Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 3.02312027804749 + 0.289809759090523CM[t] -0.293633940943942CM_G[t] -0.199249052781833D[t] + 0.153536202361446D_G[t] + 0.255960697716122PE[t] -0.283226764542751PE_G[t] + 0.0132743157206869PC[t] -0.0117482321641987PC_G[t] + 0.978572091873339PS_G[t] + 0.415924298586412O[t] -0.444540756555795O_G[t] + 0.178141200721764H[t] -0.247978402414856H_G[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) | 3.02312027804749 | 2.612232 | 1.1573 | 0.249123 | 0.124561 |
CM | 0.289809759090523 | 0.063461 | 4.5667 | 1.1e-05 | 5e-06 |
CM_G | -0.293633940943942 | 0.106148 | -2.7663 | 0.006436 | 0.003218 |
D | -0.199249052781833 | 0.130029 | -1.5323 | 0.127694 | 0.063847 |
D_G | 0.153536202361446 | 0.188746 | 0.8135 | 0.417338 | 0.208669 |
PE | 0.255960697716122 | 0.111222 | 2.3013 | 0.022849 | 0.011424 |
PE_G | -0.283226764542751 | 0.180928 | -1.5654 | 0.119744 | 0.059872 |
PC | 0.0132743157206869 | 0.131064 | 0.1013 | 0.919472 | 0.459736 |
PC_G | -0.0117482321641987 | 0.229855 | -0.0511 | 0.959309 | 0.479655 |
PS_G | 0.978572091873339 | 0.113793 | 8.5996 | 0 | 0 |
O | 0.415924298586412 | 0.072156 | 5.7642 | 0 | 0 |
O_G | -0.444540756555795 | 0.139406 | -3.1888 | 0.001763 | 0.000881 |
H | 0.178141200721764 | 0.125845 | 1.4156 | 0.159124 | 0.079562 |
H_G | -0.247978402414856 | 0.172404 | -1.4384 | 0.152564 | 0.076282 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.776966426907153 |
R-squared | 0.603676828540868 |
Adjusted R-squared | 0.566875391191092 |
F-TEST (value) | 16.4036209456513 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 140 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.80575699262366 |
Sum Squared Residuals | 1102.11812223192 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 24.0530765560902 | -0.0530765560901563 |
2 | 25 | 22.0347797620809 | 2.96522023791906 |
3 | 30 | 24.8165673304871 | 5.18343266951292 |
4 | 19 | 19.0324119867282 | -0.0324119867281819 |
5 | 22 | 20.9458040196355 | 1.05419598036454 |
6 | 22 | 22.8533923452611 | -0.85339234526115 |
7 | 25 | 23.12199774673 | 1.87800225327001 |
8 | 23 | 20.5490150747288 | 2.45098492527124 |
9 | 17 | 18.6134826537593 | -1.61348265375926 |
10 | 21 | 21.7143577556621 | -0.714357755662085 |
11 | 19 | 18.9756762393769 | 0.0243237606230659 |
12 | 19 | 23.7132941234279 | -4.71329412342788 |
13 | 15 | 22.6873745259648 | -7.68737452596483 |
14 | 16 | 17.2473501001225 | -1.24735010012250 |
15 | 23 | 22.9353989396518 | 0.0646010603481655 |
16 | 27 | 26.8942824562994 | 0.105717543700623 |
17 | 22 | 20.1951792452327 | 1.80482075476734 |
18 | 14 | 14.8309020505191 | -0.830902050519145 |
19 | 22 | 22.0620006943968 | -0.0620006943968054 |
20 | 23 | 24.8838305882861 | -1.88383058828613 |
21 | 23 | 21.1319655749382 | 1.86803442506183 |
22 | 19 | 21.7658630945607 | -2.76586309456067 |
23 | 18 | 18.1222114349989 | -0.122211434998897 |
24 | 20 | 20.1618731972673 | -0.161873197267308 |
