Multiple Linear Regression - Estimated Regression Equation |
YT[t] = -18.3591714482501 + 1.58838471475259T1[t] + 0.798757118515112X1[t] + 0.233450466257556X2[t] + 0.207082749570131X3[t] + 0.571862761699043X4[t] -0.0999815995143377`X5 `[t] + 0.00354783249216936t + 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) | -18.3591714482501 | 19.993412 | -0.9183 | 0.359947 | 0.179973 |
T1 | 1.58838471475259 | 2.002175 | 0.7933 | 0.428831 | 0.214415 |
X1 | 0.798757118515112 | 0.131148 | 6.0905 | 0 | 0 |
X2 | 0.233450466257556 | 0.134333 | 1.7379 | 0.084276 | 0.042138 |
X3 | 0.207082749570131 | 0.170009 | 1.2181 | 0.225097 | 0.112548 |
X4 | 0.571862761699043 | 0.096247 | 5.9416 | 0 | 0 |
`X5 ` | -0.0999815995143377 | 0.105485 | -0.9478 | 0.344732 | 0.172366 |
t | 0.00354783249216936 | 0.008438 | 0.4205 | 0.674741 | 0.33737 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.641530498673369 |
R-squared | 0.411561380728101 |
Adjusted R-squared | 0.384282769238676 |
F-TEST (value) | 15.087328799255 |
F-TEST (DF numerator) | 7 |
F-TEST (DF denominator) | 151 |
p-value | 7.32747196252603e-15 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 4.49056162493448 |
Sum Squared Residuals | 3044.93669980746 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 23.3005712933059 | 0.699428706694145 |
2 | 25 | 20.017522467184 | 4.98247753281596 |
3 | 17 | 21.0211399791428 | -4.02113997914275 |
4 | 18 | 18.0925500792619 | -0.092550079261901 |
5 | 18 | 17.6905678029333 | 0.309432197066652 |
6 | 16 | 17.8776483781721 | -1.87764837817211 |
7 | 20 | 20.7303968936034 | -0.73039689360339 |
8 | 16 | 22.2384819662609 | -6.23848196626085 |
9 | 18 | 22.109776689597 | -4.10977668959702 |
10 | 17 | 20.3404956440243 | -3.34049564402434 |
11 | 23 | 22.1666780037712 | 0.833321996228797 |
12 | 30 | 22.0240937482091 | 7.97590625179086 |
13 | 23 | 14.9779833304995 | 8.02201666950045 |
14 | 18 | 18.8006776299538 | -0.800677629953756 |
15 | 15 | 21.5420869454813 | -6.54208694548131 |
16 | 12 | 17.7473672648275 | -5.74736726482754 |
17 | 21 | 19.3199506278201 | 1.68004937217993 |
18 | 15 | 15.0095102272645 | -0.00951022726446759 |
19 | 20 | 19.5818010071521 | 0.418198992847863 |
20 | 31 | 26.1780117087719 | 4.8219882912281 |
21 | 27 | 25.0654667635792 | 1.93453323642076 |
22 | 34 | 26.8723465536459 | 7.12765344635406 |
23 | 21 | 19.5212510677299 | 1.47874893227007 |
24 | 31 | 20.7775429191891 | 10.2224570808109 |
25 | 19 | 19.2620873882198 | -0.262087388219846 |
26 | 16 | 20.1257631629215 | -4.12576316292152 |
27 | 20 | 21.4505453886165 | -1.45054538861649 |
28 | 21 | 18.1772639671097 | 2.82273603289032 |
29 | 22 | 21.8404586063841 | 0.159541393615926 |
30 | 17 | 19.3786812679951 | -2.37868126799509 |
31 | 24 | 20.3628830419833 | 3.63711695801675 |
32 | 25 | 30.4026260368562 | -5.40262603685615 |
33 | 26 | 26.4499559136845 | -0.449955913684469 |
34 | 25 | 24.086412180723 | 0.913587819277008 |
35 | 17 | 22.8670220283224 | -5.86702202832237 |
36 | 32 | 27.760560760874 | 4.23943923912604 |
