Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 6.80689662687928 + 0.337375488932305CM[t] -0.374730059936112D[t] + 0.174440171909908PE[t] + 0.0466548470870721PC[t] + 0.420990395069853O[t] + 0.0111700079917458`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) | 6.80689662687928 | 3.073786 | 2.2145 | 0.028283 | 0.014141 |
CM | 0.337375488932305 | 0.056942 | 5.9249 | 0 | 0 |
D | -0.374730059936112 | 0.115686 | -3.2392 | 0.001472 | 0.000736 |
PE | 0.174440171909908 | 0.101377 | 1.7207 | 0.08734 | 0.04367 |
PC | 0.0466548470870721 | 0.128182 | 0.364 | 0.716384 | 0.358192 |
O | 0.420990395069853 | 0.073288 | 5.7443 | 0 | 0 |
`H ` | 0.0111700079917458 | 0.125735 | 0.0888 | 0.929328 | 0.464664 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.613973533520472 |
R-squared | 0.376963499863614 |
Adjusted R-squared | 0.352369953805598 |
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 | 23.1938379299364 | 0.806162070063634 |
2 | 25 | 22.5527323694467 | 2.44726763055333 |
3 | 30 | 24.3584412988746 | 5.64155870112544 |
4 | 19 | 20.3508644107059 | -1.35086441070588 |
5 | 22 | 20.5948682850530 | 1.40513171494695 |
6 | 22 | 23.2090613878984 | -1.20906138789839 |
7 | 25 | 22.6272170981275 | 2.37278290187246 |
8 | 23 | 19.5679474477758 | 3.43205255222421 |
9 | 17 | 18.6438192086904 | -1.64381920869036 |
10 | 21 | 21.6733554165168 | -0.673355416516813 |
11 | 19 | 22.9460422505056 | -3.94604225050558 |
12 | 19 | 23.4343690281779 | -4.43436902817787 |
13 | 15 | 23.3722515581343 | -8.37225155813432 |
14 | 16 | 16.9717712421553 | -0.97177124215531 |
15 | 23 | 19.4780877886769 | 3.52191221132312 |
16 | 27 | 24.1261554111432 | 2.87384458885678 |
17 | 22 | 21.0629145233035 | 0.937085476696499 |
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 | -3.53155515827944 |
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 | 0.0933175832017827 |
29 | 22 | 21.590029939121 | 0.409970060879012 |
30 | 26 | 23.3698131165580 | 2.63018688344197 |
31 | 29 | 22.5640332327775 | 6.43596676722253 |
32 | 32 | 25.3444493518572 | 6.65555064814283 |
33 | 25 | 21.5634343618986 | 3.43656563810136 |
34 | 29 | 24.5257423031722 | 4.47425769682777 |
35 | 28 | 25.0974865434727 | 2.90251345652734 |
36 | 17 | 16.9418221257969 | 0.0581778742030896 |
37 | 28 | 26.1905915923489 | 1.80940840765113 |
38 | 29 | 22.9812083059895 | 6.01879169401047 |
39 | 26 | 27.7706385200149 | -1.77063852001489 |
40 | 25 | 23.5689720809701 | 1.43102791902985 |
41 | 14 | 19.3795629717581 | -5.37956297175806 |
42 | 25 | 22.0555255997719 | 2.94447440022810 |
43 | 26 | 21.7527354924592 | 4.24726450754078 |
44 | 20 | 20.3551589059586 | -0.355158905958583 |
45 | 18 | 21.4435360136149 | -3.44353601361492 |
46 | 32 | 24.7594271138453 | 7.2405728861547 |
47 | 25 | 25.1715052606450 | -0.171505260645026 |
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 | -1.52762096048366 |
55 | 26 | 24.4714984024148 | 1.52850159758519 |
56 | 24 | 21.7070397679054 | 2.29296023209459 |
57 | 22 | 21.5952738480639 | 0.404726151936134 |
58 | 14 | 15.4647300334008 | -1.46473003340083 |
59 | 24 | 22.3751950826285 | 1.62480491737149 |
60 | 24 | 22.9411121980170 | 1.05888780198303 |
61 | 24 | 23.3996176835730 | 0.600382316426967 |
62 | 24 | 20.1060692570986 | 3.89393074290137 |
63 | 19 | 18.4581362657519 | 0.54186373424815 |
