Multiple Linear Regression - Estimated Regression Equation |
y[t] = -0.377574463704221 + 0.134562581071375x1[t] + 0.0510098609463206x2[t] + 0.336315636002047x3[t] + 0.272305484877694x4[t] + 0.330922737595275x5[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) | -0.377574463704221 | 0.431842 | -0.8743 | 0.383382 | 0.191691 |
x1 | 0.134562581071375 | 0.091901 | 1.4642 | 0.145301 | 0.072651 |
x2 | 0.0510098609463206 | 0.061331 | 0.8317 | 0.406935 | 0.203467 |
x3 | 0.336315636002047 | 0.089729 | 3.7481 | 0.000257 | 0.000128 |
x4 | 0.272305484877694 | 0.0705 | 3.8625 | 0.000169 | 8.4e-05 |
x5 | 0.330922737595275 | 0.096183 | 3.4405 | 0.000759 | 0.000379 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.66880462193062 |
R-squared | 0.447299622315759 |
Adjusted R-squared | 0.428240988602509 |
F-TEST (value) | 23.4696583735062 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 145 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.674861643367005 |
Sum Squared Residuals | 66.0385444647621 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 4.17390059921299 | -0.173900599212986 |
2 | 4 | 3.85058525338894 | 0.149414746611058 |
3 | 5 | 4.86068154181098 | 0.139318458189023 |
4 | 3 | 3.54999279930057 | -0.549992799300572 |
5 | 2 | 3.00538182954518 | -1.00538182954518 |
6 | 5 | 4.06648797891354 | 0.933512021086462 |
7 | 4 | 3.32869717536919 | 0.671302824630807 |
8 | 2 | 3.44371718743986 | -1.44371718743986 |
9 | 4 | 4.40280361491558 | -0.402803614915584 |
10 | 4 | 2.34353635435463 | 1.65646364564537 |
11 | 4 | 3.88630843530261 | 0.113691564697388 |
12 | 2 | 3.01077472795195 | -1.01077472795195 |
13 | 5 | 4.960414874849 | 0.0395851251509964 |
14 | 3 | 3.41224989549425 | -0.412249895494248 |
15 | 4 | 3.98832815719525 | 0.0116718428047465 |
16 | 4 | 4.26824103384421 | -0.268241033844208 |
17 | 3 | 2.86321185670254 | 0.136788143297459 |
18 | 4 | 4.12289073826663 | -0.122890738266630 |
19 | 2 | 2.66906619354313 | -0.669066193543132 |
20 | 4 | 3.58146009124618 | 0.418539908753817 |
21 | 3 | 3.88630843530261 | -0.886308435302612 |
22 | 3 | 2.97823186877321 | 0.0217681312267863 |
23 | 4 | 4.02087101637399 | -0.0208710163739883 |
24 | 4 | 4.07188087732031 | -0.071880877320309 |
25 | 4 | 4.12289073826663 | -0.122890738266630 |
26 | 4 | 3.66501281137124 | 0.334987188628761 |
27 | 5 | 4.12289073826663 | 0.87710926173337 |
28 | 4 | 3.7192029950525 | 0.280797004947499 |
29 | 4 | 4.02087101637399 | -0.0208710163739883 |
30 | 4 | 4.02087101637399 | -0.0208710163739883 |
31 | 4 | 3.10740155143782 | 0.892598448562181 |
32 | 4 | 3.88630843530261 | 0.113691564697388 |
33 | 4 | 4.50482333680823 | -0.504823336808225 |
34 | 4 | 4.12289073826663 | -0.122890738266630 |
35 | 4 | 4.12289073826663 | -0.122890738266630 |
36 | 5 | 3.60861005201815 | 1.39138994798185 |
37 | 4 | 4.02087101637399 | -0.0208710163739883 |
38 | 4 | 3.32869717536919 | 0.671302824630807 |
