Multiple Linear Regression - Estimated Regression Equation |
Q4 [t] = + 1.07639616086863 + 0.15332101187467Q1[t] + 0.230797317115352Q2[t] + 0.247490376625303Q3[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) | 1.07639616086863 | 0.169658 | 6.3445 | 0 | 0 |
Q1 | 0.15332101187467 | 0.064714 | 2.3692 | 0.0191 | 0.00955 |
Q2 | 0.230797317115352 | 0.072552 | 3.1812 | 0.001783 | 0.000891 |
Q3 | 0.247490376625303 | 0.068065 | 3.6361 | 0.00038 | 0.00019 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.679846065001826 |
R-squared | 0.462190672098467 |
Adjusted R-squared | 0.451434485540436 |
F-TEST (value) | 42.9697523006786 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 150 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.638029844270637 |
Sum Squared Residuals | 61.062312327002 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 3 | 3.35534060670463 | -0.355340606704631 |
2 | 2 | 2.33961357209929 | -0.339613572099286 |
3 | 4 | 2.80120820632999 | 1.19879179367001 |
4 | 1 | 2.32292051258934 | -1.32292051258934 |
5 | 2 | 2.81790126583994 | -0.817901265839942 |
6 | 2 | 2.10881625498393 | -0.108816254983934 |
7 | 3 | 3.75615199520461 | -0.756151995204607 |
8 | 2 | 2.87705291296398 | -0.877052912963978 |
9 | 2 | 3.60283098332994 | -1.60283098332994 |
10 | 2 | 1.86132587835863 | 0.138674121641370 |
11 | 4 | 3.60283098332994 | 0.397169016670063 |
12 | 3 | 2.81790126583994 | 0.182098734160058 |
13 | 4 | 3.60283098332994 | 0.397169016670063 |
14 | 2 | 3.10785023007933 | -1.10785023007933 |
15 | 3 | 1.95549524310926 | 1.04450475689074 |
16 | 3 | 3.10785023007933 | -0.107850230079330 |
17 | 3 | 2.74042496059926 | 0.259575039400741 |
18 | 4 | 3.35534060670463 | 0.644659393295366 |
19 | 2 | 2.18629256022462 | -0.186292560224616 |
20 | 2 | 2.57041088921464 | -0.570410889214638 |
21 | 2 | 2.16959950071466 | -0.169599500714665 |
22 | 3 | 3.37203366621458 | -0.372033666214585 |
23 | 4 | 3.37203366621458 | 0.627966333785415 |
24 | 2 | 2.18629256022462 | -0.186292560224616 |
25 | 3 | 3.60283098332994 | -0.602830983329937 |
26 | 4 | 3.75615199520461 | 0.243848004795393 |
27 | 3 | 3.60283098332994 | -0.602830983329937 |
28 | 3 | 3.35534060670463 | -0.355340606704634 |
29 | 3 | 3.35534060670463 | -0.355340606704634 |
30 | 2 | 2.33961357209929 | -0.339613572099286 |
31 | 2 | 2.33961357209929 | -0.339613572099286 |
32 | 4 | 3.10785023007933 | 0.89214976992067 |
33 | 3 | 3.37203366621458 | -0.372033666214585 |
34 | 3 | 2.09212319547398 | 0.907876804526017 |
35 | 2 | 2.98791533722456 | -0.987915337224563 |
36 | 4 | 3.60283098332994 | 0.397169016670063 |
37 | 3 | 2.47624152446400 | 0.523758475535995 |
38 | 2 | 2.33961357209929 | -0.339613572099286 |
39 | 3 | 3.35534060670463 | -0.355340606704634 |
40 | 4 | 3.60283098332994 | 0.397169016670063 |
41 | 4 | 2.97122227771461 | 1.02877772228539 |
42 | 2 | 1.70800486648396 | 0.29199513351604 |
43 | 1 | 2.58710394872459 | -1.58710394872459 |
44 | 2 | 2.64625559584863 | -0.646255595848626 |