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 | -0.783760449496019 |
74 | 20 | 22.3164415449032 | -2.31644154490324 |
75 | 22 | 22.4948867833241 | -0.49488678332412 |
76 | 23 | 23.1806722460821 | -0.18067224608207 |
77 | 25 | 24.0413497385003 | 0.958650261499702 |
78 | 25 | 23.5553635017032 | 1.44463649829677 |
79 | 17 | 24.0589961434255 | -7.05899614342552 |
80 | 19 | 21.4206409661957 | -2.42064096619569 |
81 | 25 | 24.0966467570101 | 0.903353242989863 |
82 | 19 | 22.4163783827431 | -3.41637838274309 |
83 | 20 | 23.1586975168811 | -3.15869751688114 |
84 | 26 | 22.5902570390771 | 3.40974296092294 |
85 | 23 | 20.9631200385294 | 2.03687996147055 |
86 | 27 | 24.5966889949657 | 2.40331100503427 |
87 | 17 | 20.8979447261035 | -3.89794472610345 |
88 | 17 | 23.4526693089768 | -6.45266930897682 |
89 | 17 | 19.7140987636228 | -2.71409876362277 |
90 | 22 | 21.9657464664732 | 0.0342535335268337 |
91 | 21 | 23.7753115338017 | -2.77531153380174 |
92 | 32 | 28.8769783672484 | 3.12302163275159 |
93 | 21 | 24.8242218519478 | -3.82422185194781 |
94 | 21 | 24.4050846865295 | -3.40508468652949 |
95 | 18 | 21.2391647620643 | -3.23916476206433 |
96 | 18 | 21.2445053897907 | -3.24450538979066 |
97 | 23 | 22.9107317388236 | 0.0892682611763867 |
98 | 19 | 20.6259781030955 | -1.62597810309549 |
99 | 20 | 20.8661440442532 | -0.866144044253178 |
100 | 21 | 22.4278148330794 | -1.42781483307940 |
101 | 20 | 24.0931439799901 | -4.0931439799901 |
102 | 17 | 18.5960751594744 | -1.59607515947442 |
103 | 18 | 20.3004839077328 | -2.3004839077328 |
104 | 19 | 20.7480145734531 | -1.74801457345309 |
105 | 22 | 22.1332173240308 | -0.133217324030847 |
106 | 15 | 18.6776186614073 | -3.67761866140732 |
107 | 14 | 18.8035111382256 | -4.80351113822563 |
108 | 18 | 26.877790354651 | -8.87779035465098 |
109 | 24 | 21.5421242854055 | 2.45787571459450 |
110 | 35 | 23.6068566870257 | 11.3931433129743 |
111 | 29 | 19.3316095513897 | 9.66839044861028 |
112 | 21 | 21.9570400261406 | -0.957040026140592 |
113 | 20 | 18.4365075353462 | 1.56349246465378 |
114 | 22 | 23.2805387990828 | -1.28053879908277 |
115 | 13 | 16.6661117736317 | -3.66611177363171 |
116 | 26 | 23.2946245417577 | 2.70537545824226 |
117 | 17 | 16.7313852461565 | 0.268614753843453 |
118 | 25 | 20.0599898632173 | 4.94001013678267 |
119 | 20 | 20.8885685919793 | -0.888568591979345 |
120 | 19 | 18.1256750113904 | 0.874324988609638 |
121 | 21 | 22.6102566438842 | -1.61025664388422 |
122 | 22 | 21.0943692063585 | 0.905630793641527 |
123 | 24 | 22.8377568056261 | 1.16224319437393 |
124 | 21 | 23.0965412425226 | -2.09654124252263 |
125 | 26 | 25.6784575868679 | 0.321542413132151 |
126 | 24 | 20.6110894920294 | 3.3889105079706 |
127 | 16 | 20.3072031663297 | -4.30720316632972 |
128 | 23 | 22.4462959254319 | 0.553704074568088 |
129 | 18 | 20.7804640883523 | -2.78046408835229 |
130 | 16 | 22.4501613332031 | -6.4501613332031 |
131 | 26 | 24.0583492564563 | 1.94165074354365 |
132 | 19 | 18.9575638072141 | 0.042436192785862 |
133 | 21 | 16.6997658148324 | 4.3002341851676 |
134 | 21 | 22.3289347474948 | -1.32893474749477 |
135 | 22 | 18.5175277092119 | 3.48247229078815 |
136 | 23 | 19.7332112775698 | 3.26678872243020 |
137 | 29 | 24.9550604445391 | 4.04493955546088 |
138 | 21 | 19.0989526203443 | 1.90104737965575 |
139 | 21 | 19.9183159798312 | 1.08168402016885 |
