Multiple Linear Regression - Estimated Regression Equation |
YT[t] = -2.70676782746938 + 0.804825696596371X1[t] + 0.246618734551963X2[t] + 0.190858166207396X3[t] + 0.5682129740418X4[t] -0.100756792404192X5[t] + 0.00564436253658327t + 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) | -2.70676782746938 | 3.230753 | -0.8378 | 0.403451 | 0.201726 |
X1 | 0.804825696596371 | 0.130765 | 6.1547 | 0 | 0 |
X2 | 0.246618734551963 | 0.133141 | 1.8523 | 0.06592 | 0.03296 |
X3 | 0.190858166207396 | 0.168568 | 1.1322 | 0.25932 | 0.12966 |
X4 | 0.5682129740418 | 0.096019 | 5.9177 | 0 | 0 |
X5 | -0.100756792404192 | 0.105352 | -0.9564 | 0.340397 | 0.170199 |
t | 0.00564436253658327 | 0.008004 | 0.7052 | 0.481742 | 0.240871 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.639616097712746 |
R-squared | 0.40910875245328 |
Adjusted R-squared | 0.385784097944857 |
F-TEST (value) | 17.5397561539675 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 152 |
p-value | 2.22044604925031e-15 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 4.48508352276095 |
Sum Squared Residuals | 3057.62807933355 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 24.5869751364709 | -0.586975136470905 |
2 | 25 | 21.2987181574354 | 3.70128184256465 |
3 | 17 | 22.3859726679103 | -5.38597266791033 |
4 | 18 | 19.44541093851 | -1.44541093850998 |
5 | 18 | 19.0235142417146 | -1.02351424171457 |
6 | 16 | 19.2495257409872 | -3.24952574098718 |
7 | 20 | 20.5436429620918 | -0.543642962091785 |
8 | 16 | 21.9567214062097 | -5.95672140620968 |
9 | 18 | 21.9596456847955 | -3.9596456847955 |
10 | 17 | 20.1583618178568 | -3.15836181785682 |
11 | 23 | 21.9388979834957 | 1.06110201650432 |
12 | 30 | 21.8557785405502 | 8.14422145944982 |
13 | 23 | 14.7331473781575 | 8.2668526218425 |
14 | 18 | 18.603269980984 | -0.603269980983952 |
15 | 15 | 21.3229006529394 | -6.32290065293938 |
16 | 12 | 17.5861185544217 | -5.58611855442169 |
17 | 21 | 19.0554592926899 | 1.94454070731014 |
18 | 15 | 14.8190078084257 | 0.180992191574258 |
19 | 20 | 19.4501286955508 | 0.549871304449199 |
20 | 31 | 26.0194000461538 | 4.98059995384624 |
21 | 27 | 24.867684573156 | 2.13231542684405 |
22 | 34 | 26.750532950888 | 7.24946704911197 |
23 | 21 | 19.2804560909692 | 1.71954390903083 |
24 | 31 | 20.5997366083926 | 10.4002633916074 |
25 | 19 | 19.0701646017547 | -0.0701646017546607 |
26 | 16 | 19.9463310706596 | -3.94633107065955 |
27 | 20 | 21.3206525792539 | -1.32065257925392 |
28 | 21 | 17.996356127058 | 3.00364387294204 |
29 | 22 | 21.6836783558636 | 0.316321644136373 |
30 | 17 | 19.2404660680385 | -2.24046606803853 |
31 | 24 | 20.1645593566639 | 3.83544064333612 |
32 | 25 | 30.1993051078831 | -5.19930510788308 |
33 | 26 | 26.390560835707 | -0.390560835707007 |
34 | 25 | 23.8830734088535 | 1.11692659114645 |
35 | 17 | 22.7338898244853 | -5.73388982448527 |
36 | 32 | 27.5968576223048 | 4.4031423776952 |
37 | 33 | 23.4131876974345 | 9.5868123025655 |
38 | 13 | 21.7416158659416 | -8.74161586594163 |
39 | 32 | 27.5940197273161 | 4.40598027268392 |
