Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 7.32684596059117 + 0.356979436989242CM[t] -0.0592285666748474`CM*G`[t] -0.483865613410507D[t] + 0.175232812441502`D*G`[t] -0.0310127872102974PE[t] + 0.323284473674036`PE*G`[t] + 0.0927245043282856PC[t] -0.123099907387686`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 | 0.356979436989242 | 0.086282 | 4.1374 | 5.9e-05 | 2.9e-05 |
`CM*G` | -0.0592285666748474 | 0.115217 | -0.5141 | 0.607981 | 0.303991 |
D | -0.483865613410507 | 0.16529 | -2.9274 | 0.003963 | 0.001981 |
`D*G` | 0.175232812441502 | 0.216479 | 0.8095 | 0.419553 | 0.209777 |
PE | -0.0310127872102974 | 0.161508 | -0.192 | 0.847992 | 0.423996 |
`PE*G` | 0.323284473674036 | 0.203179 | 1.5911 | 0.113728 | 0.056864 |
PC | 0.0927245043282856 | 0.227294 | 0.4079 | 0.683904 | 0.341952 |
`PC*G` | -0.123099907387686 | 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 | 23.1455380422185 | 0.854461957781518 |
2 | 25 | 21.8668224893213 | 3.13317751067866 |
3 | 30 | 24.7061978746154 | 5.29380212538459 |
4 | 19 | 20.1022284798081 | -1.10222847980808 |
5 | 22 | 20.6284448726333 | 1.37155512736673 |
6 | 22 | 23.2539357278194 | -1.25393572781936 |
7 | 25 | 22.7327907751378 | 2.26720922486223 |
8 | 23 | 19.5095237148417 | 3.49047628515826 |
9 | 17 | 19.3533854884903 | -2.35338548849026 |
10 | 21 | 22.0243225269749 | -1.02432252697485 |
11 | 19 | 22.1598665655467 | -3.15986656554673 |
12 | 19 | 23.7278847161621 | -4.72788471616212 |
13 | 15 | 22.9278043521723 | -7.92780435217232 |
14 | 16 | 17.3287427422355 | -1.32874274223554 |
15 | 23 | 18.9743833493095 | 4.02561665069047 |
16 | 27 | 23.8541130404471 | 3.14588695955289 |
17 | 22 | 20.7140003623796 | 1.28599963762036 |
18 | 14 | 15.3283837322309 | -1.32838373223092 |
19 | 22 | 22.9515954383592 | -0.95159543835922 |
20 | 23 | 24.4257677462697 | -1.42576774626966 |
21 | 23 | 21.6110028905429 | 1.38899710945714 |
22 | 21 | 22.3792292961033 | -1.37922929610334 |
23 | 19 | 22.4316079216241 | -3.43160792162414 |
24 | 18 | 23.7752299338472 | -5.77522993384719 |
25 | 20 | 23.4608589716526 | -3.46085897165258 |
26 | 23 | 22.7985118872127 | 0.201488112787262 |
27 | 25 | 23.7720087766795 | 1.22799122332049 |
28 | 19 | 23.1342094194357 | -4.13420941943571 |
29 | 24 | 22.8883908490631 | 1.11160915093695 |
30 | 22 | 21.9164620536454 | 0.0835379463545565 |
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 | 4.46067914023782 |
37 | 28 | 25.2765897808799 | 2.72341021912010 |
38 | 17 | 15.5319101080834 | 1.46808989191663 |
39 | 28 | 26.3581819802532 | 1.64181801974678 |
40 | 29 | 22.4463344599839 | 6.55366554001613 |
41 | 26 | 26.56693529096 | -0.566935290959991 |
42 | 25 | 23.6063618825030 | 1.39363811749705 |
43 | 14 | 17.8563378961915 | -3.85633789619151 |
44 | 25 | 22.8236525160961 | 2.17634748390394 |
45 | 26 | 21.7839185806076 | 4.21608141939244 |
46 | 20 | 20.0197966730921 | -0.0197966730920678 |
47 | 18 | 21.8150714731331 | -3.81507147313315 |
48 | 32 | 24.8445122321104 | 7.15548776788959 |
49 | 25 | 24.8278172038666 | 0.172182796133373 |
50 | 25 | 22.5430131351555 | 2.45698686484448 |
51 | 23 | 21.3165270865493 | 1.68347291345067 |
52 | 21 | 22.00155939135 | -1.00155939135 |
53 | 20 | 24.0368130668541 | -4.03681306685412 |
