| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 23.6616041005634 -6.28343467972651X[t] + 0.259129910030104Y1[t] + 0.0678592356499644Y2[t] + 0.300566138661765Y3[t] + 0.11954465131137Y4[t] + 0.447120338298871M1[t] + 3.13191196265063M2[t] -10.6673105547517M3[t] -9.76717630491025M4[t] -8.14521510308711M5[t] + 3.22707368037767M6[t] -16.2457824226025M7[t] -2.16575180482806M8[t] -2.42715733581733M9[t] -1.16358422500642M10[t] + 11.8259988011420M11[t] + 0.177520173264150t + 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) | 23.6616041005634 | 11.844879 | 1.9976 | 0.048918 | 0.024459 |
| X | -6.28343467972651 | 4.411284 | -1.4244 | 0.157949 | 0.078975 |
| Y1 | 0.259129910030104 | 0.106645 | 2.4298 | 0.017185 | 0.008592 |
| Y2 | 0.0678592356499644 | 0.105736 | 0.6418 | 0.522724 | 0.261362 |
| Y3 | 0.300566138661765 | 0.106042 | 2.8344 | 0.005721 | 0.00286 |
| Y4 | 0.11954465131137 | 0.10777 | 1.1093 | 0.270411 | 0.135206 |
| M1 | 0.447120338298871 | 6.06951 | 0.0737 | 0.941447 | 0.470723 |
| M2 | 3.13191196265063 | 5.980129 | 0.5237 | 0.60182 | 0.30091 |
| M3 | -10.6673105547517 | 6.020446 | -1.7718 | 0.079962 | 0.039981 |
| M4 | -9.76717630491025 | 6.293168 | -1.552 | 0.124328 | 0.062164 |
| M5 | -8.14521510308711 | 6.263951 | -1.3003 | 0.196961 | 0.098481 |
| M6 | 3.22707368037767 | 6.315967 | 0.5109 | 0.610703 | 0.305351 |
| M7 | -16.2457824226025 | 5.835107 | -2.7841 | 0.006599 | 0.003299 |
| M8 | -2.16575180482806 | 6.512214 | -0.3326 | 0.74027 | 0.370135 |
| M9 | -2.42715733581733 | 6.296107 | -0.3855 | 0.700818 | 0.350409 |
| M10 | -1.16358422500642 | 6.445088 | -0.1805 | 0.857155 | 0.428577 |
| M11 | 11.8259988011420 | 6.103349 | 1.9376 | 0.055951 | 0.027975 |
| t | 0.177520173264150 | 0.078389 | 2.2646 | 0.026051 | 0.013026 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.811769033341268 |
| R-squared | 0.658968963491817 |
| Adjusted R-squared | 0.591555851623921 |
| F-TEST (value) | 9.77508596225523 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 86 |
| p-value | 9.9698027611339e-14 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 11.8679156254582 |
| Sum Squared Residuals | 12112.8782311977 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 110.3672031 | 102.965697210807 | 7.40150588919329 |
| 2 | 96.8602511 | 109.88093269058 | -13.0206815905799 |
| 3 | 94.1944583 | 90.4598248455911 | 3.73463345440887 |
| 4 | 99.51621961 | 90.9746491906345 | 8.54157041936552 |
| 5 | 94.06333487 | 90.8903033143095 | 3.17303155569052 |
| 6 | 97.5541476 | 98.972306478278 | -1.41815887827806 |
| 7 | 78.15062422 | 81.492375923757 | -3.34175170375705 |
| 8 | 81.2434643 | 89.956012920021 | -8.71254862002103 |
| 9 | 92.36262465 | 89.7542235666438 | 2.60840108335619 |
| 10 | 96.06324371 | 88.8717675274823 | 7.19147618251767 |
| 11 | 114.0523777 | 102.362365097059 | 11.6900126029414 |
| 12 | 110.6616666 | 99.3383059028582 | 11.3233606971418 |
| 13 | 104.9171949 | 102.746557563145 | 2.17063733685543 |
| 14 | 90.00187193 | 109.739527618820 | -19.7376556888205 |
| 15 | 95.7008067 | 92.9943753242048 | 2.70643137579516 |
| 16 | 86.02741157 | 92.4047167316436 | -6.37730516164357 |
| 17 | 84.85287668 | 86.914495556189 | -2.06161887618898 |
| 18 | 100.04328 | 97.4333779275421 | 2.60990207245786 |
