Multiple Linear Regression - Estimated Regression Equation |
YT[t] = + 8.3338907536128 -0.707921514339912T1[t] + 0.0765528746818019X1[t] + 0.247513466468538X2[t] + 0.365683209924910X3[t] -0.115580997002373X4[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) | 8.3338907536128 | 3.587474 | 2.3231 | 0.021511 | 0.010756 |
T1 | -0.707921514339912 | 0.35828 | -1.9759 | 0.04999 | 0.024995 |
X1 | 0.0765528746818019 | 0.073027 | 1.0483 | 0.296186 | 0.148093 |
X2 | 0.247513466468538 | 0.081868 | 3.0233 | 0.002938 | 0.001469 |
X3 | 0.365683209924910 | 0.071768 | 5.0953 | 1e-06 | 1e-06 |
X4 | -0.115580997002373 | 0.088948 | -1.2994 | 0.195782 | 0.097891 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.478227147881943 |
R-squared | 0.228701204971298 |
Adjusted R-squared | 0.203161509771672 |
F-TEST (value) | 8.95473509702057 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 151 |
p-value | 1.80539287519821e-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 | 4.46926005495247 | -0.469260054952466 |
2 | 4 | 3.97164437556134 | 0.0283556244386557 |
3 | 5 | 3.75906691500002 | 1.24093308499998 |
4 | 3 | 3.60596116563642 | -0.605961165636421 |
5 | 4 | 3.18748710738115 | 0.812512892618853 |
6 | 3 | 4.00658038146856 | -1.00658038146856 |
7 | 4 | 3.58778920237175 | 0.412210797628249 |
8 | 3 | 3.09017352298068 | -0.090173522980676 |
9 | 2 | 2.36139584958486 | -0.361395849584856 |
10 | 4 | 2.8980396512965 | 1.10196034870350 |
11 | 2 | 3.05114540066011 | -1.05114540066010 |
12 | 2 | 2.72707905950977 | -0.727079059509766 |
13 | 1 | 2.72707905950977 | -1.72707905950977 |
14 | 4 | 3.05114540066011 | 0.948854599339895 |
15 | 4 | 3.04855665420611 | 0.951443345793894 |
16 | 2 | 2.9745925259783 | -0.974592525978303 |
17 | 2 | 2.5951465900436 | -0.5951465900436 |
18 | 3 | 3.34027573590321 | -0.340275735903213 |
19 | 3 | 3.78251182050992 | -0.782511820509924 |
20 | 3 | 3.62940607114632 | -0.629406071146321 |
21 | 4 | 3.62790270118698 | 0.372097298813020 |
22 | 3 | 3.78251182050992 | -0.782511820509924 |
23 | 2 | 3.39824407714158 | -1.39824407714158 |
24 | 2 | 3.22210599244684 | -1.22210599244684 |
25 | 4 | 3.05114540066011 | 0.948854599339895 |
26 | 4 | 3.78251182050992 | 0.217488179490076 |
27 | 3 | 2.97459252597830 | 0.0254074740216966 |
28 | 4 | 3.41682861058501 | 0.583171389414985 |
29 | 2 | 3.05114540066011 | -1.05114540066010 |
30 | 4 | 3.55285319646452 | 0.44714680353548 |
31 | 4 | 3.30124761358264 | 0.698752386417358 |
32 | 5 | 3.36403776225465 | 1.63596223774535 |
33 | 5 | 2.8980396512965 | 2.1019603487035 |
34 | 4 | 3.05114540066011 | 0.948854599339895 |
35 | 4 | 3.83789141529429 | 0.162108584705712 |
36 | 4 | 4.01144075353502 | -0.0114407535350236 |
37 | 2 | 3.16672639766248 | -1.16672639766248 |
38 | 4 | 3.61155122872319 | 0.388448771276812 |
39 | 4 | 3.66693082350755 | 0.333069176492448 |
40 | 4 | 4.280127499901 | -0.280127499900999 |
