Multiple Linear Regression - Estimated Regression Equation |
YT[t] = + 8.33389075361305 -0.707921514339938T1[t] + 0.0765528746818012X1[t] + 0.247513466468539X2[t] + 0.36568320992491X3[t] -0.115580997002372X4[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) | 8.33389075361305 | 3.587474 | 2.3231 | 0.021511 | 0.010756 |
T1 | -0.707921514339938 | 0.35828 | -1.9759 | 0.04999 | 0.024995 |
X1 | 0.0765528746818012 | 0.073027 | 1.0483 | 0.296186 | 0.148093 |
X2 | 0.247513466468539 | 0.081868 | 3.0233 | 0.002938 | 0.001469 |
X3 | 0.36568320992491 | 0.071768 | 5.0953 | 1e-06 | 1e-06 |
X4 | -0.115580997002372 | 0.088948 | -1.2994 | 0.195782 | 0.097891 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.478227147881944 |
R-squared | 0.228701204971298 |
Adjusted R-squared | 0.203161509771673 |
F-TEST (value) | 8.9547350970206 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 151 |
p-value | 1.80539287630843e-07 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.858434433593512 |
Sum Squared Residuals | 111.273361193631 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 4 | 4.46926005495242 | -0.469260054952424 |
2 | 4 | 3.97164437556135 | 0.0283556244386497 |
3 | 5 | 3.75906691500004 | 1.24093308499996 |
4 | 3 | 3.60596116563644 | -0.605961165636439 |
5 | 4 | 3.18748710738116 | 0.812512892618836 |
6 | 3 | 4.00658038146858 | -1.00658038146858 |
7 | 4 | 3.58778920237175 | 0.412210797628248 |
8 | 3 | 3.09017352298067 | -0.0901735229806749 |
9 | 2 | 2.36139584958485 | -0.361395849584854 |
10 | 4 | 2.8980396512965 | 1.10196034870350 |
11 | 2 | 3.05114540066010 | -1.05114540066010 |
12 | 2 | 2.72707905950976 | -0.727079059509764 |
13 | 1 | 2.72707905950976 | -1.72707905950976 |
14 | 4 | 3.05114540066010 | 0.948854599339896 |
15 | 4 | 3.04855665420610 | 0.951443345793895 |
16 | 2 | 2.9745925259783 | -0.974592525978303 |
17 | 2 | 2.5951465900436 | -0.595146590043597 |
18 | 3 | 3.34027573590321 | -0.340275735903213 |
19 | 3 | 3.78251182050992 | -0.782511820509925 |
20 | 3 | 3.62940607114632 | -0.629406071146322 |
21 | 4 | 3.62790270118698 | 0.372097298813019 |
22 | 3 | 3.78251182050992 | -0.782511820509925 |
23 | 2 | 3.39824407714158 | -1.39824407714158 |
24 | 2 | 3.22210599244684 | -1.22210599244684 |
25 | 4 | 3.05114540066010 | 0.948854599339896 |
26 | 4 | 3.78251182050992 | 0.217488179490076 |
27 | 3 | 2.9745925259783 | 0.0254074740216973 |
28 | 4 | 3.41682861058501 | 0.583171389414986 |
29 | 2 | 3.05114540066010 | -1.05114540066010 |
30 | 4 | 3.55285319646452 | 0.447146803535479 |
31 | 4 | 3.30124761358264 | 0.698752386417358 |
32 | 5 | 3.36403776225465 | 1.63596223774535 |
33 | 5 | 2.8980396512965 | 2.1019603487035 |
34 | 4 | 3.05114540066010 | 0.948854599339896 |
35 | 4 | 3.83789141529429 | 0.162108584705710 |
36 | 4 | 4.01144075353503 | -0.0114407535350267 |
37 | 2 | 3.16672639766248 | -1.16672639766248 |
38 | 4 | 3.61155122872319 | 0.388448771276813 |
39 | 4 | 3.66693082350755 | 0.333069176492448 |
40 | 4 | 4.280127499901 | -0.280127499901001 |