39 | 4 | 3.79957539244261 | 0.200424607557385 |
40 | 3 | 3.38509993472228 | -0.385099934722284 |
41 | 4 | 3.85058525338894 | 0.149414746611064 |
42 | 2 | 2.6744590919499 | -0.674459091949903 |
43 | 2 | 2.96744607195967 | -0.967446071959672 |
44 | 4 | 4.31925089479053 | -0.319250894790529 |
45 | 4 | 3.57827976851124 | 0.421720231488759 |
46 | 5 | 4.45381347586190 | 0.546186524138095 |
47 | 4 | 3.88630843530261 | 0.113691564697388 |
48 | 4 | 3.66501281137124 | 0.334987188628761 |
49 | 4 | 4.02087101637399 | -0.0208710163739883 |
50 | 5 | 4.02087101637399 | 0.979128983626011 |
51 | 3 | 3.37970703631551 | -0.379707036315513 |
52 | 2 | 2.36421784948670 | -0.364217849486703 |
53 | 4 | 4.12289073826663 | -0.122890738266630 |
54 | 4 | 4.07188087732031 | -0.071880877320309 |
55 | 2 | 3.44371718743986 | -1.44371718743986 |
56 | 2 | 2.68753319531072 | -0.687533195310717 |
57 | 4 | 4.12289073826663 | -0.122890738266630 |
58 | 4 | 3.98832815719525 | 0.0116718428047465 |
59 | 4 | 3.71602267231756 | 0.283977327682441 |
60 | 3 | 3.85058525338894 | -0.850585253388936 |
61 | 2 | 2.73307634466748 | -0.733076344667483 |
62 | 4 | 4.12289073826663 | -0.122890738266630 |
63 | 5 | 3.44371718743986 | 1.55628281256014 |
64 | 4 | 4.07188087732031 | -0.071880877320309 |
65 | 5 | 5.06243459674165 | -0.062434596741645 |
66 | 4 | 3.74856553149629 | 0.251434468503706 |
67 | 3 | 3.27768731442287 | -0.277687314422872 |
68 | 3 | 2.6744590919499 | 0.325540908050097 |
69 | 4 | 3.98832815719525 | 0.0116718428047465 |
70 | 3 | 3.24196413250920 | -0.241964132509195 |
71 | 2 | 2.39454621530095 | -0.394546215300948 |
72 | 4 | 2.53450361247176 | 1.46549638752824 |
73 | 3 | 4.35179375396926 | -1.35179375396926 |
74 | 5 | 4.29317650125168 | 0.706823498748317 |
75 | 5 | 4.50482333680823 | 0.495176663191774 |
76 | 4 | 2.4401631778405 | 1.55983682215950 |
77 | 5 | 4.5297588042157 | 0.4702411957843 |
78 | 4 | 3.34169746554722 | 0.658302534452776 |
79 | 3 | 2.81220199575622 | 0.187798004243779 |
80 | 3 | 3.65201252119321 | -0.652012521193208 |
81 | 4 | 3.37970703631551 | 0.620292963684487 |
82 | 4 | 3.57827976851124 | 0.421720231488759 |
83 | 3 | 3.51426961738689 | -0.51426961738689 |
84 | 4 | 3.54999279930057 | 0.450007200699434 |
85 | 3 | 2.26219812759406 | 0.737801872405939 |
86 | 3 | 3.90920250610652 | -0.909202506106516 |
87 | 3 | 3.52726990756492 | -0.52726990756492 |
88 | 2 | 2.94137167842083 | -0.941371678420826 |
89 | 5 | 3.74856553149629 | 1.25143446850371 |
90 | 3 | 3.10740155143782 | -0.107401551437819 |
91 | 4 | 2.96744607195967 | 1.03255392804033 |
92 | 4 | 3.93731829624893 | 0.0626817037510672 |
93 | 3 | 3.37970703631551 | -0.379707036315513 |
94 | 3 | 2.99777443777392 | 0.00222556222608242 |
95 | 4 | 3.73556524131826 | 0.264434758681737 |
96 | 4 | 4.45920637426868 | -0.459206374268676 |
97 | 3 | 3.57827976851124 | -0.578279768511241 |