41 | 3 | 3.41682861058501 | -0.416828610585014 |
42 | 2 | 2.9745925259783 | -0.974592525978303 |
43 | 3 | 3.66434207705355 | -0.664342077053552 |
44 | 4 | 2.8980396512965 | 1.10196034870350 |
45 | 3 | 2.77986990784013 | 0.22013009215987 |
46 | 2 | 3.05114540066011 | -1.05114540066010 |
47 | 4 | 3.39824407714158 | 0.601755922858424 |
48 | 4 | 3.55134982650518 | 0.448650173494821 |
49 | 3 | 3.53499835404139 | -0.534998354041386 |
50 | 4 | 3.43727219946215 | 0.562727800537853 |
51 | 3 | 3.05114540066010 | -0.0511454006601048 |
52 | 4 | 2.8980396512965 | 1.10196034870350 |
53 | 2 | 2.07635763075509 | -0.0763576307550877 |
54 | 4 | 3.41941735703901 | 0.580582642960986 |
55 | 4 | 2.99094399844210 | 1.00905600155790 |
56 | 4 | 3.62940607114632 | 0.370593928853679 |
57 | 4 | 3.05114540066011 | 0.948854599339895 |
58 | 3 | 3.33768698944921 | -0.337686989449214 |
59 | 1 | 2.28484297490305 | -1.28484297490305 |
60 | 3 | 3.14555311776504 | -0.145553117765040 |
61 | 3 | 2.97459252597830 | 0.0254074740216966 |
62 | 4 | 3.14555311776504 | 0.85444688223496 |
63 | 2 | 2.8214867766147 | -0.8214867766147 |
64 | 3 | 2.72449031305577 | 0.275509686944234 |
65 | 5 | 4.24260274753977 | 0.757397252460232 |
66 | 4 | 3.22469473890084 | 0.77530526109916 |
67 | 4 | 2.97459252597830 | 1.02540747402170 |
68 | 3 | 2.97200377952430 | 0.027996220475696 |
69 | 4 | 2.8980396512965 | 1.10196034870350 |
70 | 2 | 3.22728348535484 | -1.22728348535484 |
71 | 3 | 2.8980396512965 | 0.101960348703498 |
72 | 4 | 4.280127499901 | -0.280127499900999 |
73 | 3 | 3.79886329297372 | -0.798863292973717 |
74 | 4 | 3.66434207705355 | 0.335657922946448 |
75 | 4 | 2.66687765729176 | 1.33312234270824 |
76 | 3 | 3.09017352298068 | -0.090173522980676 |
77 | 3 | 3.29865886712864 | -0.298658867128643 |
78 | 2 | 3.22210599244684 | -1.22210599244684 |
79 | 4 | 3.55134982650518 | 0.448650173494821 |
80 | 3 | 3.02997212076267 | -0.0299721207626672 |
81 | 2 | 2.72707905950977 | -0.727079059509766 |
82 | 2 | 3.70595894582812 | -1.70595894582812 |
83 | 3 | 3.78251182050992 | -0.782511820509924 |
84 | 2 | 2.78245865429413 | -0.78245865429413 |
85 | 2 | 3.05114540066011 | -1.05114540066010 |
86 | 4 | 3.26372286122141 | 0.736277138778588 |
87 | 4 | 3.26113411476741 | 0.738865885232588 |
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 | -0.650526184827964 |
93 | 3 | 3.09276226943468 | -0.0927622694346752 |
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 | -0.0511454006601048 |
99 | 2 | 2.85901152897593 | -0.85901152897593 |
100 | 4 | 3.05114540066011 | 0.948854599339895 |
101 | 3 | 3.09017352298068 | -0.090173522980676 |
102 | 3 | 2.97459252597830 | 0.0254074740216966 |
103 | 3 | 2.8980396512965 | 0.101960348703498 |
104 | 4 | 3.58778920237175 | 0.412210797628249 |
105 | 1 | 2.17185072435468 | -1.17185072435468 |
106 | 3 | 2.97459252597830 | 0.0254074740216966 |
107 | 2 | 3.01879814120687 | -1.01879814120687 |