40 | 25 | 25.6331170331415 | -0.633117033141512 |
41 | 29 | 26.8907632258501 | 2.10923677414994 |
42 | 22 | 21.8320305737771 | 0.167969426222916 |
43 | 18 | 17.05245924122 | 0.947540758780044 |
44 | 17 | 21.5731241031246 | -4.57312410312459 |
45 | 20 | 22.0446692276098 | -2.04466922760976 |
46 | 15 | 20.2957922888319 | -5.29579228883186 |
47 | 20 | 21.9969914249525 | -1.99699142495246 |
48 | 33 | 27.9610910864848 | 5.03890891351516 |
49 | 29 | 21.9922711728182 | 7.00772882718179 |
50 | 23 | 26.4609674131011 | -3.46096741310109 |
51 | 26 | 23.1055675302885 | 2.89443246971151 |
52 | 18 | 18.8307698752602 | -0.8307698752602 |
53 | 20 | 18.6699997907346 | 1.33000020926542 |
54 | 11 | 11.5812129333856 | -0.58121293338563 |
55 | 28 | 28.8095440113789 | -0.809544011378862 |
56 | 26 | 23.2735050718965 | 2.72649492810354 |
57 | 22 | 22.2026118775359 | -0.202611877535911 |
58 | 17 | 20.0774839975062 | -3.07748399750625 |
59 | 12 | 15.4292884866592 | -3.42928848665917 |
60 | 14 | 20.780061210624 | -6.78006121062399 |
61 | 17 | 20.6763094340181 | -3.67630943401805 |
62 | 21 | 21.261580521485 | -0.261580521484976 |
63 | 19 | 22.9113260083569 | -3.91132600835689 |
64 | 18 | 23.0268271622096 | -5.02682716220963 |
65 | 10 | 17.8541098959786 | -7.8541098959786 |
66 | 29 | 24.2846006276799 | 4.71539937232012 |
67 | 31 | 18.4322038562024 | 12.5677961437976 |
68 | 19 | 22.8792466318609 | -3.87924663186088 |
69 | 9 | 20.0338902827611 | -11.0338902827611 |
70 | 20 | 22.4674961633225 | -2.46749616332249 |
71 | 28 | 17.5756295114181 | 10.4243704885819 |
72 | 19 | 18.1136995485328 | 0.886300451467227 |
73 | 30 | 23.0877801178341 | 6.91221988216585 |
74 | 29 | 27.073369677065 | 1.92663032293498 |
75 | 26 | 21.4908251886057 | 4.50917481139428 |
76 | 23 | 19.5051176759053 | 3.49488232409465 |
77 | 13 | 22.7601530313896 | -9.76015303138962 |
78 | 21 | 22.6443090003536 | -1.6443090003536 |
79 | 19 | 21.5370492704958 | -2.53704927049577 |
80 | 28 | 22.93773130259 | 5.06226869740997 |
81 | 23 | 25.6175014577243 | -2.61750145772435 |
82 | 18 | 13.864639446041 | 4.13536055395896 |
83 | 21 | 20.7319285749601 | 0.268071425039858 |
84 | 20 | 21.8476069466243 | -1.84760694662434 |
85 | 23 | 20.0434165598231 | 2.95658344017692 |
86 | 21 | 20.8597333926554 | 0.140266607344571 |
87 | 21 | 21.8550198976718 | -0.855019897671836 |
88 | 15 | 22.9508811919658 | -7.9508811919658 |
89 | 28 | 27.1965037434143 | 0.80349625658569 |
90 | 19 | 17.6886416630847 | 1.31135833691528 |
91 | 26 | 21.2954140701055 | 4.70458592989447 |
92 | 10 | 13.3326243716318 | -3.3326243716318 |
93 | 16 | 17.1873143264118 | -1.18731432641177 |
94 | 22 | 21.2020388132927 | 0.797961186707265 |
95 | 19 | 18.9063046849835 | 0.093695315016467 |
96 | 31 | 28.9157779289149 | 2.08422207108509 |
97 | 31 | 25.3018849084882 | 5.69811509151183 |
98 | 29 | 24.8551287876825 | 4.14487121231755 |
99 | 19 | 17.5028282033594 | 1.49717179664061 |
100 | 22 | 18.9522887480601 | 3.04771125193991 |
101 | 23 | 22.472438197516 | 0.52756180248399 |