41 | 3 | 3.41682861058501 | -0.416828610585014 |
42 | 2 | 2.9745925259783 | -0.974592525978303 |
43 | 3 | 3.66434207705355 | -0.664342077053553 |
44 | 4 | 2.8980396512965 | 1.10196034870350 |
45 | 3 | 2.77986990784013 | 0.22013009215987 |
46 | 2 | 3.05114540066010 | -1.05114540066010 |
47 | 4 | 3.39824407714158 | 0.601755922858422 |
48 | 4 | 3.55134982650518 | 0.44865017349482 |
49 | 3 | 3.53499835404139 | -0.534998354041386 |
50 | 4 | 3.43727219946215 | 0.562727800537851 |
51 | 3 | 3.05114540066010 | -0.0511454006601039 |
52 | 4 | 2.8980396512965 | 1.10196034870350 |
53 | 2 | 2.07635763075508 | -0.0763576307550847 |
54 | 4 | 3.41941735703901 | 0.580582642960986 |
55 | 4 | 2.99094399844210 | 1.00905600155790 |
56 | 4 | 3.62940607114632 | 0.370593928853678 |
57 | 4 | 3.05114540066010 | 0.948854599339896 |
58 | 3 | 3.33768698944921 | -0.337686989449214 |
59 | 1 | 2.28484297490305 | -1.28484297490305 |
60 | 3 | 3.14555311776504 | -0.14555311776504 |
61 | 3 | 2.9745925259783 | 0.0254074740216973 |
62 | 4 | 3.14555311776504 | 0.85444688223496 |
63 | 2 | 2.8214867766147 | -0.8214867766147 |
64 | 3 | 2.72449031305576 | 0.275509686944235 |
65 | 5 | 4.24260274753977 | 0.757397252460229 |
66 | 4 | 3.22469473890084 | 0.77530526109916 |
67 | 4 | 2.97459252597830 | 1.02540747402170 |
68 | 3 | 2.97200377952430 | 0.0279962204756967 |
69 | 4 | 2.8980396512965 | 1.10196034870350 |
70 | 2 | 3.22728348535484 | -1.22728348535484 |
71 | 3 | 2.8980396512965 | 0.101960348703499 |
72 | 4 | 4.280127499901 | -0.280127499901001 |
73 | 3 | 3.79886329297372 | -0.798863292973719 |
74 | 4 | 3.66434207705355 | 0.335657922946447 |
75 | 4 | 2.66687765729176 | 1.33312234270824 |
76 | 3 | 3.09017352298067 | -0.0901735229806749 |
77 | 3 | 3.29865886712864 | -0.298658867128643 |
78 | 2 | 3.22210599244684 | -1.22210599244684 |
79 | 4 | 3.55134982650518 | 0.44865017349482 |
80 | 3 | 3.02997212076267 | -0.0299721207626679 |
81 | 2 | 2.72707905950976 | -0.727079059509764 |
82 | 2 | 3.70595894582812 | -1.70595894582812 |
83 | 3 | 3.78251182050992 | -0.782511820509925 |
84 | 2 | 2.78245865429413 | -0.78245865429413 |
85 | 2 | 3.05114540066010 | -1.05114540066010 |
86 | 4 | 3.26372286122141 | 0.736277138778588 |
87 | 4 | 3.26113411476741 | 0.738865885232587 |
88 | 4 | 3.78251182050992 | 0.217488179490076 |
89 | 2 | 2.9745925259783 | -0.974592525978303 |
90 | 2 | 3.55134982650518 | -1.55134982650518 |
91 | 4 | 2.8954509048425 | 1.10454909515750 |
92 | 2 | 2.65052618482796 | -0.650526184827963 |
93 | 3 | 3.09276226943467 | -0.0927622694346742 |
94 | 3 | 3.22210599244684 | -0.222105992446841 |
95 | 5 | 3.87541616765552 | 1.12458383234448 |
96 | 3 | 2.66687765729176 | 0.333122342708243 |
97 | 4 | 3.22469473890084 | 0.77530526109916 |
98 | 3 | 3.05114540066010 | -0.0511454006601039 |
99 | 2 | 2.85901152897593 | -0.85901152897593 |
100 | 4 | 3.05114540066010 | 0.948854599339896 |
101 | 3 | 3.09017352298067 | -0.0901735229806749 |
102 | 3 | 2.9745925259783 | 0.0254074740216973 |
