Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 6.80689662687926 + 0.337375488932305CM[t] -0.374730059936113D[t] + 0.174440171909909PE[t] + 0.0466548470870712PC[t] + 0.420990395069853O[t] + 0.0111700079917464`H `[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) | 6.80689662687926 | 3.073786 | 2.2145 | 0.028283 | 0.014141 |
CM | 0.337375488932305 | 0.056942 | 5.9249 | 0 | 0 |
D | -0.374730059936113 | 0.115686 | -3.2392 | 0.001472 | 0.000736 |
PE | 0.174440171909909 | 0.101377 | 1.7207 | 0.08734 | 0.04367 |
PC | 0.0466548470870712 | 0.128182 | 0.364 | 0.716384 | 0.358192 |
O | 0.420990395069853 | 0.073288 | 5.7443 | 0 | 0 |
`H ` | 0.0111700079917464 | 0.125735 | 0.0888 | 0.929328 | 0.464664 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.613973533520472 |
R-squared | 0.376963499863614 |
Adjusted R-squared | 0.352369953805599 |
F-TEST (value) | 15.3277408216924 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 152 |
p-value | 1.07580611086178e-13 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.42600565680683 |
Sum Squared Residuals | 1784.10224359181 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 23.1938379299365 | 0.806162070063475 |
2 | 25 | 22.5527323694467 | 2.44726763055335 |
3 | 30 | 24.3584412988746 | 5.64155870112544 |
4 | 19 | 20.3508644107059 | -1.35086441070588 |
5 | 22 | 20.5948682850530 | 1.40513171494695 |
6 | 22 | 23.2090613878984 | -1.20906138789838 |
7 | 25 | 22.6272170981275 | 2.37278290187246 |
8 | 23 | 19.5679474477758 | 3.43205255222421 |
9 | 17 | 18.6438192086904 | -1.64381920869035 |
10 | 21 | 21.6733554165168 | -0.673355416516811 |
11 | 19 | 22.9460422505056 | -3.94604225050558 |
12 | 19 | 23.4343690281779 | -4.43436902817787 |
13 | 15 | 23.3722515581343 | -8.37225155813431 |
14 | 16 | 16.9717712421553 | -0.971771242155311 |
15 | 23 | 19.4780877886769 | 3.52191221132312 |
16 | 27 | 24.1261554111432 | 2.87384458885678 |
17 | 22 | 21.0629145233035 | 0.937085476696502 |
18 | 14 | 16.3476939858197 | -2.34769398581970 |
19 | 22 | 24.0976123636836 | -2.09761236368359 |
20 | 23 | 24.0965302143664 | -1.09653021436639 |
21 | 23 | 21.5751478121951 | 1.42485218780491 |
22 | 19 | 22.5315551582794 | -3.53155515827943 |
23 | 18 | 23.9537756229784 | -5.95377562297838 |
24 | 20 | 23.2976820748665 | -3.29768207486649 |
25 | 23 | 22.5037097663004 | 0.496290233699556 |
26 | 25 | 23.3831971527993 | 1.61680284720068 |
27 | 19 | 23.4334667832308 | -4.4334667832308 |
28 | 24 | 23.9066824167982 | 0.0933175832017823 |
29 | 22 | 21.590029939121 | 0.409970060879009 |
30 | 26 | 23.369813116558 | 2.63018688344198 |
31 | 29 | 22.5640332327775 | 6.43596676722252 |
32 | 32 | 25.3444493518572 | 6.65555064814283 |
33 | 25 | 21.5634343618986 | 3.43656563810136 |
34 | 29 | 24.5257423031722 | 4.47425769682777 |
35 | 28 | 25.0974865434727 | 2.90251345652733 |
36 | 17 | 16.9418221257969 | 0.0581778742030905 |
37 | 28 | 26.1905915923489 | 1.80940840765113 |
38 | 29 | 22.9812083059895 | 6.01879169401048 |
39 | 26 | 27.7706385200149 | -1.77063852001489 |
