Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 7.52338981352697 + 0.329234589786872CM[t] -0.360242862076528D[t] + 0.196436099966937PE[t] + 0.399119446996563O[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) | 7.52338981352697 | 2.214293 | 3.3976 | 0.000865 | 0.000433 |
CM | 0.329234589786872 | 0.055051 | 5.9805 | 0 | 0 |
D | -0.360242862076528 | 0.105903 | -3.4016 | 0.000853 | 0.000427 |
PE | 0.196436099966937 | 0.085046 | 2.3098 | 0.02223 | 0.011115 |
O | 0.399119446996563 | 0.070569 | 5.6558 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.605745939016341 |
R-squared | 0.366928142634789 |
Adjusted R-squared | 0.350484717768160 |
F-TEST (value) | 22.3145813971791 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 154 |
p-value | 1.50990331349021e-14 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.39855285935688 |
Sum Squared Residuals | 1778.72487682780 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 22.9195226208873 | 1.08047737911266 |
2 | 25 | 22.3463830560465 | 2.65361694395354 |
3 | 30 | 24.2763205417966 | 5.72367945820337 |
4 | 19 | 20.2708063653626 | -1.27080636536265 |
5 | 22 | 20.5081722256164 | 1.49182777438363 |
6 | 22 | 23.1204117918552 | -1.12041179185521 |
7 | 25 | 22.6444362630495 | 2.35556373695049 |
8 | 23 | 19.3707772538392 | 3.62922274616076 |
9 | 17 | 18.8235876699938 | -1.82358766999384 |
10 | 21 | 21.6893618315462 | -0.689361831546238 |
11 | 19 | 22.7416002990848 | -3.74160029908479 |
12 | 19 | 23.4046408076239 | -4.40464080762391 |
13 | 15 | 23.1552674155735 | -8.15526741557349 |
14 | 16 | 17.0778507893901 | -1.07785078939014 |
15 | 23 | 19.4406621110489 | 3.55933788895107 |
16 | 27 | 24.1551194580711 | 2.84488054192886 |
17 | 22 | 20.9454442799962 | 1.05455572000378 |
18 | 14 | 16.5301962273129 | -2.53019622731288 |
19 | 22 | 24.1444191400076 | -2.14441914000762 |
20 | 23 | 24.0080646672178 | -1.00806466721779 |
21 | 23 | 21.5513862931887 | 1.44861370681128 |
22 | 21 | 24.4717188123923 | -3.47171881239229 |
23 | 19 | 22.3267442268275 | -3.32674422682747 |
24 | 18 | 23.8303703084389 | -5.83037030843893 |
25 | 20 | 23.1523171521758 | -3.1523171521758 |
26 | 23 | 22.4346085809263 | 0.56539141907374 |
27 | 25 | 23.3913040779972 | 1.60869592200278 |
28 | 19 | 23.3276664678502 | -4.32766646785022 |
29 | 24 | 23.8470899105413 | 0.152910089458663 |
30 | 22 | 21.6116086617062 | 0.388391338293833 |
31 | 25 | 25.1649802102494 | -0.164980210249377 |
32 | 26 | 23.1050852922967 | 2.89491470770331 |
33 | 29 | 22.8408175104868 | 6.15918248951317 |
34 | 32 | 25.2075310361039 | 6.79246896389614 |
35 | 25 | 21.5991141675808 | 3.40088583241921 |
36 | 29 | 24.4400414150955 | 4.5599585849045 |
37 | 28 | 24.9740125272788 | 3.02598747272125 |
38 | 17 | 17.1774147210595 | -0.177414721059483 |
39 | 28 | 26.0524599751178 | 1.94754002488222 |
40 | 29 | 22.9683206938046 | 6.03167930619538 |
41 | 26 | 27.5372260575766 | -1.53722605757662 |
42 | 25 | 23.4542177106075 | 1.54578228939254 |
43 | 14 | 19.578755907371 | -5.57875590737100 |
