| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 17.8062459764093 + 0.0659655162376716X[t] + 1.03333333333334M1[t] -1.02700746857109M2[t] -1.78470344546548M3[t] + 0.522992531428915M4[t] + 1.03930862288108M5[t] + 0.412221265957019M6[t] -0.198024136693129M7[t] -0.127310344158448M8[t] -0.364117240910914M9[t] + 1.8701402300858M10[t] + 0.142304023105606M11[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) | 17.8062459764093 | 1.112638 | 16.0036 | 0 | 0 |
| X | 0.0659655162376716 | 0.059181 | 1.1146 | 0.269453 | 0.134727 |
| M1 | 1.03333333333334 | 1.515497 | 0.6818 | 0.497961 | 0.248981 |
| M2 | -1.02700746857109 | 1.580703 | -0.6497 | 0.518356 | 0.259178 |
| M3 | -1.78470344546548 | 1.581412 | -1.1286 | 0.26358 | 0.13179 |
| M4 | 0.522992531428915 | 1.580703 | 0.3309 | 0.741902 | 0.370951 |
| M5 | 1.03930862288108 | 1.578005 | 0.6586 | 0.512658 | 0.256329 |
| M6 | 0.412221265957019 | 1.575495 | 0.2616 | 0.794491 | 0.397245 |
| M7 | -0.198024136693129 | 1.574399 | -0.1258 | 0.900328 | 0.450164 |
| M8 | -0.127310344158448 | 1.573201 | -0.0809 | 0.935771 | 0.467886 |
| M9 | -0.364117240910914 | 1.572949 | -0.2315 | 0.817724 | 0.408862 |
| M10 | 1.8701402300858 | 1.572751 | 1.1891 | 0.239089 | 0.119545 |
| M11 | 0.142304023105606 | 1.572721 | 0.0905 | 0.928205 | 0.464103 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.364144441329375 |
| R-squared | 0.132601174151083 |
| Adjusted R-squared | -0.0408785910187008 |
| F-TEST (value) | 0.7643610424611 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 60 |
| p-value | 0.683563158515654 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 2.72400674830111 |
| Sum Squared Residuals | 445.212765887398 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 14.2 | 18.7868068967525 | -4.58680689675246 |
| 2 | 13.5 | 16.7660454045907 | -3.26604540459065 |
| 3 | 11.9 | 16.0347356341913 | -4.13473563419133 |
| 4 | 14.6 | 18.3952040240759 | -3.79520402407586 |
| 5 | 15.6 | 18.8455545992904 | -3.24555459929035 |
| 6 | 14.1 | 18.2052741391188 | -4.10527413911876 |
| 7 | 14.9 | 17.6741873559538 | -2.77418735595381 |
| 8 | 14.2 | 17.7053218387459 | -3.50532183874589 |
| 9 | 14.6 | 17.5080942517360 | -2.90809425173603 |
| 10 | 17.2 | 19.7885275840991 | -2.58852758409911 |
| 11 | 15.4 | 18.1530430998517 | -2.75304309985166 |
| 12 | 14.3 | 18.0239321799936 | -3.72393217999359 |
| 13 | 17.5 | 19.0440724100794 | -1.54407241007939 |
| 14 | 14.5 | 17.0101178146700 | -2.51011781467003 |
| 15 | 14.4 | 16.4173356283698 | -2.01733562836982 |
| 16 | 16.6 | 18.7052419503929 | -2.10524195039291 |
| 17 | 16.7 | 19.1555925256074 | -2.45559252560741 |
| 18 | 16.6 | 18.4955224105645 | -1.89552241056451 |
| 19 | 16.9 | 17.8456976981718 | -0.94569769817176 |
| 20 | 15.7 | 17.9691839036966 | -2.26918390369658 |
| 21 | 16.4 | 17.6070425260925 | -1.20704252609254 |
| 22 | 18.4 | 19.6368068967525 | -1.23680689675247 |