108 | 3 | 3.30124761358264 | -0.301247613582642 |
109 | 2 | 3.14555311776504 | -1.14555311776504 |
110 | 2 | 2.55352972126903 | -0.55352972126903 |
111 | 2 | 2.81998340665536 | -0.81998340665536 |
112 | 4 | 2.57397331014616 | 1.42602668985384 |
113 | 5 | 4.22474790511663 | 0.775252094883365 |
114 | 5 | 2.64793743837396 | 2.35206256162604 |
115 | 3 | 2.97459252597830 | 0.0254074740216966 |
116 | 4 | 2.55611846772303 | 1.44388153227697 |
117 | 4 | 2.07894637720909 | 1.92105362279091 |
118 | 3 | 3.01211727833953 | -0.0121172783395337 |
119 | 2 | 2.84266005651214 | -0.842660056512138 |
120 | 4 | 3.95606115875066 | 0.0439388412493403 |
121 | 2 | 2.72707905950977 | -0.727079059509766 |
122 | 3 | 2.61149806250739 | 0.388501937492607 |
123 | 2 | 3.26113411476741 | -1.26113411476741 |
124 | 2 | 2.8980396512965 | -0.898039651296502 |
125 | 2 | 2.68805093718919 | -0.688050937189195 |
126 | 4 | 3.16672639766248 | 0.833273602337522 |
127 | 4 | 3.34027573590321 | 0.659724264096787 |
128 | 4 | 2.97459252597830 | 1.02540747402170 |
129 | 4 | 3.59037794882575 | 0.40962205117425 |
130 | 3 | 3.53499835404139 | -0.534998354041386 |
131 | 2 | 2.9745925259783 | -0.974592525978303 |
132 | 4 | 3.78251182050992 | 0.217488179490076 |
133 | 3 | 3.78251182050992 | -0.782511820509924 |
134 | 2 | 2.8980396512965 | -0.898039651296502 |
135 | 4 | 3.78251182050992 | 0.217488179490076 |
136 | 3 | 2.9006283977505 | 0.0993716022494987 |
137 | 3 | 3.05114540066010 | -0.0511454006601048 |
138 | 3 | 2.97459252597830 | 0.0254074740216966 |
139 | 3 | 2.72966780596377 | 0.270332194036235 |
140 | 3 | 3.13437913820925 | -0.134379138209246 |
141 | 4 | 3.62940607114632 | 0.370593928853679 |
142 | 5 | 3.84530196918193 | 1.15469803081807 |
143 | 2 | 3.01362064829887 | -1.01362064829887 |
144 | 4 | 3.10911374189847 | 0.890886258101532 |
145 | 3 | 3.70854769228212 | -0.708547692282122 |
146 | 3 | 2.36398459603886 | 0.636015403961145 |
147 | 1 | 2.47956559304123 | -1.47956559304123 |
148 | 2 | 3.05114540066011 | -1.05114540066010 |
149 | 4 | 2.80363193419157 | 1.19636806580843 |
150 | 4 | 2.81998340665536 | 1.18001659334464 |
151 | 5 | 4.03261403343246 | 0.96738596656754 |
152 | 2 | 2.80622068064557 | -0.806220680645567 |
153 | 4 | 3.37521174181044 | 0.624788258189556 |
154 | 3 | 2.97459252597830 | 0.0254074740216966 |
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 | 0.478516808529533 | 0.957033617059066 | 0.521483191470467 |
10 | 0.69957205180478 | 0.600855896390439 | 0.300427948195220 |
11 | 0.780560893564702 | 0.438878212870595 | 0.219439106435298 |
12 | 0.768244334651571 | 0.463511330696857 | 0.231755665348429 |
13 | 0.875271962661018 | 0.249456074677965 | 0.124728037338982 |
14 | 0.90977637174767 | 0.180447256504659 | 0.0902236282523297 |
15 | 0.88834616526325 | 0.223307669473501 | 0.111653834736751 |
16 | 0.870492803375496 | 0.259014393249007 | 0.129507196624504 |
