Multiple Linear Regression - Estimated Regression Equation |
D[t] = + 6.91356251488984 + 0.242424597613749CM[t] + 0.0780615601222883PC[t] -0.207313323580618PS[t] + 0.120695024728114`O `[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) | 6.91356251488984 | 1.538773 | 4.4929 | 1.4e-05 | 7e-06 |
CM | 0.242424597613749 | 0.03992 | 6.0727 | 0 | 0 |
PC | 0.0780615601222883 | 0.079487 | 0.9821 | 0.32761 | 0.163805 |
PS | -0.207313323580618 | 0.055965 | -3.7043 | 0.000295 | 0.000147 |
`O ` | 0.120695024728114 | 0.056318 | 2.1431 | 0.033675 | 0.016837 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.478897605353962 |
R-squared | 0.229342916413759 |
Adjusted R-squared | 0.209325849307623 |
F-TEST (value) | 11.4573686143788 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 154 |
p-value | 3.62416721078063e-08 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.49022072596553 |
Sum Squared Residuals | 954.98468666036 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 14 | 11.8310424560832 | 2.16895754391678 |
2 | 11 | 11.1918224154430 | -0.191822415443036 |
3 | 6 | 8.45724906608619 | -2.45724906608619 |
4 | 12 | 10.7387301736305 | 1.26126982636949 |
5 | 8 | 9.71207166409848 | -1.71207166409848 |
6 | 10 | 10.2780495959075 | -0.278049595907548 |
7 | 10 | 9.90884323634137 | 0.0911567636586304 |
8 | 11 | 9.41742231499117 | 1.58257768500883 |
9 | 16 | 10.9546002359413 | 5.04539976405866 |
10 | 11 | 10.2450074181895 | 0.754992581810542 |
11 | 13 | 12.3837944269165 | 0.616205573083486 |
12 | 12 | 13.2004733415995 | -1.20047334159949 |
13 | 8 | 12.8155345515382 | -4.81553455153818 |
14 | 12 | 10.3951099465474 | 1.60489005345256 |
15 | 11 | 9.06150806173867 | 1.93849193826133 |
16 | 4 | 7.91690488245449 | -3.91690488245449 |
17 | 9 | 10.5600404816678 | -1.56004048166784 |
18 | 8 | 9.7203777266831 | -1.72037772668309 |
19 | 8 | 10.6442728627220 | -2.64427286272197 |
20 | 14 | 12.9330962544693 | 1.06690374553071 |
21 | 15 | 11.9279697684978 | 3.07203023150217 |
22 | 16 | 14.0749966944718 | 1.92500330552823 |
23 | 9 | 11.6149217176270 | -2.61492171762696 |
24 | 14 | 14.0975632661899 | -0.0975632661898556 |
25 | 11 | 11.3773165713042 | -0.377316571304204 |
26 | 8 | 9.62338426893094 | -1.62338426893094 |
27 | 9 | 9.94427133185783 | -0.944271331857832 |
28 | 9 | 11.6647605513221 | -2.66476055132215 |
29 | 9 | 10.7499235063047 | -1.74992350630470 |
30 | 9 | 9.71824248503032 | -0.718242485030324 |
31 | 10 | 11.5174448459534 | -1.51744484595340 |
32 | 16 | 11.7296965975688 | 4.27030340243116 |
33 | 11 | 9.76733391472688 | 1.23266608527312 |
34 | 8 | 9.90395763971265 | -1.90395763971265 |
35 | 9 | 9.0890971451991 | -0.0890971451991075 |
36 | 16 | 12.2655032583566 | 3.73449674164342 |
37 | 11 | 12.2324610806385 | -1.23246108063849 |
38 | 16 | 9.58635412762801 | 6.41364587237199 |
39 | 12 | 12.4584058437585 | -0.458405843758467 |
40 | 12 | 10.2845075609983 | 1.71549243900172 |
41 | 14 | 12.9551957756588 | 1.04480422434121 |
42 | 9 | 10.5426101827241 | -1.54261018272408 |
43 | 10 | 11.0511266431649 | -1.05112664316491 |