45 | 3 | 2.09212319547398 | 0.907876804526017 |
46 | 3 | 3.20201959482996 | -0.202019594829964 |
47 | 4 | 3.37203366621458 | 0.627966333785415 |
48 | 2 | 1.93880218359931 | 0.0611978164006874 |
49 | 3 | 2.98791533722456 | 0.0120846627754373 |
50 | 4 | 3.60283098332994 | 0.397169016670063 |
51 | 2 | 1.70800486648396 | 0.29199513351604 |
52 | 2 | 3.83362830044529 | -1.83362830044529 |
53 | 3 | 2.98791533722456 | 0.0120846627754373 |
54 | 2 | 2.41708987733997 | -0.417089877339968 |
55 | 4 | 3.14286794770593 | 0.857132052294073 |
56 | 3 | 3.35534060670463 | -0.355340606704634 |
57 | 3 | 2.87705291296398 | 0.122947087036022 |
58 | 4 | 3.60283098332994 | 0.397169016670063 |
59 | 4 | 2.33961357209929 | 1.66038642790071 |
60 | 4 | 3.37203366621458 | 0.627966333785415 |
61 | 2 | 2.33961357209929 | -0.339613572099286 |
62 | 4 | 3.60283098332994 | 0.397169016670063 |
63 | 4 | 4.23443968894526 | -0.234439688945263 |
64 | 4 | 3.21871265433992 | 0.781287345660085 |
65 | 2 | 1.86132587835863 | 0.138674121641370 |
66 | 3 | 3.12454328958928 | -0.124543289589282 |
67 | 3 | 3.60283098332994 | -0.602830983329937 |
68 | 2 | 2.09212319547398 | -0.0921231954739826 |
69 | 4 | 2.97122227771461 | 1.02877772228539 |
70 | 1 | 1.70800486648396 | -0.70800486648396 |
71 | 3 | 3.37203366621458 | -0.372033666214585 |
72 | 3 | 3.14123634909923 | -0.141236349099233 |
73 | 2 | 2.87705291296398 | -0.877052912963978 |
74 | 2 | 3.60283098332994 | -1.60283098332994 |
75 | 3 | 2.97122227771461 | 0.0287777222853885 |
76 | 3 | 3.60283098332994 | -0.602830983329937 |
77 | 3 | 3.44950997145527 | -0.449509971455267 |
78 | 3 | 3.21871265433991 | -0.218712654339915 |
79 | 3 | 2.09212319547398 | 0.907876804526017 |
80 | 2 | 1.95549524310926 | 0.0445047568907363 |
81 | 2 | 2.09212319547398 | -0.0921231954739826 |
82 | 3 | 3.12454328958928 | -0.124543289589282 |
83 | 3 | 3.20201959482996 | -0.202019594829964 |
84 | 2 | 2.81626966723325 | -0.816269667233247 |
85 | 2 | 1.70800486648396 | 0.29199513351604 |
86 | 3 | 2.97122227771461 | 0.0287777222853885 |
87 | 2 | 2.33961357209929 | -0.339613572099286 |
88 | 3 | 2.74042496059926 | 0.259575039400741 |
89 | 3 | 3.37203366621458 | -0.372033666214585 |
90 | 2 | 2.49293458397396 | -0.492934583973956 |
91 | 3 | 2.49293458397396 | 0.507065416026044 |
92 | 3 | 3.12454328958928 | -0.124543289589282 |
93 | 4 | 3.60283098332994 | 0.397169016670063 |
94 | 4 | 3.60283098332994 | 0.397169016670063 |
95 | 3 | 2.83459432534989 | 0.165405674650107 |
96 | 2 | 2.33961357209929 | -0.339613572099286 |
97 | 1 | 1.70800486648396 | -0.70800486648396 |
98 | 2 | 2.18629256022462 | -0.186292560224616 |
99 | 3 | 3.37203366621458 | -0.372033666214585 |
100 | 3 | 2.81790126583994 | 0.182098734160058 |
101 | 5 | 3.60283098332994 | 1.39716901667006 |
102 | 4 | 3.44950997145527 | 0.550490028544733 |
103 | 5 | 3.50866161857930 | 1.49133838142070 |
104 | 2 | 2.70800486648396 | -0.70800486648396 |
105 | 1 | 0.570410889214638 | 0.429589110785362 |
106 | 3 | 2.64625559584863 | 0.353744404151374 |
