Multiple Linear Regression - Estimated Regression Equation |
YT[t] = + 8.56713904540317 -0.735371589104438T1[t] + 0.0759378528567064X1[t] + 0.251758435553541X2[t] + 0.366360559218664X3[t] -0.117608217425018X4[t] + 0.000361144076985856t + 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) | 8.56713904540317 | 3.75563 | 2.2811 | 0.023948 | 0.011974 |
T1 | -0.735371589104438 | 0.380985 | -1.9302 | 0.055471 | 0.027735 |
X1 | 0.0759378528567064 | 0.073314 | 1.0358 | 0.301965 | 0.150982 |
X2 | 0.251758435553541 | 0.08442 | 2.9822 | 0.003341 | 0.001671 |
X3 | 0.366360559218664 | 0.072063 | 5.0839 | 1e-06 | 1e-06 |
X4 | -0.117608217425018 | 0.089717 | -1.3109 | 0.191902 | 0.095951 |
t | 0.000361144076985856 | 0.001663 | 0.2172 | 0.828335 | 0.414167 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.478480661179188 |
R-squared | 0.228943743122473 |
Adjusted R-squared | 0.198101492847372 |
F-TEST (value) | 7.42305574594532 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 150 |
p-value | 5.69652836457379e-07 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.861155699499398 |
Sum Squared Residuals | 111.238370817045 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 4.47244135562101 | -0.472441355621013 |
2 | 4 | 3.97229172235076 | 0.0277082776492371 |
3 | 5 | 3.75816801292248 | 1.24183198707752 |
4 | 3 | 3.60665345128606 | -0.606653451286056 |
5 | 4 | 3.17943557711267 | 0.820564422887334 |
6 | 3 | 4.01100988070698 | -1.01100988070698 |
7 | 4 | 3.56642214204148 | 0.433577857958518 |
8 | 3 | 3.06627250877128 | -0.0662725087712795 |
9 | 2 | 2.33090644065104 | -0.330906440651041 |
10 | 4 | 2.87344872664353 | 1.12655127335647 |
11 | 2 | 3.02568557643392 | -1.02568557643392 |
12 | 2 | 2.69835043210066 | -0.698350432100663 |
13 | 1 | 2.69871157617765 | -1.69871157617765 |
14 | 4 | 3.02676900866488 | 0.973230991335118 |
15 | 4 | 3.03013624650176 | 0.969863753498236 |
16 | 2 | 2.95155344396215 | -0.951553443962148 |
17 | 2 | 2.56600593435707 | -0.566005934357069 |
18 | 3 | 3.31863629133478 | -0.318636291334784 |
19 | 3 | 3.76129584748714 | -0.76129584748714 |
20 | 3 | 3.60978128585071 | -0.609781285850714 |
21 | 4 | 3.60273955364778 | 0.397260446352219 |
22 | 3 | 3.7623792797181 | -0.762379279718098 |
23 | 2 | 3.37564828323163 | -1.37564828323163 |
24 | 2 | 3.20620103213158 | -1.20620103213158 |
25 | 4 | 3.03074159351173 | 0.969258406488273 |
26 | 4 | 3.76382385602604 | 0.236176143973959 |
27 | 3 | 2.95552602880899 | 0.0444739711910075 |
28 | 4 | 3.39818558496135 | 0.601814415038651 |
29 | 2 | 3.03218616981967 | -1.03218616981967 |
30 | 4 | 3.53745487376387 | 0.462545126236133 |
31 | 4 | 3.28166079976729 | 0.718339200232712 |
32 | 5 | 3.33841170223758 | 1.66158829776242 |
33 | 5 | 2.8817550404142 | 2.1182449595858 |
34 | 4 | 3.0339918902046 | 0.9660081097954 |
35 | 4 | 3.82528651799073 | 0.174713482009269 |
36 | 4 | 3.99846215100466 | 0.00153784899534324 |
37 | 2 | 3.15268353986058 | -1.15268353986058 |
38 | 4 | 3.59233700225304 | 0.407662997746964 |