37 | 33 | 23.5983866371489 | 9.40161336285113 |
38 | 13 | 21.7984983327297 | -8.79849833272967 |
39 | 32 | 27.7477901143871 | 4.25220988561288 |
40 | 25 | 25.787102563668 | -0.787102563668002 |
41 | 29 | 26.9946561977486 | 2.00534380225136 |
42 | 22 | 21.9915422579662 | 0.00845774203379345 |
43 | 18 | 17.1296141440575 | 0.870385855942537 |
44 | 17 | 21.6372078571851 | -4.63720785718513 |
45 | 20 | 22.2319210210565 | -2.23192102105651 |
46 | 15 | 20.4352937876135 | -5.43529378761353 |
47 | 20 | 22.1071288311651 | -2.10712883116511 |
48 | 33 | 28.1211719978756 | 4.87882800212443 |
49 | 29 | 22.1411505218413 | 6.85884947815874 |
50 | 23 | 26.4998596091402 | -3.49985960914021 |
51 | 26 | 23.2345975129204 | 2.76540248707957 |
52 | 18 | 18.9656042544921 | -0.965604254492144 |
53 | 20 | 18.796120045743 | 1.20387995425697 |
54 | 11 | 11.7160709940257 | -0.716070994025724 |
55 | 28 | 29.0105804767345 | -1.01058047673454 |
56 | 26 | 23.3905043460467 | 2.60949565395329 |
57 | 22 | 22.3414695454203 | -0.341469545420307 |
58 | 17 | 20.1564210484307 | -3.1564210484307 |
59 | 12 | 15.5692778789805 | -3.56927787898049 |
60 | 14 | 20.8167935559991 | -6.81679355599913 |
61 | 17 | 20.8202241820746 | -3.82022418207459 |
62 | 21 | 21.3347129501434 | -0.334712950143374 |
63 | 19 | 22.9763818374361 | -3.9763818374361 |
64 | 18 | 23.1920758880957 | -5.19207588809566 |
65 | 10 | 17.9120405565538 | -7.91204055655376 |
66 | 29 | 24.4099265188341 | 4.59007348116592 |
67 | 31 | 18.5584769188011 | 12.4415230811989 |
68 | 19 | 22.9869414093617 | -3.98694140936168 |
69 | 9 | 20.0961723263517 | -11.0961723263517 |
70 | 20 | 22.5809984574057 | -2.5809984574057 |
71 | 28 | 17.6552736410877 | 10.3447263589123 |
72 | 19 | 18.2291083555071 | 0.770891644492931 |
73 | 30 | 23.1787562563361 | 6.82124374366391 |
74 | 29 | 27.1018574495787 | 1.8981425504213 |
75 | 26 | 21.5208597487263 | 4.47914025127372 |
76 | 23 | 19.5775913896633 | 3.42240861033671 |
77 | 13 | 22.7673890269749 | -9.76738902697489 |
78 | 21 | 22.6999656986182 | -1.69996569861817 |
79 | 19 | 21.6345836806373 | -2.63458368063734 |
80 | 28 | 22.9691570142453 | 5.03084298575475 |
81 | 23 | 25.6973992029916 | -2.6973992029916 |
82 | 18 | 13.9549031616295 | 4.04509683837052 |
83 | 21 | 20.7615465591829 | 0.238453440817123 |
84 | 20 | 21.9157961866931 | -1.91579618669311 |
85 | 23 | 20.0777478836276 | 2.92225211637242 |
86 | 21 | 20.8386011500172 | 0.161398849982822 |
87 | 21 | 21.8931506037604 | -0.89315060376045 |
88 | 15 | 23.0305779438395 | -8.03057794383953 |
89 | 28 | 27.3005835439217 | 0.699416456078302 |
90 | 19 | 17.7045900098864 | 1.2954099901136 |
91 | 26 | 21.2772051999813 | 4.72279480001875 |
92 | 10 | 13.4207961925499 | -3.42079619254989 |
93 | 16 | 17.1995105289364 | -1.19951052893641 |
94 | 22 | 21.1713453970672 | 0.828654602932829 |
95 | 19 | 18.9989312859951 | 0.00106871400488 |
96 | 31 | 28.940378376922 | 2.05962162307796 |
97 | 31 | 25.2905586288165 | 5.70944137118354 |
98 | 29 | 24.8528116175613 | 4.14718838243874 |
99 | 19 | 17.5096261454999 | 1.49037385450014 |