140 | 23 | 21.9283161671274 | 1.07168383287259 |
141 | 27 | 23.0540254140307 | 3.94597458596934 |
142 | 25 | 25.4223704008277 | -0.422370400827713 |
143 | 21 | 21.0146197079921 | -0.0146197079921060 |
144 | 10 | 16.9635948368745 | -6.96359483687448 |
145 | 20 | 22.7162157947920 | -2.71621579479203 |
146 | 26 | 22.7440503441452 | 3.25594965585483 |
147 | 24 | 23.7156705027973 | 0.284329497202719 |
148 | 29 | 31.8824036716209 | -2.88240367162088 |
149 | 19 | 18.8092832019323 | 0.190716798067711 |
150 | 24 | 22.1038802098397 | 1.89611979016025 |
151 | 19 | 20.6921991090226 | -1.69219910902255 |
152 | 24 | 23.5482497311530 | 0.451750268847021 |
153 | 22 | 21.8589864571611 | 0.141013542838921 |
154 | 17 | 23.9180546657576 | -6.9180546657576 |
155 | 24 | 23.1938379299365 | 0.806162070063483 |
156 | 25 | 22.5527323694467 | 2.44726763055334 |
157 | 30 | 24.3584412988746 | 5.64155870112545 |
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 | 0.304163125120191 | 0.847918437439904 |
11 | 0.452337356991705 | 0.90467471398341 | 0.547662643008295 |
12 | 0.388213520076801 | 0.776427040153603 | 0.611786479923199 |
13 | 0.72774522495959 | 0.54450955008082 | 0.27225477504041 |
14 | 0.639425170459595 | 0.72114965908081 | 0.360574829540405 |
15 | 0.546943098459527 | 0.906113803080946 | 0.453056901540473 |
16 | 0.450275285877095 | 0.90055057175419 | 0.549724714122905 |
17 | 0.491727830322886 | 0.983455660645771 | 0.508272169677114 |
18 | 0.402736491603866 | 0.805472983207732 | 0.597263508396134 |
19 | 0.319511209266562 | 0.639022418533124 | 0.680488790733438 |
20 | 0.26302363029507 | 0.52604726059014 | 0.73697636970493 |
21 | 0.328072028225222 | 0.656144056450444 | 0.671927971774778 |
22 | 0.267182130268775 | 0.534364260537549 | 0.732817869731225 |
23 | 0.310098016762844 | 0.620196033525688 | 0.689901983237156 |
24 | 0.297119319290263 | 0.594238638580525 | 0.702880680709737 |
25 | 0.236744935246064 | 0.473489870492129 | 0.763255064753936 |
26 | 0.186233548854765 | 0.37246709770953 | 0.813766451145235 |
27 | 0.163966296963311 | 0.327932593926622 | 0.83603370303669 |
28 | 0.133167677360551 | 0.266335354721101 | 0.86683232263945 |
29 | 0.107538425330602 | 0.215076850661203 | 0.892461574669398 |
30 | 0.109353898188991 | 0.218707796377982 | 0.89064610181101 |
31 | 0.262754405595824 | 0.525508811191647 | 0.737245594404176 |
32 | 0.543667633490031 | 0.912664733019938 | 0.456332366509969 |
33 | 0.51686654290675 | 0.9662669141865 | 0.48313345709325 |
34 | 0.561855210797745 | 0.87628957840451 | 0.438144789202255 |
35 | 0.531468575211131 | 0.937062849577737 | 0.468531424788869 |
36 | 0.507283411067722 | 0.985433177864556 | 0.492716588932278 |
37 | 0.480147248913498 | 0.960294497826996 | 0.519852751086502 |
38 | 0.580055828923481 | 0.839888342153038 | 0.419944171076519 |
39 | 0.606866947595257 | 0.786266104809487 | 0.393133052404743 |
40 | 0.557665975877922 | 0.884668048244156 | 0.442334024122078 |
41 | 0.597736703494942 | 0.804526593010117 | 0.402263296505058 |
42 | 0.565712783034667 | 0.868574433930666 | 0.434287216965333 |
43 | 0.595243569231538 | 0.809512861536925 | 0.404756430768462 |
44 | 0.546910405172956 | 0.906179189654089 | 0.453089594827044 |
45 | 0.534308113997382 | 0.931383772005236 | 0.465691886002618 |
46 | 0.655120065829546 | 0.689759868340908 | 0.344879934170454 |