39 | 4 | 3.65091051160184 | 0.349089488398161 |
40 | 4 | 4.26939065045103 | -0.269390650451030 |
41 | 3 | 3.40288045796216 | -0.402880457962165 |
42 | 2 | 2.96094318996378 | -0.96094318996378 |
43 | 3 | 3.65536118166968 | -0.655361181669678 |
44 | 4 | 2.88572762526105 | 1.11427237473895 |
45 | 3 | 2.77148664567291 | 0.228513354327091 |
46 | 2 | 3.03832561912843 | -1.03832561912843 |
47 | 4 | 3.38431574107930 | 0.615684258920705 |
48 | 4 | 3.53655259086969 | 0.463447409130307 |
49 | 3 | 3.52037173424317 | -0.520371734243174 |
50 | 4 | 3.42706953787857 | 0.572930462121435 |
51 | 3 | 3.04013133951336 | -0.040131339513359 |
52 | 4 | 2.88861677787693 | 1.11138322212307 |
53 | 2 | 2.06077085619648 | -0.0607708561964836 |
54 | 4 | 3.40456923720309 | 0.595430762796915 |
55 | 4 | 2.9821800636681 | 1.01781993633190 |
56 | 4 | 3.62278247262220 | 0.377217527377796 |
57 | 4 | 3.04229820397527 | 0.957701796024726 |
58 | 3 | 3.33608814817411 | -0.336088148174114 |
59 | 1 | 2.27302579164363 | -1.27302579164363 |
60 | 3 | 3.14326436604636 | -0.143264366046361 |
61 | 3 | 2.96780492742651 | 0.0321950725734884 |
62 | 4 | 3.14398665420033 | 0.856013345799667 |
63 | 2 | 2.81665150986707 | -0.816651509867071 |
64 | 3 | 2.72013601786382 | 0.279863982136177 |
65 | 5 | 4.24415176408728 | 0.755848235912717 |
66 | 4 | 3.21836298960509 | 0.781637010394913 |
67 | 4 | 2.96997179188843 | 1.03002820811157 |
68 | 3 | 2.97333902972531 | 0.0266609702746920 |
69 | 4 | 2.89475622718569 | 1.10524377281431 |
70 | 2 | 3.21680147215313 | -1.21680147215313 |
71 | 3 | 2.89547851533966 | 0.104521484660336 |
72 | 4 | 4.28094726091458 | -0.280947260914578 |
73 | 3 | 3.79733962834788 | -0.797339628347881 |
74 | 4 | 3.66655664805624 | 0.333443351943761 |
75 | 4 | 2.66170665679757 | 1.33829334320243 |
76 | 3 | 3.09083030600632 | -0.0908303060063177 |
77 | 3 | 3.30127952106853 | -0.301279521068533 |
78 | 2 | 3.22570281228881 | -1.22570281228881 |
79 | 4 | 3.54774805725625 | 0.452251942743745 |
80 | 3 | 3.03287903016106 | -0.0328790301610601 |
81 | 2 | 2.72326937341269 | -0.723269373412687 |
82 | 2 | 3.70811007148054 | -1.70811007148054 |
83 | 3 | 3.78440906841423 | -0.784409068414235 |
84 | 2 | 2.78256517091546 | -0.782565170915462 |
85 | 2 | 3.05241023813088 | -1.05241023813088 |
86 | 4 | 3.26725623571312 | 0.732743764286884 |
87 | 4 | 3.27062347355 | 0.729376526450002 |
88 | 4 | 3.78621478879916 | 0.213785211200836 |
89 | 2 | 2.97791696158212 | -0.977916961582115 |
90 | 2 | 3.5517206421031 | -1.5517206421031 |
91 | 4 | 2.90570749063928 | 1.09429250936072 |
92 | 2 | 2.65130410540283 | -0.651304105402826 |
93 | 3 | 3.09396366155518 | -0.0939636615551816 |
94 | 3 | 3.23148111752059 | -0.231481117520586 |
95 | 5 | 3.88122265089828 | 1.11877734910172 |
96 | 3 | 2.66929068241427 | 0.330709317585726 |
97 | 4 | 3.22955845599165 | 0.770441544008352 |
98 | 3 | 3.05710511113169 | -0.0571051111316942 |
99 | 2 | 2.86392018492696 | -0.863920184926956 |