44 | 9 | 9.01824095416618 | -0.0182409541661830 |
45 | 10 | 9.77238610379368 | 0.227613896206323 |
46 | 12 | 10.0455331066649 | 1.95446689333513 |
47 | 14 | 11.7077108374113 | 2.29228916258869 |
48 | 14 | 11.6445978357722 | 2.35540216422776 |
49 | 10 | 12.1615208058980 | -2.16152080589803 |
50 | 14 | 10.3875216106370 | 3.61247838936298 |
51 | 16 | 11.6573224444570 | 4.34267755554302 |
52 | 9 | 10.4447985511974 | -1.44479855119738 |
53 | 10 | 11.6197411689180 | -1.61974116891795 |
54 | 6 | 8.71389987107078 | -2.71389987107078 |
55 | 8 | 11.4571832376643 | -3.45718323766431 |
56 | 13 | 12.3657304850061 | 0.63426951499391 |
57 | 10 | 10.7400153979336 | -0.740015397933631 |
58 | 8 | 9.18292081314097 | -1.18292081314097 |
59 | 7 | 8.95347150035757 | -1.95347150035757 |
60 | 15 | 9.9607332279818 | 5.0392667720182 |
61 | 9 | 9.77919056769218 | -0.779190567692182 |
62 | 10 | 10.3940092530522 | -0.394009253052199 |
63 | 12 | 10.4700017168594 | 1.52999828314055 |
64 | 13 | 9.90092014057782 | 3.09907985942218 |
65 | 10 | 8.56514871235365 | 1.43485128764635 |
66 | 11 | 11.5283213571443 | -0.528321357144263 |
67 | 8 | 13.3890049965955 | -5.3890049965955 |
68 | 9 | 9.08125813314308 | -0.0812581331430818 |
69 | 13 | 8.64217572431841 | 4.35782427568159 |
70 | 11 | 10.2210894768305 | 0.778910523169477 |
71 | 8 | 12.7569062413370 | -4.75690624133697 |
72 | 9 | 10.4884665639607 | -1.48846656396073 |
73 | 9 | 12.4294653906572 | -3.42946539065718 |
74 | 15 | 12.8103321334261 | 2.18966786657387 |
75 | 9 | 11.5195139422684 | -2.51951394226844 |
76 | 10 | 11.5021497886624 | -1.5021497886624 |
77 | 14 | 9.19724746761218 | 4.80275253238783 |
78 | 12 | 11.0428205805803 | 0.957179419419702 |
79 | 12 | 10.8760716252905 | 1.12392837470953 |
80 | 11 | 11.6422780633116 | -0.642278063311595 |
81 | 14 | 11.3458764393726 | 2.65412356062743 |
82 | 6 | 11.5154418949761 | -5.51544189497608 |
83 | 12 | 11.3453089417436 | 0.654691058256365 |
84 | 8 | 10.2565175723470 | -2.25651757234699 |
85 | 14 | 12.1994485802448 | 1.80055141975516 |
86 | 11 | 11.3013241074970 | -0.301324107496957 |
87 | 10 | 9.90132104576868 | 0.098678954231325 |
88 | 14 | 9.90637323483547 | 4.09362676516453 |
89 | 12 | 11.8521438971287 | 0.147856102871335 |
90 | 10 | 11.0763298088270 | -1.07632980882697 |
91 | 14 | 13.2134486264298 | 0.786551373570157 |
92 | 5 | 8.76390529720405 | -3.76390529720405 |
93 | 11 | 10.4343229451974 | 0.565677054802625 |
94 | 10 | 10.5682803989147 | -0.568280398914726 |
95 | 9 | 11.2054313432400 | -2.20543134324005 |
96 | 10 | 11.8695080507347 | -1.86950805073470 |
97 | 16 | 13.7950749050265 | 2.20492509497348 |
98 | 13 | 13.0616302912534 | -0.0616302912534297 |
99 | 9 | 10.8690164852464 | -1.86901648524635 |
100 | 10 | 11.4329617887537 | -1.43296178875366 |
101 | 10 | 11.0363329381651 | -1.03633293816512 |
102 | 7 | 9.61394321108845 | -2.61394321108845 |
103 | 9 | 10.3275239924252 | -1.32752399242516 |
104 | 8 | 10.3595316219857 | -2.35953162198573 |
105 | 14 | 12.6238331067319 | 1.37616689326811 |