40 | 25 | 23.5689720809701 | 1.43102791902985 |
41 | 14 | 19.3795629717581 | -5.37956297175806 |
42 | 25 | 22.0555255997719 | 2.9444744002281 |
43 | 26 | 21.7527354924592 | 4.24726450754078 |
44 | 20 | 20.3551589059586 | -0.355158905958581 |
45 | 18 | 21.4435360136149 | -3.44353601361491 |
46 | 32 | 24.7594271138453 | 7.2405728861547 |
47 | 25 | 25.1715052606450 | -0.171505260645027 |
48 | 25 | 21.5983872856543 | 3.40161271434573 |
49 | 23 | 20.8460981816414 | 2.15390181835858 |
50 | 21 | 22.2337553214121 | -1.23375532141214 |
51 | 20 | 24.2400778356035 | -4.24007783560355 |
52 | 15 | 16.4063035063195 | -1.40630350631953 |
53 | 30 | 26.9514189183557 | 3.04858108164434 |
54 | 24 | 25.5276209604837 | -1.52762096048365 |
55 | 26 | 24.4714984024148 | 1.52850159758519 |
56 | 24 | 21.7070397679054 | 2.29296023209459 |
57 | 22 | 21.5952738480639 | 0.404726151936135 |
58 | 14 | 15.4647300334008 | -1.46473003340083 |
59 | 24 | 22.3751950826285 | 1.62480491737149 |
60 | 24 | 22.9411121980170 | 1.05888780198303 |
61 | 24 | 23.3996176835730 | 0.60038231642697 |
62 | 24 | 20.1060692570986 | 3.89393074290138 |
63 | 19 | 18.4581362657519 | 0.541863734248147 |
64 | 31 | 27.0134028612565 | 3.98659713874353 |
65 | 22 | 26.8534365895336 | -4.85343658953355 |
66 | 27 | 21.4490897730696 | 5.55091022693044 |
67 | 19 | 17.6772560383528 | 1.32274396164716 |
68 | 25 | 22.4167664105562 | 2.58323358944378 |
69 | 20 | 25.115944649428 | -5.11594464942802 |
70 | 21 | 21.5913350604495 | -0.591335060449544 |
71 | 27 | 27.7165573575398 | -0.716557357539801 |
72 | 23 | 24.4732905256934 | -1.47329052569339 |
73 | 25 | 25.783760449496 | -0.783760449496022 |
74 | 20 | 22.3164415449032 | -2.31644154490324 |
75 | 22 | 22.4948867833241 | -0.494886783324118 |
76 | 23 | 23.1806722460821 | -0.180672246082066 |
77 | 25 | 24.0413497385003 | 0.958650261499702 |
78 | 25 | 23.5553635017032 | 1.44463649829678 |
79 | 17 | 24.0589961434255 | -7.05899614342552 |
80 | 19 | 21.4206409661957 | -2.42064096619568 |
81 | 25 | 24.0966467570101 | 0.903353242989863 |
82 | 19 | 22.4163783827431 | -3.41637838274308 |
83 | 20 | 23.1586975168811 | -3.15869751688114 |
84 | 26 | 22.5902570390771 | 3.40974296092294 |
85 | 23 | 20.9631200385294 | 2.03687996147056 |
86 | 27 | 24.5966889949657 | 2.40331100503428 |
87 | 17 | 20.8979447261035 | -3.89794472610345 |
88 | 17 | 23.4526693089768 | -6.45266930897682 |
89 | 17 | 19.7140987636228 | -2.71409876362277 |
90 | 22 | 21.9657464664732 | 0.0342535335268300 |
91 | 21 | 23.7753115338017 | -2.77531153380173 |
92 | 32 | 28.8769783672484 | 3.12302163275159 |
93 | 21 | 24.8242218519478 | -3.82422185194781 |
94 | 21 | 24.4050846865295 | -3.40508468652948 |
95 | 18 | 21.2391647620643 | -3.23916476206433 |
96 | 18 | 21.2445053897907 | -3.24450538979066 |
97 | 23 | 22.9107317388236 | 0.0892682611763867 |
98 | 19 | 20.6259781030955 | -1.62597810309550 |
99 | 20 | 20.8661440442532 | -0.866144044253181 |
100 | 21 | 22.4278148330794 | -1.42781483307941 |
101 | 20 | 24.0931439799901 | -4.0931439799901 |