107 | 3 | 2.37203366621458 | 0.627966333785415 |
108 | 4 | 4.72373190108931 | -0.723731901089308 |
109 | 2 | 2.39876521922332 | -0.398765219223323 |
110 | 2 | 1.87705291296398 | 0.122947087036022 |
111 | 3 | 2.29455736097390 | 0.705442639026097 |
112 | 4 | 4.18629256022462 | -0.186292560224616 |
113 | 2 | 2.12454328958928 | -0.124543289589282 |
114 | 3 | 2.89374597247393 | 0.106254027526071 |
115 | 3 | 2.12454328958928 | 0.875456710410718 |
116 | 4 | 3.2961889595806 | 0.703811040419403 |
117 | 4 | 4.33961357209929 | -0.339613572099286 |
118 | 2 | 2.60283098332994 | -0.602830983329937 |
119 | 3 | 4.21871265433991 | -1.21871265433991 |
120 | 2 | 1.97122227771461 | 0.0287777222853885 |
121 | 3 | 2.60283098332994 | 0.397169016670063 |
122 | 4 | 4.58710394872459 | -0.58710394872459 |
123 | 2 | 1.37203366621458 | 0.627966333785415 |
124 | 4 | 3.35534060670463 | 0.644659393295366 |
125 | 4 | 3.95549524310926 | 0.0445047568907363 |
126 | 2 | 2.35534060670463 | -0.355340606704634 |
127 | 3 | 3.60283098332994 | -0.602830983329937 |
128 | 3 | 2.49293458397396 | 0.507065416026044 |
129 | 3 | 1.70800486648396 | 1.29199513351604 |
130 | 3 | 2.10785023007933 | 0.89214976992067 |
131 | 4 | 3.98791533722456 | 0.0120846627754373 |
132 | 3 | 3.33961357209929 | -0.339613572099286 |
133 | 2 | 1.72373190108931 | 0.276268098910692 |
134 | 3 | 3.12454328958928 | -0.124543289589282 |
135 | 3 | 2.33961357209929 | 0.660386427900714 |
136 | 3 | 2.37203366621458 | 0.627966333785415 |
137 | 4 | 4.12454328958928 | -0.124543289589282 |
138 | 3 | 2.44950997145527 | 0.550490028544733 |
139 | 4 | 3.12454328958928 | 0.875456710410718 |
140 | 4 | 3.60283098332994 | 0.397169016670063 |
141 | 4 | 4.37203366621458 | -0.372033666214585 |
142 | 3 | 3.35534060670463 | -0.355340606704634 |
143 | 3 | 3.72373190108931 | -0.723731901089308 |
144 | 2 | 1.49293458397396 | 0.507065416026044 |
145 | 3 | 3.70800486648396 | -0.70800486648396 |
146 | 1 | 1.33961357209929 | -0.339613572099286 |
147 | 2 | 1.35534060670463 | 0.644659393295366 |
148 | 4 | 3.60283098332994 | 0.397169016670063 |
149 | 4 | 3.97122227771461 | 0.0287777222853885 |
150 | 3 | 2.97122227771461 | 0.0287777222853885 |
151 | 3 | 2.37203366621458 | 0.627966333785415 |
152 | 4 | 4.49293458397396 | -0.492934583973956 |
153 | 2 | 2.35534060670463 | -0.355340606704634 |
154 | 4 | 3.64625559584863 | 0.353744404151374 |
155 | 3 | NA | NA |
156 | 3 | NA | NA |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.953640409640161 | 0.0927191807196777 | 0.0463595903598389 |
8 | 0.911404157858794 | 0.177191684282412 | 0.0885958421412058 |
9 | 0.952578596116796 | 0.094842807766408 | 0.047421403883204 |
10 | 0.934594316485384 | 0.130811367029232 | 0.0654056835146162 |
11 | 0.960230221152465 | 0.0795395576950707 | 0.0397697788475354 |
12 | 0.937245261420702 | 0.125509477158596 | 0.0627547385792978 |
13 | 0.940246095777792 | 0.119507808444416 | 0.0597539042222079 |
14 | 0.927681586456393 | 0.144636827087214 | 0.0723184135436072 |