25 | 23 | 22.5011232846478 | 0.498876715352215 |
26 | 25 | 24.1338551239530 | 0.866144876046962 |
27 | 19 | 19.3285382243087 | -0.328538224308664 |
28 | 24 | 23.9548811542322 | 0.0451188457678439 |
29 | 22 | 22.1584389519411 | -0.158438951941049 |
30 | 26 | 24.0199385959575 | 1.98006140404252 |
31 | 29 | 23.0207127559547 | 5.97928724404534 |
32 | 32 | 24.7309046904592 | 7.26909530954084 |
33 | 25 | 22.0339736913512 | 2.96602630864875 |
34 | 29 | 28.7994562904100 | 0.200543709589977 |
35 | 28 | 27.8807412938904 | 0.119258706109636 |
36 | 17 | 16.9508805859068 | 0.0491194140932041 |
37 | 28 | 25.7825160599411 | 2.21748394005887 |
38 | 29 | 28.9448170203572 | 0.0551829796428413 |
39 | 26 | 25.1938589519412 | 0.80614104805876 |
40 | 25 | 23.5469889908283 | 1.45301100917168 |
41 | 14 | 14.6853688520440 | -0.68536885204396 |
42 | 25 | 22.7349055286470 | 2.26509447135304 |
43 | 26 | 26.1058683703617 | -0.105868370361661 |
44 | 20 | 19.9379576413964 | 0.0620423586036247 |
45 | 18 | 21.6877580201582 | -3.68775802015815 |
46 | 32 | 31.9498442026493 | 0.0501557973507456 |
47 | 25 | 25.029353741249 | -0.0293537412489835 |
48 | 25 | 22.3937559491003 | 2.60624405089968 |
49 | 23 | 23.253888249809 | -0.253888249809004 |
50 | 21 | 21.1133833318065 | -0.113383331806463 |
51 | 20 | 24.5006874023663 | -4.50068740236634 |
52 | 15 | 15.9313015487408 | -0.931301548740772 |
53 | 30 | 29.7335892231885 | 0.266410776811461 |
54 | 24 | 25.5232994949851 | -1.52329949498510 |
55 | 26 | 24.3081002205174 | 1.69189977948256 |
56 | 24 | 23.9586108514866 | 0.0413891485133683 |
57 | 22 | 22.1522491819777 | -0.152249181977660 |
58 | 14 | 17.0304526985932 | -3.03045269859321 |
59 | 24 | 23.9559962131739 | 0.0440037868260885 |
60 | 24 | 24.0314331791993 | -0.0314331791993214 |
61 | 24 | 23.4203206138149 | 0.579679386185118 |
62 | 24 | 23.8371641532218 | 0.162835846778242 |
63 | 19 | 18.9829124215140 | 0.0170875784859807 |
64 | 31 | 30.9504825580780 | 0.0495174419220362 |
65 | 22 | 21.9057083717531 | 0.0942916282469003 |
66 | 27 | 27.2490866133539 | -0.249086613353868 |
67 | 19 | 19.0306688916299 | -0.0306688916299072 |
68 | 25 | 22.6195635553874 | 2.38043644461262 |
69 | 20 | 24.708843473415 | -4.70884347341502 |
70 | 21 | 21.3712075935348 | -0.371207593534769 |
71 | 27 | 27.5473418577496 | -0.547341857749624 |
72 | 23 | 25.4305544100768 | -2.43055441007685 |
73 | 25 | 25.5760731741955 | -0.576073174195533 |
74 | 20 | 22.6367877902548 | -2.63678779025478 |
75 | 22 | 22.5409327698134 | -0.540932769813419 |
76 | 23 | 22.9806890296311 | 0.0193109703689074 |
77 | 25 | 23.1067942920126 | 1.89320570798738 |
78 | 25 | 23.7271406961946 | 1.2728593038054 |
79 | 17 | 23.8083960011454 | -6.80839600114543 |
80 | 19 | 19.2471065054298 | -0.247106505429782 |
81 | 25 | 24.2858797358902 | 0.714120264109787 |
82 | 19 | 19.2763766378851 | -0.276376637885127 |
83 | 20 | 19.851485440976 | 0.148514559024005 |
84 | 26 | 23.0091575229548 | 2.99084247704521 |
85 | 23 | 22.5826401145652 | 0.417359885434837 |