106 | 14 | 11.6505841258962 | 2.3494158741038 |
107 | 8 | 10.8710855815614 | -2.87108558156139 |
108 | 9 | 11.3838406817327 | -2.38384068173266 |
109 | 14 | 11.8065570170955 | 2.19344298290447 |
110 | 14 | 10.9280457006384 | 3.07195429936158 |
111 | 8 | 10.0023321444301 | -2.0023321444301 |
112 | 8 | 13.8032307385659 | -5.80323073856588 |
113 | 8 | 10.3015369547512 | -2.30153695475118 |
114 | 7 | 8.62870371163504 | -1.62870371163504 |
115 | 6 | 6.71796023966745 | -0.71796023966745 |
116 | 8 | 9.72576467560302 | -1.72576467560302 |
117 | 6 | 8.65101960720752 | -2.65101960720752 |
118 | 11 | 9.6500890332791 | 1.34991096672090 |
119 | 14 | 12.0125189710353 | 1.98748102896471 |
120 | 11 | 10.9482628225714 | 0.0517371774285888 |
121 | 11 | 11.5212662171002 | -0.52126621710015 |
122 | 11 | 9.26073169711765 | 1.73926830288235 |
123 | 14 | 10.2159532040562 | 3.7840467959438 |
124 | 8 | 9.88940998642029 | -1.88940998642029 |
125 | 20 | 11.1444832605782 | 8.85551673942181 |
126 | 11 | 10.8089527216968 | 0.191047278303235 |
127 | 8 | 9.19796519428636 | -1.19796519428636 |
128 | 11 | 10.5490978251393 | 0.450902174860745 |
129 | 10 | 10.7642501607759 | -0.764250160775898 |
130 | 14 | 13.1652959222286 | 0.83470407777136 |
131 | 11 | 10.3025715029087 | 0.697428497091296 |
132 | 9 | 10.6344308996886 | -1.63443089968863 |
133 | 9 | 9.79495267551176 | -0.79495267551176 |
134 | 8 | 10.1489480614945 | -2.14894806149447 |
135 | 10 | 12.0879439372136 | -2.08794393721360 |
136 | 13 | 11.2623617849926 | 1.73763821500737 |
137 | 13 | 10.2205219792016 | 2.77947802079842 |
138 | 12 | 9.19521483931041 | 2.80478516068959 |
139 | 8 | 10.2804355137059 | -2.28043551370592 |
140 | 13 | 10.5112361961302 | 2.48876380386983 |
141 | 14 | 11.8103783882423 | 2.18962161175772 |
142 | 12 | 11.6101202047058 | 0.389879795294225 |
143 | 14 | 11.1463545121537 | 2.85364548784626 |
144 | 15 | 10.9378876636718 | 4.06211233632824 |
145 | 13 | 10.7502403277880 | 2.24975967221197 |
146 | 16 | 11.7114660632203 | 4.28853393677966 |
147 | 9 | 12.2416514623354 | -3.24165146233536 |
148 | 9 | 10.3688060873901 | -1.36880608739013 |
149 | 9 | 10.9908122034697 | -1.99081220346971 |
150 | 8 | 11.2951532865651 | -3.29515328656511 |
151 | 7 | 9.72975263918785 | -2.72975263918785 |
152 | 16 | 12.2471045565930 | 3.75289544340698 |
153 | 11 | 14.1601974783457 | -3.1601974783457 |
154 | 9 | 10.2246601718317 | -1.22466017183167 |
155 | 11 | 10.2152354773820 | 0.78476452261799 |
156 | 9 | 10.0987924063159 | -1.09879240631595 |
157 | 14 | 12.2471045565930 | 1.75289544340698 |
158 | 13 | 11.1219166888601 | 1.87808331113989 |
159 | 16 | 14.5672839965644 | 1.43271600343556 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 0.235589506033171 | 0.471179012066341 | 0.76441049396683 |
9 | 0.342818818118287 | 0.685637636236574 | 0.657181181881713 |
10 | 0.216789627380673 | 0.433579254761347 | 0.783210372619327 |
11 | 0.223937467206284 | 0.447874934412568 | 0.776062532793716 |
12 | 0.220808547103293 | 0.441617094206587 | 0.779191452896707 |
13 | 0.73773410253037 | 0.524531794939260 | 0.262265897469630 |