98 | 3 | 3.10200865303105 | -0.102008653031048 |
99 | 4 | 4.45381347586190 | -0.453813475861905 |
100 | 2 | 3.46325975644057 | -1.46325975644057 |
101 | 4 | 2.77108591543577 | 1.22891408456423 |
102 | 4 | 4.35179375396926 | -0.351793753969263 |
103 | 4 | 3.99593554896651 | 0.00406445103348649 |
104 | 5 | 3.51426961738689 | 1.48573038261311 |
105 | 5 | 4.40280361491558 | 0.597196385084416 |
106 | 5 | 3.66501281137124 | 1.33498718862876 |
107 | 4 | 3.88630843530261 | 0.113691564697388 |
108 | 4 | 3.61400295042492 | 0.385997049575082 |
109 | 3 | 3.61400295042492 | -0.614002950424918 |
110 | 2 | 2.95215747523437 | -0.952157475234368 |
111 | 2 | 2.6365233343644 | -0.636523334364397 |
112 | 4 | 3.80718278421387 | 0.192817215786125 |
113 | 2 | 2.64952362454243 | -0.649523624542428 |
114 | 3 | 3.10740155143782 | -0.107401551437819 |
115 | 4 | 3.66501281137124 | 0.334987188628761 |
116 | 4 | 3.32869717536919 | 0.671302824630807 |
117 | 4 | 3.85058525338894 | 0.149414746611064 |
118 | 4 | 3.13233701884529 | 0.867662981154706 |
119 | 3 | 3.00538182954518 | -0.00538182954517756 |
120 | 4 | 4.07188087732031 | -0.071880877320309 |
121 | 3 | 2.6744590919499 | 0.325540908050097 |
122 | 4 | 3.66501281137124 | 0.334987188628761 |
123 | 4 | 3.71062977391079 | 0.289370226089212 |
124 | 4 | 4.40280361491558 | -0.402803614915584 |
125 | 2 | 2.52689622070050 | -0.526896220700495 |
126 | 5 | 3.84519235498216 | 1.15480764501784 |
127 | 5 | 3.61400295042492 | 1.38599704957508 |
128 | 3 | 3.54999279930057 | -0.549992799300566 |
129 | 3 | 3.74095813972503 | -0.740958139725034 |
130 | 3 | 3.13233701884529 | -0.132337018845294 |
131 | 4 | 4.07188087732031 | -0.071880877320309 |
132 | 3 | 3.63361933260841 | -0.633619332608406 |
133 | 2 | 1.97467785917385 | 0.0253221408261531 |
134 | 5 | 4.12289073826663 | 0.87710926173337 |
135 | 4 | 3.85376557612388 | 0.146234423876123 |
136 | 2 | 3.32869717536919 | -1.32869717536919 |
137 | 4 | 4.18150799098421 | -0.181507990984211 |
138 | 3 | 3.93731829624893 | -0.937318296248933 |
139 | 2 | 2.94137167842083 | -0.941371678420826 |
140 | 3 | 3.44371718743986 | -0.443717187439865 |
141 | 3 | 3.98832815719525 | -0.988328157195254 |
142 | 4 | 4.12289073826663 | -0.122890738266630 |
143 | 4 | 3.88630843530261 | 0.113691564697388 |
144 | 4 | 4.04694540991283 | -0.0469454099128343 |
145 | 2 | 2.74819184463187 | -0.748191844631869 |
146 | 5 | 3.85376557612388 | 1.14623442387612 |
147 | 4 | 3.60100266024689 | 0.398997339753113 |
148 | 4 | 4.02087101637399 | -0.0208710163739883 |
149 | 3 | 3.32869717536919 | -0.328697175369193 |
150 | 3 | 3.74856553149629 | -0.748565531496294 |
151 | 5 | 4.97888187661659 | 0.0211181233834108 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.622871122561292 | 0.754257754877417 | 0.377128877438709 |
10 | 0.699257298745655 | 0.601485402508691 | 0.300742701254345 |