102 | 15 | 16.2874647056108 | -1.28746470561081 |
103 | 20 | 21.4645212040962 | -1.46452120409622 |
104 | 18 | 19.6425371514452 | -1.64253715144523 |
105 | 23 | 22.217150234481 | 0.782849765518966 |
106 | 25 | 20.9744599375139 | 4.02554006248607 |
107 | 21 | 16.6529471075685 | 4.34705289243147 |
108 | 24 | 19.5455744278297 | 4.45442557217025 |
109 | 25 | 25.3595410763598 | -0.359541076359756 |
110 | 17 | 19.6935475859109 | -2.69354758591087 |
111 | 13 | 14.6943965458432 | -1.69439654584321 |
112 | 28 | 18.4098746117709 | 9.59012538822914 |
113 | 21 | 20.3106346801039 | 0.689365319896122 |
114 | 25 | 28.2836350486841 | -3.28363504868414 |
115 | 9 | 21.0044477704288 | -12.0044477704288 |
116 | 16 | 18.0612276169349 | -2.06122761693493 |
117 | 19 | 21.2966898433179 | -2.29668984331794 |
118 | 17 | 19.6269476477759 | -2.62694764777592 |
119 | 25 | 24.7319979920982 | 0.268002007901781 |
120 | 20 | 15.6369512420149 | 4.36304875798512 |
121 | 29 | 21.8759344009052 | 7.12406559909483 |
122 | 14 | 19.1778709228727 | -5.17787092287271 |
123 | 22 | 27.0980959242537 | -5.09809592425374 |
124 | 15 | 15.9019397751253 | -0.901939775125262 |
125 | 19 | 25.6813751580878 | -6.68137515808782 |
126 | 20 | 22.1919545613241 | -2.19195456132411 |
127 | 15 | 17.7608142090159 | -2.76081420901586 |
128 | 20 | 22.1258994239983 | -2.12589942399832 |
129 | 18 | 20.5527935376764 | -2.55279353767642 |
130 | 33 | 25.7888479793484 | 7.2111520206516 |
131 | 22 | 24.0146988185677 | -2.01469881856773 |
132 | 16 | 16.7435243851904 | -0.743524385190438 |
133 | 17 | 19.4036823708245 | -2.40368237082451 |
134 | 16 | 15.381610908457 | 0.618389091543024 |
135 | 21 | 17.3637695845882 | 3.63623041541183 |
136 | 26 | 27.9214437785666 | -1.92144377856656 |
137 | 18 | 21.4147283663736 | -3.41472836637364 |
138 | 18 | 23.276463760401 | -5.27646376040095 |
139 | 17 | 18.707861885554 | -1.70786188555397 |
140 | 22 | 24.9760915015815 | -2.97609150158152 |
141 | 30 | 24.952242458675 | 5.047757541325 |
142 | 30 | 27.6220295065553 | 2.37797049344472 |
143 | 24 | 30.0288532518421 | -6.02885325184214 |
144 | 21 | 22.3733372368221 | -1.37333723682208 |
145 | 21 | 25.7186060818219 | -4.71860608182192 |
146 | 29 | 27.7760626071577 | 1.22393739284233 |
147 | 31 | 23.567572013391 | 7.43242798660901 |
148 | 20 | 19.3381789476296 | 0.661821052370395 |
149 | 16 | 14.4271132095025 | 1.57288679049751 |
150 | 22 | 19.2888597043427 | 2.71114029565732 |
151 | 20 | 20.766728259862 | -0.766728259862021 |
152 | 28 | 27.7200998654264 | 0.279900134573624 |
153 | 38 | 27.0811321597216 | 10.9188678402784 |
154 | 22 | 19.5906715514475 | 2.40932844855246 |
155 | 20 | 26.0566974089159 | -6.05669740891587 |
156 | 17 | 18.448530410331 | -1.44853041033101 |
157 | 28 | 24.9055766121567 | 3.09442338784326 |
158 | 22 | 24.5396741854444 | -2.53967418544438 |
159 | 31 | 26.4518682878217 | 4.54813171217832 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.0986137661024837 | 0.197227532204967 | 0.901386233897516 |
11 | 0.354975571887273 | 0.709951143774546 | 0.645024428112727 |