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 | 3.13854830676792 |
59 | 22 | 22.6506184978980 | -0.650618497897962 |
60 | 14 | 16.4664066566256 | -2.46640665662557 |
61 | 24 | 22.2470641044201 | 1.75293589557994 |
62 | 24 | 22.3721702930404 | 1.62782970695965 |
63 | 24 | 23.7367153705886 | 0.2632846294114 |
64 | 24 | 20.2828725908774 | 3.71712740912255 |
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 | -0.312501645359875 |
73 | 27 | 27.4138927489721 | -0.413892748972068 |
74 | 23 | 24.9471571086258 | -1.94715710862584 |
75 | 25 | 25.9362647377293 | -0.936264737729285 |
76 | 20 | 22.2858105036534 | -2.28581050365345 |
77 | 22 | 22.7604633484450 | -0.760463348444953 |
78 | 23 | 23.5177657911834 | -0.517765791183384 |
79 | 25 | 24.1967052860024 | 0.80329471399764 |
80 | 25 | 23.5493046151028 | 1.45069538489718 |
81 | 17 | 23.6280693653108 | -6.6280693653108 |
82 | 19 | 20.5703687834139 | -1.57036878341388 |
83 | 25 | 24.2514116518747 | 0.748588348125348 |
84 | 19 | 22.7422850822930 | -3.74228508229305 |
85 | 20 | 21.8879908223272 | -1.88799082232724 |
86 | 26 | 22.6224155032293 | 3.37758449677065 |
87 | 23 | 21.1531296036157 | 1.84687039638430 |
88 | 27 | 24.5218843199494 | 2.47811568005063 |
89 | 17 | 20.2526697734074 | -3.25266977340741 |
90 | 17 | 22.3760412457908 | -5.3760412457908 |
91 | 19 | 19.9831294721654 | -0.983129472165419 |
92 | 17 | 19.6249744934655 | -2.62497449346553 |
93 | 22 | 22.5478747596857 | -0.54787475968566 |
94 | 21 | 24.1042795613991 | -3.10427956139915 |
95 | 32 | 29.0655147279217 | 2.93448527207831 |
96 | 21 | 23.7956913539753 | -2.79569135397530 |
97 | 21 | 24.7785458291776 | -3.77854582917763 |
98 | 18 | 20.7365353868179 | -2.73653538681792 |
99 | 18 | 21.5248298414760 | -3.52482984147597 |
100 | 23 | 23.1018747569259 | -0.101874756925861 |
101 | 19 | 20.1836243613537 | -1.18362436135368 |
102 | 20 | 21.7975879969896 | -1.79758799698959 |
103 | 21 | 22.6081367464553 | -1.60813674645531 |
104 | 20 | 24.1323885337656 | -4.13238853376561 |
105 | 17 | 19.1791311281402 | -2.17913112814022 |
106 | 18 | 20.2424034384410 | -2.24240343844095 |
107 | 19 | 20.8572106203013 | -1.85721062030133 |
108 | 22 | 22.4324698906192 | -0.43246989061923 |
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 | -1.33547012652286 |
116 | 25 | 21.1464414844467 | 3.85355851555328 |
117 | 20 | 18.035639851859 | 1.964360148141 |
118 | 22 | 22.0807735259196 | -0.0807735259195528 |
119 | 13 | 15.8935840669944 | -2.89358406699437 |
120 | 26 | 22.8015768436531 | 3.19842315634688 |
121 | 17 | 17.4390415770972 | -0.439041577097251 |
122 | 25 | 20.4914441148855 | 4.50855588511451 |
123 | 20 | 20.3391927870663 | -0.339192787066306 |
124 | 19 | 17.5771033710676 | 1.42289662893241 |
125 | 21 | 21.0829634567250 | -0.0829634567249715 |
126 | 22 | 21.1912795998767 | 0.808720400123346 |
127 | 24 | 22.6804071010946 | 1.31959289890544 |
128 | 21 | 23.2399778177666 | -2.23997781776660 |
129 | 26 | 25.2475192731113 | 0.752480726888736 |
130 | 24 | 20.7473200921654 | 3.25267990783464 |
131 | 16 | 20.5101872124217 | -4.51018721242169 |
132 | 23 | 22.4169385200482 | 0.583061479951772 |
133 | 18 | 20.8190080445639 | -2.8190080445639 |
134 | 16 | 22.0788724431762 | -6.0788724431762 |
135 | 26 | 21.8397598531341 | 4.16024014686593 |
