| Multiple Linear Regression - Estimated Regression Equation |
| WGM[t] = + 2.91557178759221 + 0.504267960215842WGV[t] -0.114549921346691M1[t] -0.372072749606734M2[t] -0.506544205664292M3[t] -0.430619480950859M4[t] -0.337174497527591M5[t] -0.252418510788977M6[t] -0.102987572151090M7[t] + 0.0709454377949495M8[t] + 0.154421036468811M9[t] + 0.130488026522772M10[t] + 0.0904574112721781M11[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) | 2.91557178759221 | 0.580762 | 5.0202 | 5e-06 | 2e-06 |
| WGV | 0.504267960215842 | 0.067735 | 7.4447 | 0 | 0 |
| M1 | -0.114549921346691 | 0.26824 | -0.427 | 0.670876 | 0.335438 |
| M2 | -0.372072749606734 | 0.291255 | -1.2775 | 0.206354 | 0.103177 |
| M3 | -0.506544205664292 | 0.297078 | -1.7051 | 0.093351 | 0.046676 |
| M4 | -0.430619480950859 | 0.292271 | -1.4734 | 0.145882 | 0.072941 |
| M5 | -0.337174497527591 | 0.284929 | -1.1834 | 0.241333 | 0.120667 |
| M6 | -0.252418510788977 | 0.280966 | -0.8984 | 0.372565 | 0.186283 |
| M7 | -0.102987572151090 | 0.282341 | -0.3648 | 0.716571 | 0.358286 |
| M8 | 0.0709454377949495 | 0.285673 | 0.2483 | 0.804716 | 0.402358 |
| M9 | 0.154421036468811 | 0.285173 | 0.5415 | 0.590169 | 0.295084 |
| M10 | 0.130488026522772 | 0.281971 | 0.4628 | 0.645202 | 0.322601 |
| M11 | 0.0904574112721781 | 0.278992 | 0.3242 | 0.746892 | 0.373446 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.731520033305328 |
| R-squared | 0.535121559127029 |
| Adjusted R-squared | 0.442145870952435 |
| F-TEST (value) | 5.75549984768224 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 60 |
| p-value | 1.72591126412769e-06 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.482084283828853 |
| Sum Squared Residuals | 13.9443154028867 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 7.3 | 6.78473875195064 | 0.515261248049358 |
| 2 | 7.6 | 7.13233747594964 | 0.467662524050361 |
| 3 | 7.5 | 7.14914640795683 | 0.350853592043168 |
| 4 | 7.6 | 7.22507113267026 | 0.374928867329736 |
| 5 | 7.9 | 7.16723572802878 | 0.732764271971222 |
| 6 | 7.9 | 7.2015649187458 | 0.698435081254192 |
| 7 | 8.1 | 7.50227624544845 | 0.59772375455155 |
| 8 | 8.2 | 7.978770031524 | 0.221229968476006 |
| 9 | 8 | 8.01181883417627 | -0.0118188341762713 |
| 10 | 7.5 | 7.73575184412231 | -0.235751844122311 |
| 11 | 6.8 | 7.19145326865587 | -0.391453268655875 |
| 12 | 6.5 | 6.94971546931894 | -0.449715469318944 |
| 13 | 6.6 | 7.08729952808017 | -0.487299528080174 |
| 14 | 7.6 | 7.78788582423023 | -0.187885824230232 |
| 15 | 8 | 8.00640194032376 | -0.00640194032376291 |
| 16 | 8.1 | 7.98147307299403 | 0.118526927005972 |
| 17 | 7.7 | 7.62107689222304 | 0.0789231077769633 |
| 18 | 7.5 | 7.30241851078898 | 0.197581489211023 |
| 19 | 7.6 | 7.45184944942686 | 0.148150550573135 |
| 20 | 7.8 | 7.77706284743766 | 0.0229371525623431 |
| 21 | 7.8 | 7.9109652421331 | -0.110965242133102 |
| 22 | 7.8 | 7.83660543616548 | -0.0366054361654795 |