11 | 0.773975133948668 | 0.452049732102663 | 0.226024866051332 |
12 | 0.746136225078931 | 0.507727549842138 | 0.253863774921069 |
13 | 0.754504423376951 | 0.490991153246098 | 0.245495576623049 |
14 | 0.780690095347543 | 0.438619809304914 | 0.219309904652457 |
15 | 0.700318025846144 | 0.599363948307711 | 0.299681974153856 |
16 | 0.64846550975354 | 0.70306898049292 | 0.35153449024646 |
17 | 0.570291694093831 | 0.859416611812338 | 0.429708305906169 |
18 | 0.507160164017797 | 0.985679671964406 | 0.492839835982203 |
19 | 0.460518594956866 | 0.921037189913732 | 0.539481405043134 |
20 | 0.542462212656561 | 0.915075574686878 | 0.457537787343439 |
21 | 0.59883817603314 | 0.80232364793372 | 0.40116182396686 |
22 | 0.536048620252424 | 0.927902759495152 | 0.463951379747576 |
23 | 0.460627140547107 | 0.921254281094213 | 0.539372859452893 |
24 | 0.392304264909782 | 0.784608529819563 | 0.607695735090218 |
25 | 0.340008019925463 | 0.680016039850925 | 0.659991980074537 |
26 | 0.346959450856732 | 0.693918901713465 | 0.653040549143268 |
27 | 0.351204144541816 | 0.702408289083633 | 0.648795855458184 |
28 | 0.291585606919879 | 0.583171213839757 | 0.708414393080121 |
29 | 0.236359056556522 | 0.472718113113044 | 0.763640943443478 |
30 | 0.188012972936943 | 0.376025945873887 | 0.811987027063057 |
31 | 0.275366254673022 | 0.550732509346044 | 0.724633745326978 |
32 | 0.22967498209126 | 0.45934996418252 | 0.77032501790874 |
33 | 0.208712900413570 | 0.417425800827141 | 0.79128709958643 |
34 | 0.177498277754374 | 0.354996555508748 | 0.822501722245626 |
35 | 0.148054125880101 | 0.296108251760201 | 0.8519458741199 |
36 | 0.394959869234456 | 0.789919738468912 | 0.605040130765544 |
37 | 0.339675498579513 | 0.679350997159026 | 0.660324501420487 |
38 | 0.316933966114869 | 0.633867932229738 | 0.683066033885131 |
39 | 0.286314548923521 | 0.572629097847042 | 0.713685451076479 |
40 | 0.259241190737361 | 0.518482381474721 | 0.740758809262639 |
41 | 0.223036088562334 | 0.446072177124669 | 0.776963911437666 |
42 | 0.227714369228471 | 0.455428738456942 | 0.77228563077153 |
43 | 0.291005218896122 | 0.582010437792244 | 0.708994781103878 |
44 | 0.25090818395845 | 0.5018163679169 | 0.74909181604155 |
45 | 0.255703334735448 | 0.511406669470896 | 0.744296665264552 |
46 | 0.246176370630193 | 0.492352741260386 | 0.753823629369807 |
47 | 0.207072210664389 | 0.414144421328778 | 0.79292778933561 |
48 | 0.185958919319355 | 0.371917838638709 | 0.814041080680645 |
49 | 0.152522846235174 | 0.305045692470347 | 0.847477153764826 |
50 | 0.185558746873597 | 0.371117493747195 | 0.814441253126403 |
51 | 0.166284139267588 | 0.332568278535176 | 0.833715860732412 |
52 | 0.140619156221054 | 0.281238312442108 | 0.859380843778946 |
53 | 0.116617830867788 | 0.233235661735575 | 0.883382169132212 |
54 | 0.0944173912779607 | 0.188834782555921 | 0.90558260872204 |
55 | 0.160807975485153 | 0.321615950970307 | 0.839192024514847 |