100 | 4 | 3.05782739928567 | 0.942172600714334 |
101 | 3 | 3.09985890793096 | -0.099858907930964 |
102 | 3 | 2.98261183458293 | 0.0173881654170684 |
103 | 3 | 2.90703512580321 | 0.0929648741967886 |
104 | 4 | 3.60145311750911 | 0.398546882490891 |
105 | 1 | 2.16902410800006 | -1.16902410800006 |
106 | 3 | 2.98405641089087 | 0.0159435891091249 |
107 | 2 | 3.02007573201638 | -1.02007573201638 |
108 | 3 | 3.3094688936952 | -0.309468893695199 |
109 | 2 | 3.16096042581867 | -1.16096042581867 |
110 | 2 | 2.56092806270834 | -0.560928062708337 |
111 | 2 | 2.82658354928247 | -0.826583549282474 |
112 | 4 | 2.58258913408584 | 1.41741086591416 |
113 | 5 | 4.23754180279918 | 0.76245819720082 |
114 | 5 | 2.66225536885641 | 2.33774463114359 |
115 | 3 | 2.98730670758375 | 0.0126932924162523 |
116 | 4 | 2.56008883341036 | 1.43991116658964 |
117 | 4 | 2.08087798336368 | 1.91912201663632 |
118 | 3 | 3.0226576281031 | -0.0226576281030992 |
119 | 2 | 2.85460106576317 | -0.854601065763168 |
120 | 4 | 3.97058588819965 | 0.0294141118003487 |
121 | 2 | 2.73771513649212 | -0.737715136492121 |
122 | 3 | 2.62046806314409 | 0.379531936855911 |
123 | 2 | 3.28362466032149 | -1.28362466032149 |
124 | 2 | 2.91461915141991 | -0.914619151419914 |
125 | 2 | 2.69748934823175 | -0.697489348231753 |
126 | 4 | 3.18482536271232 | 0.815174637287684 |
127 | 4 | 3.35800099572624 | 0.641999004273758 |
128 | 4 | 2.99200158058456 | 1.00799841941544 |
129 | 4 | 3.60747562567386 | 0.39252437432614 |
130 | 3 | 3.54962440447903 | -0.549624404479028 |
131 | 2 | 2.99308501281552 | -0.993085012815521 |
132 | 4 | 3.80210512818654 | 0.197894871813458 |
133 | 3 | 3.80246627226353 | -0.802466272263528 |
134 | 2 | 2.91823059218977 | -0.918230592189773 |
135 | 4 | 3.8031885604175 | 0.196811439582501 |
136 | 3 | 2.91594678658385 | 0.0840532134161509 |
137 | 3 | 3.07118973013414 | -0.0711897301341425 |
138 | 3 | 2.99561302135442 | 0.0043869786455776 |
139 | 3 | 2.74120963611797 | 0.258790363882029 |
140 | 3 | 3.14960170398193 | -0.149601703981933 |
141 | 4 | 3.653479719166 | 0.346520280833998 |
142 | 5 | 3.86210632734971 | 1.13789367265029 |
143 | 2 | 3.03908910630766 | -1.03908910630766 |
144 | 4 | 3.12892401018497 | 0.871075989815035 |
145 | 3 | 3.72785605457076 | -0.727856054570756 |
146 | 3 | 2.37737708543821 | 0.622622914561792 |
147 | 1 | 2.49534644694021 | -1.49534644694021 |
148 | 2 | 3.07516231498099 | -1.07516231498099 |
149 | 4 | 2.82376502350443 | 1.17623497649557 |
150 | 4 | 2.84066816828492 | 1.15933183171508 |
151 | 5 | 4.05771920744292 | 0.942280792557081 |
152 | 2 | 2.82184236197549 | -0.821842361975493 |
153 | 4 | 3.40466432377616 | 0.595335676223836 |
154 | 3 | 3.00139132658620 | -0.00139132658619608 |
155 | 2 | 3.36811302988185 | -1.36811302988185 |
156 | 4 | 3.32680380939052 | 0.67319619060948 |
157 | 2 | 2.47382952384526 | -0.473829523845264 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.814900628656109 | 0.370198742687782 | 0.185099371343891 |