86 | 27 | 24.3160454603099 | 2.68395453969006 |
87 | 17 | 17.1640440206979 | -0.164044020697871 |
88 | 17 | 16.6060563169582 | 0.393943683041799 |
89 | 17 | 17.2909912366521 | -0.290991236652071 |
90 | 22 | 22.3161047928413 | -0.316104792841313 |
91 | 21 | 20.9143536065983 | 0.085646393401681 |
92 | 32 | 29.3916308982389 | 2.60836910176113 |
93 | 21 | 20.5922193050101 | 0.407780694989933 |
94 | 21 | 24.6541958327448 | -3.65419583274485 |
95 | 18 | 18.3978405680709 | -0.397840568070873 |
96 | 18 | 20.702242927377 | -2.70224292737698 |
97 | 23 | 23.074936113401 | -0.0749361134009955 |
98 | 19 | 19.2720973995629 | -0.272097399562895 |
99 | 20 | 21.3489771868437 | -1.34897718684369 |
100 | 21 | 22.9747333242637 | -1.97473332426375 |
101 | 20 | 19.6346876192706 | 0.365312380729391 |
102 | 17 | 18.7373756573030 | -1.73737565730303 |
103 | 18 | 20.0886322714171 | -2.08863227141706 |
104 | 19 | 20.5565277383226 | -1.55652773832264 |
105 | 22 | 22.8708337361754 | -0.870833736175399 |
106 | 15 | 15.03017071542 | -0.0301707154199975 |
107 | 14 | 19.2920653920197 | -5.29206539201971 |
108 | 18 | 26.452765239334 | -8.45276523933401 |
109 | 24 | 24.3540193970066 | -0.354019397006586 |
110 | 35 | 23.5479032051727 | 11.4520967948273 |
111 | 29 | 18.5117113246981 | 10.4882886753019 |
112 | 21 | 21.7579634256110 | -0.757963425611031 |
113 | 20 | 20.1992008424665 | -0.199200842466506 |
114 | 22 | 21.8261869833736 | 0.173813016626372 |
115 | 13 | 13.4637990996297 | -0.463799099629735 |
116 | 26 | 22.7249972369739 | 3.27500276302615 |
117 | 17 | 17.3800726955620 | -0.38007269556197 |
118 | 25 | 20.2010303611278 | 4.79896963887217 |
119 | 20 | 20.4619097982583 | -0.461909798258281 |
120 | 19 | 18.7284953373628 | 0.271504662637237 |
121 | 21 | 20.9065953910951 | 0.0934046089049144 |
122 | 22 | 21.3995620605385 | 0.600437939461491 |
123 | 24 | 23.0354878539738 | 0.964512146026208 |
124 | 21 | 23.2581325967219 | -2.25813259672187 |
125 | 26 | 25.7893432652187 | 0.210656734781317 |
126 | 24 | 20.4831749246143 | 3.51682507538568 |
127 | 16 | 20.4510861279594 | -4.45108612795943 |
128 | 23 | 22.9001321942388 | 0.099867805761226 |
129 | 18 | 20.1267808197177 | -2.12678081971768 |
130 | 16 | 16.1919539344285 | -0.191953934428511 |
131 | 26 | 25.7746298864891 | 0.225370113510852 |
132 | 19 | 19.6130953042636 | -0.613095304263595 |
133 | 21 | 17.1966579118187 | 3.80334208818127 |
134 | 21 | 22.2011921513117 | -1.20119215131171 |
135 | 22 | 18.6074918570167 | 3.39250814298333 |
136 | 23 | 19.8460996237850 | 3.15390037621497 |
137 | 29 | 25.2991718207792 | 3.70082817922083 |
138 | 21 | 19.5382658099568 | 1.46173419004319 |
139 | 21 | 21.3784089773461 | -0.378408977346122 |
140 | 23 | 22.8386894466138 | 0.161310553386206 |
141 | 27 | 23.6109919925434 | 3.38900800745662 |
142 | 25 | 24.9031793200022 | 0.0968206799977803 |
143 | 21 | 20.9251658522983 | 0.0748341477016993 |
144 | 10 | 16.7806836535453 | -6.78068365354529 |