14 | 0.665403506201861 | 0.669192987596278 | 0.334596493798139 |
15 | 0.59293297471546 | 0.81413405056908 | 0.40706702528454 |
16 | 0.703434262151917 | 0.593131475696165 | 0.296565737848083 |
17 | 0.651376517986246 | 0.697246964027508 | 0.348623482013754 |
18 | 0.639394034048031 | 0.721211931903938 | 0.360605965951969 |
19 | 0.618323437398896 | 0.763353125202208 | 0.381676562601104 |
20 | 0.570876615192512 | 0.858246769614975 | 0.429123384807488 |
21 | 0.614211303342006 | 0.771577393315988 | 0.385788696657994 |
22 | 0.557711427084538 | 0.884577145830925 | 0.442288572915462 |
23 | 0.580037847299371 | 0.839924305401258 | 0.419962152700629 |
24 | 0.516703110098772 | 0.966593779802457 | 0.483296889901228 |
25 | 0.44724761082293 | 0.89449522164586 | 0.55275238917707 |
26 | 0.394895264410714 | 0.789790528821429 | 0.605104735589286 |
27 | 0.335595508434919 | 0.671191016869838 | 0.664404491565081 |
28 | 0.335612964296846 | 0.671225928593692 | 0.664387035703154 |
29 | 0.300167613269913 | 0.600335226539827 | 0.699832386730087 |
30 | 0.247377970434517 | 0.494755940869033 | 0.752622029565483 |
31 | 0.209704921176245 | 0.419409842352491 | 0.790295078823755 |
32 | 0.264843772357165 | 0.52968754471433 | 0.735156227642835 |
33 | 0.227487134881908 | 0.454974269763817 | 0.772512865118092 |
34 | 0.213565404880003 | 0.427130809760006 | 0.786434595119997 |
35 | 0.172389738074743 | 0.344779476149487 | 0.827610261925257 |
36 | 0.215966629276413 | 0.431933258552825 | 0.784033370723587 |
37 | 0.198861663572392 | 0.397723327144784 | 0.801138336427608 |
38 | 0.572142554759667 | 0.855714890480666 | 0.427857445240333 |
39 | 0.521822365677327 | 0.956355268645346 | 0.478177634322673 |
40 | 0.493144137956084 | 0.986288275912168 | 0.506855862043916 |
41 | 0.446619002185238 | 0.893238004370475 | 0.553380997814762 |
42 | 0.413288765850545 | 0.82657753170109 | 0.586711234149455 |
43 | 0.371759675422921 | 0.743519350845843 | 0.628240324577078 |
44 | 0.322842550221853 | 0.645685100443707 | 0.677157449778147 |
45 | 0.277156990653631 | 0.554313981307262 | 0.72284300934637 |
46 | 0.264584440408213 | 0.529168880816425 | 0.735415559591787 |
47 | 0.254071789037173 | 0.508143578074347 | 0.745928210962827 |
48 | 0.244186753078403 | 0.488373506156807 | 0.755813246921597 |
49 | 0.242094385941828 | 0.484188771883655 | 0.757905614058172 |
50 | 0.28515494697261 | 0.57030989394522 | 0.71484505302739 |
51 | 0.360061535483996 | 0.720123070967992 | 0.639938464516004 |
52 | 0.329822271101935 | 0.65964454220387 | 0.670177728898065 |
53 | 0.305238207388361 | 0.610476414776722 | 0.694761792611639 |
54 | 0.309637640390206 | 0.619275280780411 | 0.690362359609794 |
55 | 0.335346018810081 | 0.670692037620161 | 0.66465398118992 |
56 | 0.293035451789950 | 0.586070903579899 | 0.70696454821005 |
57 | 0.255824641382392 | 0.511649282764784 | 0.744175358617608 |
58 | 0.224832480944034 | 0.449664961888068 | 0.775167519055966 |
59 | 0.209040074410851 | 0.418080148821702 | 0.790959925589149 |
60 | 0.333571347503498 | 0.667142695006996 | 0.666428652496502 |