11 | 0.832742451356617 | 0.334515097286766 | 0.167257548643383 |
12 | 0.753553513237782 | 0.492892973524437 | 0.246446486762218 |
13 | 0.731787354144662 | 0.536425291710675 | 0.268212645855338 |
14 | 0.921384959384112 | 0.157230081231776 | 0.0786150406158878 |
15 | 0.918143259084963 | 0.163713481830074 | 0.0818567409150371 |
16 | 0.886271201335923 | 0.227457597328153 | 0.113728798664077 |
17 | 0.839610862753665 | 0.320778274492669 | 0.160389137246335 |
18 | 0.799566878492577 | 0.400866243014847 | 0.200433121507423 |
19 | 0.740015147632863 | 0.519969704734274 | 0.259984852367137 |
20 | 0.6816190039514 | 0.636761992097199 | 0.318380996048600 |
21 | 0.699069517404997 | 0.601860965190005 | 0.300930482595003 |
22 | 0.641802759355697 | 0.716394481288606 | 0.358197240644303 |
23 | 0.60242926640345 | 0.7951414671931 | 0.39757073359655 |
24 | 0.560393627690797 | 0.879212744618406 | 0.439606372309203 |
25 | 0.666259128042566 | 0.667481743914868 | 0.333740871957434 |
26 | 0.631404493970282 | 0.737191012059436 | 0.368595506029718 |
27 | 0.584168585916401 | 0.831662828167197 | 0.415831414083599 |
28 | 0.558615220264388 | 0.882769559471224 | 0.441384779735612 |
29 | 0.576751849851059 | 0.846496300297882 | 0.423248150148941 |
30 | 0.62391965893079 | 0.75216068213842 | 0.37608034106921 |
31 | 0.61996959935479 | 0.76006080129042 | 0.38003040064521 |
32 | 0.677085744253664 | 0.645828511492672 | 0.322914255746336 |
33 | 0.85505346900773 | 0.289893061984539 | 0.144946530992269 |
34 | 0.831333767231654 | 0.337332465536693 | 0.168666232768346 |
35 | 0.79176167375563 | 0.416476652488739 | 0.208238326244370 |
36 | 0.74828187648857 | 0.50343624702286 | 0.25171812351143 |
37 | 0.860312112734253 | 0.279375774531494 | 0.139687887265747 |
38 | 0.829750113999746 | 0.340499772000509 | 0.170249886000254 |
39 | 0.793452361269935 | 0.413095277460131 | 0.206547638730065 |
40 | 0.760699959156569 | 0.478600081686863 | 0.239300040843432 |
41 | 0.745107246560874 | 0.509785506878253 | 0.254892753439126 |
42 | 0.772255768068697 | 0.455488463862606 | 0.227744231931303 |
43 | 0.755948480310672 | 0.488103039378657 | 0.244051519689328 |
44 | 0.768504355005526 | 0.462991289988948 | 0.231495644994474 |
45 | 0.726401866632919 | 0.547196266734162 | 0.273598133367081 |
46 | 0.764600550724695 | 0.47079889855061 | 0.235399449275305 |
47 | 0.73366409938386 | 0.532671801232281 | 0.266335900616140 |
48 | 0.693200899184437 | 0.613598201631127 | 0.306799100815563 |
49 | 0.67740691295642 | 0.645186174087161 | 0.322593087043580 |
50 | 0.641442802938396 | 0.717114394123208 | 0.358557197061604 |
51 | 0.594958167923672 | 0.810083664152656 | 0.405041832076328 |
52 | 0.598786386037036 | 0.802427227925929 | 0.401213613962964 |
53 | 0.563279566782059 | 0.873440866435882 | 0.436720433217941 |
54 | 0.522883942336094 | 0.954232115327811 | 0.477116057663906 |
55 | 0.509730233095537 | 0.980539533808926 | 0.490269766904463 |
56 | 0.465225306538893 | 0.930450613077787 | 0.534774693461107 |
57 | 0.452115247684887 | 0.904230495369775 | 0.547884752315113 |