145 | 20 | 22.3335982628498 | -2.33359826284984 |
146 | 26 | 22.8946259893632 | 3.10537401063678 |
147 | 24 | 25.1619579556401 | -1.16195795564013 |
148 | 29 | 32.2243102755247 | -3.22431027552474 |
149 | 19 | 19.1101399599375 | -0.110139959937496 |
150 | 24 | 22.7318187197821 | 1.26818128021791 |
151 | 19 | 20.4358843511594 | -1.43588435115941 |
152 | 24 | 23.8793968053101 | 0.120603194689921 |
153 | 22 | 22.4251622938296 | -0.425162293829623 |
154 | 17 | 24.8854842560364 | -7.88548425603638 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
17 | 0.9781439190994 | 0.0437121618011982 | 0.0218560809005991 |
18 | 0.952678714586764 | 0.0946425708264729 | 0.0473212854132364 |
19 | 0.911993910286692 | 0.176012179426617 | 0.0880060897133083 |
20 | 0.87145432898861 | 0.257091342022781 | 0.128545671011391 |
21 | 0.91806502448838 | 0.163869951023239 | 0.0819349755116194 |
22 | 0.88002917131513 | 0.239941657369742 | 0.119970828684871 |
23 | 0.824802716681744 | 0.350394566636512 | 0.175197283318256 |
24 | 0.758894199585343 | 0.482211600829315 | 0.241105800414657 |
25 | 0.687160189875773 | 0.625679620248453 | 0.312839810124227 |
26 | 0.611583870646597 | 0.776832258706806 | 0.388416129353403 |
27 | 0.52774211350732 | 0.94451577298536 | 0.47225788649268 |
28 | 0.444573530441326 | 0.889147060882653 | 0.555426469558673 |
29 | 0.392732038035119 | 0.785464076070239 | 0.60726796196488 |
30 | 0.376879607086252 | 0.753759214172504 | 0.623120392913748 |
31 | 0.675120118948892 | 0.649759762102216 | 0.324879881051108 |
32 | 0.875295391886869 | 0.249409216226262 | 0.124704608113131 |
33 | 0.864752972994647 | 0.270494054010706 | 0.135247027005353 |
34 | 0.824311348798671 | 0.351377302402657 | 0.175688651201329 |
35 | 0.777567578593383 | 0.444864842813234 | 0.222432421406617 |
36 | 0.725067200271602 | 0.549865599456795 | 0.274932799728398 |
37 | 0.691724632948161 | 0.616550734103678 | 0.308275367051839 |
38 | 0.632718770275743 | 0.734562459448515 | 0.367281229724257 |
39 | 0.574508580369953 | 0.850982839260094 | 0.425491419630047 |
40 | 0.517639934828353 | 0.964720130343294 | 0.482360065171647 |
41 | 0.457760845518981 | 0.915521691037961 | 0.54223915448102 |
42 | 0.423686422663947 | 0.847372845327894 | 0.576313577336053 |
43 | 0.364693067032239 | 0.729386134064478 | 0.635306932967761 |
44 | 0.309177713692308 | 0.618355427384616 | 0.690822286307692 |
45 | 0.346863408857198 | 0.693726817714396 | 0.653136591142802 |
46 | 0.293979346420560 | 0.587958692841121 | 0.70602065357944 |
47 | 0.257810609876425 | 0.515621219752849 | 0.742189390123575 |
48 | 0.237512843565904 | 0.475025687131808 | 0.762487156434096 |
49 | 0.195101720189184 | 0.390203440378368 | 0.804898279810816 |
50 | 0.157854472254950 | 0.315708944509899 | 0.84214552774505 |
51 | 0.256800478201724 | 0.513600956403449 | 0.743199521798276 |
52 | 0.216865090359544 | 0.433730180719088 | 0.783134909640456 |
53 | 0.178067907090909 | 0.356135814181818 | 0.821932092909091 |
