Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 13.7057371438104 + 0.324108497176835x[t] + 1.14327246228138M1[t] + 0.439706450988726M2[t] + 1.83383716930753M3[t] + 1.71023841287010M4[t] + 1.09272498914167M5[t] + 1.90756098740434M6[t] + 2.40680372186540M7[t] + 2.79780553151221M8[t] + 2.16600472664307M9[t] + 1.47795465102299M10[t] + 0.411061338553018M11[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) | 13.7057371438104 | 1.711689 | 8.0071 | 0 | 0 |
x | 0.324108497176835 | 0.056197 | 5.7674 | 0 | 0 |
M1 | 1.14327246228138 | 1.495494 | 0.7645 | 0.445816 | 0.222908 |
M2 | 0.439706450988726 | 1.501932 | 0.2928 | 0.770121 | 0.38506 |
M3 | 1.83383716930753 | 1.495763 | 1.226 | 0.222164 | 0.111082 |
M4 | 1.71023841287010 | 1.5348 | 1.1143 | 0.266978 | 0.133489 |
M5 | 1.09272498914167 | 1.53657 | 0.7111 | 0.478129 | 0.239064 |
M6 | 1.90756098740434 | 1.541815 | 1.2372 | 0.217992 | 0.108996 |
M7 | 2.40680372186540 | 1.531582 | 1.5714 | 0.118243 | 0.059121 |
M8 | 2.79780553151221 | 1.527569 | 1.8315 | 0.069058 | 0.034529 |
M9 | 2.16600472664307 | 1.523508 | 1.4217 | 0.15724 | 0.07862 |
M10 | 1.47795465102299 | 1.52233 | 0.9709 | 0.333229 | 0.166614 |
M11 | 0.411061338553018 | 1.528798 | 0.2689 | 0.788403 | 0.394201 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.467233839799462 |
R-squared | 0.218307461053750 |
Adjusted R-squared | 0.154058759222551 |
F-TEST (value) | 3.39785014843275 |
F-TEST (DF numerator) | 12 |
F-TEST (DF denominator) | 146 |
p-value | 0.00021079102177457 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.87855041641 |
Sum Squared Residuals | 2196.30038656459 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 22.6276135383358 | 1.37238646166418 |
2 | 25 | 22.2481560242200 | 2.75184397578002 |
3 | 30 | 21.0494187651241 | 8.9505812348759 |
4 | 19 | 21.2499285058635 | -2.24992850586349 |
5 | 22 | 20.6324150821351 | 1.36758491786493 |
6 | 22 | 20.7990340860441 | 1.20096591395593 |
7 | 25 | 22.5947108092125 | 2.40528919078753 |
8 | 23 | 21.6892786301519 | 1.31072136984806 |
9 | 17 | 21.7056948196365 | -4.70569481963647 |
10 | 21 | 20.6935362468396 | 0.306463753160447 |
11 | 19 | 21.5712939174306 | -2.57129391743060 |
12 | 19 | 23.4289920591154 | -4.42899205911543 |
13 | 15 | 22.3035050411590 | -7.30350504115896 |
14 | 16 | 19.9793965439821 | -3.97939654398212 |
15 | 23 | 20.4012017707704 | 2.59879822922958 |
16 | 27 | 19.3052775228025 | 7.69472247719752 |
17 | 22 | 21.6047405736656 | 0.395259426334421 |
18 | 14 | 20.4749255888672 | -6.47492558886723 |
19 | 22 | 22.5947108092125 | -0.594710809212473 |
20 | 23 | 26.5509060878045 | -3.55090608780447 |
21 | 23 | 24.622671294228 | -1.62267129422799 |
22 | 21 | 26.2033806988458 | -5.20338069884575 |
23 | 19 | 20.9230769230769 | -1.92307692307692 |
24 | 18 | 23.7531005562923 | -5.75310055629226 |
25 | 20 | 21.0070710524516 | -1.00707105245162 |
26 | 23 | 19.3311795496285 | 3.66882045037155 |
27 | 25 | 22.0217442566546 | 2.9782557433454 |
28 | 19 | 22.222253997394 | -3.222253997394 |
