Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 6.22294541070322 + 0.329668770012704CM[t] -0.307335861753657D[t] + 0.178919946656884PE[t] + 0.0935033736509635PC[t] + 0.407206747380311O[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) | 6.22294541070322 | 2.34676 | 2.6517 | 0.008893 | 0.004447 |
CM | 0.329668770012704 | 0.057216 | 5.7619 | 0 | 0 |
D | -0.307335861753657 | 0.110252 | -2.7876 | 0.006018 | 0.003009 |
PE | 0.178919946656884 | 0.102502 | 1.7455 | 0.082998 | 0.041499 |
PC | 0.0935033736509635 | 0.130989 | 0.7138 | 0.476473 | 0.238236 |
O | 0.407206747380311 | 0.074276 | 5.4824 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.617279978710385 |
R-squared | 0.381034572116694 |
Adjusted R-squared | 0.359837125956307 |
F-TEST (value) | 17.9754942757563 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 146 |
p-value | 7.23865412055602e-14 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.40954750236372 |
Sum Squared Residuals | 1697.2520689477 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 25 | 25.4532988015174 | -0.453298801517387 |
2 | 25 | 23.0680794340608 | 1.93192056593915 |
3 | 19 | 22.6517316308325 | -3.65173163083251 |
4 | 18 | 24.0429568620695 | -6.04295686206954 |
5 | 18 | 20.0535404745316 | -2.05354047453161 |
6 | 22 | 20.4237942998698 | 1.57620570013019 |
7 | 23 | 21.0325770794913 | 1.96742292050875 |
8 | 23 | 24.7881531544984 | -1.78815315449844 |
9 | 25 | 23.421800401002 | 1.57819959899801 |
10 | 23 | 19.6649494699891 | 3.3350505300109 |
11 | 24 | 23.5098291553823 | 0.49017084461772 |
12 | 32 | 24.7435744555164 | 7.25642554448355 |
13 | 30 | 23.9531340972797 | 6.04686590272026 |
14 | 32 | 28.8360534590547 | 3.16394654094532 |
15 | 24 | 23.7796402943158 | 0.220359705684247 |
16 | 29 | 31.5905023612761 | -2.59050236127607 |
17 | 17 | 23.5174995460139 | -6.51749954601387 |
18 | 30 | 27.3032652174204 | 2.69673478257962 |
19 | 25 | 22.4501919872836 | 2.54980801271637 |
20 | 25 | 25.0419327093183 | -0.0419327093182908 |
21 | 26 | 24.0368658283291 | 1.96313417167091 |
22 | 23 | 19.4619773264038 | 3.53802267359619 |
23 | 25 | 23.9185044825808 | 1.08149551741919 |
24 | 25 | 23.9185044825808 | 1.08149551741919 |
25 | 35 | 23.484924484195 | 11.515075515805 |
26 | 19 | 23.2098425923333 | -4.20984259233326 |
27 | 20 | 22.1783765475357 | -2.17837654753568 |
28 | 21 | 22.0589888013667 | -1.05898880136675 |
29 | 21 | 21.3511876103775 | -0.351187610377524 |
30 | 23 | 21.8749557458123 | 1.12504425418771 |
31 | 24 | 20.2074689413755 | 3.79253105862445 |
32 | 23 | 20.9185348079907 | 2.08146519200926 |
33 | 19 | 20.3719345754117 | -1.37193457541170 |
34 | 17 | 23.6164899347315 | -6.61648993473145 |
35 | 24 | 23.6400772460686 | 0.359922753931377 |
36 | 27 | 23.4092288249468 | 3.59077117505316 |
37 | 27 | 24.8959554500055 | 2.10404454999448 |
38 | 25 | 24.9708026623725 | 0.0291973376274716 |