12 | 0.749205672924374 | 0.501588654151252 | 0.250794327075626 |
13 | 0.743994274618463 | 0.512011450763075 | 0.256005725381537 |
14 | 0.727142351575679 | 0.545715296848642 | 0.272857648424321 |
15 | 0.689806032322999 | 0.620387935354002 | 0.310193967677001 |
16 | 0.607520523040911 | 0.784958953918178 | 0.392479476959089 |
17 | 0.552963977005474 | 0.894072045989052 | 0.447036022994526 |
18 | 0.524489297213624 | 0.951021405572752 | 0.475510702786376 |
19 | 0.469705119785148 | 0.939410239570297 | 0.530294880214852 |
20 | 0.498689321613758 | 0.997378643227515 | 0.501310678386242 |
21 | 0.431176180699654 | 0.862352361399307 | 0.568823819300346 |
22 | 0.419451092528738 | 0.838902185057477 | 0.580548907471262 |
23 | 0.376937483513752 | 0.753874967027504 | 0.623062516486248 |
24 | 0.530934349054127 | 0.938131301891747 | 0.469065650945873 |
25 | 0.488778271623547 | 0.977556543247095 | 0.511221728376453 |
26 | 0.505724304437271 | 0.988551391125458 | 0.494275695562729 |
27 | 0.438393462196286 | 0.876786924392572 | 0.561606537803714 |
28 | 0.379359317119068 | 0.758718634238137 | 0.620640682880932 |
29 | 0.317823247581353 | 0.635646495162706 | 0.682176752418647 |
30 | 0.278075108364166 | 0.556150216728331 | 0.721924891635834 |
31 | 0.269604109958724 | 0.539208219917449 | 0.730395890041276 |
32 | 0.399006591421525 | 0.79801318284305 | 0.600993408578475 |
33 | 0.343222070528927 | 0.686444141057854 | 0.656777929471073 |
34 | 0.313641715491668 | 0.627283430983335 | 0.686358284508332 |
35 | 0.356773406558775 | 0.71354681311755 | 0.643226593441225 |
36 | 0.323998275685865 | 0.64799655137173 | 0.676001724314135 |
37 | 0.438555192615725 | 0.87711038523145 | 0.561444807384275 |
38 | 0.745624437903073 | 0.508751124193854 | 0.254375562096927 |
39 | 0.7299817348089 | 0.5400365303822 | 0.2700182651911 |
40 | 0.693934084025518 | 0.612131831948964 | 0.306065915974482 |
41 | 0.656722991738823 | 0.686554016522354 | 0.343277008261177 |
42 | 0.60963548605611 | 0.78072902788778 | 0.39036451394389 |
43 | 0.559432351693984 | 0.881135296612032 | 0.440567648306016 |
44 | 0.55279891173134 | 0.89440217653732 | 0.44720108826866 |
45 | 0.540193248509558 | 0.919613502980883 | 0.459806751490442 |
46 | 0.584175010022566 | 0.831649979954867 | 0.415824989977434 |
47 | 0.547117591212123 | 0.905764817575755 | 0.452882408787877 |
48 | 0.537011624774243 | 0.925976750451514 | 0.462988375225757 |
49 | 0.589669637022597 | 0.820660725954807 | 0.410330362977403 |
50 | 0.568422033221753 | 0.863155933556493 | 0.431577966778247 |
51 | 0.538178226534436 | 0.923643546931127 | 0.461821773465564 |
52 | 0.491057984345914 | 0.982115968691829 | 0.508942015654086 |
53 | 0.445536972695211 | 0.891073945390421 | 0.55446302730479 |
54 | 0.404935211723214 | 0.809870423446429 | 0.595064788276786 |
55 | 0.366544629337198 | 0.733089258674396 | 0.633455370662802 |
56 | 0.33576260610805 | 0.6715252122161 | 0.66423739389195 |
57 | 0.29273382043106 | 0.585467640862121 | 0.70726617956894 |
58 | 0.267371541827075 | 0.534743083654151 | 0.732628458172925 |