29 | 24 | 21.9288490708424 | 2.07115092915758 |
30 | 22 | 21.1231425832209 | 0.876857416779095 |
31 | 25 | 23.8911447979198 | 1.10885520208018 |
32 | 26 | 24.6062551047435 | 1.39374489525654 |
33 | 29 | 24.2985627970511 | 4.70143720294885 |
34 | 32 | 23.2864042242542 | 8.71359577574576 |
35 | 25 | 19.6266429343696 | 5.37335706563042 |
36 | 29 | 24.0772090534691 | 4.9227909465309 |
37 | 28 | 25.5445900129273 | 2.45540998707269 |
38 | 17 | 18.3588540580979 | -1.35885405809794 |
39 | 28 | 25.9110462227766 | 2.08895377722337 |
40 | 29 | 23.5186879861013 | 5.48131201389865 |
41 | 26 | 24.1976085510803 | 1.80239144891974 |
42 | 25 | 22.7436850691051 | 2.25631493089492 |
43 | 14 | 21.9464938148588 | -7.9464938148588 |
44 | 25 | 22.0133871273288 | 2.98661287267123 |
45 | 26 | 22.3539118139901 | 3.64608818600986 |
46 | 20 | 20.0453192524859 | -0.0453192524858794 |
47 | 18 | 20.5989684259001 | -2.59896842590009 |
48 | 32 | 24.4013175506459 | 7.59868244935407 |
49 | 25 | 24.2481560242200 | 0.751843975780029 |
50 | 25 | 21.5999390298663 | 3.4000609701337 |
51 | 23 | 23.9663952397156 | -0.966395239715616 |
52 | 21 | 21.2499285058635 | -0.249928505863495 |
53 | 20 | 21.2806320764887 | -1.28063207648874 |
54 | 15 | 19.1784916001599 | -4.17849160015989 |
55 | 30 | 25.1875787866272 | 4.81242121337284 |
56 | 24 | 24.9303636019203 | -0.930363601920293 |
57 | 26 | 23.0021288083438 | 2.99787119165619 |
58 | 24 | 20.6935362468395 | 3.30646375316045 |
59 | 22 | 18.0061004484854 | 3.9938995515146 |
60 | 14 | 18.2432561042861 | -4.24325610428605 |
61 | 24 | 20.3588540580979 | 3.64114594190206 |
62 | 24 | 20.9517220355126 | 3.04827796448737 |
63 | 24 | 21.6976357594778 | 2.30236424052223 |
64 | 24 | 21.2499285058635 | 2.75007149413650 |
65 | 19 | 18.0395471047204 | 0.960452895279612 |
66 | 31 | 25.0124445493429 | 5.98755545065707 |
67 | 22 | 26.1599042781577 | -4.15990427815767 |
68 | 27 | 22.6616041216824 | 4.33839587831756 |
69 | 19 | 18.7887183450449 | 0.211281654955056 |
70 | 25 | 21.6658617383701 | 3.33413826162994 |
71 | 20 | 23.1918364033148 | -3.19183640331477 |
72 | 21 | 19.8637985901702 | 1.13620140982977 |
73 | 27 | 24.5722645213968 | 2.42773547860319 |
74 | 23 | 23.5445900129273 | -0.544590012927316 |
75 | 25 | 23.9663952397156 | 1.03360476028438 |
76 | 20 | 22.8704709917477 | -2.87047099174767 |
77 | 21 | 19.0118725962509 | 1.98812740374911 |
78 | 22 | 22.4195765719282 | -0.419576571928247 |
79 | 23 | 22.2706023120356 | 0.729397687964362 |
80 | 25 | 25.5785805962740 | -0.578580596273965 |
81 | 25 | 23.3262373055206 | 1.67376269447936 |
82 | 17 | 21.0176447440164 | -4.01764474401639 |
83 | 19 | 20.9230769230769 | -1.92307692307692 |
84 | 25 | 20.1879070873471 | 4.81209291265293 |
85 | 19 | 22.3035050411590 | -3.30350504115896 |
86 | 20 | 20.9517220355126 | -0.95172203551263 |
87 | 26 | 22.3458527538314 | 3.65414724616856 |
88 | 23 | 20.277603014333 | 2.72239698566701 |
89 | 27 | 23.8735000539034 | 3.12649994609657 |
90 | 17 | 21.7713595775746 | -4.77135957757458 |