54 | 0.157302909894546 | 0.314605819789092 | 0.842697090105454 |
55 | 0.134616436637033 | 0.269232873274067 | 0.865383563362967 |
56 | 0.107048573529798 | 0.214097147059595 | 0.892951426470202 |
57 | 0.083867523503024 | 0.167735047006048 | 0.916132476496976 |
58 | 0.077320359354139 | 0.154640718708278 | 0.922679640645861 |
59 | 0.0594794119156925 | 0.118958823831385 | 0.940520588084307 |
60 | 0.0450917930999588 | 0.0901835861999176 | 0.954908206900041 |
61 | 0.0340407865065312 | 0.0680815730130623 | 0.965959213493469 |
62 | 0.0251008652225183 | 0.0502017304450367 | 0.974899134777482 |
63 | 0.0182198508884628 | 0.0364397017769255 | 0.981780149111537 |
64 | 0.0130801582591190 | 0.0261603165182379 | 0.986919841740881 |
65 | 0.00925198340388186 | 0.0185039668077637 | 0.990748016596118 |
66 | 0.00642834076443957 | 0.0128566815288791 | 0.99357165923556 |
67 | 0.00440463726453305 | 0.0088092745290661 | 0.995595362735467 |
68 | 0.00415915290483558 | 0.00831830580967115 | 0.995840847095164 |
69 | 0.0131662642707638 | 0.0263325285415275 | 0.986833735729236 |
70 | 0.00942216817813516 | 0.0188443363562703 | 0.990577831821865 |
71 | 0.00719711130772487 | 0.0143942226154497 | 0.992802888692275 |
72 | 0.00680486571222828 | 0.0136097314244566 | 0.993195134287772 |
73 | 0.00547168149788901 | 0.0109433629957780 | 0.994528318502111 |
74 | 0.00512801934547278 | 0.0102560386909456 | 0.994871980654527 |
75 | 0.00356313123272169 | 0.00712626246544338 | 0.996436868767278 |
76 | 0.00240588868914902 | 0.00481177737829805 | 0.99759411131085 |
77 | 0.00188171899761454 | 0.00376343799522908 | 0.998118281002385 |
78 | 0.00142105769126224 | 0.00284211538252449 | 0.998578942308738 |
79 | 0.0096888857900115 | 0.019377771580023 | 0.990311114209989 |
80 | 0.00686204526039376 | 0.0137240905207875 | 0.993137954739606 |
81 | 0.00489910203177253 | 0.00979820406354506 | 0.995100897968227 |
82 | 0.00336855938993868 | 0.00673711877987735 | 0.996631440610061 |
83 | 0.00228020708047745 | 0.00456041416095490 | 0.997719792919523 |
84 | 0.00238675831104824 | 0.00477351662209648 | 0.997613241688952 |
85 | 0.00160619323335109 | 0.00321238646670219 | 0.998393806766649 |
86 | 0.00171173245986687 | 0.00342346491973374 | 0.998288267540133 |
87 | 0.00112938382009561 | 0.00225876764019122 | 0.998870616179904 |
88 | 0.00073680612352729 | 0.00147361224705458 | 0.999263193876473 |
89 | 0.000472528054133025 | 0.00094505610826605 | 0.999527471945867 |
90 | 0.000330282107795487 | 0.000660564215590974 | 0.999669717892204 |
91 | 0.000205304603126307 | 0.000410609206252613 | 0.999794695396874 |
92 | 0.000201460186368584 | 0.000402920372737168 | 0.999798539813631 |
93 | 0.000124963400784965 | 0.000249926801569930 | 0.999875036599215 |
94 | 0.000173165978625656 | 0.000346331957251311 | 0.999826834021374 |
95 | 0.000106637225481205 | 0.000213274450962409 | 0.999893362774519 |
96 | 0.000101490198423701 | 0.000202980396847402 | 0.999898509801576 |
97 | 6.04314352437458e-05 | 0.000120862870487492 | 0.999939568564756 |