136 | 19 | 19.5541578161299 | -0.554157816129855 |
137 | 21 | 17.4196809202405 | 3.58031907975947 |
138 | 21 | 22.2211700720996 | -1.22117007209955 |
139 | 22 | 18.6437797801546 | 3.35622021984542 |
140 | 23 | 19.5840897553837 | 3.41591024461629 |
141 | 29 | 24.946615986352 | 4.05338401364798 |
142 | 21 | 20.3365274401464 | 0.663472559853618 |
143 | 21 | 20.0461944449213 | 0.953805555078684 |
144 | 23 | 22.5123933224215 | 0.487606677578455 |
145 | 27 | 23.1222502568711 | 3.87774974312893 |
146 | 25 | 25.6519318180701 | -0.651931818070076 |
147 | 21 | 21.0615436711115 | -0.0615436711115204 |
148 | 10 | 17.4578058960550 | -7.45780589605502 |
149 | 20 | 22.7513670629223 | -2.75136706292233 |
150 | 26 | 22.3735599452575 | 3.62644005474245 |
151 | 24 | 24.2251070127566 | -0.225107012756570 |
152 | 29 | 32.1262672519407 | -3.12626725194067 |
153 | 19 | 19.5422299608837 | -0.542229960883653 |
154 | 24 | 22.8924708289908 | 1.10752917100924 |
155 | 19 | 21.1609605753186 | -2.16096057531862 |
156 | 24 | 23.1830384814002 | 0.81696151859982 |
157 | 22 | 22.2559762228679 | -0.255976222867863 |
158 | 17 | 24.2411685019621 | -7.24116850196213 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
14 | 0.973563485975858 | 0.0528730280482846 | 0.0264365140241423 |
15 | 0.945574431549052 | 0.108851136901897 | 0.0544255684509485 |
16 | 0.903533838411931 | 0.192932323176138 | 0.0964661615880688 |
17 | 0.847422592109532 | 0.305154815780937 | 0.152577407890468 |
18 | 0.773350155076146 | 0.453299689847708 | 0.226649844923854 |
19 | 0.793838553659489 | 0.412322892681022 | 0.206161446340511 |
20 | 0.760872614315812 | 0.478254771368376 | 0.239127385684188 |
21 | 0.742599677834574 | 0.514800644330852 | 0.257400322165426 |
22 | 0.707672116283652 | 0.584655767432696 | 0.292327883716348 |
23 | 0.664309633563626 | 0.671380732872747 | 0.335690366436374 |
24 | 0.655544505977978 | 0.688910988044044 | 0.344455494022022 |
25 | 0.644259769053714 | 0.711480461892571 | 0.355740230946286 |
26 | 0.568202658847986 | 0.863594682304028 | 0.431797341152014 |
27 | 0.494576364001745 | 0.98915272800349 | 0.505423635998255 |
28 | 0.441639286460324 | 0.883278572920647 | 0.558360713539676 |
29 | 0.410066048658141 | 0.820132097316283 | 0.589933951341859 |
30 | 0.343647598634996 | 0.687295197269991 | 0.656352401365004 |
31 | 0.315321751715943 | 0.630643503431886 | 0.684678248284057 |
32 | 0.310633333425846 | 0.621266666851692 | 0.689366666574154 |
33 | 0.40056325298966 | 0.80112650597932 | 0.59943674701034 |
34 | 0.546658816577625 | 0.90668236684475 | 0.453341183422375 |
35 | 0.508482156519824 | 0.983035686960352 | 0.491517843480176 |
36 | 0.56429387988445 | 0.8714122402311 | 0.43570612011555 |
37 | 0.618421431891703 | 0.763157136216594 | 0.381578568108297 |
38 | 0.581625981652318 | 0.836748036695364 | 0.418374018347682 |
39 | 0.530543824495599 | 0.938912351008803 | 0.469456175504401 |
40 | 0.652368209827993 | 0.695263580344015 | 0.347631790172007 |
41 | 0.598359417413505 | 0.80328116517299 | 0.401640582586495 |
42 | 0.544732527194889 | 0.910534945610222 | 0.455267472805111 |
43 | 0.545338236168203 | 0.909323527663595 | 0.454661763831797 |
44 | 0.504648912956551 | 0.990702174086898 | 0.495351087043449 |
45 | 0.543671463996991 | 0.912657072006019 | 0.456328536003009 |
