 36 | 91.1277721 | 98.5417151891453 | -7.4139430891453 |
| 37 | 85.01249943 | 104.183408192521 | -19.1709087625214 |
| 38 | 83.90390242 | 103.675499764744 | -19.7715973447436 |
| 39 | 104.8626302 | 116.104625758077 | -11.2419955580769 |
| 40 | 110.9039108 | 109.501235862521 | 1.40267493747864 |
| 41 | 95.43714373 | 109.620263295855 | -14.1831195658547 |
| 42 | 111.6238727 | 115.740374341410 | -4.11650164141025 |
| 43 | 108.8925403 | 103.213733062521 | 5.67880723747863 |
| 44 | 96.17511682 | 100.707041789188 | -4.53192496918803 |
| 45 | 101.9740205 | 102.860643415855 | -0.886622915854707 |
| 46 | 99.11953031 | 111.764955155855 | -12.6454248458547 |
| 47 | 86.78158147 | 92.6722150058547 | -5.89063353585469 |
| 48 | 118.4195003 | 102.934143739188 | 15.4853565608120 |
| 49 | 118.7441447 | 108.575836742564 | 10.1683079574359 |
| 50 | 106.5296192 | 108.067928314786 | -1.53830911478633 |
| 51 | 134.7772694 | 120.497054308120 | 14.2802150918803 |
| 52 | 104.6778714 | 113.893664412564 | -9.2157930125641 |
| 53 | 105.2954304 | 114.012691845897 | -8.71726144589743 |
| 54 | 139.4139849 | 120.132802891453 | 19.281182008547 |
| 55 | 103.6060491 | 107.606161612564 | -4.00011251256409 |
| 56 | 99.78182974 | 105.099470339231 | -5.31764059923076 |
| 57 | 103.4610301 | 107.253071965897 | -3.79204186589743 |
| 58 | 120.0594945 | 116.157383705897 | 3.90211079410256 |
| 59 | 96.71377168 | 97.0646435558974 | -0.350871875897444 |
| 60 | 107.1308929 | 107.326572289231 | -0.195679389230766 |
| 61 | 105.3608372 | 112.968265292607 | -7.60742809260684 |
| 62 | 111.6942359 | 112.460356864829 | -0.766120964829072 |
| 63 | 132.0519998 | 124.889482858162 | 7.16251694183761 |
| 64 | 126.8037879 | 118.286092962607 | 8.51769493739316 |
| 65 | 154.4824253 | 118.405120395940 | 36.0773049040598 |
| 66 | 141.5570984 | 124.525231441496 | 17.0318669585043 |
| 67 | 109.9506882 | 111.998590162607 | -2.04790196260683 |
| 68 | 127.904198 | 109.491898889274 | 18.4122991107265 |
| 69 | 133.0888617 | 111.645500515940 | 21.4433611840598 |
| 70 | 120.0796299 | 120.549812255940 | -0.470182355940181 |
| 71 | 117.5557142 | 101.457072105940 | 16.0986420940598 |
| 72 | 143.0362309 | 111.719000839274 | 31.3172300607265 |
| 73 | 159.982927 | 115.597424338291 | 44.3855026617094 |
| 74 | 128.5991124 | 115.089515910513 | 13.5095964894872 |
| 75 | 149.7373327 | 127.518641903846 | 22.2186907961538 |
| 76 | 126.8169313 | 120.915252008291 | 5.9016792917094 |
| 77 | 140.9639674 | 121.034279441624 | 19.9296879583761 |
| 78 | 137.6691981 | 127.154390487179 | 10.5148076128205 |
| 79 | 117.9402337 | 114.627749208291 | 3.31248449170940 |
| 80 | 122.3095247 | 112.121057934957 | 10.1884667650427 |
| 81 | 127.7804207 | 114.274659561624 | 13.5057611383761 |
| 82 | 136.1677176 | 123.178971301624 | 12.9887462983761 |
| 83 | 116.2405856 | 104.086231151624 | 12.1543544483761 |
| 84 | 123.1576893 | 114.348159884957 | 8.80952941504274 |
| 85 | 116.3400234 | 119.989852888333 | -3.64982948833333 |
| 86 | 108.6119282 | 119.481944460556 | -10.8700162605556 |
| 87 | 125.8982264 | 131.911070453889 | -6.01284405388889 |
| 88 | 112.8003105 | 125.307680558333 | -12.5073700583333 |
| 89 | 107.5182447 | 125.426707991667 | -17.9084632916667 |
| 90 | 135.0955413 | 131.546819037222 | 3.54872226277779 |