44 | 25 | 22.2009169616070 | 2.79908303839302 |
45 | 26 | 21.6497612690894 | 4.35023873091056 |
46 | 20 | 20.2777775899621 | -0.277777589962093 |
47 | 18 | 21.3936536676476 | -3.39365366764764 |
48 | 32 | 24.6915228350423 | 7.3084771649577 |
49 | 25 | 25.0057447771052 | -0.00574477710516708 |
50 | 25 | 21.7733073959194 | 3.22669260408062 |
51 | 23 | 20.8806505825134 | 2.11934941748661 |
52 | 21 | 22.1435265985227 | -1.14352659852267 |
53 | 20 | 24.0382307040061 | -4.03823070400614 |
54 | 15 | 16.54804088047 | -1.54804088047002 |
55 | 30 | 26.5568707700849 | 3.4431292299151 |
56 | 24 | 25.3320291034943 | -1.33202910349435 |
57 | 26 | 24.2975804365833 | 1.70241956341668 |
58 | 24 | 21.7691681767531 | 2.23083182324693 |
59 | 22 | 21.5029020721061 | 0.49709792789394 |
60 | 14 | 15.6686115909104 | -1.66861159091044 |
61 | 24 | 22.2134114557324 | 1.78658854426764 |
62 | 24 | 22.9674236057737 | 1.03257639422631 |
63 | 24 | 23.3813825900001 | 0.618617409999919 |
64 | 24 | 19.9168107503488 | 4.08318924965119 |
65 | 19 | 18.5538514711877 | 0.446148528812339 |
66 | 31 | 26.8500297441038 | 4.14997025589623 |
67 | 22 | 26.5873830278616 | -4.58738302786159 |
68 | 27 | 21.4718389472868 | 5.52816105271322 |
69 | 19 | 17.7456910891974 | 1.25430891080260 |
70 | 25 | 22.284193400973 | 2.71580659902702 |
71 | 20 | 24.9978764644748 | -4.99787646447479 |
72 | 21 | 21.4843334414122 | -0.484333441412164 |
73 | 27 | 27.4818888698591 | -0.481888869859067 |
74 | 23 | 24.3831470665241 | -1.38314706652415 |
75 | 25 | 25.765831063715 | -0.765831063715015 |
76 | 20 | 22.2320983443908 | -2.23209834439081 |
77 | 21 | 19.2916948861692 | 1.70830511383083 |
78 | 22 | 22.4433739815876 | -0.443373981587572 |
79 | 23 | 22.9947576371289 | 0.0052423628711022 |
80 | 25 | 24.1135839782121 | 0.88641602178786 |
81 | 25 | 23.382279678031 | 1.61772032196899 |
82 | 17 | 23.8260579787784 | -6.82605797877844 |
83 | 19 | 21.4486989876275 | -2.44869898762751 |
84 | 25 | 23.9479830400407 | 1.05201695995932 |
85 | 19 | 22.4000991781963 | -3.40009917819633 |
86 | 20 | 23.1964890435980 | -3.19648904359797 |
87 | 26 | 22.5745514058398 | 3.42544859416018 |
88 | 23 | 20.7608974538614 | 2.23910254613858 |
89 | 27 | 24.3426494160364 | 2.65735058396358 |
90 | 17 | 20.9151599852433 | -3.91515998524332 |
91 | 17 | 23.3690612063689 | -6.36906120636888 |
92 | 19 | 20.1648769286661 | -1.16487692866605 |
93 | 17 | 19.7761439478985 | -2.77614394789849 |
94 | 22 | 22.0930526075082 | -0.0930526075081821 |
95 | 21 | 23.4736834293323 | -2.47368342933229 |
96 | 32 | 28.629497197371 | 3.37050280262897 |
97 | 21 | 24.6938678781467 | -3.69386787814674 |
98 | 21 | 24.3053938966841 | -3.30539389668408 |
99 | 18 | 21.2754028473198 | -3.27540284731985 |
100 | 18 | 21.3010609605777 | -3.30106096057775 |
101 | 23 | 22.8214066442916 | 0.178593355708382 |
102 | 19 | 20.6789502123254 | -1.67895021232541 |
103 | 20 | 20.9840929018925 | -0.98409290189246 |
104 | 21 | 22.2948388665069 | -1.29483886650688 |
105 | 20 | 23.7876463720903 | -3.78764637209027 |
106 | 17 | 18.8584432937121 | -1.85844329371212 |