47 | 0.62359228919704 | 0.75281542160592 | 0.37640771080296 |
48 | 0.609212712933452 | 0.781574574133096 | 0.390787287066548 |
49 | 0.565242477253371 | 0.869515045493258 | 0.434757522746629 |
50 | 0.522665017079655 | 0.95466996584069 | 0.477334982920345 |
51 | 0.582939217483258 | 0.834121565033484 | 0.417060782516742 |
52 | 0.545218339411399 | 0.909563321177203 | 0.454781660588601 |
53 | 0.595403437830661 | 0.809193124338677 | 0.404596562169339 |
54 | 0.56556297822273 | 0.868874043554541 | 0.434437021777271 |
55 | 0.522985056535732 | 0.954029886928536 | 0.477014943464268 |
56 | 0.490315071654591 | 0.980630143309183 | 0.509684928345409 |
57 | 0.441726326062757 | 0.883452652125515 | 0.558273673937243 |
58 | 0.401885733439674 | 0.803771466879348 | 0.598114266560326 |
59 | 0.367298137342021 | 0.734596274684041 | 0.63270186265798 |
60 | 0.325895728927786 | 0.651791457855571 | 0.674104271072214 |
61 | 0.284262193665279 | 0.568524387330558 | 0.71573780633472 |
62 | 0.299724557771075 | 0.599449115542151 | 0.700275442228925 |
63 | 0.261428901630255 | 0.522857803260511 | 0.738571098369745 |
64 | 0.26580440123006 | 0.53160880246012 | 0.73419559876994 |
65 | 0.360321377224498 | 0.720642754448997 | 0.639678622775502 |
66 | 0.448895721923045 | 0.89779144384609 | 0.551104278076955 |
67 | 0.411007696955101 | 0.822015393910203 | 0.588992303044899 |
68 | 0.389890735766869 | 0.779781471533738 | 0.610109264233131 |
69 | 0.471999191817478 | 0.943998383634956 | 0.528000808182522 |
70 | 0.426356301738342 | 0.852712603476683 | 0.573643698261658 |
71 | 0.387418702801506 | 0.774837405603011 | 0.612581297198494 |
72 | 0.357365532804649 | 0.714731065609297 | 0.642634467195351 |
73 | 0.324819324812948 | 0.649638649625896 | 0.675180675187052 |
74 | 0.304696665279569 | 0.609393330559139 | 0.69530333472043 |
75 | 0.265700496302875 | 0.53140099260575 | 0.734299503697125 |
76 | 0.229115117037877 | 0.458230234075755 | 0.770884882962123 |
77 | 0.200436082402065 | 0.40087216480413 | 0.799563917597935 |
78 | 0.175548368617213 | 0.351096737234426 | 0.824451631382787 |
79 | 0.287626527636521 | 0.575253055273042 | 0.712373472363479 |
80 | 0.265943273546381 | 0.531886547092763 | 0.734056726453619 |
81 | 0.231877933461132 | 0.463755866922265 | 0.768122066538867 |
82 | 0.230595632840884 | 0.461191265681769 | 0.769404367159116 |
83 | 0.229240437203921 | 0.458480874407842 | 0.770759562796079 |
84 | 0.230780344412659 | 0.461560688825317 | 0.769219655587341 |
85 | 0.209983013635230 | 0.419966027270460 | 0.79001698636477 |
86 | 0.195102568498852 | 0.390205136997704 | 0.804897431501148 |
87 | 0.202217159374713 | 0.404434318749426 | 0.797782840625287 |
88 | 0.299743741716408 | 0.599487483432817 | 0.700256258283592 |
89 | 0.279799467196004 | 0.559598934392009 | 0.720200532803996 |
90 | 0.24333774863356 | 0.48667549726712 | 0.75666225136644 |
91 | 0.230967455911562 | 0.461934911823124 | 0.769032544088438 |
92 | 0.225649470280327 | 0.451298940560653 | 0.774350529719673 |
93 | 0.232771486307609 | 0.465542972615218 | 0.767228513692391 |
94 | 0.229087213511671 | 0.458174427023342 | 0.770912786488329 |
95 | 0.219868614062428 | 0.439737228124855 | 0.780131385937572 |
96 | 0.212745507682769 | 0.425491015365538 | 0.787254492317231 |
97 | 0.179586439967164 | 0.359172879934329 | 0.820413560032836 |