102 | 17 | 18.5960751594744 | -1.59607515947442 |
103 | 18 | 20.3004839077328 | -2.30048390773280 |
104 | 19 | 20.7480145734531 | -1.74801457345310 |
105 | 22 | 22.1332173240308 | -0.133217324030845 |
106 | 15 | 18.6776186614073 | -3.67761866140732 |
107 | 14 | 18.8035111382256 | -4.80351113822563 |
108 | 18 | 26.8777903546510 | -8.87779035465097 |
109 | 24 | 21.5421242854055 | 2.4578757145945 |
110 | 35 | 23.6068566870257 | 11.3931433129743 |
111 | 29 | 19.3316095513897 | 9.66839044861029 |
112 | 21 | 21.9570400261406 | -0.957040026140595 |
113 | 20 | 18.4365075353462 | 1.56349246465377 |
114 | 22 | 23.2805387990828 | -1.28053879908277 |
115 | 13 | 16.6661117736317 | -3.66611177363172 |
116 | 26 | 23.2946245417577 | 2.70537545824226 |
117 | 17 | 16.7313852461565 | 0.268614753843451 |
118 | 25 | 20.0599898632173 | 4.94001013678267 |
119 | 20 | 20.8885685919793 | -0.888568591979344 |
120 | 19 | 18.1256750113904 | 0.874324988609644 |
121 | 21 | 22.6102566438842 | -1.61025664388422 |
122 | 22 | 21.0943692063585 | 0.905630793641523 |
123 | 24 | 22.8377568056261 | 1.16224319437393 |
124 | 21 | 23.0965412425226 | -2.09654124252263 |
125 | 26 | 25.6784575868678 | 0.321542413132153 |
126 | 24 | 20.6110894920294 | 3.38891050797060 |
127 | 16 | 20.3072031663297 | -4.30720316632972 |
128 | 23 | 22.4462959254319 | 0.553704074568086 |
129 | 18 | 20.7804640883523 | -2.78046408835229 |
130 | 16 | 22.4501613332031 | -6.45016133320309 |
131 | 26 | 24.0583492564563 | 1.94165074354365 |
132 | 19 | 18.9575638072141 | 0.0424361927858609 |
133 | 21 | 16.6997658148324 | 4.30023418516759 |
134 | 21 | 22.3289347474948 | -1.32893474749477 |
135 | 22 | 18.5175277092118 | 3.48247229078815 |
136 | 23 | 19.7332112775698 | 3.2667887224302 |
137 | 29 | 24.9550604445391 | 4.04493955546088 |
138 | 21 | 19.0989526203442 | 1.90104737965575 |
139 | 21 | 19.9183159798311 | 1.08168402016885 |
140 | 23 | 21.9283161671274 | 1.07168383287259 |
141 | 27 | 23.0540254140307 | 3.94597458596934 |
142 | 25 | 25.4223704008277 | -0.422370400827714 |
143 | 21 | 21.0146197079921 | -0.0146197079921077 |
144 | 10 | 16.9635948368745 | -6.96359483687447 |
145 | 20 | 22.7162157947920 | -2.71621579479203 |
146 | 26 | 22.7440503441452 | 3.25594965585483 |
147 | 24 | 23.7156705027973 | 0.284329497202718 |
148 | 29 | 31.8824036716209 | -2.88240367162089 |
149 | 19 | 18.8092832019323 | 0.190716798067704 |
150 | 24 | 22.1038802098397 | 1.89611979016026 |
151 | 19 | 20.6921991090226 | -1.69219910902255 |
152 | 24 | 23.5482497311530 | 0.451750268847024 |
153 | 22 | 21.8589864571611 | 0.141013542838923 |
154 | 17 | 23.9180546657576 | -6.91805466575759 |
155 | 24 | 23.1938379299365 | 0.806162070063492 |
156 | 25 | 22.5527323694467 | 2.44726763055334 |
157 | 30 | 24.3584412988746 | 5.64155870112544 |
158 | 19 | 20.3508644107059 | -1.35086441070588 |
159 | 22 | 20.5948682850530 | 1.40513171494695 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.152081562560096 | 0.304163125120192 | 0.847918437439904 |