17 | 0.839516689581751 | 0.320966620836497 | 0.160483310418249 |
18 | 0.783254306418867 | 0.433491387162266 | 0.216745693581133 |
19 | 0.726656408485754 | 0.546687183028493 | 0.273343591514246 |
20 | 0.660211848210979 | 0.679576303578042 | 0.339788151789021 |
21 | 0.660847588270225 | 0.67830482345955 | 0.339152411729775 |
22 | 0.606481242314824 | 0.787037515370351 | 0.393518757685176 |
23 | 0.590115278290766 | 0.819769443418467 | 0.409884721709234 |
24 | 0.61994931817988 | 0.760101363640239 | 0.380050681820120 |
25 | 0.642192163329237 | 0.715615673341527 | 0.357807836670763 |
26 | 0.594939606764987 | 0.810120786470026 | 0.405060393235013 |
27 | 0.535235464913179 | 0.929529070173643 | 0.464764535086821 |
28 | 0.506216372845768 | 0.987567254308464 | 0.493783627154232 |
29 | 0.537069153889377 | 0.925861692221246 | 0.462930846110623 |
30 | 0.573510510680005 | 0.852978978639989 | 0.426489489319995 |
31 | 0.580690575485695 | 0.838618849028609 | 0.419309424514304 |
32 | 0.6579805656958 | 0.6840388686084 | 0.3420194343042 |
33 | 0.908650861958865 | 0.182698276082271 | 0.0913491380411354 |
34 | 0.908266076530464 | 0.183467846939073 | 0.0917339234695363 |
35 | 0.8867807279168 | 0.226438544166402 | 0.113219272083201 |
36 | 0.862641423852393 | 0.274717152295214 | 0.137358576147607 |
37 | 0.886842904853329 | 0.226314190293342 | 0.113157095146671 |
38 | 0.860436524869457 | 0.279126950261087 | 0.139563475130544 |
39 | 0.830740036478443 | 0.338519927043115 | 0.169259963521558 |
40 | 0.797717614157092 | 0.404564771685817 | 0.202282385842908 |
41 | 0.767001447984224 | 0.465997104031552 | 0.232998552015776 |
42 | 0.766880912704317 | 0.466238174591366 | 0.233119087295683 |
43 | 0.74326116351356 | 0.51347767297288 | 0.25673883648644 |
44 | 0.78116407744393 | 0.43767184511214 | 0.21883592255607 |
45 | 0.747904851060332 | 0.504190297879335 | 0.252095148939668 |
46 | 0.762661150139035 | 0.47467769972193 | 0.237338849860965 |
47 | 0.739085139073838 | 0.521829721852325 | 0.260914860926162 |
48 | 0.70263236295738 | 0.59473527408524 | 0.29736763704262 |
49 | 0.674812173905653 | 0.650375652188694 | 0.325187826094347 |
50 | 0.646777248494004 | 0.706445503011993 | 0.353222751505997 |
51 | 0.598483745067875 | 0.803032509864249 | 0.401516254932125 |
52 | 0.625391459057926 | 0.749217081884147 | 0.374608540942074 |
53 | 0.579830328944868 | 0.840339342110263 | 0.420169671055132 |
54 | 0.545669462891496 | 0.908661074217009 | 0.454330537108504 |
55 | 0.542212335675389 | 0.915575328649223 | 0.457787664324611 |
56 | 0.505987687540508 | 0.988024624918983 | 0.494012312459492 |
57 | 0.51225637394826 | 0.97548725210348 | 0.48774362605174 |
58 | 0.466837074967294 | 0.933674149934588 | 0.533162925032706 |
59 | 0.541974097130315 | 0.91605180573937 | 0.458025902869685 |
60 | 0.49397201601642 | 0.98794403203284 | 0.50602798398358 |