| 19 | 80.91713823 | 79.7684089515314 | 1.14872927846861 |
| 20 | 74.06539709 | 88.591185440573 | -14.5257883505730 |
| 21 | 77.30281369 | 89.8592351629742 | -12.5564214729742 |
| 22 | 97.23043249 | 87.7415468915675 | 9.48888559843252 |
| 23 | 90.75515676 | 101.946351447309 | -11.1911946873085 |
| 24 | 100.5614455 | 90.126176983432 | 10.4352685165680 |
| 25 | 92.01293267 | 99.229096226296 | -7.21616355629606 |
| 26 | 99.24012138 | 100.977671539818 | -1.73755015981768 |
| 27 | 105.8672755 | 90.822008171181 | 15.0452673288190 |
| 28 | 90.9920463 | 92.7102838223847 | -1.71823752238474 |
| 29 | 93.30624423 | 92.255181224768 | 1.05106300523195 |
| 30 | 91.17419413 | 106.251116277723 | -15.0769221477229 |
| 31 | 77.33295039 | 82.8815927261962 | -5.54864233619617 |
| 32 | 91.1277721 | 92.3250994300588 | -1.19732733005881 |
| 33 | 85.01249943 | 94.512436678903 | -9.49993724890296 |
| 34 | 83.90390242 | 90.8899015923685 | -6.98599917236852 |
| 35 | 104.8626302 | 105.846366057431 | -0.98373585743099 |
| 36 | 110.9039108 | 99.3647453857263 | 11.5391654142737 |
| 37 | 95.43714373 | 101.912850781344 | -6.47570705134366 |
| 38 | 111.6238727 | 107.344174340609 | 4.27969835939079 |
| 39 | 108.8925403 | 101.188682813707 | 7.70385748629318 |
| 40 | 96.17511682 | 98.7304027003058 | -2.55528588030577 |
| 41 | 101.9740205 | 100.065286492016 | 1.90873400798395 |
| 42 | 99.11953031 | 113.368861038547 | -14.2493307285474 |
| 43 | 86.78158147 | 89.578407445564 | -2.79682597556398 |
| 44 | 118.4195003 | 100.667777273347 | 17.7517230266529 |
| 45 | 118.7441447 | 107.780244021966 | 10.9639006780336 |
| 46 | 106.5296192 | 107.402778693284 | -0.873159493284235 |
| 47 | 134.7772694 | 125.461114425716 | 9.31615497428449 |
| 48 | 104.6778714 | 124.183299576964 | -19.5054281769645 |
| 49 | 105.2954304 | 115.292686480784 | -9.9972560807843 |
| 50 | 139.4139849 | 123.302610099755 | 16.1113748002447 |
| 51 | 103.6060491 | 112.893948455889 | -9.28789935588896 |
| 52 | 99.78182974 | 103.595350012062 | -3.81352027206218 |
| 53 | 103.4610301 | 112.302670672971 | -8.84164057297146 |
| 54 | 120.0594945 | 117.862399589339 | 2.19709491066137 |
| 55 | 96.71377168 | 97.6878119246435 | -0.974040244643523 |
| 56 | 107.1308929 | 107.670824844534 | -0.539931944533667 |
| 57 | 105.3608372 | 114.130869341622 | -8.77003214162232 |
| 58 | 111.6942359 | 110.787510011797 | 0.906725888202717 |
| 59 | 132.0519998 | 125.815849226604 | 6.23615057339612 |
| 60 | 126.8037879 | 120.585748038344 | 6.21803986165644 |
| 61 | 154.4824253 | 122.923886670643 | 31.5585386293567 |
| 62 | 141.5570984 | 139.478400065832 | 2.07869833416769 |
| 63 | 109.9506882 | 125.241837104027 | -15.2911489040269 |
| 64 | 127.904198 | 124.944087996815 | 2.96011000318453 |
| 65 | 133.0888617 | 128.674991372773 | 4.41387032722707 |
| 66 | 120.0796299 | 131.741642851762 | -11.6620129517616 |
| 67 | 117.5557142 | 111.044893001384 | 6.51082119861605 |
| 68 | 143.0362309 | 127.470205635242 | 15.5660252647582 |
| 69 | 159.982927 | 124.244042852636 | 35.7388841473638 |
| 70 | 128.5991124 | 129.491832684023 | -0.89272028402333 |
| 71 | 149.7373327 | 143.033300567204 | 6.70403213279556 |
| 72 | 126.8169313 | 142.872347887312 | -16.0554165873124 |