103 | 3 | 2.8980396512965 | 0.101960348703499 |
104 | 4 | 3.58778920237175 | 0.412210797628248 |
105 | 1 | 2.17185072435468 | -1.17185072435468 |
106 | 3 | 2.9745925259783 | 0.0254074740216973 |
107 | 2 | 3.01879814120687 | -1.01879814120687 |
108 | 3 | 3.30124761358264 | -0.301247613582642 |
109 | 2 | 3.14555311776504 | -1.14555311776504 |
110 | 2 | 2.55352972126903 | -0.553529721269027 |
111 | 2 | 2.81998340665536 | -0.81998340665536 |
112 | 4 | 2.57397331014616 | 1.42602668985384 |
113 | 5 | 4.22474790511664 | 0.775252094883364 |
114 | 5 | 2.64793743837396 | 2.35206256162604 |
115 | 3 | 2.9745925259783 | 0.0254074740216973 |
116 | 4 | 2.55611846772303 | 1.44388153227697 |
117 | 4 | 2.07894637720908 | 1.92105362279092 |
118 | 3 | 3.01211727833953 | -0.0121172783395329 |
119 | 2 | 2.84266005651214 | -0.842660056512136 |
120 | 4 | 3.95606115875066 | 0.0439388412493387 |
121 | 2 | 2.72707905950976 | -0.727079059509764 |
122 | 3 | 2.61149806250739 | 0.388501937492608 |
123 | 2 | 3.26113411476741 | -1.26113411476741 |
124 | 2 | 2.8980396512965 | -0.898039651296502 |
125 | 2 | 2.68805093718919 | -0.688050937189193 |
126 | 4 | 3.16672639766248 | 0.833273602337524 |
127 | 4 | 3.34027573590321 | 0.659724264096787 |
128 | 4 | 2.97459252597830 | 1.02540747402170 |
129 | 4 | 3.59037794882575 | 0.409622051174249 |
130 | 3 | 3.53499835404139 | -0.534998354041386 |
131 | 2 | 2.9745925259783 | -0.974592525978303 |
132 | 4 | 3.78251182050992 | 0.217488179490076 |
133 | 3 | 3.78251182050992 | -0.782511820509925 |
134 | 2 | 2.8980396512965 | -0.898039651296502 |
135 | 4 | 3.78251182050992 | 0.217488179490076 |
136 | 3 | 2.9006283977505 | 0.0993716022494993 |
137 | 3 | 3.05114540066010 | -0.0511454006601039 |
138 | 3 | 2.9745925259783 | 0.0254074740216973 |
139 | 3 | 2.72966780596376 | 0.270332194036237 |
140 | 3 | 3.13437913820924 | -0.134379138209244 |
141 | 4 | 3.62940607114632 | 0.370593928853678 |
142 | 5 | 3.84530196918193 | 1.15469803081807 |
143 | 2 | 3.01362064829887 | -1.01362064829887 |
144 | 4 | 3.10911374189847 | 0.890886258101531 |
145 | 3 | 3.70854769228212 | -0.708547692282123 |
146 | 3 | 2.36398459603885 | 0.636015403961147 |
147 | 1 | 2.47956559304123 | -1.47956559304123 |
148 | 2 | 3.05114540066010 | -1.05114540066010 |
149 | 4 | 2.80363193419157 | 1.19636806580843 |
150 | 4 | 2.81998340665536 | 1.18001659334464 |
151 | 5 | 4.03261403343246 | 0.967385966567537 |
152 | 2 | 2.80622068064556 | -0.806220680645565 |
153 | 4 | 3.37521174181044 | 0.624788258189556 |
154 | 3 | 2.9745925259783 | 0.0254074740216973 |
155 | 2 | 3.34027573590321 | -1.34027573590321 |
156 | 4 | 3.30124761358264 | 0.698752386417358 |
157 | 2 | 2.45688894318445 | -0.456888943184449 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.478516808529534 | 0.957033617059067 | 0.521483191470466 |
10 | 0.699572051804781 | 0.600855896390437 | 0.300427948195219 |
11 | 0.780560893564702 | 0.438878212870595 | 0.219439106435298 |