98 | 3.5639879179104e-05 | 7.1279758358208e-05 | 0.99996436012082 |
99 | 2.31470773180972e-05 | 4.62941546361943e-05 | 0.999976852922682 |
100 | 1.53749740572701e-05 | 3.07499481145403e-05 | 0.999984625025943 |
101 | 8.75228222649496e-06 | 1.75045644529899e-05 | 0.999991247717773 |
102 | 5.90585401899174e-06 | 1.18117080379835e-05 | 0.999994094145981 |
103 | 4.49052739001114e-06 | 8.98105478002227e-06 | 0.99999550947261 |
104 | 3.28687920748496e-06 | 6.57375841496991e-06 | 0.999996713120793 |
105 | 1.79588682881190e-06 | 3.59177365762379e-06 | 0.999998204113171 |
106 | 9.39938048657008e-07 | 1.87987609731402e-06 | 0.99999906006195 |
107 | 3.37899972234571e-06 | 6.75799944469141e-06 | 0.999996621000278 |
108 | 0.000360074540067842 | 0.000720149080135683 | 0.999639925459932 |
109 | 0.000219138956284162 | 0.000438277912568324 | 0.999780861043716 |
110 | 0.0632485219714483 | 0.126497043942897 | 0.936751478028552 |
111 | 0.464922955463394 | 0.929845910926788 | 0.535077044536606 |
112 | 0.415909187218632 | 0.831818374437263 | 0.584090812781368 |
113 | 0.361588090503173 | 0.723176181006345 | 0.638411909496827 |
114 | 0.305875462980007 | 0.611750925960013 | 0.694124537019994 |
115 | 0.254077437629412 | 0.508154875258824 | 0.745922562370588 |
116 | 0.239451286850621 | 0.478902573701242 | 0.76054871314938 |
117 | 0.193732305390424 | 0.387464610780848 | 0.806267694609576 |
118 | 0.26079500319118 | 0.52159000638236 | 0.73920499680882 |
119 | 0.211947516692657 | 0.423895033385315 | 0.788052483307343 |
120 | 0.166686983300123 | 0.333373966600246 | 0.833313016699877 |
121 | 0.127652654362295 | 0.255305308724590 | 0.872347345637705 |
122 | 0.0998213697896844 | 0.199642739579369 | 0.900178630210316 |
123 | 0.0777366484025935 | 0.155473296805187 | 0.922263351597407 |
124 | 0.0583586884614695 | 0.116717376922939 | 0.94164131153853 |
125 | 0.0414177901424689 | 0.0828355802849379 | 0.95858220985753 |
126 | 0.0435735189374731 | 0.0871470378749462 | 0.956426481062527 |
127 | 0.0525358887988513 | 0.105071777597703 | 0.947464111201149 |
128 | 0.0344645801326764 | 0.0689291602653527 | 0.965535419867324 |
129 | 0.0239851270000138 | 0.0479702540000276 | 0.976014872999986 |
130 | 0.0143835707712485 | 0.0287671415424969 | 0.985616429228751 |
131 | 0.0081525596018272 | 0.0163051192036544 | 0.991847440398173 |
132 | 0.00450649590766619 | 0.00901299181533239 | 0.995493504092334 |
133 | 0.00421390984816502 | 0.00842781969633004 | 0.995786090151835 |
134 | 0.00213309845124953 | 0.00426619690249906 | 0.99786690154875 |
135 | 0.00139834635399111 | 0.00279669270798222 | 0.99860165364601 |
136 | 0.000808516029532804 | 0.00161703205906561 | 0.999191483970467 |
137 | 0.000956961837372133 | 0.00191392367474427 | 0.999043038162628 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 41 | 0.338842975206612 | NOK |
5% type I error level | 57 | 0.471074380165289 | NOK |
10% type I error level | 64 | 0.528925619834711 | NOK |