11 | 0.452337356991705 | 0.90467471398341 | 0.547662643008295 |
12 | 0.388213520076802 | 0.776427040153604 | 0.611786479923198 |
13 | 0.72774522495959 | 0.54450955008082 | 0.27225477504041 |
14 | 0.639425170459596 | 0.721149659080809 | 0.360574829540404 |
15 | 0.546943098459525 | 0.90611380308095 | 0.453056901540475 |
16 | 0.450275285877095 | 0.90055057175419 | 0.549724714122905 |
17 | 0.491727830322884 | 0.983455660645769 | 0.508272169677116 |
18 | 0.402736491603864 | 0.805472983207727 | 0.597263508396136 |
19 | 0.31951120926656 | 0.63902241853312 | 0.68048879073344 |
20 | 0.263023630295069 | 0.526047260590139 | 0.73697636970493 |
21 | 0.328072028225221 | 0.656144056450442 | 0.671927971774779 |
22 | 0.267182130268775 | 0.53436426053755 | 0.732817869731225 |
23 | 0.310098016762845 | 0.62019603352569 | 0.689901983237155 |
24 | 0.297119319290263 | 0.594238638580525 | 0.702880680709737 |
25 | 0.236744935246065 | 0.473489870492131 | 0.763255064753935 |
26 | 0.186233548854765 | 0.37246709770953 | 0.813766451145235 |
27 | 0.163966296963311 | 0.327932593926621 | 0.83603370303669 |
28 | 0.13316767736055 | 0.2663353547211 | 0.86683232263945 |
29 | 0.107538425330600 | 0.215076850661201 | 0.8924615746694 |
30 | 0.109353898188990 | 0.218707796377979 | 0.89064610181101 |
31 | 0.262754405595823 | 0.525508811191646 | 0.737245594404177 |
32 | 0.543667633490033 | 0.912664733019934 | 0.456332366509967 |
33 | 0.51686654290675 | 0.9662669141865 | 0.48313345709325 |
34 | 0.561855210797746 | 0.876289578404507 | 0.438144789202254 |
35 | 0.531468575211132 | 0.937062849577735 | 0.468531424788868 |
36 | 0.50728341106772 | 0.98543317786456 | 0.49271658893228 |
37 | 0.480147248913496 | 0.960294497826991 | 0.519852751086504 |
38 | 0.58005582892348 | 0.83988834215304 | 0.41994417107652 |
39 | 0.60686694759526 | 0.78626610480948 | 0.39313305240474 |
40 | 0.55766597587792 | 0.88466804824416 | 0.44233402412208 |
41 | 0.597736703494942 | 0.804526593010116 | 0.402263296505058 |
42 | 0.565712783034664 | 0.868574433930672 | 0.434287216965336 |
43 | 0.595243569231536 | 0.809512861536928 | 0.404756430768464 |
44 | 0.546910405172955 | 0.90617918965409 | 0.453089594827045 |
45 | 0.53430811399738 | 0.93138377200524 | 0.46569188600262 |
46 | 0.655120065829547 | 0.689759868340906 | 0.344879934170453 |
47 | 0.623592289197042 | 0.752815421605916 | 0.376407710802958 |
48 | 0.609212712933453 | 0.781574574133094 | 0.390787287066547 |
49 | 0.565242477253369 | 0.869515045493261 | 0.434757522746631 |
50 | 0.522665017079657 | 0.954669965840687 | 0.477334982920343 |
51 | 0.582939217483258 | 0.834121565033484 | 0.417060782516742 |
52 | 0.5452183394114 | 0.9095633211772 | 0.4547816605886 |
53 | 0.595403437830661 | 0.809193124338678 | 0.404596562169339 |
54 | 0.565562978222728 | 0.868874043554545 | 0.434437021777272 |
55 | 0.522985056535733 | 0.954029886928534 | 0.477014943464267 |
56 | 0.490315071654591 | 0.980630143309182 | 0.509684928345409 |
57 | 0.441726326062757 | 0.883452652125514 | 0.558273673937243 |