61 | 0.445477687859768 | 0.890955375719535 | 0.554522312140232 |
62 | 0.447618843646287 | 0.895237687292574 | 0.552381156353713 |
63 | 0.44083103773445 | 0.8816620754689 | 0.55916896226555 |
64 | 0.400882215253697 | 0.801764430507395 | 0.599117784746303 |
65 | 0.397559041866029 | 0.795118083732059 | 0.602440958133971 |
66 | 0.383459154389235 | 0.766918308778469 | 0.616540845610765 |
67 | 0.399251196884879 | 0.798502393769758 | 0.600748803115121 |
68 | 0.354464382014966 | 0.708928764029931 | 0.645535617985034 |
69 | 0.379850194668842 | 0.759700389337683 | 0.620149805331158 |
70 | 0.437905199823255 | 0.87581039964651 | 0.562094800176745 |
71 | 0.392299320940246 | 0.784598641880491 | 0.607700679059754 |
72 | 0.352293967569651 | 0.704587935139303 | 0.647706032430349 |
73 | 0.347125138708278 | 0.694250277416555 | 0.652874861291722 |
74 | 0.310781580130208 | 0.621563160260415 | 0.689218419869792 |
75 | 0.362378445684524 | 0.724756891369047 | 0.637621554315476 |
76 | 0.319356808447106 | 0.638713616894213 | 0.680643191552894 |
77 | 0.283300405288823 | 0.566600810577646 | 0.716699594711177 |
78 | 0.321851423751781 | 0.643702847503563 | 0.678148576248219 |
79 | 0.291059779450707 | 0.582119558901413 | 0.708940220549293 |
80 | 0.253275024400287 | 0.506550048800574 | 0.746724975599713 |
81 | 0.244351734330950 | 0.488703468661901 | 0.75564826566905 |
82 | 0.351224131811134 | 0.702448263622269 | 0.648775868188866 |
83 | 0.341637645416440 | 0.683275290832879 | 0.65836235458356 |
84 | 0.335701150201321 | 0.671402300402641 | 0.66429884979868 |
85 | 0.358114743350772 | 0.716229486701543 | 0.641885256649228 |
86 | 0.347211491902517 | 0.694422983805033 | 0.652788508097483 |
87 | 0.337073240768096 | 0.674146481536191 | 0.662926759231904 |
88 | 0.298166686522729 | 0.596333373045458 | 0.701833313477271 |
89 | 0.308525269033448 | 0.617050538066896 | 0.691474730966552 |
90 | 0.403136734160616 | 0.806273468321233 | 0.596863265839384 |
91 | 0.436304403286227 | 0.872608806572453 | 0.563695596713773 |
92 | 0.412238897217148 | 0.824477794434295 | 0.587761102782852 |
93 | 0.367113806244689 | 0.734227612489379 | 0.632886193755311 |
94 | 0.325254368996302 | 0.650508737992603 | 0.674745631003698 |
95 | 0.349558824738263 | 0.699117649476525 | 0.650441175261737 |
96 | 0.317927959281954 | 0.635855918563907 | 0.682072040718046 |
97 | 0.31310622021519 | 0.62621244043038 | 0.68689377978481 |
98 | 0.271719176708364 | 0.543438353416728 | 0.728280823291636 |
99 | 0.265633691472606 | 0.531267382945212 | 0.734366308527394 |
100 | 0.270002741131277 | 0.540005482262555 | 0.729997258868723 |
101 | 0.231443931650197 | 0.462887863300393 | 0.768556068349803 |
102 | 0.195678467407947 | 0.391356934815895 | 0.804321532592053 |
103 | 0.164652391764421 | 0.329304783528842 | 0.835347608235579 |
104 | 0.144129921653128 | 0.288259843306256 | 0.855870078346872 |
105 | 0.162573636733919 | 0.325147273467837 | 0.837426363266081 |
