Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 7.32684596059117 + 0.356979436989241CM[t] -0.0592285666748476`CM*G`[t] -0.483865613410506D[t] + 0.175232812441501`D*G`[t] -0.0310127872102981PE[t] + 0.323284473674037`PE*G`[t] + 0.0927245043282869PC[t] -0.123099907387688`PC*G`[t] + 0.509759645731013O[t] -0.132008906567604`O*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) | 7.32684596059117 | 2.279284 | 3.2145 | 0.001606 | 0.000803 |
CM | 0.356979436989241 | 0.086282 | 4.1374 | 5.9e-05 | 2.9e-05 |
`CM*G` | -0.0592285666748476 | 0.115217 | -0.5141 | 0.607981 | 0.303991 |
D | -0.483865613410506 | 0.16529 | -2.9274 | 0.003963 | 0.001981 |
`D*G` | 0.175232812441501 | 0.216479 | 0.8095 | 0.419553 | 0.209777 |
PE | -0.0310127872102981 | 0.161508 | -0.192 | 0.847992 | 0.423996 |
`PE*G` | 0.323284473674037 | 0.203179 | 1.5911 | 0.113728 | 0.056864 |
PC | 0.0927245043282869 | 0.227294 | 0.4079 | 0.683904 | 0.341952 |
`PC*G` | -0.123099907387688 | 0.276833 | -0.4447 | 0.65721 | 0.328605 |
O | 0.509759645731013 | 0.103161 | 4.9414 | 2e-06 | 1e-06 |
`O*G` | -0.132008906567604 | 0.106177 | -1.2433 | 0.21574 | 0.10787 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.623397994765618 |
R-squared | 0.388625059877793 |
Adjusted R-squared | 0.347034927896691 |
F-TEST (value) | 9.34416510277905 |
F-TEST (DF numerator) | 10 |
F-TEST (DF denominator) | 147 |
p-value | 6.79212242005178e-12 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.41759903161865 |
Sum Squared Residuals | 1716.95752171535 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 23.1455380422184 | 0.854461957781564 |
2 | 25 | 21.8668224893214 | 3.13317751067865 |
3 | 30 | 24.7061978746154 | 5.29380212538457 |
4 | 19 | 20.1022284798081 | -1.10222847980806 |
5 | 22 | 20.6284448726333 | 1.37155512736673 |
6 | 22 | 23.2539357278194 | -1.25393572781936 |
7 | 25 | 22.7327907751378 | 2.26720922486224 |
8 | 23 | 19.5095237148417 | 3.49047628515826 |
9 | 17 | 19.3533854884903 | -2.35338548849026 |
10 | 21 | 22.0243225269749 | -1.02432252697486 |
11 | 19 | 22.1598665655467 | -3.15986656554674 |
12 | 19 | 23.7278847161621 | -4.72788471616212 |
13 | 15 | 22.9278043521723 | -7.92780435217232 |
14 | 16 | 17.3287427422355 | -1.32874274223553 |
15 | 23 | 18.9743833493095 | 4.02561665069046 |
16 | 27 | 23.8541130404471 | 3.14588695955291 |
17 | 22 | 20.7140003623796 | 1.28599963762037 |
18 | 14 | 15.3283837322309 | -1.32838373223092 |
19 | 22 | 22.9515954383592 | -0.951595438359213 |
20 | 23 | 24.4257677462697 | -1.42576774626966 |
21 | 23 | 21.6110028905429 | 1.38899710945714 |
22 | 21 | 22.3792292961033 | -1.37922929610334 |
23 | 19 | 22.4316079216241 | -3.43160792162413 |
24 | 18 | 23.7752299338472 | -5.77522993384719 |
25 | 20 | 23.4608589716526 | -3.46085897165258 |
26 | 23 | 22.7985118872127 | 0.20148811278726 |
27 | 25 | 23.7720087766795 | 1.22799122332049 |
28 | 19 | 23.1342094194357 | -4.13420941943572 |
29 | 24 | 22.8883908490631 | 1.11160915093695 |
30 | 22 | 21.9164620536454 | 0.0835379463545559 |