| 23 | 16.9 | 17.8232155186633 | -0.923215518663301 |
| 24 | 16.5 | 17.6809114955577 | -1.18091149555769 |
| 25 | 18.3 | 18.8857551711090 | -0.585755171108976 |
| 26 | 15.1 | 16.7198695432243 | -1.61986954322428 |
| 27 | 15.7 | 15.9094011533397 | -0.209401153339747 |
| 28 | 18.1 | 18.1247454075014 | -0.0247454075014015 |
| 29 | 16.8 | 18.7070270151912 | -1.90702701519124 |
| 30 | 18.9 | 18.2316603456138 | 0.668339654386175 |
| 31 | 19 | 17.6873804592013 | 1.31261954079865 |
| 32 | 18.1 | 17.9296045939540 | 0.170395406046027 |
| 33 | 17.8 | 17.7059908004490 | 0.0940091995509578 |
| 34 | 21.5 | 20.1117586136637 | 1.3882413863363 |
| 35 | 17.1 | 18.2981672355745 | -1.19816723557453 |
| 36 | 18.7 | 18.3075838998156 | 0.392416100184425 |
| 37 | 19 | 19.1496172360597 | -0.149617236059662 |
| 38 | 16.4 | 17.2146109150068 | -0.814610915006818 |
| 39 | 16.9 | 16.3117908023895 | 0.588209197610455 |
| 40 | 18.6 | 18.6326798825315 | -0.0326798825314726 |
| 41 | 19.3 | 19.2413476967164 | 0.0586523032836177 |
| 42 | 19.4 | 18.5351017203071 | 0.864898279692886 |
| 43 | 17.6 | 17.8720839046668 | -0.272083904666826 |
| 44 | 18.6 | 17.8570425260925 | 0.742957473907466 |
| 45 | 18.1 | 17.6400252842114 | 0.45997471578863 |
| 46 | 20.4 | 19.9468448230695 | 0.453155176930476 |
| 47 | 18.1 | 18.2124120644656 | -0.112412064465561 |
| 48 | 19.6 | 17.9843528702510 | 1.61564712974902 |
| 49 | 19.9 | 19.0110896519606 | 0.888910348039446 |
| 50 | 19.2 | 16.9837316081750 | 2.21626839182503 |
| 51 | 17.8 | 16.3117908023895 | 1.48820919761046 |
| 52 | 19.2 | 18.5271350565512 | 0.6728649434488 |
| 53 | 22 | 18.9774856317657 | 3.0225143682343 |
| 54 | 21.1 | 18.3042224134753 | 2.79577758652474 |
| 55 | 19.5 | 17.7071701140726 | 1.79282988592735 |
| 56 | 22.2 | 17.7646908033598 | 4.4353091966402 |
| 57 | 20.9 | 17.6532183874589 | 3.24678161254109 |
| 58 | 22.2 | 19.7951241357229 | 2.40487586427712 |
| 59 | 23.5 | 18.1662362030992 | 5.33376379690081 |
| 60 | 21.5 | 17.8722114926469 | 3.62778850735306 |
| 61 | 24.3 | 18.997896548713 | 5.30210345128698 |
| 62 | 22.8 | 16.8056247143333 | 5.99437528566675 |
| 63 | 20.3 | 16.0149459793200 | 4.28505402067998 |
| 64 | 23.7 | 18.4149936789472 | 5.28500632105284 |
| 65 | 23.3 | 18.7729925314289 | 4.52700746857109 |
| 66 | 19.6 | 17.9282189709205 | 1.67178102907947 |
| 67 | 18 | 17.1134804679336 | 0.886519532066396 |
| 68 | 17.3 | 16.8741563341512 | 0.425843665848771 |
| 69 | 16.8 | 16.4856287500521 | 0.314371249947881 |
| 70 | 18.2 | 18.6209379466923 | -0.420937946692322 |
| 71 | 16.5 | 16.8469258783458 | -0.346925878345760 |
| 72 | 16 | 16.7310080617352 | -0.731008061735223 |
| 73 | 18.4 | 17.7247620853260 | 0.675237914674042 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.034408847286182 | 0.068817694572364 | 0.965591152713818 |
| 17 | 0.0165160347273925 | 0.0330320694547850 | 0.983483965272608 |