| 91 | 115.5096488 | 119.020177758333 | -3.51052895833333 |
| 92 | 115.8640759 | 116.513486485 | -0.649410584999993 |
| 93 | 104.5883906 | 118.667088111667 | -14.0786975116667 |
| 94 | 163.7213386 | 127.571399851667 | 36.1499387483333 |
| 95 | 113.4482275 | 108.478659701667 | 4.96956779833334 |
| 96 | 98.0428844 | 118.740588435 | -20.697704035 |
| 97 | 116.7868521 | 124.382281438376 | -7.59542933837607 |
| 98 | 126.5330444 | 123.874373010598 | 2.65867138940171 |
| 99 | 113.0336597 | 136.303499003932 | -23.2698393039316 |
| 100 | 124.3392163 | 129.700109108376 | -5.36089280837607 |
| 101 | 109.8298759 | 129.819136541709 | -19.9892606417094 |
| 102 | 124.4434777 | 135.939247587265 | -11.4957698872650 |
| 103 | 111.5039454 | 123.412606308376 | -11.9086609083761 |
| 104 | 102.0350019 | 120.905915035043 | -18.8709131350427 |
| 105 | 116.8726598 | 123.059516661709 | -6.1868568617094 |
| 106 | 112.2073122 | 131.963828401709 | -19.7565162017094 |
| 107 | 101.1513902 | 112.871088251709 | -11.7196980517094 |
| 108 | 124.4255108 | 123.133016985043 | 1.29249381495726 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0969837326446764 | 0.193967465289353 | 0.903016267355324 |
| 18 | 0.0366702572823415 | 0.073340514564683 | 0.963329742717658 |
| 19 | 0.0145325802642958 | 0.0290651605285917 | 0.985467419735704 |
| 20 | 0.0096085695622418 | 0.0192171391244836 | 0.990391430437758 |
| 21 | 0.00371235418948817 | 0.00742470837897633 | 0.996287645810512 |
| 22 | 0.00178293121667593 | 0.00356586243335186 | 0.998217068783324 |
| 23 | 0.00081747096488756 | 0.00163494192977512 | 0.999182529035112 |
| 24 | 0.000309403244306179 | 0.000618806488612357 | 0.999690596755694 |
| 25 | 0.000479715526223488 | 0.000959431052446977 | 0.999520284473776 |
| 26 | 0.000181006569468291 | 0.000362013138936581 | 0.999818993430532 |
| 27 | 0.000422123914812614 | 0.000844247829625228 | 0.999577876085187 |
| 28 | 0.000177869237214638 | 0.000355738474429276 | 0.999822130762785 |
| 29 | 8.91331760153943e-05 | 0.000178266352030789 | 0.999910866823985 |
| 30 | 0.000204106635675157 | 0.000408213271350313 | 0.999795893364325 |
| 31 | 0.000609331691667317 | 0.00121866338333463 | 0.999390668308333 |
| 32 | 0.000306031471105927 | 0.000612062942211854 | 0.999693968528894 |
| 33 | 0.000222716096548830 | 0.000445432193097660 | 0.999777283903451 |
| 34 | 0.000120154690938949 | 0.000240309381877897 | 0.99987984530906 |
| 35 | 6.21472805330555e-05 | 0.000124294561066111 | 0.999937852719467 |
| 36 | 0.000169171507775609 | 0.000338343015551217 | 0.999830828492224 |
| 37 | 0.000125310707444065 | 0.00025062141488813 | 0.999874689292556 |
| 38 | 0.000144849464127118 | 0.000289698928254236 | 0.999855150535873 |
| 39 | 9.95345156116222e-05 | 0.000199069031223244 | 0.999900465484388 |
| 40 | 9.77874073622333e-05 | 0.000195574814724467 | 0.999902212592638 |
| 41 | 6.7770858998776e-05 | 0.000135541717997552 | 0.999932229141001 |
| 42 | 0.00030250727518946 | 0.00060501455037892 | 0.99969749272481 |
| 43 | 0.000313805779567022 | 0.000627611559134044 | 0.999686194220433 |
| 44 | 0.000225028032105345 | 0.000450056064210691 | 0.999774971967895 |
| 45 | 0.000254966590590436 | 0.000509933181180872 | 0.99974503340941 |