58 | 0.401885733439674 | 0.803771466879348 | 0.598114266560326 |
59 | 0.367298137342021 | 0.734596274684042 | 0.632701862657979 |
60 | 0.325895728927786 | 0.651791457855572 | 0.674104271072214 |
61 | 0.284262193665279 | 0.568524387330559 | 0.715737806334721 |
62 | 0.299724557771075 | 0.599449115542151 | 0.700275442228924 |
63 | 0.261428901630255 | 0.522857803260509 | 0.738571098369745 |
64 | 0.265804401230059 | 0.531608802460117 | 0.734195598769941 |
65 | 0.360321377224498 | 0.720642754448997 | 0.639678622775501 |
66 | 0.448895721923045 | 0.89779144384609 | 0.551104278076955 |
67 | 0.4110076969551 | 0.8220153939102 | 0.5889923030449 |
68 | 0.38989073576687 | 0.77978147153374 | 0.61010926423313 |
69 | 0.47199919181748 | 0.94399838363496 | 0.52800080818252 |
70 | 0.426356301738342 | 0.852712603476684 | 0.573643698261658 |
71 | 0.387418702801505 | 0.77483740560301 | 0.612581297198495 |
72 | 0.357365532804649 | 0.714731065609298 | 0.642634467195351 |
73 | 0.324819324812949 | 0.649638649625899 | 0.67518067518705 |
74 | 0.304696665279571 | 0.609393330559141 | 0.69530333472043 |
75 | 0.265700496302874 | 0.531400992605748 | 0.734299503697126 |
76 | 0.229115117037878 | 0.458230234075757 | 0.770884882962122 |
77 | 0.200436082402063 | 0.400872164804126 | 0.799563917597937 |
78 | 0.175548368617216 | 0.351096737234432 | 0.824451631382784 |
79 | 0.28762652763652 | 0.57525305527304 | 0.71237347236348 |
80 | 0.265943273546382 | 0.531886547092764 | 0.734056726453618 |
81 | 0.231877933461133 | 0.463755866922265 | 0.768122066538867 |
82 | 0.230595632840887 | 0.461191265681773 | 0.769404367159113 |
83 | 0.229240437203919 | 0.458480874407838 | 0.770759562796081 |
84 | 0.23078034441266 | 0.46156068882532 | 0.76921965558734 |
85 | 0.209983013635230 | 0.419966027270461 | 0.79001698636477 |
86 | 0.19510256849885 | 0.3902051369977 | 0.80489743150115 |
87 | 0.202217159374712 | 0.404434318749423 | 0.797782840625288 |
88 | 0.299743741716408 | 0.599487483432816 | 0.700256258283592 |
89 | 0.279799467196003 | 0.559598934392007 | 0.720200532803997 |
90 | 0.243337748633561 | 0.486675497267121 | 0.75666225136644 |
91 | 0.230967455911560 | 0.461934911823121 | 0.76903254408844 |
92 | 0.225649470280327 | 0.451298940560653 | 0.774350529719673 |
93 | 0.232771486307608 | 0.465542972615216 | 0.767228513692392 |
94 | 0.229087213511668 | 0.458174427023336 | 0.770912786488332 |
95 | 0.219868614062428 | 0.439737228124857 | 0.780131385937572 |
96 | 0.212745507682768 | 0.425491015365535 | 0.787254492317232 |
97 | 0.179586439967165 | 0.359172879934331 | 0.820413560032835 |
98 | 0.154199292176412 | 0.308398584352824 | 0.845800707823588 |
99 | 0.127877935719618 | 0.255755871439236 | 0.872122064280382 |
100 | 0.107406561164753 | 0.214813122329506 | 0.892593438835247 |
101 | 0.119529831573143 | 0.239059663146286 | 0.880470168426857 |
102 | 0.0993795967937933 | 0.198759193587587 | 0.900620403206207 |
103 | 0.0881240918238202 | 0.176248183647640 | 0.91187590817618 |
104 | 0.0766956892481051 | 0.153391378496210 | 0.923304310751895 |