| 23 | 7.5 | 7.59486763682855 | -0.0948676368285478 |
| 24 | 7.5 | 7.4035566335132 | 0.096443366486798 |
| 25 | 7.1 | 7.3394335081881 | -0.239433508188095 |
| 26 | 7.5 | 7.63660543616548 | -0.136605436165478 |
| 27 | 7.5 | 7.60298757215109 | -0.102987572151090 |
| 28 | 7.6 | 7.62848550084294 | -0.0284855008429378 |
| 29 | 7.7 | 7.4193697081367 | 0.280630291863300 |
| 30 | 7.7 | 7.30241851078898 | 0.397581489211023 |
| 31 | 7.9 | 7.50227624544845 | 0.397723754551551 |
| 32 | 8.1 | 7.72663605141607 | 0.373363948583927 |
| 33 | 8.2 | 7.81011165008993 | 0.389888349910065 |
| 34 | 8.2 | 7.68532504810073 | 0.514674951899273 |
| 35 | 8.2 | 7.54444084080696 | 0.655559159193035 |
| 36 | 7.9 | 7.45398342953479 | 0.446016570465214 |
| 37 | 7.3 | 7.3394335081881 | -0.0394335081880947 |
| 38 | 6.9 | 7.48532504810073 | -0.585325048100726 |
| 39 | 6.6 | 7.45170718408634 | -0.851707184086337 |
| 40 | 6.7 | 7.4267783167566 | -0.726778316756601 |
| 41 | 6.9 | 7.26808932007195 | -0.368089320071947 |
| 42 | 7 | 7.2015649187458 | -0.201564918745809 |
| 43 | 7.1 | 7.3509958573837 | -0.250995857383697 |
| 44 | 7.2 | 7.57535566335132 | -0.375355663351320 |
| 45 | 7.1 | 7.65883126202518 | -0.558831262025182 |
| 46 | 6.9 | 7.63489825207914 | -0.734898252079142 |
| 47 | 7 | 7.64529443285013 | -0.645294432850132 |
| 48 | 6.8 | 7.35312983749162 | -0.553129837491618 |
| 49 | 6.4 | 6.986445936037 | -0.586445936037005 |
| 50 | 6.7 | 6.77934990379855 | -0.0793499037985468 |
| 51 | 6.6 | 6.49359805967624 | 0.106401940323763 |
| 52 | 6.4 | 6.36781560030333 | 0.0321843996966681 |
| 53 | 6.3 | 6.56211417576977 | -0.262114175769769 |
| 54 | 6.2 | 6.64687016250838 | -0.446870162508383 |
| 55 | 6.5 | 6.84672789716785 | -0.346727897167854 |
| 56 | 6.8 | 6.97023411109231 | -0.170234111092309 |
| 57 | 6.8 | 6.90242932170142 | -0.102429321701418 |
| 58 | 6.4 | 6.62636233164746 | -0.226362331647457 |
| 59 | 6.1 | 6.43505132833211 | -0.335051328332111 |
| 60 | 5.8 | 6.19331352899518 | -0.393313528995180 |
| 61 | 6.1 | 6.28047079173483 | -0.180470791734826 |
| 62 | 7.2 | 6.67849631175538 | 0.521503688244622 |
| 63 | 7.3 | 6.79615883580574 | 0.503841164194258 |
| 64 | 6.9 | 6.67037637643284 | 0.229623623567163 |
| 65 | 6.1 | 6.56211417576977 | -0.462114175769769 |
| 66 | 5.8 | 6.44516297842205 | -0.645162978422046 |
| 67 | 6.2 | 6.74587430512469 | -0.545874305124685 |
| 68 | 7.1 | 7.17194129517865 | -0.0719412951786467 |
| 69 | 7.7 | 7.3058436898741 | 0.394156310125908 |
| 70 | 7.9 | 7.18105708788488 | 0.718942912115117 |
| 71 | 7.7 | 6.88889249252637 | 0.811107507473631 |
| 72 | 7.4 | 6.54630110114627 | 0.85369889885373 |
| 73 | 7.5 | 6.48217797582116 | 1.01782202417884 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.35071097737773 | 0.70142195475546 | 0.64928902262227 |
| 17 | 0.237898775184069 | 0.475797550368137 | 0.762101224815931 |