39 | 18 | 21.7264936732396 | -3.72649367323957 |
40 | 22 | 21.3140264833287 | 0.685973516671312 |
41 | 26 | 21.6459438389444 | 4.35405616105558 |
42 | 26 | 27.8524328742633 | -1.85243287426331 |
43 | 23 | 24.3542863674797 | -1.35428636747969 |
44 | 16 | 22.3334525022709 | -6.33345250227089 |
45 | 27 | 21.3459572758954 | 5.6540427241046 |
46 | 25 | 23.7582002787617 | 1.24179972123827 |
47 | 14 | 16.3119174378617 | -2.31191743786168 |
48 | 19 | 20.738067388979 | -1.73806738897899 |
49 | 20 | 24.7550954948359 | -4.75509549483586 |
50 | 26 | 24.2919482618048 | 1.70805173819516 |
51 | 16 | 20.1780310192004 | -4.1780310192004 |
52 | 18 | 21.0735339555876 | -3.07353395558755 |
53 | 22 | 20.9759116555639 | 1.02408834443607 |
54 | 25 | 21.4958028961485 | 3.50419710385151 |
55 | 29 | 22.4314363126676 | 6.56856368733238 |
56 | 21 | 20.0288700866456 | 0.971129913354392 |
57 | 22 | 23.8267585627793 | -1.82675856277927 |
58 | 22 | 23.0348457628383 | -1.03484576283827 |
59 | 32 | 24.9877094269387 | 7.01229057306132 |
60 | 23 | 19.9630107926281 | 3.03698920737188 |
61 | 31 | 26.6966440713575 | 4.30335592864250 |
62 | 18 | 21.2132142294192 | -3.21321422941924 |
63 | 23 | 23.1448438297063 | -0.144843829706266 |
64 | 24 | 22.2300301523853 | 1.76996984761468 |
65 | 19 | 17.7249865310024 | 1.27501346899761 |
66 | 26 | 25.6956278435125 | 0.304372156487544 |
67 | 14 | 15.8175645184084 | -1.81756451840838 |
68 | 20 | 20.5239986732194 | -0.523998673219369 |
69 | 22 | 21.0558616664308 | 0.944138333569198 |
70 | 24 | 22.7325724490062 | 1.26742755099384 |
71 | 25 | 22.2652637857581 | 2.73473621424193 |
72 | 21 | 24.6819147568961 | -3.68191475689609 |
73 | 21 | 24.6819147568961 | -3.68191475689609 |
74 | 28 | 24.8511685460168 | 3.1488314539832 |
75 | 24 | 21.4702542646195 | 2.52974573538049 |
76 | 15 | 18.7840137331429 | -3.7840137331429 |
77 | 21 | 23.6183646141654 | -2.61836461416543 |
78 | 23 | 22.9021431348083 | 0.0978568651917416 |
79 | 24 | 22.7391481659886 | 1.26085183401142 |
80 | 21 | 23.0174097013384 | -2.01740970133844 |
81 | 21 | 25.0518817936013 | -4.05188179360135 |
82 | 13 | 16.5346871154700 | -3.53468711547003 |
83 | 17 | 18.9997209006796 | -1.99972090067956 |
84 | 29 | 19.1716010434584 | 9.82839895654158 |
85 | 25 | 22.3319414186083 | 2.66805858139173 |
86 | 16 | 17.1142805963692 | -1.11428059636921 |
87 | 20 | 20.3762617067911 | -0.376261706791088 |
88 | 25 | 21.7501294601545 | 3.24987053984549 |
89 | 25 | 21.7572829496484 | 3.24271705035162 |
90 | 21 | 21.6072716282330 | -0.607271628232959 |
91 | 23 | 22.3372503367166 | 0.662749663283391 |
92 | 22 | 26.4730987266287 | -4.47309872662868 |
93 | 19 | 20.2760272253931 | -1.27602722539309 |
94 | 26 | 24.2709483402501 | 1.72905165974987 |
95 | 25 | 23.9283487370753 | 1.07165126292473 |
96 | 19 | 18.6059866791910 | 0.394013320808964 |
97 | 25 | 22.4501919872836 | 2.54980801271637 |
98 | 24 | 23.9200052558457 | 0.0799947441542706 |