15 | 0.934566782839005 | 0.130866434321989 | 0.0654332171609947 |
16 | 0.932281051856716 | 0.135437896286569 | 0.0677189481432844 |
17 | 0.912188834346024 | 0.175622331307951 | 0.0878111656539755 |
18 | 0.943052175647028 | 0.113895648705943 | 0.0569478243529717 |
19 | 0.92942504622922 | 0.141149907541559 | 0.0705749537707797 |
20 | 0.917914700991134 | 0.164170598017732 | 0.0820852990088658 |
21 | 0.88857856748649 | 0.222842865027022 | 0.111421432513511 |
22 | 0.857257951703201 | 0.285484096593597 | 0.142742048296799 |
23 | 0.862112552417483 | 0.275774895165034 | 0.137887447582517 |
24 | 0.83086652144435 | 0.338266957111301 | 0.169133478555650 |
25 | 0.810744589784024 | 0.378510820431951 | 0.189255410215976 |
26 | 0.793287639791108 | 0.413424720417784 | 0.206712360208892 |
27 | 0.772649796026682 | 0.454700407946637 | 0.227350203973318 |
28 | 0.727869019815989 | 0.544261960368022 | 0.272130980184011 |
29 | 0.680144282781603 | 0.639711434436794 | 0.319855717218397 |
30 | 0.634280291990666 | 0.731439416018668 | 0.365719708009334 |
31 | 0.586143634878096 | 0.827712730243807 | 0.413856365121904 |
32 | 0.733871276782383 | 0.532257446435233 | 0.266128723217617 |
33 | 0.69284535057358 | 0.61430929885284 | 0.30715464942642 |
34 | 0.752466991191753 | 0.495066017616493 | 0.247533008808247 |
35 | 0.787451636797771 | 0.425096726404458 | 0.212548363202229 |
36 | 0.779489503371634 | 0.441020993256731 | 0.220510496628366 |
37 | 0.767180192312907 | 0.465639615374186 | 0.232819807687093 |
38 | 0.732461287618452 | 0.535077424763095 | 0.267538712381548 |
39 | 0.69355851269896 | 0.612882974602079 | 0.306441487301040 |
40 | 0.681890182425455 | 0.63621963514909 | 0.318109817574545 |
41 | 0.765440997391671 | 0.469118005216658 | 0.234559002608329 |
42 | 0.730081573913542 | 0.539836852172916 | 0.269918426086458 |
43 | 0.879950138780336 | 0.240099722439327 | 0.120049861219664 |
44 | 0.872828148351847 | 0.254343703296307 | 0.127171851648153 |
45 | 0.895131549166631 | 0.209736901666738 | 0.104868450833369 |
46 | 0.871711962037091 | 0.256576075925818 | 0.128288037962909 |
47 | 0.88260956490517 | 0.23478087018966 | 0.11739043509483 |
48 | 0.855909643413307 | 0.288180713173386 | 0.144090356586693 |
49 | 0.827951704900328 | 0.344096590199344 | 0.172048295099672 |
50 | 0.814125145328291 | 0.371749709343418 | 0.185874854671709 |
51 | 0.78574851447763 | 0.428502971044741 | 0.214251485522370 |
52 | 0.93970033207259 | 0.120599335854819 | 0.0602996679274097 |
53 | 0.92420137592457 | 0.151597248150859 | 0.0757986240754297 |
54 | 0.912214617881641 | 0.175570764236718 | 0.087785382118359 |
55 | 0.931541509012683 | 0.136916981974634 | 0.0684584909873169 |
56 | 0.91943586665333 | 0.161128266693340 | 0.0805641333466699 |
57 | 0.901856638916617 | 0.196286722166767 | 0.0981433610833833 |
58 | 0.89231720519143 | 0.21536558961714 | 0.10768279480857 |
59 | 0.971693338249056 | 0.0566133235018884 | 0.0283066617509442 |
60 | 0.972282704315376 | 0.0554345913692477 | 0.0277172956846238 |