| 73 | 140.9639674 | 131.585025224154 | 9.37894217584638 |
| 74 | 137.6691981 | 139.159562374336 | -1.49036427433584 |
| 75 | 117.9402337 | 121.281958444108 | -3.34172474410787 |
| 76 | 122.3095247 | 118.535776191719 | 3.77374850828066 |
| 77 | 127.7804207 | 120.829585517564 | 6.95083518243584 |
| 78 | 136.1677176 | 127.769833313526 | 8.39788428647392 |
| 79 | 116.2405856 | 109.973916450410 | 6.26666914958952 |
| 80 | 123.1576893 | 121.803598330747 | 1.35409096925263 |
| 81 | 116.3400234 | 125.334855283980 | -8.99483188397974 |
| 82 | 108.6119282 | 120.491912150278 | -11.8799839502782 |
| 83 | 125.8982264 | 130.890658242176 | -4.99243184217618 |
| 84 | 112.8003105 | 121.974897113968 | -9.17458661396786 |
| 85 | 107.5182447 | 117.240691613604 | -9.72244691360394 |
| 86 | 135.0955413 | 122.117271069856 | 12.9782702301440 |
| 87 | 115.5096488 | 113.412928648912 | 2.09672015108772 |
| 88 | 115.8640759 | 108.133270868367 | 7.73080503163253 |
| 89 | 104.5883906 | 116.352870050945 | -11.7644794509451 |
| 90 | 163.7213386 | 122.414725067645 | 41.3066135323553 |
| 91 | 113.4482275 | 115.442485342446 | -1.99425784244561 |
| 92 | 98.0428844 | 117.338766702915 | -19.2958823029154 |
| 93 | 116.7868521 | 126.276815261274 | -9.48996316127435 |
| 94 | 126.5330444 | 123.488269169199 | 3.04477523080139 |
| 95 | 113.0336597 | 129.812647596502 | -16.7789878965019 |
| 96 | 124.3392163 | 119.119619411395 | 5.21959688860474 |
| 97 | 109.8298759 | 126.927926329224 | -17.0980504292238 |
| 98 | 124.4434777 | 123.905267710393 | 0.538209989606686 |
| 99 | 111.5039454 | 114.870082192380 | -3.36613679238022 |
| 100 | 102.0350019 | 110.576887026067 | -8.541885126067 |
| 101 | 116.8726598 | 111.702454978464 | 5.17020482153624 |
| 102 | 112.2073122 | 124.312382295638 | -12.1050700956385 |
| 103 | 101.1513902 | 100.422091724068 | 0.729298475932147 |
| 104 | 124.4255108 | 114.825871512562 | 9.59963928743815 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.101298808199809 | 0.202597616399617 | 0.898701191800191 |
| 22 | 0.0455331256275007 | 0.0910662512550014 | 0.9544668743725 |
| 23 | 0.153679177269815 | 0.307358354539631 | 0.846320822730184 |
| 24 | 0.0871958875357022 | 0.174391775071404 | 0.912804112464298 |
| 25 | 0.053211084862781 | 0.106422169725562 | 0.94678891513722 |
| 26 | 0.0667792145675758 | 0.133558429135152 | 0.933220785432424 |
| 27 | 0.129966154977016 | 0.259932309954031 | 0.870033845022984 |
| 28 | 0.0833525233000579 | 0.166705046600116 | 0.916647476699942 |
| 29 | 0.0580599326981458 | 0.116119865396292 | 0.941940067301854 |
| 30 | 0.0372795311947863 | 0.0745590623895726 | 0.962720468805214 |
| 31 | 0.0240083600187689 | 0.0480167200375378 | 0.975991639981231 |
| 32 | 0.0388405749041345 | 0.077681149808269 | 0.961159425095865 |
| 33 | 0.0260847981203916 | 0.0521695962407831 | 0.973915201879608 |
| 34 | 0.0223062062520292 | 0.0446124125040584 | 0.97769379374797 |
| 35 | 0.0141335873214194 | 0.0282671746428389 | 0.98586641267858 |
| 36 | 0.0103956026912548 | 0.0207912053825095 | 0.989604397308745 |
| 37 | 0.00624190359949097 | 0.0124838071989819 | 0.99375809640051 |
| 38 | 0.0119056839603030 | 0.0238113679206059 | 0.988094316039697 |
| 39 | 0.00893977300290678 | 0.0178795460058136 | 0.991060226997093 |