91 | 17 | 24.5393617922735 | -7.53936179227349 |
92 | 19 | 19.7446276470909 | -0.744627647090923 |
93 | 17 | 21.0574778252828 | -4.05747782528279 |
94 | 22 | 22.3140787327237 | -0.314078732723729 |
95 | 21 | 20.2748599287233 | 0.725140071276748 |
96 | 32 | 23.7531005562923 | 8.24689944370774 |
97 | 21 | 24.8963730185736 | -3.89637301857364 |
98 | 21 | 23.5445900129273 | -2.54459001292732 |
99 | 18 | 21.6976357594778 | -3.69763575947777 |
100 | 18 | 22.5463624945708 | -4.54636249457084 |
101 | 23 | 22.2529575680193 | 0.74704243198075 |
102 | 19 | 20.4749255888672 | -1.47492558886723 |
103 | 20 | 22.5947108092125 | -2.59471080921247 |
104 | 21 | 22.3374956245056 | -1.33749562450561 |
105 | 20 | 23.3262373055206 | -3.32623730552064 |
106 | 17 | 23.2864042242542 | -6.28640422425423 |
107 | 18 | 20.9230769230769 | -2.92307692307692 |
108 | 19 | 21.4843410760544 | -2.48434107605441 |
109 | 22 | 22.9517220355126 | -0.951722035512628 |
110 | 15 | 19.6552880468053 | -4.65528804680529 |
111 | 14 | 19.7529847764168 | -5.75298477641675 |
112 | 18 | 24.4910134776319 | -6.49101347763185 |
113 | 24 | 21.6047405736656 | 2.39525942633442 |
114 | 35 | 23.7160105606356 | 11.2839894393644 |
115 | 29 | 19.0295173402673 | 9.97048265973272 |
116 | 21 | 21.6892786301519 | -0.689278630151937 |
117 | 25 | 22.0298033168133 | 2.9701966831867 |
118 | 20 | 20.6935362468395 | -0.693536246839551 |
119 | 22 | 22.2195109117843 | -0.219510911784265 |
120 | 13 | 20.1879070873471 | -7.18790708734707 |
121 | 26 | 24.2481560242200 | 1.75184397578003 |
122 | 17 | 18.6829625552748 | -1.68296255527478 |
123 | 25 | 22.6699612510083 | 2.33003874899173 |
124 | 20 | 20.277603014333 | -0.277603014332988 |
125 | 19 | 20.9565235793119 | -1.95652357931191 |
126 | 21 | 22.0954680747514 | -1.09546807475141 |
127 | 22 | 20.9741683233283 | 1.02583167667171 |
128 | 24 | 22.9857126188593 | 1.01428738114072 |
129 | 21 | 21.7056948196365 | -0.705694819636464 |
130 | 26 | 25.8792722016689 | 0.120727798331079 |
131 | 24 | 21.2471854202538 | 2.75281457974624 |
132 | 16 | 18.8914730986397 | -2.89147309863973 |
133 | 23 | 20.3588540580979 | 2.64114594190206 |
134 | 18 | 19.3311795496285 | -1.33117954962845 |
135 | 16 | 22.3458527538314 | -6.34585275383144 |
136 | 26 | 23.8427964832782 | 2.15720351672182 |
137 | 19 | 20.6324150821351 | -1.63241508213507 |
138 | 21 | 21.4472510803977 | -0.447251080397741 |
139 | 21 | 21.6223853176820 | -0.622385317681966 |
140 | 22 | 23.6339296132130 | -1.63392961321295 |
141 | 23 | 25.5949967857585 | -2.59499678575849 |
142 | 29 | 24.9069467101384 | 4.09305328986159 |
143 | 21 | 21.8954024146074 | -0.89540241460743 |
144 | 21 | 20.5120155845239 | 0.487984415476095 |
145 | 23 | 21.6552880468053 | 1.34471195319471 |
146 | 27 | 23.5445900129273 | 3.45540998707268 |
147 | 25 | 25.5869377255998 | -0.586937725599795 |
148 | 21 | 21.8981455002172 | -0.898145500217166 |
149 | 10 | 19.9841980877814 | -9.9841980877814 |
150 | 20 | 22.7436850691051 | -2.74368506910508 |