106 | 0.133791883418129 | 0.267583766836258 | 0.866208116581871 |
107 | 0.148599568030555 | 0.297199136061111 | 0.851400431969444 |
108 | 0.123657803260759 | 0.247315606521518 | 0.87634219673924 |
109 | 0.134110664532349 | 0.268221329064698 | 0.86588933546765 |
110 | 0.119995857836530 | 0.239991715673059 | 0.88000414216347 |
111 | 0.116161724073132 | 0.232323448146265 | 0.883838275926868 |
112 | 0.164494776612273 | 0.328989553224547 | 0.835505223387727 |
113 | 0.153006333726774 | 0.306012667453548 | 0.846993666273226 |
114 | 0.490404398897515 | 0.98080879779503 | 0.509595601102485 |
115 | 0.439381482237435 | 0.878762964474871 | 0.560618517762565 |
116 | 0.513323613650870 | 0.97335277269826 | 0.48667638634913 |
117 | 0.838863886463529 | 0.322272227072942 | 0.161136113536471 |
118 | 0.812805302051598 | 0.374389395896803 | 0.187194697948402 |
119 | 0.786819161717193 | 0.426361676565614 | 0.213180838282807 |
120 | 0.744550375205668 | 0.510899249588664 | 0.255449624794332 |
121 | 0.711509073442546 | 0.576981853114909 | 0.288490926557454 |
122 | 0.681053678082919 | 0.637892643834163 | 0.318946321917081 |
123 | 0.684366803406942 | 0.631266393186116 | 0.315633196593058 |
124 | 0.65495541313343 | 0.690089173733139 | 0.345044586866570 |
125 | 0.64431083639607 | 0.71137832720786 | 0.35568916360393 |
126 | 0.651380011786686 | 0.697239976426628 | 0.348619988213314 |
127 | 0.638289798638442 | 0.723420402723115 | 0.361710201361558 |
128 | 0.716684175536018 | 0.566631648927964 | 0.283315824463982 |
129 | 0.664317821510786 | 0.671364356978429 | 0.335682178489214 |
130 | 0.642266389266562 | 0.715467221466876 | 0.357733610733438 |
131 | 0.621088869934561 | 0.757822260130877 | 0.378911130065439 |
132 | 0.553176344118871 | 0.893647311762258 | 0.446823655881129 |
133 | 0.597149550747421 | 0.805700898505159 | 0.402850449252579 |
134 | 0.5445755807565 | 0.910848838487 | 0.4554244192435 |
135 | 0.47431672118837 | 0.94863344237674 | 0.52568327881163 |
136 | 0.415346516010255 | 0.83069303202051 | 0.584653483989745 |
137 | 0.342274581821334 | 0.684549163642668 | 0.657725418178666 |
138 | 0.277347193606546 | 0.554694387213091 | 0.722652806393454 |
139 | 0.228488327468747 | 0.456976654937493 | 0.771511672531253 |
140 | 0.184861908683889 | 0.369723817367778 | 0.815138091316111 |
141 | 0.176974519404652 | 0.353949038809303 | 0.823025480595349 |
142 | 0.182597227441930 | 0.365194454883859 | 0.81740277255807 |
143 | 0.131544370816263 | 0.263088741632526 | 0.868455629183737 |
144 | 0.109943167222919 | 0.219886334445838 | 0.89005683277708 |
145 | 0.0741942899200109 | 0.148388579840022 | 0.92580571007999 |
146 | 0.123552961809528 | 0.247105923619055 | 0.876447038190472 |
147 | 0.0776491481155252 | 0.155298296231050 | 0.922350851884475 |
148 | 0.0988286351840012 | 0.197657270368002 | 0.901171364815999 |
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 |