56 | 0.163305809984068 | 0.326611619968136 | 0.836694190015932 |
57 | 0.136389754894473 | 0.272779509788945 | 0.863610245105527 |
58 | 0.110625949184111 | 0.221251898368221 | 0.88937405081589 |
59 | 0.0962885000160055 | 0.192577000032011 | 0.903711499983994 |
60 | 0.104739422171841 | 0.209478844343683 | 0.895260577828159 |
61 | 0.097743947367106 | 0.195487894734212 | 0.902256052632894 |
62 | 0.0793058663109155 | 0.158611732621831 | 0.920694133689084 |
63 | 0.245756631549167 | 0.491513263098335 | 0.754243368450833 |
64 | 0.209897950455607 | 0.419795900911214 | 0.790102049544393 |
65 | 0.176642283877388 | 0.353284567754777 | 0.823357716122612 |
66 | 0.152145551010056 | 0.304291102020112 | 0.847854448989944 |
67 | 0.128907288744385 | 0.25781457748877 | 0.871092711255615 |
68 | 0.11021045054715 | 0.2204209010943 | 0.88978954945285 |
69 | 0.0889237504413444 | 0.177847500882689 | 0.911076249558656 |
70 | 0.0725725969719455 | 0.145145193943891 | 0.927427403028054 |
71 | 0.0642921802372247 | 0.128584360474449 | 0.935707819762775 |
72 | 0.144730570273127 | 0.289461140546254 | 0.855269429726873 |
73 | 0.230543094207136 | 0.461086188414272 | 0.769456905792864 |
74 | 0.230119189204843 | 0.460238378409686 | 0.769880810795157 |
75 | 0.216374099399639 | 0.432748198799277 | 0.783625900600361 |
76 | 0.357059826347454 | 0.714119652694907 | 0.642940173652546 |
77 | 0.335787395004985 | 0.67157479000997 | 0.664212604995015 |
78 | 0.352199493930447 | 0.704398987860895 | 0.647800506069553 |
79 | 0.312387849360779 | 0.624775698721558 | 0.687612150639221 |
80 | 0.32017391239418 | 0.64034782478836 | 0.67982608760582 |
81 | 0.309766993290319 | 0.619533986580639 | 0.69023300670968 |
82 | 0.289794966815046 | 0.579589933630092 | 0.710205033184954 |
83 | 0.273128958210655 | 0.54625791642131 | 0.726871041789345 |
84 | 0.251461186188479 | 0.502922372376958 | 0.748538813811521 |
85 | 0.258694583201476 | 0.517389166402953 | 0.741305416798524 |
86 | 0.291635449020187 | 0.583270898040375 | 0.708364550979813 |
87 | 0.276545413108937 | 0.553090826217873 | 0.723454586891063 |
88 | 0.317836359485684 | 0.635672718971367 | 0.682163640514317 |
89 | 0.436235594329587 | 0.872471188659174 | 0.563764405670413 |
90 | 0.391725574969366 | 0.783451149938733 | 0.608274425030634 |
91 | 0.447669993704599 | 0.895339987409197 | 0.552330006295401 |
92 | 0.400694005562742 | 0.801388011125485 | 0.599305994437258 |
93 | 0.370126357517414 | 0.740252715034828 | 0.629873642482586 |
94 | 0.327030332087733 | 0.654060664175465 | 0.672969667912267 |
95 | 0.293423456024596 | 0.586846912049192 | 0.706576543975404 |
96 | 0.275647721584822 | 0.551295443169645 | 0.724352278415178 |
97 | 0.283395717350284 | 0.566791434700569 | 0.716604282649716 |
98 | 0.244364066522229 | 0.488728133044458 | 0.755635933477771 |
99 | 0.230792353352420 | 0.461584706704839 | 0.76920764664758 |