| 46 | 0.000312185377088081 | 0.000624370754176162 | 0.999687814622912 |
| 47 | 0.000369981162879416 | 0.000739962325758832 | 0.99963001883712 |
| 48 | 0.00650842603567148 | 0.0130168520713430 | 0.993491573964329 |
| 49 | 0.0171566001491189 | 0.0343132002982377 | 0.982843399850881 |
| 50 | 0.0135316569558187 | 0.0270633139116373 | 0.986468343044181 |
| 51 | 0.0214402928132259 | 0.0428805856264519 | 0.978559707186774 |
| 52 | 0.0195662811266752 | 0.0391325622533505 | 0.980433718873325 |
| 53 | 0.0203505884835867 | 0.0407011769671735 | 0.979649411516413 |
| 54 | 0.0537373865031828 | 0.107474773006366 | 0.946262613496817 |
| 55 | 0.0440377287911653 | 0.0880754575823307 | 0.955962271208835 |
| 56 | 0.0425649504129392 | 0.0851299008258784 | 0.95743504958706 |
| 57 | 0.0439370555346221 | 0.0878741110692441 | 0.956062944465378 |
| 58 | 0.0538423283270369 | 0.107684656654074 | 0.946157671672963 |
| 59 | 0.0636132935277611 | 0.127226587055522 | 0.936386706472239 |
| 60 | 0.0813297741483767 | 0.162659548296753 | 0.918670225851623 |
| 61 | 0.125383207150756 | 0.250766414301512 | 0.874616792849244 |
| 62 | 0.122843711548185 | 0.245687423096371 | 0.877156288451814 |
| 63 | 0.105193076084196 | 0.210386152168392 | 0.894806923915804 |
| 64 | 0.0873686908377483 | 0.174737381675497 | 0.912631309162252 |
| 65 | 0.292376266892768 | 0.584752533785536 | 0.707623733107232 |
| 66 | 0.286122913422245 | 0.572245826844491 | 0.713877086577755 |
| 67 | 0.263971966921069 | 0.527943933842139 | 0.73602803307893 |
| 68 | 0.252813856608212 | 0.505627713216424 | 0.747186143391788 |
| 69 | 0.262254540245287 | 0.524509080490574 | 0.737745459754713 |
| 70 | 0.351196010458396 | 0.702392020916792 | 0.648803989541604 |
| 71 | 0.363814262518266 | 0.727628525036532 | 0.636185737481734 |
| 72 | 0.39909873389439 | 0.79819746778878 | 0.60090126610561 |
| 73 | 0.542771592027513 | 0.914456815944974 | 0.457228407972487 |
| 74 | 0.530757534696219 | 0.938484930607562 | 0.469242465303781 |
| 75 | 0.561898650492966 | 0.876202699014069 | 0.438101349507034 |
| 76 | 0.526056486144465 | 0.94788702771107 | 0.473943513855535 |
| 77 | 0.598066775152311 | 0.803866449695377 | 0.401933224847689 |
| 78 | 0.52642679543818 | 0.94714640912364 | 0.47357320456182 |
| 79 | 0.469952687413514 | 0.939905374827027 | 0.530047312586486 |
| 80 | 0.403010398588755 | 0.80602079717751 | 0.596989601411245 |
| 81 | 0.354342703155057 | 0.708685406310114 | 0.645657296844943 |
| 82 | 0.290172139345715 | 0.58034427869143 | 0.709827860654285 |
| 83 | 0.220480383266680 | 0.440960766533360 | 0.77951961673332 |
| 84 | 0.169074760326590 | 0.338149520653181 | 0.83092523967341 |
| 85 | 0.130004908880454 | 0.260009817760908 | 0.869995091119546 |
| 86 | 0.152128567261591 | 0.304257134523181 | 0.84787143273841 |
| 87 | 0.117323762914511 | 0.234647525829021 | 0.88267623708549 |
| 88 | 0.109374261566929 | 0.218748523133859 | 0.89062573843307 |
| 89 | 0.0874817884447473 | 0.174963576889495 | 0.912518211555253 |
| 90 | 0.0473159219787511 | 0.0946318439575023 | 0.952684078021249 |
| 91 | 0.0226813798636342 | 0.0453627597272684 | 0.977318620136366 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 27 | 0.36 | NOK |
| 5% type I error level | 36 | 0.48 | NOK |
| 10% type I error level | 41 | 0.546666666666667 | NOK |