31 | 25 | 26.1159579815043 | -1.11595798150433 |
32 | 26 | 23.6733945502657 | 2.32660544973434 |
33 | 29 | 23.581934424098 | 5.41806557590197 |
34 | 32 | 25.0399562059333 | 6.96004379406672 |
35 | 25 | 22.2389211119954 | 2.76107888800462 |
36 | 29 | 24.5393208597622 | 4.46067914023781 |
37 | 28 | 25.2765897808799 | 2.72341021912009 |
38 | 17 | 15.5319101080834 | 1.46808989191663 |
39 | 28 | 26.3581819802532 | 1.64181801974678 |
40 | 29 | 22.4463344599839 | 6.55366554001613 |
41 | 26 | 26.56693529096 | -0.566935290959992 |
42 | 25 | 23.606361882503 | 1.39363811749705 |
43 | 14 | 17.8563378961915 | -3.85633789619151 |
44 | 25 | 22.8236525160961 | 2.17634748390394 |
45 | 26 | 21.7839185806076 | 4.21608141939244 |
46 | 20 | 20.0197966730921 | -0.0197966730920708 |
47 | 18 | 21.8150714731331 | -3.81507147313315 |
48 | 32 | 24.8445122321104 | 7.15548776788959 |
49 | 25 | 24.8278172038666 | 0.172182796133374 |
50 | 25 | 22.5430131351555 | 2.45698686484448 |
51 | 23 | 21.3165270865493 | 1.68347291345067 |
52 | 21 | 22.00155939135 | -1.00155939135 |
53 | 20 | 24.0368130668541 | -4.03681306685413 |
54 | 15 | 16.4264490613949 | -1.42644906139486 |
55 | 30 | 24.7567213971447 | 5.24327860285527 |
56 | 24 | 25.2751706249969 | -1.27517062499689 |
57 | 26 | 24.2545640683195 | 1.74543593168049 |
58 | 24 | 20.8614516932321 | 3.13854830676793 |
59 | 22 | 22.650618497898 | -0.650618497897962 |
60 | 14 | 16.4664066566256 | -2.46640665662557 |
61 | 24 | 22.2470641044201 | 1.75293589557994 |
62 | 24 | 22.3721702930403 | 1.62782970695965 |
63 | 24 | 23.7367153705886 | 0.263284629411397 |
64 | 24 | 20.2828725908775 | 3.71712740912254 |
65 | 19 | 17.90493791052 | 1.09506208948001 |
66 | 31 | 27.8340246944428 | 3.16597530555724 |
67 | 22 | 27.1571704728309 | -5.15717047283094 |
68 | 27 | 20.7982471039359 | 6.2017528960641 |
69 | 19 | 17.2396182162998 | 1.76038178370016 |
70 | 25 | 22.3026563619312 | 2.69734363806884 |
71 | 20 | 24.7999565993862 | -4.79995659938623 |
72 | 21 | 21.3125016453599 | -0.312501645359874 |
73 | 27 | 27.4138927489721 | -0.413892748972069 |
74 | 23 | 24.9471571086258 | -1.94715710862584 |
75 | 25 | 25.9362647377293 | -0.936264737729286 |
76 | 20 | 22.2858105036534 | -2.28581050365344 |
77 | 22 | 22.760463348445 | -0.760463348444952 |
78 | 23 | 23.5177657911834 | -0.517765791183388 |
79 | 25 | 24.1967052860024 | 0.803294713997641 |
80 | 25 | 23.5493046151028 | 1.45069538489718 |
81 | 17 | 23.6280693653108 | -6.6280693653108 |
82 | 19 | 20.5703687834139 | -1.57036878341388 |
83 | 25 | 24.2514116518747 | 0.748588348125346 |
84 | 19 | 22.7422850822931 | -3.74228508229305 |
85 | 20 | 21.8879908223272 | -1.88799082232724 |
86 | 26 | 22.6224155032293 | 3.37758449677065 |
87 | 23 | 21.1531296036157 | 1.84687039638429 |
88 | 27 | 24.5218843199494 | 2.47811568005063 |
89 | 17 | 20.2526697734074 | -3.25266977340741 |
90 | 17 | 22.3760412457908 | -5.3760412457908 |
91 | 19 | 19.9831294721654 | -0.98312947216542 |
92 | 17 | 19.6249744934655 | -2.62497449346553 |