46 | 0.488071435448853 | 0.976142870897705 | 0.511928564551148 |
47 | 0.491751501995867 | 0.983503003991735 | 0.508248498004133 |
48 | 0.600326453223506 | 0.799347093552988 | 0.399673546776494 |
49 | 0.549650766987107 | 0.900698466025785 | 0.450349233012893 |
50 | 0.518881295275454 | 0.96223740944909 | 0.481118704724546 |
51 | 0.509331138425358 | 0.981337723149283 | 0.490668861574642 |
52 | 0.459587586423106 | 0.919175172846213 | 0.540412413576894 |
53 | 0.491938001021854 | 0.983876002043707 | 0.508061998978147 |
54 | 0.456141792701001 | 0.912283585402002 | 0.543858207298999 |
55 | 0.618527099540189 | 0.762945800919623 | 0.381472900459811 |
56 | 0.575510735373065 | 0.84897852925387 | 0.424489264626935 |
57 | 0.535549846207916 | 0.928900307584169 | 0.464450153792084 |
58 | 0.519585531384092 | 0.960828937231816 | 0.480414468615908 |
59 | 0.471739241060611 | 0.943478482121222 | 0.528260758939389 |
60 | 0.435964021817484 | 0.871928043634968 | 0.564035978182516 |
61 | 0.398157482727049 | 0.796314965454098 | 0.601842517272951 |
62 | 0.362365709510587 | 0.724731419021175 | 0.637634290489413 |
63 | 0.31785357983526 | 0.63570715967052 | 0.68214642016474 |
64 | 0.326647962170927 | 0.653295924341854 | 0.673352037829073 |
65 | 0.286011796068072 | 0.572023592136144 | 0.713988203931928 |
66 | 0.326478630228336 | 0.652957260456673 | 0.673521369771664 |
67 | 0.385743769977070 | 0.771487539954141 | 0.61425623002293 |
68 | 0.499026387530035 | 0.99805277506007 | 0.500973612469965 |
69 | 0.45154536487852 | 0.90309072975704 | 0.54845463512148 |
70 | 0.436022161394265 | 0.87204432278853 | 0.563977838605735 |
71 | 0.510501642219656 | 0.978996715560688 | 0.489498357780344 |
72 | 0.462360329078122 | 0.924720658156244 | 0.537639670921878 |
73 | 0.4175062465648 | 0.8350124931296 | 0.5824937534352 |
74 | 0.384046985004067 | 0.768093970008133 | 0.615953014995933 |
75 | 0.349629313926797 | 0.699258627853595 | 0.650370686073203 |
76 | 0.324814181075246 | 0.649628362150493 | 0.675185818924754 |
77 | 0.283690820396231 | 0.567381640792462 | 0.716309179603769 |
78 | 0.249370704845817 | 0.498741409691633 | 0.750629295154183 |
79 | 0.214519905851015 | 0.429039811702031 | 0.785480094148985 |
80 | 0.189274440119874 | 0.378548880239748 | 0.810725559880126 |
81 | 0.300038704743211 | 0.600077409486423 | 0.699961295256789 |
82 | 0.271083570647963 | 0.542167141295925 | 0.728916429352037 |
83 | 0.234284830549141 | 0.468569661098283 | 0.765715169450859 |
84 | 0.232605380948609 | 0.465210761897218 | 0.767394619051391 |
85 | 0.208125856627594 | 0.416251713255189 | 0.791874143372406 |
86 | 0.207625900657262 | 0.415251801314523 | 0.792374099342738 |
87 | 0.183973932344488 | 0.367947864688977 | 0.816026067655512 |
88 | 0.171303222619938 | 0.342606445239876 | 0.828696777380062 |
89 | 0.164056901412649 | 0.328113802825299 | 0.83594309858735 |
90 | 0.199583836833028 | 0.399167673666056 | 0.800416163166972 |
91 | 0.169873153050196 | 0.339746306100392 | 0.830126846949804 |
92 | 0.151180336888609 | 0.302360673777217 | 0.848819663111391 |
93 | 0.127355090184568 | 0.254710180369136 | 0.872644909815432 |
94 | 0.117270958065542 | 0.234541916131085 | 0.882729041934458 |
95 | 0.113812105284465 | 0.227624210568931 | 0.886187894715535 |