59 | 0.249510500844237 | 0.499021001688474 | 0.750489499155763 |
60 | 0.308670878298286 | 0.617341756596572 | 0.691329121701714 |
61 | 0.294097713731882 | 0.588195427463764 | 0.705902286268118 |
62 | 0.25509957966582 | 0.510199159331641 | 0.74490042033418 |
63 | 0.239430065579774 | 0.478860131159548 | 0.760569934420226 |
64 | 0.265644227426384 | 0.531288454852768 | 0.734355772573616 |
65 | 0.330364327637464 | 0.660728655274929 | 0.669635672362536 |
66 | 0.338966844575648 | 0.677933689151295 | 0.661033155424352 |
67 | 0.683800498206362 | 0.632399003587276 | 0.316199501793638 |
68 | 0.673315481045092 | 0.653369037909816 | 0.326684518954908 |
69 | 0.841190161183828 | 0.317619677632344 | 0.158809838816172 |
70 | 0.819138327521376 | 0.361723344957248 | 0.180861672478624 |
71 | 0.930851738061275 | 0.138296523877451 | 0.0691482619387253 |
72 | 0.914656901731175 | 0.170686196537649 | 0.0853430982688247 |
73 | 0.938282933785067 | 0.123434132429866 | 0.0617170662149329 |
74 | 0.926386103955744 | 0.147227792088511 | 0.0736138960442556 |
75 | 0.927628103388979 | 0.144743793222043 | 0.0723718966110213 |
76 | 0.921532903260819 | 0.156934193478362 | 0.0784670967391811 |
77 | 0.969328781764506 | 0.0613424364709884 | 0.0306712182354942 |
78 | 0.961667340439293 | 0.076665319121414 | 0.038332659560707 |
79 | 0.95410748689714 | 0.0917850262057179 | 0.0458925131028589 |
80 | 0.956601951586903 | 0.0867960968261945 | 0.0433980484130972 |
81 | 0.94866640143641 | 0.10266719712718 | 0.0513335985635901 |
82 | 0.947674557240555 | 0.104650885518891 | 0.0523254427594455 |
83 | 0.933876863951651 | 0.132246272096698 | 0.0661231360483489 |
84 | 0.920778464987114 | 0.158443070025772 | 0.079221535012886 |
85 | 0.911255843490232 | 0.177488313019536 | 0.088744156509768 |
86 | 0.893685955156079 | 0.212628089687843 | 0.106314044843921 |
87 | 0.871647292220026 | 0.256705415559949 | 0.128352707779974 |
88 | 0.919379775763868 | 0.161240448472264 | 0.0806202242361318 |
89 | 0.902611562542193 | 0.194776874915614 | 0.0973884374578069 |
90 | 0.88176524363347 | 0.236469512733059 | 0.118234756366529 |
91 | 0.88139741398992 | 0.237205172020159 | 0.11860258601008 |
92 | 0.871398039668186 | 0.257203920663629 | 0.128601960331815 |
93 | 0.849132483499532 | 0.301735033000937 | 0.150867516500468 |
94 | 0.820422351999574 | 0.359155296000851 | 0.179577648000426 |
95 | 0.787017743228047 | 0.425964513543906 | 0.212982256771953 |
96 | 0.755715717519414 | 0.488568564961172 | 0.244284282480586 |
97 | 0.773221498701841 | 0.453557002596318 | 0.226778501298159 |
98 | 0.769991622825097 | 0.460016754349807 | 0.230008377174903 |
99 | 0.734360026106277 | 0.531279947787446 | 0.265639973893723 |
100 | 0.712285342532018 | 0.575429314935964 | 0.287714657467982 |
101 | 0.673804180886969 | 0.652391638226062 | 0.326195819113031 |
102 | 0.632880695737512 | 0.734238608524976 | 0.367119304262488 |
103 | 0.591795492302649 | 0.816409015394702 | 0.408204507697351 |
104 | 0.54863121933782 | 0.902737561324361 | 0.45136878066218 |