100 | 0.406862075422453 | 0.813724150844906 | 0.593137924577547 |
101 | 0.505924454010173 | 0.988151091979655 | 0.494075545989827 |
102 | 0.46716016386319 | 0.93432032772638 | 0.53283983613681 |
103 | 0.417584726688242 | 0.835169453376484 | 0.582415273311758 |
104 | 0.595057059461622 | 0.809885881076755 | 0.404942940538378 |
105 | 0.578429378339288 | 0.843141243321425 | 0.421570621660712 |
106 | 0.724383829931213 | 0.551232340137575 | 0.275616170068787 |
107 | 0.68336704394789 | 0.633265912104221 | 0.316632956052111 |
108 | 0.659326785907293 | 0.681346428185415 | 0.340673214092707 |
109 | 0.639855310195112 | 0.720289379609775 | 0.360144689804888 |
110 | 0.681436620554469 | 0.637126758891062 | 0.318563379445531 |
111 | 0.663338668885203 | 0.673322662229594 | 0.336661331114797 |
112 | 0.614786971284004 | 0.770426057431991 | 0.385213028715996 |
113 | 0.624436536921387 | 0.751126926157226 | 0.375563463078613 |
114 | 0.577426301329159 | 0.845147397341681 | 0.422573698670841 |
115 | 0.528560778059842 | 0.942878443880316 | 0.471439221940158 |
116 | 0.537568526155266 | 0.924862947689467 | 0.462431473844734 |
117 | 0.478974028036779 | 0.957948056073558 | 0.521025971963221 |
118 | 0.553704618856142 | 0.892590762287716 | 0.446295381143858 |
119 | 0.492298755550039 | 0.984597511100077 | 0.507701244449961 |
120 | 0.431800599400765 | 0.86360119880153 | 0.568199400599235 |
121 | 0.401592822365193 | 0.803185644730385 | 0.598407177634807 |
122 | 0.354547936252085 | 0.70909587250417 | 0.645452063747915 |
123 | 0.306197777160525 | 0.61239555432105 | 0.693802222839475 |
124 | 0.263308522532820 | 0.526617045065641 | 0.73669147746718 |
125 | 0.224076638152746 | 0.448153276305491 | 0.775923361847255 |
126 | 0.406503574197925 | 0.813007148395849 | 0.593496425802075 |
127 | 0.744223702062177 | 0.511552595875646 | 0.255776297937823 |
128 | 0.688420812151832 | 0.623158375696336 | 0.311579187848168 |
129 | 0.720008229149283 | 0.559983541701435 | 0.279991770850717 |
130 | 0.651749150180826 | 0.696501699638349 | 0.348250849819174 |
131 | 0.574426780156198 | 0.851146439687605 | 0.425573219843802 |
132 | 0.508373046918126 | 0.983253906163748 | 0.491626953081874 |
133 | 0.444038709736349 | 0.888077419472698 | 0.555961290263651 |
134 | 0.588082812532794 | 0.823834374934412 | 0.411917187467206 |
135 | 0.49476124883644 | 0.98952249767288 | 0.50523875116356 |
136 | 0.559695188101687 | 0.880609623796625 | 0.440304811898313 |
137 | 0.4628541900963 | 0.9257083801926 | 0.5371458099037 |
138 | 0.540675740447357 | 0.918648519105287 | 0.459324259552643 |
139 | 0.460642210174210 | 0.921284420348419 | 0.53935778982579 |
140 | 0.338860717194898 | 0.677721434389797 | 0.661139282805102 |
141 | 0.496850782298951 | 0.993701564597903 | 0.503149217701049 |
142 | 0.335624696102007 | 0.671249392204014 | 0.664375303897993 |
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 | 0 | 0 | OK |