151 | 26 | 22.5947108092125 | 3.40528919078753 |
152 | 24 | 25.5785805962740 | -1.57858059627396 |
153 | 29 | 28.1878647631732 | 0.812135236826824 |
154 | 19 | 22.3140787327237 | -3.31407873272373 |
155 | 24 | 20.5989684259001 | 3.40103157409991 |
156 | 19 | 19.2155815958166 | -0.215581595816563 |
157 | 24 | 23.9240475270431 | 0.075952472956865 |
158 | 22 | 21.2758305326895 | 0.724169467310533 |
159 | 17 | 25.5869377255998 | -8.5869377255998 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
16 | 0.96623021520765 | 0.0675395695847 | 0.03376978479235 |
17 | 0.930967911833863 | 0.138064176332273 | 0.0690320881661366 |
18 | 0.943126595332907 | 0.113746809334187 | 0.0568734046670934 |
19 | 0.911161442861403 | 0.177677114277193 | 0.0888385571385967 |
20 | 0.881777107577307 | 0.236445784845386 | 0.118222892422693 |
21 | 0.85143950853018 | 0.297120982939641 | 0.148560491469820 |
22 | 0.816782713687218 | 0.366434572625565 | 0.183217286312782 |
23 | 0.750226540723055 | 0.499546918553891 | 0.249773459276945 |
24 | 0.698011675113096 | 0.603976649773809 | 0.301988324886904 |
25 | 0.62221925968065 | 0.755561480638701 | 0.377780740319351 |
26 | 0.58095010091082 | 0.838099798178361 | 0.419049899089180 |
27 | 0.521674992965865 | 0.95665001406827 | 0.478325007034135 |
28 | 0.510232149579109 | 0.979535700841782 | 0.489767850420891 |
29 | 0.446533467972737 | 0.893066935945474 | 0.553466532027263 |
30 | 0.419988583842592 | 0.839977167685184 | 0.580011416157408 |
31 | 0.353669275872203 | 0.707338551744407 | 0.646330724127796 |
32 | 0.311494381941058 | 0.622988763882117 | 0.688505618058942 |
33 | 0.463675543842037 | 0.927351087684075 | 0.536324456157963 |
34 | 0.737453047508821 | 0.525093904982358 | 0.262546952491179 |
35 | 0.776951025450949 | 0.446097949098103 | 0.223048974549051 |
36 | 0.880907815159552 | 0.238184369680896 | 0.119092184840448 |
37 | 0.897191946690415 | 0.205616106619169 | 0.102808053309585 |
38 | 0.876206677496205 | 0.24758664500759 | 0.123793322503795 |
39 | 0.849055843506871 | 0.301888312986257 | 0.150944156493129 |
40 | 0.867048659347995 | 0.265902681304009 | 0.132951340652005 |
41 | 0.836291859166923 | 0.327416281666154 | 0.163708140833077 |
42 | 0.821626313304448 | 0.356747373391105 | 0.178373686695552 |
43 | 0.906064909082036 | 0.187870181835928 | 0.0939350909179638 |
44 | 0.892798235133133 | 0.214403529733735 | 0.107201764866867 |
45 | 0.886527244670229 | 0.226945510659542 | 0.113472755329771 |
46 | 0.860472350379897 | 0.279055299240206 | 0.139527649620103 |
47 | 0.840925162978728 | 0.318149674042544 | 0.159074837021272 |
48 | 0.916189003733474 | 0.167621992533051 | 0.0838109962665256 |
49 | 0.896235302046465 | 0.207529395907071 | 0.103764697953535 |
50 | 0.886330090541927 | 0.227339818916147 | 0.113669909458073 |
51 | 0.881700133719807 | 0.236599732560385 | 0.118299866280193 |
52 | 0.857995788359688 | 0.284008423280624 | 0.142004211640312 |
53 | 0.834256036026851 | 0.331487927946298 | 0.165743963973149 |