93 | 22 | 22.5478747596857 | -0.54787475968566 |
94 | 21 | 24.1042795613992 | -3.10427956139915 |
95 | 32 | 29.0655147279217 | 2.93448527207831 |
96 | 21 | 23.7956913539753 | -2.7956913539753 |
97 | 21 | 24.7785458291776 | -3.77854582917763 |
98 | 18 | 20.7365353868179 | -2.73653538681792 |
99 | 18 | 21.524829841476 | -3.52482984147597 |
100 | 23 | 23.1018747569259 | -0.101874756925861 |
101 | 19 | 20.1836243613537 | -1.18362436135368 |
102 | 20 | 21.7975879969896 | -1.7975879969896 |
103 | 21 | 22.6081367464553 | -1.60813674645531 |
104 | 20 | 24.1323885337656 | -4.13238853376562 |
105 | 17 | 19.1791311281402 | -2.17913112814022 |
106 | 18 | 20.242403438441 | -2.24240343844095 |
107 | 19 | 20.8572106203013 | -1.85721062030133 |
108 | 22 | 22.4324698906192 | -0.432469890619229 |
109 | 15 | 17.5105239414586 | -2.51052394145862 |
110 | 14 | 19.2004413271801 | -5.2004413271801 |
111 | 18 | 26.572667808271 | -8.572667808271 |
112 | 24 | 21.8885366074199 | 2.11146339258007 |
113 | 35 | 23.9587116001398 | 11.0412883998602 |
114 | 29 | 18.8471180464216 | 10.1528819535784 |
115 | 21 | 22.3354701265229 | -1.33547012652287 |
116 | 25 | 21.1464414844467 | 3.85355851555328 |
117 | 20 | 18.035639851859 | 1.964360148141 |
118 | 22 | 22.0807735259196 | -0.080773525919554 |
119 | 13 | 15.8935840669944 | -2.89358406699437 |
120 | 26 | 22.8015768436531 | 3.19842315634688 |
121 | 17 | 17.4390415770972 | -0.43904157709725 |
122 | 25 | 20.4914441148855 | 4.50855588511451 |
123 | 20 | 20.3391927870663 | -0.339192787066305 |
124 | 19 | 17.5771033710676 | 1.4228966289324 |
125 | 21 | 21.082963456725 | -0.0829634567249685 |
126 | 22 | 21.1912795998767 | 0.808720400123346 |
127 | 24 | 22.6804071010946 | 1.31959289890544 |
128 | 21 | 23.2399778177666 | -2.2399778177666 |
129 | 26 | 25.2475192731113 | 0.752480726888739 |
130 | 24 | 20.7473200921654 | 3.25267990783464 |
131 | 16 | 20.5101872124217 | -4.51018721242169 |
132 | 23 | 22.4169385200482 | 0.583061479951775 |
133 | 18 | 20.8190080445639 | -2.8190080445639 |
134 | 16 | 22.0788724431762 | -6.07887244317621 |
135 | 26 | 21.8397598531341 | 4.16024014686593 |
136 | 19 | 19.5541578161299 | -0.554157816129854 |
137 | 21 | 17.4196809202405 | 3.58031907975947 |
138 | 21 | 22.2211700720996 | -1.22117007209955 |
139 | 22 | 18.6437797801546 | 3.35622021984542 |
140 | 23 | 19.5840897553837 | 3.4159102446163 |
141 | 29 | 24.946615986352 | 4.05338401364798 |
142 | 21 | 20.3365274401464 | 0.663472559853616 |
143 | 21 | 20.0461944449213 | 0.95380555507868 |
144 | 23 | 22.5123933224215 | 0.487606677578453 |
145 | 27 | 23.1222502568711 | 3.87774974312893 |
146 | 25 | 25.6519318180701 | -0.651931818070076 |
147 | 21 | 21.0615436711115 | -0.0615436711115192 |
148 | 10 | 17.457805896055 | -7.45780589605502 |
149 | 20 | 22.7513670629223 | -2.75136706292233 |
150 | 26 | 22.3735599452575 | 3.62644005474245 |
151 | 24 | 24.2251070127566 | -0.22510701275657 |
152 | 29 | 32.1262672519407 | -3.12626725194067 |
153 | 19 | 19.5422299608837 | -0.542229960883653 |