61 | 0.966455609513124 | 0.0670887809737518 | 0.0335443904868759 |
62 | 0.961384812462658 | 0.0772303750746847 | 0.0386151875373424 |
63 | 0.953090128881763 | 0.0938197422364734 | 0.0469098711182367 |
64 | 0.958630682899012 | 0.0827386342019754 | 0.0413693171009877 |
65 | 0.947891045211729 | 0.104217909576542 | 0.0521089547882711 |
66 | 0.934800903799464 | 0.130398192401071 | 0.0651990962005357 |
67 | 0.933980117039374 | 0.132039765921252 | 0.0660198829606259 |
68 | 0.91788880491181 | 0.164222390176380 | 0.0821111950881902 |
69 | 0.942383570724387 | 0.115232858551226 | 0.057616429275613 |
70 | 0.945271596904096 | 0.109456806191809 | 0.0547284030959045 |
71 | 0.93605611176071 | 0.127887776478579 | 0.0639438882392895 |
72 | 0.920508073989695 | 0.158983852020610 | 0.0794919260103051 |
73 | 0.936654170436566 | 0.126691659126869 | 0.0633458295634343 |
74 | 0.986798069335282 | 0.0264038613294368 | 0.0132019306647184 |
75 | 0.982303706710571 | 0.0353925865788578 | 0.0176962932894289 |
76 | 0.983586386693701 | 0.0328272266125972 | 0.0164136133062986 |
77 | 0.982505121806679 | 0.0349897563866428 | 0.0174948781933214 |
78 | 0.977853885116912 | 0.0442922297661763 | 0.0221461148830881 |
79 | 0.984664317607383 | 0.0306713647852348 | 0.0153356823926174 |
80 | 0.98030197127581 | 0.0393960574483806 | 0.0196980287241903 |
81 | 0.974005000038767 | 0.0519899999224661 | 0.0259949999612331 |
82 | 0.96716971175935 | 0.0656605764812994 | 0.0328302882406497 |
83 | 0.96098539000444 | 0.0780292199911187 | 0.0390146099955593 |
84 | 0.967462660789194 | 0.0650746784216112 | 0.0325373392108056 |
85 | 0.963666271528989 | 0.0726674569420221 | 0.0363337284710111 |
86 | 0.953281100855389 | 0.0934377982892223 | 0.0467188991446111 |
87 | 0.943605388187049 | 0.112789223625902 | 0.056394611812951 |
88 | 0.931669266846843 | 0.136661466306314 | 0.0683307331531572 |
89 | 0.926812137931876 | 0.146375724136247 | 0.0731878620681235 |
90 | 0.92070526429826 | 0.158589471403481 | 0.0792947357017403 |
91 | 0.915602333696864 | 0.168795332606273 | 0.0843976663031364 |
92 | 0.900162901476088 | 0.199674197047824 | 0.099837098523912 |
93 | 0.88470839802676 | 0.230583203946480 | 0.115291601973240 |
94 | 0.86708329411985 | 0.265833411760301 | 0.132916705880151 |
95 | 0.841664748165799 | 0.316670503668403 | 0.158335251834202 |
96 | 0.817666002137199 | 0.364667995725602 | 0.182333997862801 |
97 | 0.814955787055712 | 0.370088425888577 | 0.185044212944288 |
98 | 0.782382985993964 | 0.435234028012073 | 0.217617014006036 |
99 | 0.773440329724786 | 0.453119340550428 | 0.226559670275214 |
100 | 0.737354693419422 | 0.525290613161156 | 0.262645306580578 |
101 | 0.848464807992446 | 0.303070384015109 | 0.151535192007554 |
102 | 0.836793628319744 | 0.326412743360512 | 0.163206371680256 |
103 | 0.926776131238278 | 0.146447737523445 | 0.0732238687617223 |
104 | 0.927521160185263 | 0.144957679629474 | 0.0724788398147369 |
105 | 0.91990074541909 | 0.160198509161821 | 0.0800992545809105 |
106 | 0.903211333817759 | 0.193577332364482 | 0.096788666182241 |