99 | 20 | 23.2238928907365 | -3.22389289073650 |
100 | 21 | 16.9301303152302 | 4.06986968476979 |
101 | 14 | 19.4379655479216 | -5.43796554792157 |
102 | 22 | 22.42564060147 | -0.425640601470004 |
103 | 14 | 18.5884437025044 | -4.58844370250436 |
104 | 20 | 24.0398174691597 | -4.03981746915974 |
105 | 21 | 20.0685074930445 | 0.931492506955491 |
106 | 22 | 21.7912541228114 | 0.208745877188611 |
107 | 19 | 19.7482955543503 | -0.748295554350274 |
108 | 28 | 26.3854636760682 | 1.61453632393183 |
109 | 25 | 25.2967521815657 | -0.296752181565735 |
110 | 17 | 17.1643703033141 | -0.164370303314113 |
111 | 21 | 22.2756777556324 | -1.27567775563236 |
112 | 27 | 23.1680675452721 | 3.83193245472791 |
113 | 29 | 22.9439524851634 | 6.05604751483657 |
114 | 19 | 19.0138116175289 | -0.0138116175289485 |
115 | 22 | 22.0576735269149 | -0.057673526914894 |
116 | 20 | 22.6010193942657 | -2.60101939426567 |
117 | 24 | 22.3737040698735 | 1.62629593012651 |
118 | 17 | 18.7057000886548 | -1.70570008865482 |
119 | 21 | 22.1301592667587 | -1.13015926675866 |
120 | 22 | 20.6454649651647 | 1.35453503483533 |
121 | 26 | 22.4331679971329 | 3.56683200286707 |
122 | 19 | 18.2476659645214 | 0.752334035478633 |
123 | 17 | 19.5605028295302 | -2.56050282953017 |
124 | 17 | 16.7744846451152 | 0.225515354884836 |
125 | 19 | 22.3960836772225 | -3.39608367722249 |
126 | 17 | 20.7661980938339 | -3.7661980938339 |
127 | 15 | 15.9681278429511 | -0.96812784295114 |
128 | 27 | 27.4596907499014 | -0.459690749901438 |
129 | 19 | 21.4904939780402 | -2.49049397804015 |
130 | 21 | 22.5910476037890 | -1.59104760378895 |
131 | 25 | 20.4433008500144 | 4.55669914998562 |
132 | 19 | 23.5524525059058 | -4.55245250590583 |
133 | 18 | 26.7527056444788 | -8.75270564447884 |
134 | 15 | 23.2083418190683 | -8.20834181906835 |
135 | 20 | 23.0554998008741 | -3.05549980087412 |
136 | 29 | 25.0023595487702 | 3.99764045122981 |
137 | 19 | 18.6620160588657 | 0.337983941134325 |
138 | 20 | 24.2147738802086 | -4.21477388020858 |
139 | 29 | 24.6136474567571 | 4.38635254324295 |
140 | 24 | 25.5030292513553 | -1.50302925135531 |
141 | 24 | 20.7791817412382 | 3.22081825876184 |
142 | 23 | 22.0843034585049 | 0.915696541495112 |
143 | 23 | 19.4619773264038 | 3.53802267359619 |
144 | 19 | 23.3204184317127 | -4.32041843171271 |
145 | 22 | 22.5773307931086 | -0.57733079310862 |
146 | 22 | 18.9509765762350 | 3.04902342376504 |
147 | 25 | 21.7501294601545 | 3.24987053984549 |
148 | 21 | 20.8170760315631 | 0.182923968436935 |
149 | 22 | 23.460254096309 | -1.46025409630901 |
150 | 21 | 21.605396948799 | -0.605396948798987 |
151 | 18 | 20.3890070411402 | -2.38900704114018 |
152 | 10 | 17.0138804138089 | -7.01388041380888 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.147113918133767 | 0.294227836267535 | 0.852886081866233 |
10 | 0.135204929387749 | 0.270409858775498 | 0.864795070612251 |