154 | 24 | 22.8924708289908 | 1.10752917100924 |
155 | 19 | 21.1609605753186 | -2.16096057531863 |
156 | 24 | 23.1830384814002 | 0.816961518599816 |
157 | 22 | 22.2559762228679 | -0.255976222867862 |
158 | 17 | 24.2411685019621 | -7.24116850196213 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
14 | 0.973563485975858 | 0.0528730280482844 | 0.0264365140241422 |
15 | 0.945574431549052 | 0.108851136901897 | 0.0544255684509483 |
16 | 0.903533838411931 | 0.192932323176138 | 0.096466161588069 |
17 | 0.84742259210953 | 0.305154815780939 | 0.15257740789047 |
18 | 0.773350155076144 | 0.453299689847711 | 0.226649844923856 |
19 | 0.793838553659489 | 0.412322892681023 | 0.206161446340512 |
20 | 0.760872614315812 | 0.478254771368376 | 0.239127385684188 |
21 | 0.742599677834574 | 0.514800644330852 | 0.257400322165426 |
22 | 0.707672116283653 | 0.584655767432695 | 0.292327883716347 |
23 | 0.664309633563628 | 0.671380732872745 | 0.335690366436372 |
24 | 0.655544505977979 | 0.688910988044042 | 0.344455494022021 |
25 | 0.644259769053716 | 0.711480461892569 | 0.355740230946284 |
26 | 0.568202658847986 | 0.863594682304028 | 0.431797341152014 |
27 | 0.494576364001744 | 0.989152728003488 | 0.505423635998256 |
28 | 0.441639286460324 | 0.883278572920648 | 0.558360713539676 |
29 | 0.410066048658135 | 0.82013209731627 | 0.589933951341865 |
30 | 0.343647598634995 | 0.68729519726999 | 0.656352401365005 |
31 | 0.315321751715943 | 0.630643503431886 | 0.684678248284057 |
32 | 0.310633333425843 | 0.621266666851687 | 0.689366666574157 |
33 | 0.400563252989661 | 0.801126505979322 | 0.599436747010339 |
34 | 0.546658816577626 | 0.906682366844748 | 0.453341183422374 |
35 | 0.508482156519823 | 0.983035686960354 | 0.491517843480177 |
36 | 0.564293879884452 | 0.871412240231096 | 0.435706120115548 |
37 | 0.618421431891703 | 0.763157136216595 | 0.381578568108297 |
38 | 0.581625981652316 | 0.836748036695367 | 0.418374018347684 |
39 | 0.530543824495601 | 0.938912351008797 | 0.469456175504399 |
40 | 0.652368209827994 | 0.695263580344012 | 0.347631790172006 |
41 | 0.598359417413507 | 0.803281165172986 | 0.401640582586493 |
42 | 0.54473252719489 | 0.91053494561022 | 0.45526747280511 |
43 | 0.545338236168202 | 0.909323527663596 | 0.454661763831798 |
44 | 0.504648912956552 | 0.990702174086896 | 0.495351087043448 |
45 | 0.543671463996992 | 0.912657072006016 | 0.456328536003008 |
46 | 0.488071435448851 | 0.976142870897702 | 0.511928564551149 |
47 | 0.491751501995865 | 0.98350300399173 | 0.508248498004135 |
48 | 0.600326453223505 | 0.79934709355299 | 0.399673546776495 |
49 | 0.549650766987107 | 0.900698466025785 | 0.450349233012893 |
50 | 0.518881295275455 | 0.96223740944909 | 0.481118704724545 |
51 | 0.509331138425358 | 0.981337723149283 | 0.490668861574642 |
52 | 0.459587586423106 | 0.919175172846211 | 0.540412413576894 |
53 | 0.491938001021851 | 0.983876002043703 | 0.508061998978149 |
54 | 0.456141792701001 | 0.912283585402001 | 0.543858207298999 |