105 | 0.0607958138954348 | 0.121591627790870 | 0.939204186104565 |
106 | 0.0600019237639292 | 0.120003847527858 | 0.93999807623607 |
107 | 0.0758206550231696 | 0.151641310046339 | 0.92417934497683 |
108 | 0.271128028956533 | 0.542256057913066 | 0.728871971043467 |
109 | 0.250684771183485 | 0.50136954236697 | 0.749315228816515 |
110 | 0.69781707575857 | 0.60436584848286 | 0.30218292424143 |
111 | 0.906547886023399 | 0.186904227953202 | 0.093452113976601 |
112 | 0.883225574503502 | 0.233548850992996 | 0.116774425496498 |
113 | 0.85998654658264 | 0.280026906834719 | 0.140013453417360 |
114 | 0.833416878070445 | 0.33316624385911 | 0.166583121929555 |
115 | 0.857597735214886 | 0.284804529570228 | 0.142402264785114 |
116 | 0.839959623386584 | 0.320080753226833 | 0.160040376613416 |
117 | 0.804196695946771 | 0.391606608106458 | 0.195803304053229 |
118 | 0.846911202071809 | 0.306177595856382 | 0.153088797928191 |
119 | 0.812525199021854 | 0.374949601956291 | 0.187474800978146 |
120 | 0.776141083673704 | 0.447717832652592 | 0.223858916326296 |
121 | 0.736494629908617 | 0.527010740182765 | 0.263505370091383 |
122 | 0.688584829734065 | 0.622830340531869 | 0.311415170265935 |
123 | 0.639642744195598 | 0.720714511608804 | 0.360357255804402 |
124 | 0.595179618530144 | 0.809640762939711 | 0.404820381469856 |
125 | 0.537464408785764 | 0.925071182428473 | 0.462535591214236 |
126 | 0.534549818756306 | 0.930900362487387 | 0.465450181243694 |
127 | 0.570829755077969 | 0.858340489844063 | 0.429170244922031 |
128 | 0.508115228685312 | 0.983769542629375 | 0.491884771314688 |
129 | 0.468187017304523 | 0.936374034609046 | 0.531812982695477 |
130 | 0.64405923789145 | 0.7118815242171 | 0.35594076210855 |
131 | 0.615148768436642 | 0.769702463126717 | 0.384851231563358 |
132 | 0.552844378593497 | 0.894311242813006 | 0.447155621406503 |
133 | 0.56390679329217 | 0.87218641341566 | 0.43609320670783 |
134 | 0.521090831414262 | 0.957818337171475 | 0.478909168585738 |
135 | 0.505370676694288 | 0.989258646611423 | 0.494629323305712 |
136 | 0.51068001172829 | 0.97863997654342 | 0.48931998827171 |
137 | 0.54834047525324 | 0.903319049493521 | 0.451659524746761 |
138 | 0.803743322159 | 0.392513355682 | 0.196256677841 |
139 | 0.740544028973054 | 0.518911942053892 | 0.259455971026946 |
140 | 0.677686389382795 | 0.64462722123441 | 0.322313610617205 |
141 | 0.720288336762335 | 0.55942332647533 | 0.279711663237665 |
142 | 0.720924584206979 | 0.558150831586042 | 0.279075415793021 |
143 | 0.630904741141986 | 0.738190517716027 | 0.369095258858014 |
144 | 0.763077086073738 | 0.473845827852523 | 0.236922913926262 |
145 | 0.748831576802836 | 0.502336846394328 | 0.251168423197164 |
146 | 0.643513687301471 | 0.712972625397058 | 0.356486312698529 |
147 | 0.639744992816221 | 0.720510014367558 | 0.360255007183779 |
148 | 0.591219617887185 | 0.81756076422563 | 0.408780382112815 |
149 | 0.509717023091222 | 0.980565953817557 | 0.490282976908778 |
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 |