61 | 0.293963541095796 | 0.587927082191593 | 0.706036458904204 |
62 | 0.255290341867435 | 0.51058068373487 | 0.744709658132565 |
63 | 0.233108431501274 | 0.466216863002547 | 0.766891568498726 |
64 | 0.259642331638994 | 0.519284663277988 | 0.740357668361006 |
65 | 0.234542204496860 | 0.469084408993721 | 0.76545779550314 |
66 | 0.202186609794219 | 0.404373219588438 | 0.797813390205781 |
67 | 0.363171118834518 | 0.726342237669035 | 0.636828881165482 |
68 | 0.319797590559764 | 0.639595181119527 | 0.680202409440236 |
69 | 0.404860037524773 | 0.809720075049546 | 0.595139962475227 |
70 | 0.364329294797118 | 0.728658589594236 | 0.635670705202882 |
71 | 0.488108032847822 | 0.976216065695644 | 0.511891967152178 |
72 | 0.458478233259545 | 0.916956466519089 | 0.541521766740455 |
73 | 0.496375459379312 | 0.992750918758623 | 0.503624540620688 |
74 | 0.485645266293597 | 0.971290532587194 | 0.514354733706403 |
75 | 0.48653581989566 | 0.97307163979132 | 0.51346418010434 |
76 | 0.457323389289663 | 0.914646778579326 | 0.542676610710337 |
77 | 0.579774700835159 | 0.840450598329682 | 0.420225299164841 |
78 | 0.540515900006416 | 0.918968199987168 | 0.459484099993584 |
79 | 0.504147456936067 | 0.991705086127867 | 0.495852543063933 |
80 | 0.461863308514521 | 0.923726617029041 | 0.538136691485479 |
81 | 0.46818406420157 | 0.93636812840314 | 0.53181593579843 |
82 | 0.638507482149569 | 0.722985035700863 | 0.361492517850431 |
83 | 0.597049953518176 | 0.805900092963648 | 0.402950046481824 |
84 | 0.587188293609786 | 0.825623412780428 | 0.412811706390214 |
85 | 0.564313354570428 | 0.871373290859144 | 0.435686645429572 |
86 | 0.518613333268896 | 0.962773333462207 | 0.481386666731104 |
87 | 0.4722170653416 | 0.9444341306832 | 0.5277829346584 |
88 | 0.560670321460608 | 0.878659357078783 | 0.439329678539392 |
89 | 0.51507135925827 | 0.96985728148346 | 0.48492864074173 |
90 | 0.476070044753591 | 0.952140089507183 | 0.523929955246409 |
91 | 0.43366398403397 | 0.86732796806794 | 0.56633601596603 |
92 | 0.479635231525602 | 0.959270463051204 | 0.520364768474398 |
93 | 0.436930012425028 | 0.873860024850056 | 0.563069987574972 |
94 | 0.392838407710917 | 0.785676815421835 | 0.607161592289083 |
95 | 0.378806788846362 | 0.757613577692724 | 0.621193211153638 |
96 | 0.363988468216653 | 0.727976936433305 | 0.636011531783347 |
97 | 0.348851025826101 | 0.697702051652201 | 0.6511489741739 |
98 | 0.306803657906248 | 0.613607315812496 | 0.693196342093752 |
99 | 0.286186693114404 | 0.572373386228807 | 0.713813306885596 |
100 | 0.258917305742133 | 0.517834611484266 | 0.741082694257867 |
101 | 0.228138003304278 | 0.456276006608557 | 0.771861996695722 |
102 | 0.226290472003373 | 0.452580944006746 | 0.773709527996627 |
103 | 0.200408991796687 | 0.400817983593373 | 0.799591008203313 |
104 | 0.195538689376072 | 0.391077378752144 | 0.804461310623928 |
105 | 0.170482449693594 | 0.340964899387189 | 0.829517550306406 |
106 | 0.166118642336269 | 0.332237284672537 | 0.833881357663731 |
107 | 0.172873395227815 | 0.345746790455630 | 0.827126604772185 |