12 | 0.768244334651571 | 0.463511330696857 | 0.231755665348429 |
13 | 0.875271962661018 | 0.249456074677964 | 0.124728037338982 |
14 | 0.90977637174767 | 0.18044725650466 | 0.09022362825233 |
15 | 0.88834616526325 | 0.223307669473501 | 0.111653834736751 |
16 | 0.870492803375496 | 0.259014393249007 | 0.129507196624504 |
17 | 0.839516689581751 | 0.320966620836498 | 0.160483310418249 |
18 | 0.783254306418867 | 0.433491387162267 | 0.216745693581134 |
19 | 0.726656408485754 | 0.546687183028493 | 0.273343591514246 |
20 | 0.660211848210979 | 0.679576303578042 | 0.339788151789021 |
21 | 0.660847588270224 | 0.678304823459552 | 0.339152411729776 |
22 | 0.606481242314824 | 0.787037515370353 | 0.393518757685176 |
23 | 0.590115278290767 | 0.819769443418466 | 0.409884721709233 |
24 | 0.619949318179881 | 0.760101363640239 | 0.380050681820119 |
25 | 0.642192163329236 | 0.715615673341527 | 0.357807836670764 |
26 | 0.594939606764986 | 0.810120786470027 | 0.405060393235014 |
27 | 0.535235464913179 | 0.929529070173642 | 0.464764535086821 |
28 | 0.506216372845769 | 0.987567254308462 | 0.493783627154231 |
29 | 0.537069153889378 | 0.925861692221244 | 0.462930846110622 |
30 | 0.573510510680005 | 0.85297897863999 | 0.426489489319995 |
31 | 0.580690575485696 | 0.838618849028608 | 0.419309424514304 |
32 | 0.657980565695803 | 0.684038868608393 | 0.342019434304197 |
33 | 0.908650861958864 | 0.182698276082271 | 0.0913491380411355 |
34 | 0.908266076530464 | 0.183467846939073 | 0.0917339234695364 |
35 | 0.886780727916799 | 0.226438544166402 | 0.113219272083201 |
36 | 0.862641423852392 | 0.274717152295215 | 0.137358576147608 |
37 | 0.886842904853328 | 0.226314190293343 | 0.113157095146672 |
38 | 0.860436524869458 | 0.279126950261084 | 0.139563475130542 |
39 | 0.830740036478442 | 0.338519927043115 | 0.169259963521558 |
40 | 0.79771761415709 | 0.404564771685819 | 0.202282385842909 |
41 | 0.767001447984225 | 0.465997104031551 | 0.232998552015775 |
42 | 0.766880912704316 | 0.466238174591367 | 0.233119087295684 |
43 | 0.74326116351356 | 0.513477672972881 | 0.256738836486440 |
44 | 0.781164077443932 | 0.437671845112136 | 0.218835922556068 |
45 | 0.747904851060334 | 0.504190297879333 | 0.252095148939666 |
46 | 0.762661150139035 | 0.47467769972193 | 0.237338849860965 |
47 | 0.73908513907384 | 0.52182972185232 | 0.26091486092616 |
48 | 0.702632362957381 | 0.594735274085238 | 0.297367637042619 |
49 | 0.674812173905653 | 0.650375652188694 | 0.325187826094347 |
50 | 0.646777248494002 | 0.706445503011995 | 0.353222751505998 |
51 | 0.598483745067876 | 0.803032509864247 | 0.401516254932124 |
52 | 0.625391459057925 | 0.74921708188415 | 0.374608540942075 |
53 | 0.579830328944867 | 0.840339342110265 | 0.420169671055133 |
54 | 0.545669462891495 | 0.90866107421701 | 0.454330537108505 |
55 | 0.542212335675389 | 0.915575328649223 | 0.457787664324611 |
56 | 0.50598768754051 | 0.98802462491898 | 0.49401231245949 |
57 | 0.51225637394826 | 0.97548725210348 | 0.48774362605174 |