100 | 22 | 18.9524275113635 | 3.0475724886365 |
101 | 23 | 22.4963923849776 | 0.503607615022413 |
102 | 15 | 16.287535418075 | -1.28753541807505 |
103 | 20 | 21.4228525089516 | -1.4228525089516 |
104 | 18 | 19.6658145225114 | -1.66581452251145 |
105 | 23 | 22.2563692427647 | 0.743630757235343 |
106 | 25 | 20.9086574355098 | 4.09134256449023 |
107 | 21 | 16.6722771524643 | 4.32772284753566 |
108 | 24 | 19.5680077116824 | 4.4319922883176 |
109 | 25 | 25.3550235068465 | -0.35502350684648 |
110 | 17 | 19.619766860822 | -2.61976686082202 |
111 | 13 | 14.6659551691233 | -1.66595516912328 |
112 | 28 | 18.4262616637208 | 9.57373833627919 |
113 | 21 | 20.4196764510916 | 0.580323548908432 |
114 | 25 | 28.3159565386191 | -3.31595653861912 |
115 | 9 | 21.1551764227403 | -12.1551764227403 |
116 | 16 | 18.006110633023 | -2.00611063302303 |
117 | 19 | 21.2544613841651 | -2.25446138416515 |
118 | 17 | 19.6108037739653 | -2.61080377396526 |
119 | 25 | 24.6763915340849 | 0.323608465915102 |
120 | 20 | 15.5671337387445 | 4.4328662612555 |
121 | 29 | 21.8716126114376 | 7.12838738856236 |
122 | 14 | 19.1167857657226 | -5.11678576572262 |
123 | 22 | 27.0867941796051 | -5.0867941796051 |
124 | 15 | 15.9355784175142 | -0.935578417514243 |
125 | 19 | 25.626332592574 | -6.62633259257396 |
126 | 20 | 22.092892026745 | -2.09289202674502 |
127 | 15 | 17.7095654037931 | -2.70956540379314 |
128 | 20 | 22.1149283807381 | -2.11492838073814 |
129 | 18 | 20.5115649579609 | -2.51156495796087 |
130 | 33 | 25.7620025241802 | 7.23799747581976 |
131 | 22 | 24.0135738555549 | -2.01357385555486 |
132 | 16 | 16.6900618439135 | -0.69006184391349 |
133 | 17 | 19.3420422957593 | -2.34204229575932 |
134 | 16 | 15.3134803176989 | 0.686519682301068 |
135 | 21 | 17.2994992608764 | 3.70050073912356 |
136 | 26 | 27.7996968946194 | -1.79969689461943 |
137 | 18 | 21.304233865906 | -3.30423386590599 |
138 | 18 | 23.2073200148495 | -5.20732001484945 |
139 | 17 | 18.6825913123659 | -1.6825913123659 |
140 | 22 | 24.9799528930422 | -2.97995289304224 |
141 | 30 | 24.9254198082097 | 5.07458019179029 |
142 | 30 | 27.5705627248667 | 2.42943727513332 |
143 | 24 | 29.9683835869881 | -5.9683835869881 |
144 | 21 | 22.2960469748642 | -1.29604697486422 |
145 | 21 | 25.6227704527493 | -4.62277045274928 |
146 | 29 | 27.6739609431583 | 1.32603905684171 |
147 | 31 | 23.464342466474 | 7.53565753352599 |
148 | 20 | 19.2655893559701 | 0.734410644029935 |
149 | 16 | 14.3261339717709 | 1.67386602822906 |
150 | 22 | 19.2236647882233 | 2.77633521177669 |
151 | 20 | 20.7522347250232 | -0.752234725023152 |
152 | 28 | 27.5610774834422 | 0.438922516557777 |
153 | 38 | 26.890415116 | 11.109584884 |
154 | 22 | 19.4362722728422 | 2.56372772715776 |
155 | 20 | 25.9470773992814 | -5.9470773992814 |
156 | 17 | 18.31008307594 | -1.31008307593998 |
157 | 28 | 24.8140500775851 | 3.18594992241494 |
158 | 22 | 24.4230458313632 | -2.4230458313632 |
159 | 31 | 26.3398127723852 | 4.66018722761482 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