| 18 | 0.00568714487622783 | 0.0113742897524557 | 0.994312855123772 |
| 19 | 0.00222517700515862 | 0.00445035401031723 | 0.997774822994841 |
| 20 | 0.00073152702209578 | 0.00146305404419156 | 0.999268472977904 |
| 21 | 0.000440695015921012 | 0.000881390031842024 | 0.999559304984079 |
| 22 | 0.00137059440022768 | 0.00274118880045536 | 0.998629405599772 |
| 23 | 0.00919990173344255 | 0.0183998034668851 | 0.990800098266557 |
| 24 | 0.0288774476543625 | 0.057754895308725 | 0.971122552345637 |
| 25 | 0.0390655243693445 | 0.078131048738689 | 0.960934475630655 |
| 26 | 0.0390602628314886 | 0.0781205256629771 | 0.960939737168511 |
| 27 | 0.0693268188162819 | 0.138653637632564 | 0.930673181183718 |
| 28 | 0.0860921807517459 | 0.172184361503492 | 0.913907819248254 |
| 29 | 0.0827856466816494 | 0.165571293363299 | 0.91721435331835 |
| 30 | 0.120085877416420 | 0.240171754832839 | 0.87991412258358 |
| 31 | 0.132632838399620 | 0.265265676799241 | 0.86736716160038 |
| 32 | 0.154552374725552 | 0.309104749451105 | 0.845447625274448 |
| 33 | 0.141687525085788 | 0.283375050171575 | 0.858312474914212 |
| 34 | 0.155586350424021 | 0.311172700848042 | 0.844413649575979 |
| 35 | 0.138989182781183 | 0.277978365562365 | 0.861010817218817 |
| 36 | 0.131445088575046 | 0.262890177150092 | 0.868554911424954 |
| 37 | 0.129933025230844 | 0.259866050461688 | 0.870066974769156 |
| 38 | 0.183272214290956 | 0.366544428581911 | 0.816727785709044 |
| 39 | 0.187517462101556 | 0.375034924203111 | 0.812482537898444 |
| 40 | 0.192092941216756 | 0.384185882433513 | 0.807907058783244 |
| 41 | 0.251973407050812 | 0.503946814101625 | 0.748026592949188 |
| 42 | 0.238366252700967 | 0.476732505401934 | 0.761633747299033 |
| 43 | 0.210449122591403 | 0.420898245182805 | 0.789550877408597 |
| 44 | 0.232712776326307 | 0.465425552652614 | 0.767287223673693 |
| 45 | 0.224573156749101 | 0.449146313498201 | 0.775426843250899 |
| 46 | 0.196250343606907 | 0.392500687213813 | 0.803749656393093 |
| 47 | 0.293876728822875 | 0.58775345764575 | 0.706123271177125 |
| 48 | 0.297357922907768 | 0.594715845815536 | 0.702642077092232 |
| 49 | 0.451506581877229 | 0.903013163754458 | 0.548493418122771 |
| 50 | 0.677119431413356 | 0.645761137173287 | 0.322880568586644 |
| 51 | 0.797704234284973 | 0.404591531430054 | 0.202295765715027 |
| 52 | 0.98792783755546 | 0.0241443248890812 | 0.0120721624445406 |
| 53 | 0.99646646393302 | 0.00706707213395907 | 0.00353353606697954 |
| 54 | 0.99150889504209 | 0.0169822099158212 | 0.00849110495791059 |
| 55 | 0.98613339586209 | 0.0277332082758209 | 0.0138666041379104 |
| 56 | 0.977369920385756 | 0.0452601592284885 | 0.0226300796142443 |
| 57 | 0.959617899573769 | 0.0807642008524625 | 0.0403821004262313 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 5 | 0.119047619047619 | NOK |
| 5% type I error level | 12 | 0.285714285714286 | NOK |
| 10% type I error level | 17 | 0.404761904761905 | NOK |