107 | 0.896118616900545 | 0.207762766198911 | 0.103881383099455 |
108 | 0.907742913888804 | 0.184514172222391 | 0.0922570861111957 |
109 | 0.906512999874817 | 0.186974000250366 | 0.0934870001251832 |
110 | 0.883832379550567 | 0.232335240898867 | 0.116167620449433 |
111 | 0.878755641924758 | 0.242488716150484 | 0.121244358075242 |
112 | 0.85065022285205 | 0.298699554295902 | 0.149349777147951 |
113 | 0.823086009940657 | 0.353827980118686 | 0.176913990059343 |
114 | 0.785493786256711 | 0.429012427486578 | 0.214506213743289 |
115 | 0.804477020146362 | 0.391045959707277 | 0.195522979853638 |
116 | 0.843334196470653 | 0.313331607058694 | 0.156665803529347 |
117 | 0.817865233916009 | 0.364269532167983 | 0.182134766083991 |
118 | 0.819342842123326 | 0.361314315753347 | 0.180657157876674 |
119 | 0.911346730830036 | 0.177306538339928 | 0.0886532691699638 |
120 | 0.88491325707545 | 0.230173485849100 | 0.115086742924550 |
121 | 0.860414917308698 | 0.279170165382605 | 0.139585082691302 |
122 | 0.863115706754717 | 0.273768586490566 | 0.136884293245283 |
123 | 0.849087003225375 | 0.301825993549249 | 0.150912996774625 |
124 | 0.840803257980424 | 0.318393484039152 | 0.159196742019576 |
125 | 0.798851971875008 | 0.402296056249983 | 0.201148028124992 |
126 | 0.77885964506833 | 0.442280709863339 | 0.221140354931669 |
127 | 0.804239530132885 | 0.391520939734229 | 0.195760469867115 |
128 | 0.7756534441729 | 0.448693111654199 | 0.224346555827100 |
129 | 0.952516867993328 | 0.0949662640133446 | 0.0474831320066723 |
130 | 0.968246952770584 | 0.0635060944588329 | 0.0317530472294165 |
131 | 0.958579843927095 | 0.0828403121458095 | 0.0414201560729047 |
132 | 0.941976274509904 | 0.116047450980192 | 0.0580237254900962 |
133 | 0.933189527800162 | 0.133620944399676 | 0.0668104721998381 |
134 | 0.912347219341293 | 0.175305561317415 | 0.0876527806587074 |
135 | 0.952340086498154 | 0.095319827003691 | 0.0476599135018455 |
136 | 0.930292188030068 | 0.139415623939864 | 0.0697078119699321 |
137 | 0.909595181687358 | 0.180809636625284 | 0.0904048183126422 |
138 | 0.910729929130197 | 0.178540141739606 | 0.0892700708698029 |
139 | 0.925591828833931 | 0.148816342332138 | 0.0744081711660689 |
140 | 0.891580807796973 | 0.216838384406055 | 0.108419192203027 |
141 | 0.961068389728592 | 0.0778632205428169 | 0.0389316102714084 |
142 | 0.944564795481105 | 0.110870409037790 | 0.0554352045188952 |
143 | 0.93503112063782 | 0.12993775872436 | 0.06496887936218 |
144 | 0.948029290240872 | 0.103941419518255 | 0.0519707097591276 |
145 | 0.90047880952389 | 0.199042380952222 | 0.0995211904761108 |
146 | 0.826290093983226 | 0.347419812033549 | 0.173709906016775 |
147 | 0.916336529456709 | 0.167326941086582 | 0.0836634705432912 |
148 | 0.782645537831845 | 0.434708924336309 | 0.217354462168155 |
149 | 0.527216052493395 | 0.94556789501321 | 0.472783947506605 |
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 | 7 | 0.048951048951049 | OK |
10% type I error level | 27 | 0.188811188811189 | NOK |