58 | 0.414411920865886 | 0.828823841731772 | 0.585588079134114 |
59 | 0.52149514598771 | 0.95700970802458 | 0.47850485401229 |
60 | 0.475400568939524 | 0.950801137879048 | 0.524599431060476 |
61 | 0.427909184554166 | 0.855818369108332 | 0.572090815445834 |
62 | 0.417684313987474 | 0.835368627974948 | 0.582315686012526 |
63 | 0.422143213933684 | 0.844286427867369 | 0.577856786066316 |
64 | 0.3775280752033 | 0.7550561504066 | 0.6224719247967 |
65 | 0.362932474531370 | 0.725864949062739 | 0.63706752546863 |
66 | 0.342147391618936 | 0.684294783237873 | 0.657852608381064 |
67 | 0.344306272112153 | 0.688612544224307 | 0.655693727887847 |
68 | 0.302059315114574 | 0.604118630229148 | 0.697940684885426 |
69 | 0.315523637189989 | 0.631047274379978 | 0.684476362810011 |
70 | 0.400164310430221 | 0.800328620860441 | 0.59983568956978 |
71 | 0.357493939045512 | 0.714987878091024 | 0.642506060954488 |
72 | 0.326958603441712 | 0.653917206883423 | 0.673041396558288 |
73 | 0.331325288406838 | 0.662650576813676 | 0.668674711593162 |
74 | 0.294533441551453 | 0.589066883102906 | 0.705466558448547 |
75 | 0.344599280604297 | 0.689198561208593 | 0.655400719395703 |
76 | 0.305235845811362 | 0.610471691622725 | 0.694764154188638 |
77 | 0.273866907082256 | 0.547733814164512 | 0.726133092917744 |
78 | 0.318243755162415 | 0.636487510324831 | 0.681756244837584 |
79 | 0.290438117301476 | 0.580876234602952 | 0.709561882698524 |
80 | 0.254522822402585 | 0.50904564480517 | 0.745477177597415 |
81 | 0.24711436623242 | 0.49422873246484 | 0.75288563376758 |
82 | 0.352291216391647 | 0.704582432783293 | 0.647708783608353 |
83 | 0.340236436660959 | 0.680472873321918 | 0.659763563339041 |
84 | 0.332616475110168 | 0.665232950220336 | 0.667383524889832 |
85 | 0.352752788214958 | 0.705505576429916 | 0.647247211785042 |
86 | 0.342613323767172 | 0.685226647534345 | 0.657386676232828 |
87 | 0.332812688798489 | 0.665625377596978 | 0.66718731120151 |
88 | 0.293970487367053 | 0.587940974734106 | 0.706029512632947 |
89 | 0.303840583222297 | 0.607681166444593 | 0.696159416777703 |
90 | 0.403484817307944 | 0.806969634615889 | 0.596515182692056 |
91 | 0.434422112669342 | 0.868844225338684 | 0.565577887330658 |
92 | 0.412318545315396 | 0.824637090630791 | 0.587681454684604 |
93 | 0.369736985285203 | 0.739473970570406 | 0.630263014714797 |
94 | 0.32830919541267 | 0.65661839082534 | 0.67169080458733 |
95 | 0.345531679402732 | 0.691063358805464 | 0.654468320597268 |
96 | 0.311205698474319 | 0.622411396948637 | 0.688794301525681 |
97 | 0.303595100013991 | 0.607190200027982 | 0.696404899986009 |
98 | 0.262792153922191 | 0.525584307844381 | 0.73720784607781 |
99 | 0.258093273491288 | 0.516186546982577 | 0.741906726508712 |
100 | 0.259745593382293 | 0.519491186764585 | 0.740254406617707 |
101 | 0.221931927710361 | 0.443863855420723 | 0.778068072289639 |
102 | 0.186724530726387 | 0.373449061452775 | 0.813275469273613 |
103 | 0.156157534318704 | 0.312315068637409 | 0.843842465681296 |