107 | 18 | 20.30476490105 | -2.30476490104999 |
108 | 19 | 20.7232952142418 | -1.72329521424176 |
109 | 22 | 22.0389043755593 | -0.0389043755592504 |
110 | 15 | 18.8157193573635 | -3.81571935736346 |
111 | 14 | 18.861999276682 | -4.86199927668202 |
112 | 18 | 26.5818597583357 | -8.58185975833566 |
113 | 24 | 21.3056871420727 | 2.69431285792725 |
114 | 35 | 23.5534349220095 | 11.4465650779905 |
115 | 29 | 19.0762800298061 | 9.9237199701939 |
116 | 21 | 22.0417363809924 | -1.04173638099239 |
117 | 25 | 20.5444758044082 | 4.45552419559183 |
118 | 20 | 18.5089007496991 | 1.49109925030089 |
119 | 22 | 23.2362627165489 | -1.23626271654894 |
120 | 13 | 16.9054517371134 | -3.90545173711341 |
121 | 26 | 23.2642019681974 | 2.73579803180261 |
122 | 17 | 16.9131469392496 | 0.086853060750385 |
123 | 25 | 20.0565256122386 | 4.94347438776143 |
124 | 20 | 20.7365685384335 | -0.736568538433521 |
125 | 19 | 18.1234647525965 | 0.876535247403452 |
126 | 21 | 22.6645711067815 | -1.66457110678147 |
127 | 22 | 21.1231934913047 | 0.876806508695295 |
128 | 24 | 22.6833128479695 | 1.31668715203046 |
129 | 21 | 22.9743948303731 | -1.97439483037314 |
130 | 26 | 25.4835144819727 | 0.516485518027266 |
131 | 24 | 20.5416986515047 | 3.45830134849535 |
132 | 16 | 20.2876990779592 | -4.28769907795923 |
133 | 23 | 22.416094802762 | 0.583905197238016 |
134 | 18 | 20.8568725341281 | -2.85687253412808 |
135 | 16 | 22.3718680588102 | -6.37186805881019 |
136 | 26 | 24.1096817742539 | 1.89031822574610 |
137 | 19 | 19.1060773622303 | -0.106077362230300 |
138 | 21 | 16.8689201952978 | 4.13107980470218 |
139 | 21 | 22.1745348708123 | -1.17453487081232 |
140 | 22 | 18.4274184863950 | 3.57258151360503 |
141 | 23 | 19.7126245957160 | 3.28737540428395 |
142 | 29 | 24.8046824956432 | 4.19531750435677 |
143 | 21 | 19.0872807685126 | 1.91271923148739 |
144 | 21 | 19.9875926955894 | 1.01240730441057 |
145 | 23 | 21.8742005254187 | 1.12579947458127 |
146 | 27 | 23.0469709516756 | 3.95302904832437 |
147 | 25 | 25.4101595306039 | -0.410159530603869 |
148 | 21 | 21.0090818901432 | -0.00908189014322001 |
149 | 10 | 17.0947435019867 | -7.09474350198672 |
150 | 20 | 22.6171022316943 | -2.6171022316943 |
151 | 26 | 22.5278065082894 | 3.4721934917106 |
152 | 24 | 23.6999168617234 | 0.300083138276562 |
153 | 29 | 31.7712548047923 | -2.77125480479230 |
154 | 19 | 19.0639037936453 | -0.0639037936452667 |
155 | 24 | 22.0565210656926 | 1.94347893430741 |
156 | 19 | 20.8133697677130 | -1.81336976771304 |
157 | 24 | 23.4382220860418 | 0.56177791395819 |
158 | 22 | 21.8105629152717 | 0.189437084728275 |
159 | 17 | 23.6804511429986 | -6.68045114299861 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 0.313908091714112 | 0.627816183428223 | 0.686091908285888 |
9 | 0.184161427812675 | 0.368322855625350 | 0.815838572187325 |
10 | 0.113055352943660 | 0.226110705887320 | 0.88694464705634 |
11 | 0.228358723830182 | 0.456717447660365 | 0.771641276169818 |
12 | 0.209735537529444 | 0.419471075058889 | 0.790264462470556 |