55 | 0.618527099540189 | 0.762945800919621 | 0.381472900459811 |
56 | 0.575510735373064 | 0.848978529253872 | 0.424489264626936 |
57 | 0.535549846207916 | 0.928900307584168 | 0.464450153792084 |
58 | 0.51958553138409 | 0.96082893723182 | 0.48041446861591 |
59 | 0.471739241060609 | 0.943478482121218 | 0.528260758939391 |
60 | 0.435964021817483 | 0.871928043634966 | 0.564035978182517 |
61 | 0.39815748272705 | 0.7963149654541 | 0.60184251727295 |
62 | 0.362365709510587 | 0.724731419021174 | 0.637634290489413 |
63 | 0.317853579835259 | 0.635707159670518 | 0.682146420164741 |
64 | 0.326647962170926 | 0.653295924341853 | 0.673352037829074 |
65 | 0.286011796068073 | 0.572023592136147 | 0.713988203931927 |
66 | 0.326478630228336 | 0.652957260456673 | 0.673521369771664 |
67 | 0.38574376997707 | 0.771487539954139 | 0.61425623002293 |
68 | 0.499026387530038 | 0.998052775060075 | 0.500973612469962 |
69 | 0.451545364878518 | 0.903090729757037 | 0.548454635121482 |
70 | 0.436022161394261 | 0.872044322788523 | 0.563977838605739 |
71 | 0.510501642219655 | 0.97899671556069 | 0.489498357780346 |
72 | 0.462360329078122 | 0.924720658156244 | 0.537639670921878 |
73 | 0.417506246564802 | 0.835012493129604 | 0.582493753435198 |
74 | 0.384046985004066 | 0.768093970008131 | 0.615953014995934 |
75 | 0.349629313926796 | 0.699258627853592 | 0.650370686073204 |
76 | 0.324814181075245 | 0.64962836215049 | 0.675185818924755 |
77 | 0.283690820396231 | 0.567381640792462 | 0.716309179603769 |
78 | 0.249370704845817 | 0.498741409691633 | 0.750629295154183 |
79 | 0.214519905851017 | 0.429039811702034 | 0.785480094148983 |
80 | 0.189274440119874 | 0.378548880239748 | 0.810725559880126 |
81 | 0.300038704743208 | 0.600077409486417 | 0.699961295256792 |
82 | 0.271083570647962 | 0.542167141295924 | 0.728916429352038 |
83 | 0.234284830549142 | 0.468569661098284 | 0.765715169450858 |
84 | 0.232605380948608 | 0.465210761897216 | 0.767394619051392 |
85 | 0.208125856627596 | 0.416251713255192 | 0.791874143372404 |
86 | 0.207625900657261 | 0.415251801314522 | 0.79237409934274 |
87 | 0.183973932344489 | 0.367947864688978 | 0.81602606765551 |
88 | 0.171303222619938 | 0.342606445239876 | 0.828696777380062 |
89 | 0.164056901412647 | 0.328113802825294 | 0.835943098587353 |
90 | 0.199583836833028 | 0.399167673666056 | 0.800416163166972 |
91 | 0.169873153050197 | 0.339746306100394 | 0.830126846949803 |
92 | 0.151180336888608 | 0.302360673777216 | 0.848819663111392 |
93 | 0.127355090184567 | 0.254710180369135 | 0.872644909815433 |
94 | 0.117270958065543 | 0.234541916131085 | 0.882729041934457 |
95 | 0.113812105284465 | 0.227624210568931 | 0.886187894715535 |
96 | 0.102033509259048 | 0.204067018518096 | 0.897966490740952 |
97 | 0.104042702923084 | 0.208085405846168 | 0.895957297076916 |
98 | 0.0925341672177336 | 0.185068334435467 | 0.907465832782266 |
99 | 0.0914691248151193 | 0.182938249630239 | 0.90853087518488 |
100 | 0.0724366793297467 | 0.144873358659493 | 0.927563320670253 |
101 | 0.0572382950334733 | 0.114476590066947 | 0.942761704966527 |