58 | 0.466837074967294 | 0.933674149934589 | 0.533162925032705 |
59 | 0.541974097130315 | 0.91605180573937 | 0.458025902869685 |
60 | 0.493972016016417 | 0.987944032032835 | 0.506027983983583 |
61 | 0.445477687859766 | 0.890955375719532 | 0.554522312140234 |
62 | 0.447618843646286 | 0.895237687292571 | 0.552381156353714 |
63 | 0.440831037734451 | 0.881662075468902 | 0.559168962265549 |
64 | 0.400882215253698 | 0.801764430507397 | 0.599117784746302 |
65 | 0.397559041866031 | 0.795118083732062 | 0.602440958133969 |
66 | 0.383459154389234 | 0.766918308778468 | 0.616540845610766 |
67 | 0.399251196884878 | 0.798502393769756 | 0.600748803115122 |
68 | 0.354464382014967 | 0.708928764029934 | 0.645535617985033 |
69 | 0.37985019466884 | 0.75970038933768 | 0.62014980533116 |
70 | 0.437905199823253 | 0.875810399646507 | 0.562094800176747 |
71 | 0.392299320940243 | 0.784598641880486 | 0.607700679059757 |
72 | 0.352293967569652 | 0.704587935139303 | 0.647706032430349 |
73 | 0.34712513870828 | 0.69425027741656 | 0.65287486129172 |
74 | 0.310781580130204 | 0.621563160260407 | 0.689218419869796 |
75 | 0.362378445684524 | 0.724756891369049 | 0.637621554315476 |
76 | 0.319356808447107 | 0.638713616894214 | 0.680643191552893 |
77 | 0.283300405288826 | 0.566600810577651 | 0.716699594711174 |
78 | 0.321851423751779 | 0.643702847503558 | 0.678148576248221 |
79 | 0.291059779450706 | 0.582119558901411 | 0.708940220549295 |
80 | 0.253275024400289 | 0.506550048800579 | 0.74672497559971 |
81 | 0.244351734330951 | 0.488703468661902 | 0.755648265669049 |
82 | 0.351224131811136 | 0.702448263622273 | 0.648775868188864 |
83 | 0.341637645416435 | 0.683275290832869 | 0.658362354583565 |
84 | 0.335701150201324 | 0.671402300402648 | 0.664298849798676 |
85 | 0.358114743350772 | 0.716229486701544 | 0.641885256649228 |
86 | 0.347211491902511 | 0.694422983805023 | 0.652788508097489 |
87 | 0.337073240768094 | 0.674146481536188 | 0.662926759231906 |
88 | 0.298166686522728 | 0.596333373045457 | 0.701833313477272 |
89 | 0.30852526903345 | 0.6170505380669 | 0.69147473096655 |
90 | 0.403136734160616 | 0.806273468321232 | 0.596863265839384 |
91 | 0.436304403286227 | 0.872608806572455 | 0.563695596713773 |
92 | 0.412238897217148 | 0.824477794434295 | 0.587761102782853 |
93 | 0.367113806244687 | 0.734227612489374 | 0.632886193755313 |
94 | 0.325254368996299 | 0.650508737992598 | 0.674745631003701 |
95 | 0.349558824738267 | 0.699117649476534 | 0.650441175261733 |
96 | 0.317927959281961 | 0.635855918563922 | 0.682072040718039 |
97 | 0.313106220215192 | 0.626212440430383 | 0.686893779784808 |
98 | 0.271719176708363 | 0.543438353416726 | 0.728280823291637 |
99 | 0.265633691472607 | 0.531267382945215 | 0.734366308527393 |
100 | 0.270002741131279 | 0.540005482262559 | 0.72999725886872 |
101 | 0.231443931650196 | 0.462887863300392 | 0.768556068349804 |
102 | 0.195678467407945 | 0.391356934815890 | 0.804321532592055 |
103 | 0.164652391764419 | 0.329304783528838 | 0.835347608235581 |