13 | 0.81275056304401 | 0.374498873911982 | 0.187249436955991 |
14 | 0.74190122158433 | 0.516197556831339 | 0.258098778415670 |
15 | 0.693429293364596 | 0.613141413270807 | 0.306570706635404 |
16 | 0.62476569885514 | 0.750468602289719 | 0.375234301144860 |
17 | 0.544875030289121 | 0.910249939421758 | 0.455124969710879 |
18 | 0.519120707484585 | 0.96175858503083 | 0.480879292515415 |
19 | 0.454185870152810 | 0.908371740305619 | 0.54581412984719 |
20 | 0.451890113889269 | 0.903780227778537 | 0.548109886110731 |
21 | 0.438511594078955 | 0.87702318815791 | 0.561488405921045 |
22 | 0.37533295715466 | 0.75066591430932 | 0.62466704284534 |
23 | 0.352144474222603 | 0.704288948445205 | 0.647855525777397 |
24 | 0.384517196995652 | 0.769034393991304 | 0.615482803004348 |
25 | 0.400964584236053 | 0.801929168472106 | 0.599035415763947 |
26 | 0.336307554187925 | 0.672615108375850 | 0.663692445812075 |
27 | 0.294853399922711 | 0.589706799845423 | 0.705146600077289 |
28 | 0.315916371387688 | 0.631832742775376 | 0.684083628612312 |
29 | 0.264856394702076 | 0.529712789404151 | 0.735143605297924 |
30 | 0.214634392561454 | 0.429268785122908 | 0.785365607438546 |
31 | 0.173124834581063 | 0.346249669162126 | 0.826875165418937 |
32 | 0.179223094879201 | 0.358446189758401 | 0.8207769051208 |
33 | 0.361651415217500 | 0.723302830434999 | 0.6383485847825 |
34 | 0.59728455328745 | 0.8054308934251 | 0.40271544671255 |
35 | 0.571475634319893 | 0.857048731360213 | 0.428524365680107 |
36 | 0.675196021333216 | 0.649607957333567 | 0.324803978666784 |
37 | 0.679234296222423 | 0.641531407555154 | 0.320765703777577 |
38 | 0.627616884363965 | 0.744766231272069 | 0.372383115636035 |
39 | 0.588863865476317 | 0.822272269047366 | 0.411136134523683 |
40 | 0.68532488483786 | 0.629350230324279 | 0.314675115162139 |
41 | 0.655914904165825 | 0.68817019166835 | 0.344085095834175 |
42 | 0.611267501492562 | 0.777464997014877 | 0.388732498507438 |
43 | 0.680532468743455 | 0.63893506251309 | 0.319467531256545 |
44 | 0.65832080898886 | 0.683358382022279 | 0.341679191011140 |
45 | 0.675512812030156 | 0.648974375939688 | 0.324487187969844 |
46 | 0.62900258110614 | 0.74199483778772 | 0.37099741889386 |
47 | 0.624138230638205 | 0.75172353872359 | 0.375861769361795 |
48 | 0.754353108638781 | 0.491293782722438 | 0.245646891361219 |
49 | 0.717021540602141 | 0.565956918795718 | 0.282978459397859 |
50 | 0.719902362680314 | 0.560195274639371 | 0.280097637319686 |
51 | 0.688933476314936 | 0.622133047370129 | 0.311066523685064 |
52 | 0.653625703909832 | 0.692748592180335 | 0.346374296090168 |
53 | 0.689469892175614 | 0.621060215648773 | 0.310530107824386 |
54 | 0.65294711015571 | 0.694105779688579 | 0.347052889844290 |
55 | 0.645234269684252 | 0.709531460631496 | 0.354765730315748 |
56 | 0.613021738006507 | 0.773956523986986 | 0.386978261993493 |
57 | 0.574416392160035 | 0.85116721567993 | 0.425583607839965 |
58 | 0.544291477785167 | 0.911417044429666 | 0.455708522214833 |
59 | 0.497213344533111 | 0.994426689066222 | 0.502786655466889 |