102 | 0.0463257253238616 | 0.0926514506477232 | 0.953674274676138 |
103 | 0.036834983585444 | 0.0736699671708881 | 0.963165016414556 |
104 | 0.0389300929345071 | 0.0778601858690143 | 0.961069907065493 |
105 | 0.0319443154390982 | 0.0638886308781964 | 0.968055684560902 |
106 | 0.0276040168058955 | 0.0552080336117909 | 0.972395983194105 |
107 | 0.0235469039257525 | 0.047093807851505 | 0.976453096074247 |
108 | 0.0173587129539882 | 0.0347174259079764 | 0.982641287046012 |
109 | 0.015908328054881 | 0.031816656109762 | 0.984091671945119 |
110 | 0.0219082784332123 | 0.0438165568664245 | 0.978091721566788 |
111 | 0.115708228944401 | 0.231416457888802 | 0.8842917710556 |
112 | 0.10625911269956 | 0.21251822539912 | 0.89374088730044 |
113 | 0.457094732753294 | 0.914189465506589 | 0.542905267246706 |
114 | 0.785650296352116 | 0.428699407295768 | 0.214349703647884 |
115 | 0.744341869519475 | 0.51131626096105 | 0.255658130480525 |
116 | 0.821956543487791 | 0.356086913024418 | 0.178043456512209 |
117 | 0.79992250278695 | 0.400154994426101 | 0.200077497213051 |
118 | 0.755167335094305 | 0.48966532981139 | 0.244832664905695 |
119 | 0.76423389306938 | 0.471532213861242 | 0.235766106930621 |
120 | 0.73572130083281 | 0.528557398334381 | 0.264278699167191 |
121 | 0.681943379315359 | 0.636113241369282 | 0.318056620684641 |
122 | 0.702685906931684 | 0.594628186136632 | 0.297314093068316 |
123 | 0.647613683969825 | 0.704772632060351 | 0.352386316030175 |
124 | 0.588376998460726 | 0.823246003078548 | 0.411623001539274 |
125 | 0.54754566981672 | 0.90490866036656 | 0.45245433018328 |
126 | 0.500740088478051 | 0.9985198230439 | 0.49925991152195 |
127 | 0.444779663144029 | 0.889559326288058 | 0.555220336855971 |
128 | 0.384399277539521 | 0.768798555079043 | 0.615600722460479 |
129 | 0.328686665659969 | 0.657373331319937 | 0.671313334340031 |
130 | 0.30965183619047 | 0.61930367238094 | 0.69034816380953 |
131 | 0.313115128060602 | 0.626230256121203 | 0.686884871939398 |
132 | 0.382163147058334 | 0.764326294116669 | 0.617836852941666 |
133 | 0.352283373971767 | 0.704566747943534 | 0.647716626028233 |
134 | 0.302238893426928 | 0.604477786853855 | 0.697761106573072 |
135 | 0.243829218590008 | 0.487658437180016 | 0.756170781409992 |
136 | 0.18622514553572 | 0.372450291071441 | 0.81377485446428 |
137 | 0.179780522002676 | 0.359561044005353 | 0.820219477997324 |
138 | 0.126146196590667 | 0.252292393181334 | 0.873853803409333 |
139 | 0.0969933788038216 | 0.193986757607643 | 0.903006621196178 |
140 | 0.0729144525093624 | 0.145828905018725 | 0.927085547490638 |
141 | 0.0844151126656436 | 0.168830225331287 | 0.915584887334356 |
142 | 0.14343692152721 | 0.286873843054419 | 0.85656307847279 |
143 | 0.0822635621176883 | 0.164527124235377 | 0.917736437882312 |
144 | 0.0444199958049525 | 0.088839991609905 | 0.955580004195048 |
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 | 4 | 0.0305343511450382 | OK |
10% type I error level | 11 | 0.083969465648855 | OK |