104 | 0.144129921653128 | 0.288259843306255 | 0.855870078346872 |
105 | 0.162573636733919 | 0.325147273467838 | 0.837426363266081 |
106 | 0.133791883418128 | 0.267583766836256 | 0.866208116581872 |
107 | 0.148599568030554 | 0.297199136061108 | 0.851400431969446 |
108 | 0.123657803260759 | 0.247315606521517 | 0.876342196739241 |
109 | 0.134110664532346 | 0.268221329064693 | 0.865889335467654 |
110 | 0.119995857836527 | 0.239991715673054 | 0.880004142163473 |
111 | 0.116161724073133 | 0.232323448146267 | 0.883838275926867 |
112 | 0.164494776612278 | 0.328989553224556 | 0.835505223387722 |
113 | 0.153006333726771 | 0.306012667453541 | 0.84699366627323 |
114 | 0.490404398897513 | 0.980808797795025 | 0.509595601102487 |
115 | 0.439381482237435 | 0.87876296447487 | 0.560618517762565 |
116 | 0.513323613650873 | 0.973352772698253 | 0.486676386349127 |
117 | 0.83886388646353 | 0.32227222707294 | 0.16113611353647 |
118 | 0.8128053020516 | 0.374389395896801 | 0.187194697948401 |
119 | 0.786819161717192 | 0.426361676565616 | 0.213180838282808 |
120 | 0.744550375205665 | 0.51089924958867 | 0.255449624794335 |
121 | 0.711509073442543 | 0.576981853114914 | 0.288490926557457 |
122 | 0.681053678082917 | 0.637892643834167 | 0.318946321917083 |
123 | 0.68436680340694 | 0.631266393186121 | 0.315633196593061 |
124 | 0.65495541313343 | 0.690089173733139 | 0.345044586866569 |
125 | 0.644310836396074 | 0.711378327207853 | 0.355689163603926 |
126 | 0.651380011786689 | 0.697239976426623 | 0.348619988213311 |
127 | 0.638289798638437 | 0.723420402723125 | 0.361710201361563 |
128 | 0.716684175536015 | 0.56663164892797 | 0.283315824463985 |
129 | 0.664317821510782 | 0.671364356978435 | 0.335682178489218 |
130 | 0.64226638926656 | 0.715467221466879 | 0.357733610733440 |
131 | 0.621088869934563 | 0.757822260130875 | 0.378911130065437 |
132 | 0.553176344118875 | 0.89364731176225 | 0.446823655881125 |
133 | 0.597149550747423 | 0.805700898505155 | 0.402850449252577 |
134 | 0.5445755807565 | 0.910848838487 | 0.4554244192435 |
135 | 0.474316721188373 | 0.948633442376747 | 0.525683278811627 |
136 | 0.415346516010257 | 0.830693032020514 | 0.584653483989743 |
137 | 0.342274581821334 | 0.684549163642667 | 0.657725418178666 |
138 | 0.277347193606545 | 0.554694387213089 | 0.722652806393455 |
139 | 0.228488327468749 | 0.456976654937499 | 0.77151167253125 |
140 | 0.184861908683887 | 0.369723817367774 | 0.815138091316113 |
141 | 0.176974519404651 | 0.353949038809302 | 0.82302548059535 |
142 | 0.182597227441929 | 0.365194454883857 | 0.817402772558071 |
143 | 0.131544370816265 | 0.263088741632530 | 0.868455629183735 |
144 | 0.109943167222918 | 0.219886334445836 | 0.890056832777082 |
145 | 0.0741942899200113 | 0.148388579840023 | 0.925805710079989 |
146 | 0.123552961809527 | 0.247105923619054 | 0.876447038190473 |
147 | 0.0776491481155255 | 0.155298296231051 | 0.922350851884474 |
148 | 0.0988286351840017 | 0.197657270368003 | 0.901171364815998 |
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 |