105 | 0.506340488687242 | 0.987319022625516 | 0.493659511312758 |
106 | 0.492691634388543 | 0.985383268777087 | 0.507308365611457 |
107 | 0.500002089027185 | 0.99999582194563 | 0.499997910972815 |
108 | 0.539303621396917 | 0.921392757206165 | 0.460696378603083 |
109 | 0.501865343762256 | 0.996269312475488 | 0.498134656237744 |
110 | 0.460704289802822 | 0.921408579605645 | 0.539295710197178 |
111 | 0.413743913231613 | 0.827487826463226 | 0.586256086768387 |
112 | 0.7406188406695 | 0.518762318661001 | 0.2593811593305 |
113 | 0.775579162293001 | 0.448841675413997 | 0.224420837706999 |
114 | 0.751192493702792 | 0.497615012594416 | 0.248807506297208 |
115 | 0.875459864023444 | 0.249080271953112 | 0.124540135976556 |
116 | 0.847093187395818 | 0.305813625208364 | 0.152906812604182 |
117 | 0.817630525758243 | 0.364738948483514 | 0.182369474241757 |
118 | 0.784169778505269 | 0.431660442989463 | 0.215830221494731 |
119 | 0.75623961941945 | 0.4875207611611 | 0.24376038058055 |
120 | 0.804970576588137 | 0.390058846823727 | 0.195029423411863 |
121 | 0.884059519069933 | 0.231880961860133 | 0.115940480930067 |
122 | 0.865249738023542 | 0.269500523952917 | 0.134750261976459 |
123 | 0.844910324733052 | 0.310179350533897 | 0.155089675266948 |
124 | 0.806900129855564 | 0.386199740288873 | 0.193099870144436 |
125 | 0.811564180355852 | 0.376871639288295 | 0.188435819644148 |
126 | 0.768212231461183 | 0.463575537077634 | 0.231787768538817 |
127 | 0.736867409455641 | 0.526265181088718 | 0.263132590544359 |
128 | 0.690330756079321 | 0.619338487841358 | 0.309669243920679 |
129 | 0.645015922560204 | 0.709968154879591 | 0.354984077439796 |
130 | 0.765893935019667 | 0.468212129960667 | 0.234106064980334 |
131 | 0.713580282724145 | 0.572839434551711 | 0.286419717275856 |
132 | 0.653407430680831 | 0.693185138638338 | 0.346592569319169 |
133 | 0.615380189803281 | 0.769239620393437 | 0.384619810196719 |
134 | 0.54569034141003 | 0.90861931717994 | 0.45430965858997 |
135 | 0.571000707376548 | 0.857998585246904 | 0.428999292623452 |
136 | 0.500535746389736 | 0.998928507220527 | 0.499464253610264 |
137 | 0.453408493907197 | 0.906816987814394 | 0.546591506092803 |
138 | 0.470186630788955 | 0.94037326157791 | 0.529813369211045 |
139 | 0.396281266677954 | 0.792562533355908 | 0.603718733322046 |
140 | 0.322837797121087 | 0.645675594242173 | 0.677162202878913 |
141 | 0.425940533040582 | 0.851881066081163 | 0.574059466959418 |
142 | 0.3759469279344 | 0.7518938558688 | 0.6240530720656 |
143 | 0.303350492215239 | 0.606700984430479 | 0.696649507784761 |
144 | 0.227185895699065 | 0.45437179139813 | 0.772814104300935 |
145 | 0.333525544777945 | 0.667051089555889 | 0.666474455222055 |
146 | 0.254150574218036 | 0.508301148436071 | 0.745849425781964 |
147 | 0.252870623285587 | 0.505741246571175 | 0.747129376714413 |
148 | 0.159612301285357 | 0.319224602570713 | 0.840387698714643 |
149 | 0.0863434141037003 | 0.172686828207401 | 0.9136565858963 |
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 | 4 | 0.0285714285714286 | OK |