60 | 0.457758574709084 | 0.915517149418168 | 0.542241425290916 |
61 | 0.421560516161258 | 0.843121032322515 | 0.578439483838742 |
62 | 0.37875670660946 | 0.75751341321892 | 0.62124329339054 |
63 | 0.335740404334552 | 0.671480808669104 | 0.664259595665448 |
64 | 0.356503041758516 | 0.713006083517033 | 0.643496958241484 |
65 | 0.314203826821476 | 0.628407653642952 | 0.685796173178524 |
66 | 0.328798541588361 | 0.657597083176721 | 0.67120145841164 |
67 | 0.386766831145141 | 0.773533662290282 | 0.613233168854859 |
68 | 0.460372895375259 | 0.920745790750519 | 0.539627104624741 |
69 | 0.420219324718961 | 0.840438649437921 | 0.57978067528104 |
70 | 0.403698209936378 | 0.807396419872756 | 0.596301790063622 |
71 | 0.461526333698883 | 0.923052667397766 | 0.538473666301117 |
72 | 0.417422107553176 | 0.834844215106352 | 0.582577892446824 |
73 | 0.37638820216516 | 0.75277640433032 | 0.62361179783484 |
74 | 0.340676462671655 | 0.68135292534331 | 0.659323537328345 |
75 | 0.302708572746511 | 0.605417145493022 | 0.69729142725349 |
76 | 0.279100202788534 | 0.558200405577068 | 0.720899797211466 |
77 | 0.251680858250261 | 0.503361716500521 | 0.748319141749739 |
78 | 0.217539790976247 | 0.435079581952495 | 0.782460209023753 |
79 | 0.188646320569137 | 0.377292641138275 | 0.811353679430863 |
80 | 0.161109146881336 | 0.322218293762673 | 0.838890853118664 |
81 | 0.142432352034499 | 0.284864704068999 | 0.8575676479655 |
82 | 0.232412287423974 | 0.464824574847949 | 0.767587712576026 |
83 | 0.214487351911849 | 0.428974703823699 | 0.78551264808815 |
84 | 0.186502118395167 | 0.373004236790333 | 0.813497881604833 |
85 | 0.185563848053983 | 0.371127696107966 | 0.814436151946017 |
86 | 0.179814665337771 | 0.359629330675543 | 0.820185334662229 |
87 | 0.182409793807212 | 0.364819587614425 | 0.817590206192788 |
88 | 0.172639636431485 | 0.345279272862971 | 0.827360363568515 |
89 | 0.162585478391337 | 0.325170956782673 | 0.837414521608663 |
90 | 0.167948517213653 | 0.335897034427306 | 0.832051482786347 |
91 | 0.241334617742729 | 0.482669235485457 | 0.758665382257271 |
92 | 0.20893943701761 | 0.41787887403522 | 0.79106056298239 |
93 | 0.193705913068455 | 0.387411826136909 | 0.806294086931545 |
94 | 0.162983760088996 | 0.325967520177992 | 0.837016239911004 |
95 | 0.146929950032658 | 0.293859900065317 | 0.853070049967342 |
96 | 0.151256538778794 | 0.302513077557588 | 0.848743461221206 |
97 | 0.152081860366667 | 0.304163720733334 | 0.847918139633333 |
98 | 0.147047161493748 | 0.294094322987496 | 0.852952838506252 |
99 | 0.141381205888916 | 0.282762411777833 | 0.858618794111084 |
100 | 0.137412310693485 | 0.27482462138697 | 0.862587689306515 |
101 | 0.112949386229247 | 0.225898772458493 | 0.887050613770753 |
102 | 0.095119274613827 | 0.190238549227654 | 0.904880725386173 |
103 | 0.0775192624770602 | 0.155038524954120 | 0.92248073752294 |
104 | 0.062875943915877 | 0.125751887831754 | 0.937124056084123 |
105 | 0.0637898211862556 | 0.127579642372511 | 0.936210178813744 |
106 | 0.0551237573644963 | 0.110247514728993 | 0.944876242635504 |