11 | 0.151322698005990 | 0.302645396011979 | 0.84867730199401 |
12 | 0.819711963916198 | 0.360576072167603 | 0.180288036083802 |
13 | 0.830747706692281 | 0.338504586615438 | 0.169252293307719 |
14 | 0.797727953636923 | 0.404544092726154 | 0.202272046363077 |
15 | 0.727906104178603 | 0.544187791642794 | 0.272093895821397 |
16 | 0.744451556620712 | 0.511096886758575 | 0.255548443379288 |
17 | 0.823275176139317 | 0.353449647721365 | 0.176724823860683 |
18 | 0.798485781493355 | 0.403028437013290 | 0.201514218506645 |
19 | 0.740455900164672 | 0.519088199670655 | 0.259544099835328 |
20 | 0.736798303204102 | 0.526403393591796 | 0.263201696795898 |
21 | 0.706517213583423 | 0.586965572833154 | 0.293482786416577 |
22 | 0.680585496393455 | 0.63882900721309 | 0.319414503606545 |
23 | 0.6325115063118 | 0.734976987376399 | 0.367488493688200 |
24 | 0.577850573776035 | 0.84429885244793 | 0.422149426223965 |
25 | 0.919679192576848 | 0.160641614846305 | 0.0803208074231523 |
26 | 0.931141293286804 | 0.137717413426392 | 0.0688587067131958 |
27 | 0.926219338131326 | 0.147561323737348 | 0.073780661868674 |
28 | 0.913648507857964 | 0.172702984284072 | 0.0863514921420358 |
29 | 0.891038372952032 | 0.217923254095936 | 0.108961627047968 |
30 | 0.868474416186977 | 0.263051167626045 | 0.131525583813023 |
31 | 0.870342371029732 | 0.259315257940536 | 0.129657628970268 |
32 | 0.859064040054363 | 0.281871919891273 | 0.140935959945637 |
33 | 0.835388511952966 | 0.329222976094067 | 0.164611488047034 |
34 | 0.920910662399446 | 0.158178675201108 | 0.079089337600554 |
35 | 0.897611586829606 | 0.204776826340789 | 0.102388413170395 |
36 | 0.89006733117937 | 0.219865337641261 | 0.109932668820631 |
37 | 0.869847930496138 | 0.260304139007724 | 0.130152069503862 |
38 | 0.837721483962726 | 0.324557032074548 | 0.162278516037274 |
39 | 0.850083220591615 | 0.299833558816771 | 0.149916779408385 |
40 | 0.817254558224886 | 0.365490883550228 | 0.182745441775114 |
41 | 0.825696415084154 | 0.348607169831691 | 0.174303584915846 |
42 | 0.792172170301872 | 0.415655659396256 | 0.207827829698128 |
43 | 0.763164746166377 | 0.473670507667245 | 0.236835253833623 |
44 | 0.860863789672403 | 0.278272420655193 | 0.139136210327597 |
45 | 0.886371862666966 | 0.227256274666068 | 0.113628137333034 |
46 | 0.866032150620482 | 0.267935698759037 | 0.133967849379518 |
47 | 0.876228088499946 | 0.247543823000108 | 0.123771911500054 |
48 | 0.861526297306554 | 0.276947405386893 | 0.138473702693446 |
49 | 0.885861690299387 | 0.228276619401225 | 0.114138309700613 |
50 | 0.865057761395704 | 0.269884477208593 | 0.134942238604296 |
51 | 0.88308141701592 | 0.233837165968159 | 0.116918582984080 |
52 | 0.87906021764974 | 0.24187956470052 | 0.12093978235026 |
53 | 0.853804964500572 | 0.292390070998856 | 0.146195035499428 |
54 | 0.850278707029725 | 0.299442585940551 | 0.149721292970275 |
55 | 0.904371287905732 | 0.191257424188537 | 0.0956287120942685 |