| 40 | 0.00558347298549548 | 0.0111669459709910 | 0.994416527014504 |
| 41 | 0.00331049849906298 | 0.00662099699812597 | 0.996689501500937 |
| 42 | 0.00283771662099467 | 0.00567543324198934 | 0.997162283379005 |
| 43 | 0.00193910376994642 | 0.00387820753989285 | 0.998060896230054 |
| 44 | 0.0138240042926694 | 0.0276480085853389 | 0.98617599570733 |
| 45 | 0.0170191094616752 | 0.0340382189233503 | 0.982980890538325 |
| 46 | 0.0121326800392462 | 0.0242653600784925 | 0.987867319960754 |
| 47 | 0.00853981385882133 | 0.0170796277176427 | 0.991460186141179 |
| 48 | 0.0268150278942892 | 0.0536300557885784 | 0.973184972105711 |
| 49 | 0.0218398952738579 | 0.0436797905477158 | 0.978160104726142 |
| 50 | 0.0390831869256892 | 0.0781663738513785 | 0.96091681307431 |
| 51 | 0.0298194846369666 | 0.0596389692739333 | 0.970180515363033 |
| 52 | 0.0218000679474995 | 0.0436001358949991 | 0.9781999320525 |
| 53 | 0.0239756790568834 | 0.0479513581137667 | 0.976024320943117 |
| 54 | 0.0313503303594864 | 0.0627006607189728 | 0.968649669640514 |
| 55 | 0.0267977649901678 | 0.0535955299803356 | 0.973202235009832 |
| 56 | 0.0246674916182160 | 0.0493349832364319 | 0.975332508381784 |
| 57 | 0.037504829671087 | 0.075009659342174 | 0.962495170328913 |
| 58 | 0.0358829600926190 | 0.0717659201852379 | 0.964117039907381 |
| 59 | 0.0310044068111917 | 0.0620088136223834 | 0.968995593188808 |
| 60 | 0.0234720244472488 | 0.0469440488944975 | 0.976527975552751 |
| 61 | 0.121438276736431 | 0.242876553472863 | 0.878561723263569 |
| 62 | 0.0957286725098613 | 0.191457345019723 | 0.904271327490139 |
| 63 | 0.0913074120518481 | 0.182614824103696 | 0.908692587948152 |
| 64 | 0.0672330263337453 | 0.134466052667491 | 0.932766973666255 |
| 65 | 0.0516318425136341 | 0.103263685027268 | 0.948368157486366 |
| 66 | 0.0676447256811783 | 0.135289451362357 | 0.932355274318822 |
| 67 | 0.0561579690180069 | 0.112315938036014 | 0.943842030981993 |
| 68 | 0.0476412004424604 | 0.0952824008849208 | 0.95235879955754 |
| 69 | 0.160187502246349 | 0.320375004492698 | 0.839812497753651 |
| 70 | 0.284651138370100 | 0.569302276740199 | 0.7153488616299 |
| 71 | 0.369721157646260 | 0.739442315292521 | 0.63027884235374 |
| 72 | 0.421997812349855 | 0.84399562469971 | 0.578002187650145 |
| 73 | 0.442636542795373 | 0.885273085590746 | 0.557363457204627 |
| 74 | 0.363160191391225 | 0.726320382782451 | 0.636839808608775 |
| 75 | 0.288064507115483 | 0.576129014230965 | 0.711935492884517 |
| 76 | 0.214394161434061 | 0.428788322868122 | 0.785605838565939 |
| 77 | 0.154686239391888 | 0.309372478783775 | 0.845313760608112 |
| 78 | 0.107559446375643 | 0.215118892751286 | 0.892440553624357 |
| 79 | 0.0665925565834213 | 0.133185113166843 | 0.933407443416579 |
| 80 | 0.0391650460353018 | 0.0783300920706036 | 0.960834953964698 |
| 81 | 0.0250037028401406 | 0.0500074056802811 | 0.97499629715986 |
| 82 | 0.0206972482534763 | 0.0413944965069527 | 0.979302751746524 |
| 83 | 0.0162524764013677 | 0.0325049528027355 | 0.983747523598632 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 3 | 0.0476190476190476 | NOK |
| 5% type I error level | 22 | 0.349206349206349 | NOK |
| 10% type I error level | 37 | 0.587301587301587 | NOK |