11 | 0.482919301614958 | 0.965838603229916 | 0.517080698385042 |
12 | 0.554073239343644 | 0.891853521312711 | 0.445926760656356 |
13 | 0.778571207452893 | 0.442857585094215 | 0.221428792547107 |
14 | 0.804401377897167 | 0.391197244205667 | 0.195598622102833 |
15 | 0.744773564280576 | 0.510452871438848 | 0.255226435719424 |
16 | 0.66423254463189 | 0.671534910736221 | 0.33576745536811 |
17 | 0.62352776774613 | 0.752944464507739 | 0.37647223225387 |
18 | 0.581415909333899 | 0.837168181332201 | 0.418584090666101 |
19 | 0.541563815283281 | 0.916872369433438 | 0.458436184716719 |
20 | 0.562150479533602 | 0.875699040932797 | 0.437849520466398 |
21 | 0.485348761129402 | 0.970697522258804 | 0.514651238870598 |
22 | 0.455924906437962 | 0.911849812875924 | 0.544075093562038 |
23 | 0.418029313423605 | 0.836058626847209 | 0.581970686576396 |
24 | 0.525131871059442 | 0.949736257881115 | 0.474868128940558 |
25 | 0.496594569472841 | 0.993189138945682 | 0.503405430527159 |
26 | 0.528430312047999 | 0.943139375904003 | 0.471569687952001 |
27 | 0.462456469163947 | 0.924912938327894 | 0.537543530836053 |
28 | 0.399432869722767 | 0.798865739445533 | 0.600567130277233 |
29 | 0.337499119939794 | 0.674998239879588 | 0.662500880060206 |
30 | 0.303449426252635 | 0.606898852505269 | 0.696550573747365 |
31 | 0.292068810897148 | 0.584137621794295 | 0.707931189102852 |
32 | 0.427890514331057 | 0.855781028662114 | 0.572109485668943 |
33 | 0.367770972580548 | 0.735541945161097 | 0.632229027419452 |
34 | 0.338921624250193 | 0.677843248500386 | 0.661078375749807 |
35 | 0.389911976046698 | 0.779823952093395 | 0.610088023953302 |
36 | 0.35418446066544 | 0.70836892133088 | 0.64581553933456 |
37 | 0.465426892273875 | 0.930853784547751 | 0.534573107726125 |
38 | 0.761514402351724 | 0.476971195296553 | 0.238485597648277 |
39 | 0.748042922363758 | 0.503914155272485 | 0.251957077636242 |
40 | 0.711410768934748 | 0.577178462130504 | 0.288589231065252 |
41 | 0.676447198133764 | 0.647105603732472 | 0.323552801866236 |
42 | 0.62816507684451 | 0.74366984631098 | 0.37183492315549 |
43 | 0.576422723698906 | 0.847154552602189 | 0.423577276301094 |
44 | 0.564043835542673 | 0.871912328914655 | 0.435956164457327 |
45 | 0.547145831190928 | 0.905708337618144 | 0.452854168809072 |
46 | 0.579192685522073 | 0.841614628955854 | 0.420807314477927 |
47 | 0.535476535517342 | 0.929046928965315 | 0.464523464482658 |
48 | 0.52598491184851 | 0.948030176302981 | 0.47401508815149 |
49 | 0.586210353983298 | 0.827579292033405 | 0.413789646016702 |
50 | 0.557321331543701 | 0.885357336912599 | 0.442678668456299 |
51 | 0.526419736329641 | 0.947160527340718 | 0.473580263670359 |
52 | 0.476679027266428 | 0.953358054532855 | 0.523320972733572 |
53 | 0.433008721292444 | 0.866017442584888 | 0.566991278707556 |
54 | 0.388214689123759 | 0.776429378247518 | 0.611785310876241 |
55 | 0.347336244766195 | 0.69467248953239 | 0.652663755233805 |
56 | 0.318722802009979 | 0.637445604019959 | 0.681277197990021 |
57 | 0.275855712367904 | 0.551711424735808 | 0.724144287632096 |