56 | 0.883282358456327 | 0.233435283087346 | 0.116717641543673 |
57 | 0.870283911696183 | 0.259432176607633 | 0.129716088303817 |
58 | 0.845076912113268 | 0.309846175773463 | 0.154923087886732 |
59 | 0.921730461188856 | 0.156539077622287 | 0.0782695388111437 |
60 | 0.914205320988204 | 0.171589358023592 | 0.085794679011796 |
61 | 0.927037970698423 | 0.145924058603154 | 0.0729620293015768 |
62 | 0.926410300514618 | 0.147179398970763 | 0.0735896994853815 |
63 | 0.907967446639198 | 0.184065106721604 | 0.0920325533608019 |
64 | 0.892262470821927 | 0.215475058356146 | 0.107737529178073 |
65 | 0.870526786504726 | 0.258946426990549 | 0.129473213495274 |
66 | 0.843722067471357 | 0.312555865057286 | 0.156277932528643 |
67 | 0.825152557478366 | 0.349694885043268 | 0.174847442521634 |
68 | 0.793877320402195 | 0.41224535919561 | 0.206122679597805 |
69 | 0.761382803574883 | 0.477234392850235 | 0.238617196425117 |
70 | 0.73037574243301 | 0.539248515133979 | 0.269624257566989 |
71 | 0.719970579052439 | 0.560058841895122 | 0.280029420947561 |
72 | 0.724630118287694 | 0.550739763424613 | 0.275369881712306 |
73 | 0.728209467445385 | 0.54358106510923 | 0.271790532554615 |
74 | 0.730759892194187 | 0.538480215611626 | 0.269240107805813 |
75 | 0.712594367724636 | 0.574811264550728 | 0.287405632275364 |
76 | 0.722949416259338 | 0.554101167481323 | 0.277050583740662 |
77 | 0.707119697299662 | 0.585760605400677 | 0.292880302700338 |
78 | 0.665637809561558 | 0.668724380876884 | 0.334362190438442 |
79 | 0.628401039922027 | 0.743197920155945 | 0.371598960077973 |
80 | 0.597497994979551 | 0.805004010040898 | 0.402502005020449 |
81 | 0.610007713865865 | 0.77998457226827 | 0.389992286134135 |
82 | 0.610191774619665 | 0.77961645076067 | 0.389808225380335 |
83 | 0.588329579156292 | 0.823340841687415 | 0.411670420843708 |
84 | 0.895353758953012 | 0.209292482093976 | 0.104646241046988 |
85 | 0.89391009971313 | 0.212179800573740 | 0.106089900286870 |
86 | 0.872964848514785 | 0.254070302970430 | 0.127035151485215 |
87 | 0.845831992317135 | 0.308336015365730 | 0.154168007682865 |
88 | 0.84269573455656 | 0.31460853088688 | 0.15730426544344 |
89 | 0.848594816129995 | 0.302810367740009 | 0.151405183870005 |
90 | 0.81867903242369 | 0.362641935152619 | 0.181320967576309 |
91 | 0.7993433846374 | 0.4013132307252 | 0.2006566153626 |
92 | 0.816281806089001 | 0.367436387821998 | 0.183718193910999 |
93 | 0.788735866258767 | 0.422528267482466 | 0.211264133741233 |
94 | 0.763505591588213 | 0.472988816823573 | 0.236494408411787 |
95 | 0.752174256241793 | 0.495651487516413 | 0.247825743758207 |
96 | 0.729933462692475 | 0.540133074615051 | 0.270066537307525 |
97 | 0.714808699178056 | 0.570382601643888 | 0.285191300821944 |
98 | 0.674953886687793 | 0.650092226624413 | 0.325046113312207 |
99 | 0.65727278251119 | 0.685454434977620 | 0.342727217488810 |
100 | 0.667301315932173 | 0.665397368135654 | 0.332698684067827 |