96 | 0.102033509259048 | 0.204067018518096 | 0.897966490740952 |
97 | 0.104042702923085 | 0.208085405846170 | 0.895957297076915 |
98 | 0.0925341672177332 | 0.185068334435466 | 0.907465832782267 |
99 | 0.0914691248151188 | 0.182938249630238 | 0.908530875184881 |
100 | 0.0724366793297473 | 0.144873358659495 | 0.927563320670253 |
101 | 0.0572382950334735 | 0.114476590066947 | 0.942761704966527 |
102 | 0.0463257253238612 | 0.0926514506477225 | 0.953674274676139 |
103 | 0.036834983585444 | 0.073669967170888 | 0.963165016414556 |
104 | 0.038930092934507 | 0.077860185869014 | 0.961069907065493 |
105 | 0.0319443154390978 | 0.0638886308781955 | 0.968055684560902 |
106 | 0.0276040168058954 | 0.0552080336117908 | 0.972395983194105 |
107 | 0.0235469039257523 | 0.0470938078515045 | 0.976453096074248 |
108 | 0.0173587129539882 | 0.0347174259079764 | 0.982641287046012 |
109 | 0.0159083280548811 | 0.0318166561097621 | 0.984091671945119 |
110 | 0.0219082784332125 | 0.0438165568664251 | 0.978091721566787 |
111 | 0.115708228944400 | 0.231416457888801 | 0.8842917710556 |
112 | 0.106259112699560 | 0.212518225399121 | 0.89374088730044 |
113 | 0.457094732753297 | 0.914189465506593 | 0.542905267246703 |
114 | 0.785650296352116 | 0.428699407295767 | 0.214349703647884 |
115 | 0.744341869519473 | 0.511316260961054 | 0.255658130480527 |
116 | 0.821956543487791 | 0.356086913024417 | 0.178043456512209 |
117 | 0.79992250278695 | 0.4001549944261 | 0.20007749721305 |
118 | 0.755167335094304 | 0.489665329811391 | 0.244832664905696 |
119 | 0.76423389306938 | 0.471532213861242 | 0.235766106930621 |
120 | 0.73572130083281 | 0.528557398334381 | 0.264278699167190 |
121 | 0.68194337931536 | 0.636113241369281 | 0.318056620684641 |
122 | 0.702685906931684 | 0.594628186136633 | 0.297314093068316 |
123 | 0.647613683969824 | 0.704772632060352 | 0.352386316030176 |
124 | 0.588376998460726 | 0.823246003078548 | 0.411623001539274 |
125 | 0.54754566981672 | 0.90490866036656 | 0.45245433018328 |
126 | 0.500740088478052 | 0.998519823043896 | 0.499259911521948 |
127 | 0.444779663144027 | 0.889559326288054 | 0.555220336855973 |
128 | 0.384399277539522 | 0.768798555079045 | 0.615600722460478 |
129 | 0.328686665659967 | 0.657373331319934 | 0.671313334340033 |
130 | 0.309651836190470 | 0.619303672380941 | 0.69034816380953 |
131 | 0.313115128060602 | 0.626230256121203 | 0.686884871939399 |
132 | 0.382163147058339 | 0.764326294116678 | 0.617836852941661 |
133 | 0.35228337397177 | 0.70456674794354 | 0.64771662602823 |
134 | 0.302238893426928 | 0.604477786853856 | 0.697761106573072 |
135 | 0.243829218590009 | 0.487658437180017 | 0.756170781409991 |
136 | 0.186225145535720 | 0.372450291071439 | 0.81377485446428 |
137 | 0.179780522002677 | 0.359561044005353 | 0.820219477997324 |
138 | 0.126146196590667 | 0.252292393181334 | 0.873853803409333 |
139 | 0.0969933788038216 | 0.193986757607643 | 0.903006621196178 |
140 | 0.072914452509362 | 0.145828905018724 | 0.927085547490638 |
141 | 0.0844151126656436 | 0.168830225331287 | 0.915584887334356 |
142 | 0.143436921527209 | 0.286873843054419 | 0.85656307847279 |
143 | 0.0822635621176883 | 0.164527124235377 | 0.917736437882312 |
144 | 0.0444199958049524 | 0.0888399916099047 | 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 |