58 | 0.247829977005935 | 0.49565995401187 | 0.752170022994065 |
59 | 0.229544224760973 | 0.459088449521945 | 0.770455775239027 |
60 | 0.264607003917429 | 0.529214007834858 | 0.735392996082571 |
61 | 0.24812764027652 | 0.496255280553041 | 0.75187235972348 |
62 | 0.2141301810355 | 0.428260362071 | 0.7858698189645 |
63 | 0.196907532926841 | 0.393815065853682 | 0.803092467073159 |
64 | 0.217946681722194 | 0.435893363444389 | 0.782053318277806 |
65 | 0.266979412065807 | 0.533958824131614 | 0.733020587934193 |
66 | 0.275929127254051 | 0.551858254508101 | 0.724070872745949 |
67 | 0.63776942013587 | 0.724461159728261 | 0.36223057986413 |
68 | 0.621918172530881 | 0.756163654938239 | 0.378081827469119 |
69 | 0.795195289203808 | 0.409609421592385 | 0.204804710796192 |
70 | 0.767814750635934 | 0.464370498728133 | 0.232185249364067 |
71 | 0.912753156491534 | 0.174493687016931 | 0.0872468435084657 |
72 | 0.893727121804519 | 0.212545756390963 | 0.106272878195482 |
73 | 0.924292609592878 | 0.151414780814245 | 0.0757073904071225 |
74 | 0.912497020729957 | 0.175005958540085 | 0.0875029792700426 |
75 | 0.916330968011296 | 0.167338063977407 | 0.0836690319887037 |
76 | 0.910662472173307 | 0.178675055653386 | 0.0893375278266929 |
77 | 0.962094085816428 | 0.0758118283671447 | 0.0379059141835724 |
78 | 0.952685243442334 | 0.0946295131153326 | 0.0473147565576663 |
79 | 0.94347392980676 | 0.11305214038648 | 0.0565260701932399 |
80 | 0.947942852549188 | 0.104114294901625 | 0.0520571474508123 |
81 | 0.938265238808533 | 0.123469522382935 | 0.0617347611914673 |
82 | 0.937582724026703 | 0.124834551946594 | 0.062417275973297 |
83 | 0.922053336251284 | 0.155893327497431 | 0.0779466637487156 |
84 | 0.906574250002528 | 0.186851499994944 | 0.0934257499974718 |
85 | 0.896763278206496 | 0.206473443587007 | 0.103236721793504 |
86 | 0.878080050015044 | 0.243839899969911 | 0.121919949984956 |
87 | 0.853375575666525 | 0.293248848666951 | 0.146624424333475 |
88 | 0.905330192016902 | 0.189339615966195 | 0.0946698079830975 |
89 | 0.886155588871522 | 0.227688822256956 | 0.113844411128478 |
90 | 0.863647711730099 | 0.272704576539803 | 0.136352288269901 |
91 | 0.865827478842622 | 0.268345042314757 | 0.134172521157378 |
92 | 0.854384780881698 | 0.291230438236603 | 0.145615219118302 |
93 | 0.829831700773177 | 0.340336598453647 | 0.170168299226823 |
94 | 0.79955374740597 | 0.400892505188061 | 0.200446252594031 |
95 | 0.763688446644035 | 0.472623106711929 | 0.236311553355965 |
96 | 0.731055574998138 | 0.537888850003724 | 0.268944425001862 |
97 | 0.751741927331529 | 0.496516145336941 | 0.248258072668471 |
98 | 0.749346506853056 | 0.501306986293889 | 0.250653493146944 |
99 | 0.712234696431953 | 0.575530607136094 | 0.287765303568047 |
100 | 0.689744864923867 | 0.620510270152265 | 0.310255135076133 |
101 | 0.649434922236285 | 0.70113015552743 | 0.350565077763715 |
102 | 0.606634845790476 | 0.786730308419047 | 0.393365154209524 |
103 | 0.563244216748731 | 0.873511566502539 | 0.436755783251269 |