98 | 0.154199292176411 | 0.308398584352821 | 0.84580070782359 |
99 | 0.127877935719618 | 0.255755871439236 | 0.872122064280382 |
100 | 0.107406561164754 | 0.214813122329507 | 0.892593438835246 |
101 | 0.119529831573143 | 0.239059663146285 | 0.880470168426857 |
102 | 0.0993795967937931 | 0.198759193587586 | 0.900620403206207 |
103 | 0.0881240918238203 | 0.176248183647641 | 0.91187590817618 |
104 | 0.076695689248106 | 0.153391378496212 | 0.923304310751894 |
105 | 0.0607958138954348 | 0.121591627790870 | 0.939204186104565 |
106 | 0.0600019237639285 | 0.120003847527857 | 0.939998076236072 |
107 | 0.0758206550231698 | 0.151641310046340 | 0.92417934497683 |
108 | 0.271128028956533 | 0.542256057913066 | 0.728871971043467 |
109 | 0.250684771183485 | 0.50136954236697 | 0.749315228816515 |
110 | 0.697817075758572 | 0.604365848482857 | 0.302182924241428 |
111 | 0.906547886023399 | 0.186904227953202 | 0.093452113976601 |
112 | 0.883225574503502 | 0.233548850992996 | 0.116774425496498 |
113 | 0.85998654658264 | 0.280026906834719 | 0.140013453417360 |
114 | 0.833416878070443 | 0.333166243859113 | 0.166583121929557 |
115 | 0.857597735214885 | 0.284804529570229 | 0.142402264785115 |
116 | 0.839959623386584 | 0.320080753226832 | 0.160040376613416 |
117 | 0.80419669594677 | 0.391606608106459 | 0.195803304053229 |
118 | 0.846911202071808 | 0.306177595856384 | 0.153088797928192 |
119 | 0.812525199021855 | 0.374949601956291 | 0.187474800978145 |
120 | 0.776141083673704 | 0.447717832652593 | 0.223858916326296 |
121 | 0.736494629908617 | 0.527010740182766 | 0.263505370091383 |
122 | 0.688584829734065 | 0.62283034053187 | 0.311415170265935 |
123 | 0.639642744195599 | 0.720714511608803 | 0.360357255804402 |
124 | 0.595179618530144 | 0.809640762939713 | 0.404820381469856 |
125 | 0.537464408785764 | 0.925071182428472 | 0.462535591214236 |
126 | 0.534549818756306 | 0.930900362487389 | 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 | 0.711881524217099 | 0.355940762108550 |
131 | 0.615148768436642 | 0.769702463126716 | 0.384851231563358 |
132 | 0.552844378593497 | 0.894311242813007 | 0.447155621406503 |
133 | 0.56390679329217 | 0.87218641341566 | 0.43609320670783 |
134 | 0.521090831414262 | 0.957818337171477 | 0.478909168585738 |
135 | 0.505370676694289 | 0.989258646611423 | 0.494629323305711 |
136 | 0.51068001172829 | 0.97863997654342 | 0.48931998827171 |
137 | 0.548340475253241 | 0.903319049493519 | 0.451659524746759 |
138 | 0.803743322159 | 0.392513355681999 | 0.196256677841000 |
139 | 0.740544028973054 | 0.518911942053893 | 0.259455971026946 |
140 | 0.677686389382796 | 0.644627221234408 | 0.322313610617204 |
141 | 0.720288336762336 | 0.559423326475328 | 0.279711663237664 |
142 | 0.72092458420698 | 0.55815083158604 | 0.27907541579302 |
143 | 0.630904741141985 | 0.738190517716031 | 0.369095258858015 |
144 | 0.763077086073737 | 0.473845827852526 | 0.236922913926263 |
145 | 0.748831576802837 | 0.502336846394327 | 0.251168423197163 |
146 | 0.643513687301472 | 0.712972625397057 | 0.356486312698528 |
147 | 0.639744992816221 | 0.720510014367559 | 0.360255007183779 |
148 | 0.591219617887186 | 0.817560764225627 | 0.408780382112814 |
149 | 0.50971702309122 | 0.98056595381756 | 0.49028297690878 |
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 |