108 | 0.171712629452345 | 0.343425258904691 | 0.828287370547655 |
109 | 0.160755339583248 | 0.321510679166497 | 0.839244660416752 |
110 | 0.176160338063148 | 0.352320676126297 | 0.823839661936852 |
111 | 0.161029826226595 | 0.32205965245319 | 0.838970173773405 |
112 | 0.367626060365253 | 0.735252120730505 | 0.632373939634747 |
113 | 0.369610873904905 | 0.73922174780981 | 0.630389126095095 |
114 | 0.345690559558931 | 0.691381119117863 | 0.654309440441069 |
115 | 0.305500010037403 | 0.611000020074807 | 0.694499989962597 |
116 | 0.280031343751001 | 0.560062687502003 | 0.719968656248999 |
117 | 0.302416655324319 | 0.604833310648638 | 0.697583344675681 |
118 | 0.267756133198954 | 0.535512266397908 | 0.732243866801046 |
119 | 0.244186556429497 | 0.488373112858995 | 0.755813443570503 |
120 | 0.204927181546315 | 0.409854363092631 | 0.795072818453685 |
121 | 0.170933679438313 | 0.341867358876625 | 0.829066320561687 |
122 | 0.152767440045206 | 0.305534880090411 | 0.847232559954794 |
123 | 0.170194283419401 | 0.340388566838803 | 0.829805716580599 |
124 | 0.153260525842903 | 0.306521051685806 | 0.846739474157097 |
125 | 0.777018655569678 | 0.445962688860644 | 0.222981344430322 |
126 | 0.7302031790998 | 0.539593641800401 | 0.269796820900201 |
127 | 0.683783645446439 | 0.632432709107123 | 0.316216354553561 |
128 | 0.628603078023767 | 0.742793843952465 | 0.371396921976233 |
129 | 0.569952302350397 | 0.860095395299207 | 0.430047697649604 |
130 | 0.509859555505773 | 0.980280888988454 | 0.490140444494227 |
131 | 0.449768159031913 | 0.899536318063825 | 0.550231840968087 |
132 | 0.397268396252225 | 0.79453679250445 | 0.602731603747775 |
133 | 0.338502315733256 | 0.677004631466513 | 0.661497684266744 |
134 | 0.301943763009144 | 0.603887526018288 | 0.698056236990856 |
135 | 0.268161895235183 | 0.536323790470367 | 0.731838104764817 |
136 | 0.223333251537706 | 0.446666503075413 | 0.776666748462294 |
137 | 0.232225226645593 | 0.464450453291185 | 0.767774773354407 |
138 | 0.224873655694368 | 0.449747311388737 | 0.775126344305632 |
139 | 0.220587122987082 | 0.441174245974164 | 0.779412877012918 |
140 | 0.192896607291697 | 0.385793214583393 | 0.807103392708303 |
141 | 0.195930784657198 | 0.391861569314397 | 0.804069215342802 |
142 | 0.144739436343638 | 0.289478872687276 | 0.855260563656362 |
143 | 0.179916487793164 | 0.359832975586329 | 0.820083512206836 |
144 | 0.205977498852605 | 0.41195499770521 | 0.794022501147395 |
145 | 0.174092086256251 | 0.348184172512503 | 0.825907913743749 |
146 | 0.365779709003272 | 0.731559418006544 | 0.634220290996728 |
147 | 0.333267838520732 | 0.666535677041463 | 0.666732161479268 |
148 | 0.239512993705293 | 0.479025987410587 | 0.760487006294707 |
149 | 0.186035428981169 | 0.372070857962339 | 0.81396457101883 |
150 | 0.262533562656282 | 0.525067125312564 | 0.737466437343718 |
151 | 0.252524953019549 | 0.505049906039097 | 0.747475046980451 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 0 | 0 | OK |
5% type I error level | 0 | 0 | OK |
10% type I error level | 0 | 0 | OK |