54 | 0.83172541058149 | 0.33654917883702 | 0.16827458941851 |
55 | 0.850452341271356 | 0.299095317457288 | 0.149547658728644 |
56 | 0.820926743843008 | 0.358146512313985 | 0.179073256156992 |
57 | 0.802279810657317 | 0.395440378685365 | 0.197720189342683 |
58 | 0.785405079488895 | 0.429189841022209 | 0.214594920511105 |
59 | 0.785166599651033 | 0.429666800697934 | 0.214833400348967 |
60 | 0.787860735142463 | 0.424278529715073 | 0.212139264857537 |
61 | 0.78638592726879 | 0.427228145462421 | 0.213614072731211 |
62 | 0.767538961926053 | 0.464922076147893 | 0.232461038073947 |
63 | 0.747832956712784 | 0.504334086574433 | 0.252167043287216 |
64 | 0.726006158504322 | 0.547987682991355 | 0.273993841495677 |
65 | 0.686202250942933 | 0.627595498114133 | 0.313797749057067 |
66 | 0.73943726505249 | 0.521125469895021 | 0.260562734947511 |
67 | 0.748613216711446 | 0.502773566577108 | 0.251386783288554 |
68 | 0.757273255435754 | 0.485453489128492 | 0.242726744564246 |
69 | 0.718661171310079 | 0.562677657379843 | 0.281338828689921 |
70 | 0.7085113920557 | 0.5829772158886 | 0.2914886079443 |
71 | 0.699629665021119 | 0.600740669957763 | 0.300370334978881 |
72 | 0.66047390964837 | 0.67905218070326 | 0.33952609035163 |
73 | 0.630092805631273 | 0.739814388737454 | 0.369907194368727 |
74 | 0.588083375999979 | 0.823833248000041 | 0.411916624000021 |
75 | 0.562960210960587 | 0.874079578078826 | 0.437039789039413 |
76 | 0.548647579510011 | 0.902704840979978 | 0.451352420489989 |
77 | 0.518073066840272 | 0.963853866319455 | 0.481926933159728 |
78 | 0.469533633268316 | 0.939067266536633 | 0.530466366731684 |
79 | 0.42377624413341 | 0.84755248826682 | 0.57622375586659 |
80 | 0.379172241904872 | 0.758344483809744 | 0.620827758095128 |
81 | 0.344408737425747 | 0.688817474851494 | 0.655591262574253 |
82 | 0.351341152528082 | 0.702682305056163 | 0.648658847471918 |
83 | 0.317436713091947 | 0.634873426183893 | 0.682563286908053 |
84 | 0.342058960868048 | 0.684117921736096 | 0.657941039131952 |
85 | 0.328751119159408 | 0.657502238318817 | 0.671248880840592 |
86 | 0.289794102211854 | 0.579588204423708 | 0.710205897788146 |
87 | 0.320066806925737 | 0.640133613851474 | 0.679933193074263 |
88 | 0.313884723445954 | 0.627769446891909 | 0.686115276554046 |
89 | 0.305770250230682 | 0.611540500461364 | 0.694229749769318 |
90 | 0.334727196906527 | 0.669454393813053 | 0.665272803093473 |
91 | 0.52320395666414 | 0.95359208667172 | 0.47679604333586 |
92 | 0.478356509186592 | 0.956713018373184 | 0.521643490813408 |
93 | 0.472272742577407 | 0.944545485154814 | 0.527727257422593 |
94 | 0.426667889748671 | 0.853335779497342 | 0.573332110251329 |
95 | 0.379868373440733 | 0.759736746881467 | 0.620131626559267 |
96 | 0.584204798344197 | 0.831590403311606 | 0.415795201655803 |
97 | 0.601174823590053 | 0.797650352819893 | 0.398825176409946 |
98 | 0.573936965603423 | 0.852126068793153 | 0.426063034396577 |
99 | 0.5706451853805 | 0.858709629239001 | 0.429354814619501 |
100 | 0.574740603442823 | 0.850518793114353 | 0.425259396557177 |