101 | 0.731732280741544 | 0.536535438516912 | 0.268267719258456 |
102 | 0.689556628718428 | 0.620886742563143 | 0.310443371281572 |
103 | 0.706910873967355 | 0.586178252065291 | 0.293089126032645 |
104 | 0.703711648041687 | 0.592576703916627 | 0.296288351958313 |
105 | 0.657874572048852 | 0.684250855902296 | 0.342125427951148 |
106 | 0.608807423443618 | 0.782385153112763 | 0.391192576556382 |
107 | 0.578591254625464 | 0.842817490749071 | 0.421408745374536 |
108 | 0.543076998973998 | 0.913846002052004 | 0.456923001026002 |
109 | 0.494397114162215 | 0.98879422832443 | 0.505602885837785 |
110 | 0.469936065535816 | 0.939872131071633 | 0.530063934464184 |
111 | 0.422574989445845 | 0.84514997889169 | 0.577425010554155 |
112 | 0.407576998516981 | 0.815153997033962 | 0.592423001483019 |
113 | 0.555655365602816 | 0.888689268794368 | 0.444344634397184 |
114 | 0.502362079366627 | 0.995275841266747 | 0.497637920633373 |
115 | 0.445274186667016 | 0.890548373334031 | 0.554725813332984 |
116 | 0.39963288423628 | 0.79926576847256 | 0.60036711576372 |
117 | 0.364042840594064 | 0.728085681188128 | 0.635957159405936 |
118 | 0.358037241397422 | 0.716074482794845 | 0.641962758602578 |
119 | 0.3169745189728 | 0.6339490379456 | 0.6830254810272 |
120 | 0.299089436679119 | 0.598178873358237 | 0.700910563320881 |
121 | 0.502007865878346 | 0.995984268243307 | 0.497992134121653 |
122 | 0.449640962311486 | 0.899281924622971 | 0.550359037688514 |
123 | 0.41888991813859 | 0.83777983627718 | 0.581110081861409 |
124 | 0.360158381950802 | 0.720316763901604 | 0.639841618049198 |
125 | 0.452013328835182 | 0.904026657670364 | 0.547986671164818 |
126 | 0.442513438441593 | 0.885026876883185 | 0.557486561558407 |
127 | 0.377437750691911 | 0.754875501383823 | 0.622562249308088 |
128 | 0.442771813267866 | 0.885543626535732 | 0.557228186732134 |
129 | 0.428790909169518 | 0.857581818339036 | 0.571209090830482 |
130 | 0.359890392160190 | 0.719780784320381 | 0.64010960783981 |
131 | 0.342725780942418 | 0.685451561884835 | 0.657274219057582 |
132 | 0.37090822015628 | 0.74181644031256 | 0.62909177984372 |
133 | 0.368727275553479 | 0.737454551106957 | 0.631272724446521 |
134 | 0.465466397609644 | 0.930932795219287 | 0.534533602390356 |
135 | 0.4275089755833 | 0.8550179511666 | 0.5724910244167 |
136 | 0.457543195538408 | 0.915086391076815 | 0.542456804461592 |
137 | 0.365229323053411 | 0.730458646106822 | 0.634770676946589 |
138 | 0.49131736372947 | 0.98263472745894 | 0.50868263627053 |
139 | 0.401642970020619 | 0.803285940041238 | 0.598357029979381 |
140 | 0.371278519224822 | 0.742557038449644 | 0.628721480775178 |
141 | 0.4788765290502 | 0.9577530581004 | 0.5211234709498 |
142 | 0.346946180089848 | 0.693892360179696 | 0.653053819910152 |
143 | 0.245004102295685 | 0.49000820459137 | 0.754995897704315 |
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 |