107 | 0.0490025614394577 | 0.0980051228789154 | 0.950997438560542 |
108 | 0.0421038220666769 | 0.0842076441333539 | 0.957896177933323 |
109 | 0.0321670700054552 | 0.0643341400109104 | 0.967832929994545 |
110 | 0.0334237492536641 | 0.0668474985073282 | 0.966576250746336 |
111 | 0.043875132073119 | 0.087750264146238 | 0.956124867926881 |
112 | 0.144453178232742 | 0.288906356465483 | 0.855546821767258 |
113 | 0.129192154690002 | 0.258384309380004 | 0.870807845309998 |
114 | 0.538394111787916 | 0.923211776424167 | 0.461605888212084 |
115 | 0.888138364029625 | 0.223723271940750 | 0.111861635970375 |
116 | 0.86092682812201 | 0.278146343755980 | 0.139073171877990 |
117 | 0.90239189134391 | 0.195216217312181 | 0.0976081086560904 |
118 | 0.881391745659575 | 0.23721650868085 | 0.118608254340425 |
119 | 0.858284891281352 | 0.283430217437295 | 0.141715108718648 |
120 | 0.894615113812526 | 0.210769772374948 | 0.105384886187474 |
121 | 0.87655186336812 | 0.246896273263759 | 0.123448136631879 |
122 | 0.844490577281067 | 0.311018845437867 | 0.155509422718933 |
123 | 0.871604045375132 | 0.256791909249736 | 0.128395954624868 |
124 | 0.837921861731835 | 0.324156276536329 | 0.162078138268165 |
125 | 0.80599531994001 | 0.388009360119982 | 0.194004680059991 |
126 | 0.765495653261683 | 0.469008693476634 | 0.234504346738317 |
127 | 0.734103367401864 | 0.531793265196272 | 0.265896632598136 |
128 | 0.698287304790342 | 0.603425390419316 | 0.301712695209658 |
129 | 0.645833838520459 | 0.708332322959083 | 0.354166161479541 |
130 | 0.586880510831911 | 0.826238978336178 | 0.413119489168089 |
131 | 0.586817344832592 | 0.826365310334816 | 0.413182655167408 |
132 | 0.589229045267082 | 0.821541909465835 | 0.410770954732918 |
133 | 0.541871641549675 | 0.91625671690065 | 0.458128358450325 |
134 | 0.495158390907884 | 0.990316781815767 | 0.504841609092116 |
135 | 0.649441511758549 | 0.701116976482903 | 0.350558488241451 |
136 | 0.612907870488338 | 0.774184259023325 | 0.387092129511662 |
137 | 0.545655076054474 | 0.908689847891052 | 0.454344923945526 |
138 | 0.549902165955774 | 0.900195668088451 | 0.450097834044226 |
139 | 0.475549976571105 | 0.95109995314221 | 0.524450023428895 |
140 | 0.454475219699718 | 0.908950439399436 | 0.545524780300282 |
141 | 0.424878335520443 | 0.849756671040887 | 0.575121664479556 |
142 | 0.491065817282313 | 0.982131634564626 | 0.508934182717687 |
143 | 0.616683573847295 | 0.766632852305411 | 0.383316426152705 |
144 | 0.542083881601001 | 0.915832236797998 | 0.457916118398999 |
145 | 0.466931403195775 | 0.93386280639155 | 0.533068596804225 |
146 | 0.492273938949524 | 0.984547877899049 | 0.507726061050476 |
147 | 0.438778444456133 | 0.877556888912266 | 0.561221555543867 |
148 | 0.327473281349775 | 0.65494656269955 | 0.672526718650225 |
149 | 0.561540225645244 | 0.876919548709513 | 0.438459774354756 |
150 | 0.539603645709571 | 0.920792708580858 | 0.460396354290429 |
151 | 0.400811779071350 | 0.801623558142699 | 0.59918822092865 |
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 | 5 | 0.0347222222222222 | OK |