101 | 0.544640272866396 | 0.910719454267209 | 0.455359727133604 |
102 | 0.510350006437611 | 0.979299987124778 | 0.489649993562389 |
103 | 0.537968277621515 | 0.92406344475697 | 0.462031722378485 |
104 | 0.489145649034604 | 0.978291298069208 | 0.510854350965396 |
105 | 0.472396661735125 | 0.94479332347025 | 0.527603338264875 |
106 | 0.552991469974734 | 0.894017060050532 | 0.447008530025266 |
107 | 0.542706899247044 | 0.914586201505913 | 0.457293100752956 |
108 | 0.504285195584127 | 0.991429608831747 | 0.495714804415873 |
109 | 0.462981537734121 | 0.925963075468242 | 0.537018462265879 |
110 | 0.484155497807546 | 0.968310995615093 | 0.515844502192454 |
111 | 0.494425791349429 | 0.988851582698858 | 0.505574208650571 |
112 | 0.590849207585634 | 0.818301584828733 | 0.409150792414366 |
113 | 0.638278149547836 | 0.723443700904328 | 0.361721850452164 |
114 | 0.940063189042126 | 0.119873621915747 | 0.0599368109578736 |
115 | 0.988005498604872 | 0.0239890027902566 | 0.0119945013951283 |
116 | 0.982264326410049 | 0.0354713471799022 | 0.0177356735899511 |
117 | 0.983462496950042 | 0.0330750060999151 | 0.0165375030499576 |
118 | 0.975607767644914 | 0.0487844647101728 | 0.0243922323550864 |
119 | 0.968015146785035 | 0.06396970642993 | 0.031984853214965 |
120 | 0.985666985969932 | 0.0286660280601352 | 0.0143330140300676 |
121 | 0.97863334937441 | 0.042733301251179 | 0.0213666506255895 |
122 | 0.970636769151523 | 0.0587264616969543 | 0.0293632308484771 |
123 | 0.992798009907925 | 0.0144039801841503 | 0.00720199009207515 |
124 | 0.98823457163062 | 0.0235308567387598 | 0.0117654283693799 |
125 | 0.987197310753243 | 0.0256053784935135 | 0.0128026892467568 |
126 | 0.979713805488178 | 0.040572389023644 | 0.020286194511822 |
127 | 0.96837482212067 | 0.0632503557586582 | 0.0316251778793291 |
128 | 0.963025712688952 | 0.0739485746220952 | 0.0369742873110476 |
129 | 0.956114586740964 | 0.0877708265180719 | 0.0438854132590359 |
130 | 0.939018853049577 | 0.121962293900846 | 0.0609811469504232 |
131 | 0.915160309763752 | 0.169679380472496 | 0.0848396902362482 |
132 | 0.890134568873956 | 0.219730862252088 | 0.109865431126044 |
133 | 0.885825647476292 | 0.228348705047416 | 0.114174352523708 |
134 | 0.83608474062885 | 0.327830518742300 | 0.163915259371150 |
135 | 0.794223257853069 | 0.411553484293863 | 0.205776742146931 |
136 | 0.722250613756782 | 0.555498772486436 | 0.277749386243218 |
137 | 0.82337481466202 | 0.353250370675959 | 0.176625185337980 |
138 | 0.783033272108509 | 0.433933455782982 | 0.216966727891491 |
139 | 0.725657476825725 | 0.54868504634855 | 0.274342523174275 |
140 | 0.626752400884829 | 0.746495198230342 | 0.373247599115171 |
141 | 0.501647666117784 | 0.996704667764431 | 0.498352333882216 |
142 | 0.550907406851049 | 0.898185186297902 | 0.449092593148951 |
143 | 0.493612995924665 | 0.98722599184933 | 0.506387004075335 |
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 | 10 | 0.078125 | NOK |
10% type I error level | 16 | 0.125 | NOK |