104 | 0.135850666687528 | 0.271701333375057 | 0.864149333312472 |
105 | 0.154521807826980 | 0.309043615653959 | 0.84547819217302 |
106 | 0.126389578056595 | 0.25277915611319 | 0.873610421943405 |
107 | 0.147116171318016 | 0.294232342636032 | 0.852883828681984 |
108 | 0.125466006542988 | 0.250932013085976 | 0.874533993457012 |
109 | 0.142388097480975 | 0.284776194961950 | 0.857611902519025 |
110 | 0.134249274770545 | 0.268498549541089 | 0.865750725229455 |
111 | 0.156567620039172 | 0.313135240078343 | 0.843432379960828 |
112 | 0.196927678406044 | 0.393855356812088 | 0.803072321593956 |
113 | 0.174779015909973 | 0.349558031819947 | 0.825220984090027 |
114 | 0.494603095411647 | 0.989206190823294 | 0.505396904588353 |
115 | 0.439937068265967 | 0.879874136531933 | 0.560062931734034 |
116 | 0.489532870961681 | 0.979065741923362 | 0.510467129038319 |
117 | 0.812484260504027 | 0.375031478991945 | 0.187515739495973 |
118 | 0.78330397396203 | 0.433392052075939 | 0.216696026037970 |
119 | 0.758389021497587 | 0.483221957004826 | 0.241610978502413 |
120 | 0.714836369087296 | 0.570327261825408 | 0.285163630912704 |
121 | 0.685925220541633 | 0.628149558916734 | 0.314074779458367 |
122 | 0.645633969832881 | 0.708732060334238 | 0.354366030167119 |
123 | 0.653255383837443 | 0.693489232325114 | 0.346744616162557 |
124 | 0.628217451867937 | 0.743565096264126 | 0.371782548132063 |
125 | 0.653823162852743 | 0.692353674294513 | 0.346176837147257 |
126 | 0.635566767138124 | 0.728866465723752 | 0.364433232861876 |
127 | 0.606239950423034 | 0.787520099153931 | 0.393760049576966 |
128 | 0.673062408081664 | 0.653875183836671 | 0.326937591918336 |
129 | 0.617273765919448 | 0.765452468161104 | 0.382726234080552 |
130 | 0.592981099961349 | 0.814037800077303 | 0.407018900038651 |
131 | 0.579906861267479 | 0.840186277465042 | 0.420093138732521 |
132 | 0.511701066609348 | 0.976597866781303 | 0.488298933390652 |
133 | 0.614894134511224 | 0.770211730977553 | 0.385105865488776 |
134 | 0.586084325050544 | 0.827831349898912 | 0.413915674949456 |
135 | 0.562946829378229 | 0.874106341243542 | 0.437053170621771 |
136 | 0.483144039632516 | 0.966288079265032 | 0.516855960367484 |
137 | 0.487487325135399 | 0.974974650270798 | 0.512512674864601 |
138 | 0.436938933493837 | 0.873877866987675 | 0.563061066506163 |
139 | 0.355541990837327 | 0.711083981674653 | 0.644458009162673 |
140 | 0.288796039099582 | 0.577592078199164 | 0.711203960900418 |
141 | 0.240407881704033 | 0.480815763408066 | 0.759592118295967 |
142 | 0.195794658850956 | 0.391589317701912 | 0.804205341149044 |
143 | 0.144131629985642 | 0.288263259971283 | 0.855868370014358 |
144 | 0.0947164893389675 | 0.189432978677935 | 0.905283510661033 |
145 | 0.084726664148586 | 0.169453328297172 | 0.915273335851414 |
146 | 0.0857080830678513 | 0.171416166135703 | 0.914291916932149 |
147 | 0.0528165441478915 | 0.105633088295783 | 0.947183455852109 |
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 |