| 18 | 0.182552329960932 | 0.365104659921865 | 0.817447670039068 |
| 19 | 0.153535132161482 | 0.307070264322963 | 0.846464867838518 |
| 20 | 0.105703620270108 | 0.211407240540217 | 0.894296379729892 |
| 21 | 0.0608014228005666 | 0.121602845601133 | 0.939198577199433 |
| 22 | 0.0366805083899434 | 0.0733610167798869 | 0.963319491610057 |
| 23 | 0.0354858809824934 | 0.0709717619649869 | 0.964514119017507 |
| 24 | 0.0522655216811885 | 0.104531043362377 | 0.947734478318812 |
| 25 | 0.0300482175171959 | 0.0600964350343918 | 0.969951782482804 |
| 26 | 0.017489712144259 | 0.034979424288518 | 0.98251028785574 |
| 27 | 0.0106624122921564 | 0.0213248245843128 | 0.989337587707844 |
| 28 | 0.00644289634414518 | 0.0128857926882904 | 0.993557103655855 |
| 29 | 0.00398889920048017 | 0.00797779840096034 | 0.99601110079952 |
| 30 | 0.00279006064106351 | 0.00558012128212702 | 0.997209939358936 |
| 31 | 0.00198169688183665 | 0.00396339376367329 | 0.998018303118163 |
| 32 | 0.00135054085252655 | 0.00270108170505310 | 0.998649459147473 |
| 33 | 0.00123293291427859 | 0.00246586582855718 | 0.998767067085721 |
| 34 | 0.00234292938130617 | 0.00468585876261235 | 0.997657070618694 |
| 35 | 0.0150392984274363 | 0.0300785968548727 | 0.984960701572564 |
| 36 | 0.029966390101779 | 0.059932780203558 | 0.97003360989822 |
| 37 | 0.0194743244105599 | 0.0389486488211197 | 0.98052567558944 |
| 38 | 0.0238977660322970 | 0.0477955320645939 | 0.976102233967703 |
| 39 | 0.0648076839239375 | 0.129615367847875 | 0.935192316076062 |
| 40 | 0.104129008185812 | 0.208258016371625 | 0.895870991814188 |
| 41 | 0.108514920814685 | 0.21702984162937 | 0.891485079185315 |
| 42 | 0.115032689016598 | 0.230065378033197 | 0.884967310983402 |
| 43 | 0.111909347961154 | 0.223818695922309 | 0.888090652038846 |
| 44 | 0.0937596658966695 | 0.187519331793339 | 0.90624033410333 |
| 45 | 0.090301789230568 | 0.180603578461136 | 0.909698210769432 |
| 46 | 0.117543666759234 | 0.235087333518469 | 0.882456333240766 |
| 47 | 0.146602472896256 | 0.293204945792513 | 0.853397527103744 |
| 48 | 0.261994860391232 | 0.523989720782463 | 0.738005139608768 |
| 49 | 0.91065925339365 | 0.178681493212702 | 0.0893407466063509 |
| 50 | 0.951311275685405 | 0.0973774486291894 | 0.0486887243145947 |
| 51 | 0.922015828766453 | 0.155968342467094 | 0.0779841712335469 |
| 52 | 0.906830523304695 | 0.18633895339061 | 0.093169476695305 |
| 53 | 0.859685689293041 | 0.280628621413918 | 0.140314310706959 |
| 54 | 0.808463343729427 | 0.383073312541146 | 0.191536656270573 |
| 55 | 0.705761219190918 | 0.588477561618165 | 0.294238780809082 |
| 56 | 0.613192626768459 | 0.773614746463082 | 0.386807373231541 |
| 57 | 0.546072797120358 | 0.907854405759284 | 0.453927202879642 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 6 | 0.142857142857143 | NOK |
| 5% type I error level | 12 | 0.285714285714286 | NOK |
| 10% type I error level | 17 | 0.404761904761905 | NOK |