104 | 0.518654156668534 | 0.962691686662932 | 0.481345843331466 |
105 | 0.475880650474406 | 0.951761300948813 | 0.524119349525594 |
106 | 0.46361214111995 | 0.927224282239899 | 0.53638785888005 |
107 | 0.47077904927371 | 0.94155809854742 | 0.52922095072629 |
108 | 0.509532807449636 | 0.980934385100728 | 0.490467192550364 |
109 | 0.470971756762878 | 0.941943513525756 | 0.529028243237122 |
110 | 0.428611691000273 | 0.857223382000545 | 0.571388308999727 |
111 | 0.381451505416846 | 0.762903010833691 | 0.618548494583154 |
112 | 0.711288640363238 | 0.577422719273525 | 0.288711359636762 |
113 | 0.747397544448189 | 0.505204911103622 | 0.252602455551811 |
114 | 0.720032266639849 | 0.559935466720302 | 0.279967733360151 |
115 | 0.854652166059168 | 0.290695667881664 | 0.145347833940832 |
116 | 0.822716200104192 | 0.354567599791616 | 0.177283799895808 |
117 | 0.789598373374736 | 0.420803253250528 | 0.210401626625264 |
118 | 0.752405016530783 | 0.495189966938434 | 0.247594983469217 |
119 | 0.721776844050078 | 0.556446311899843 | 0.278223155949921 |
120 | 0.773892573829068 | 0.452214852341864 | 0.226107426170932 |
121 | 0.86094268064034 | 0.27811463871932 | 0.13905731935966 |
122 | 0.838493713445111 | 0.323012573109779 | 0.161506286554889 |
123 | 0.8144281484347 | 0.371143703130601 | 0.1855718515653 |
124 | 0.771549295854048 | 0.456901408291903 | 0.228450704145952 |
125 | 0.774698277617689 | 0.450603444764622 | 0.225301722382311 |
126 | 0.725912210291747 | 0.548175579416507 | 0.274087789708253 |
127 | 0.690676886270889 | 0.618646227458223 | 0.309323113729111 |
128 | 0.639778003698588 | 0.720443992602824 | 0.360221996301412 |
129 | 0.590736886156087 | 0.818526227687826 | 0.409263113843913 |
130 | 0.718503215808757 | 0.562993568382487 | 0.281496784191243 |
131 | 0.660323778713816 | 0.679352442572368 | 0.339676221286184 |
132 | 0.595126930986174 | 0.809746138027651 | 0.404873069013826 |
133 | 0.553718763961046 | 0.892562472077908 | 0.446281236038954 |
134 | 0.481445774757762 | 0.962891549515525 | 0.518554225242238 |
135 | 0.50489983869972 | 0.99020032260056 | 0.49510016130028 |
136 | 0.432400563387953 | 0.864801126775906 | 0.567599436612047 |
137 | 0.38385109062999 | 0.767702181259981 | 0.61614890937001 |
138 | 0.39624875461526 | 0.79249750923052 | 0.60375124538474 |
139 | 0.323763162155535 | 0.64752632431107 | 0.676236837844465 |
140 | 0.254403000965545 | 0.50880600193109 | 0.745596999034455 |
141 | 0.344047179913995 | 0.68809435982799 | 0.655952820086005 |
142 | 0.294575906829285 | 0.58915181365857 | 0.705424093170715 |
143 | 0.226445586897252 | 0.452891173794503 | 0.773554413102748 |
144 | 0.159698858380338 | 0.319397716760676 | 0.840301141619662 |
145 | 0.239930077553042 | 0.479860155106083 | 0.760069922446958 |
146 | 0.169348307271413 | 0.338696614542826 | 0.830651692728587 |
147 | 0.160521283906014 | 0.321042567812029 | 0.839478716093986 |
148 | 0.087308090660505 | 0.17461618132101 | 0.912691909339495 |
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 | 2 | 0.0144927536231884 | OK |