Multiple Linear Regression - Estimated Regression Equation |
YT[t] = -18.3591714482512 + 1.58838471475270T1[t] + 0.79875711851511X1[t] + 0.233450466257558X2[t] + 0.207082749570129X3[t] + 0.571862761699044X4[t] -0.0999815995143383`X5 `[t] + 0.00354783249216934t + 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) | -18.3591714482512 | 19.993412 | -0.9183 | 0.359947 | 0.179973 |
T1 | 1.58838471475270 | 2.002175 | 0.7933 | 0.428831 | 0.214415 |
X1 | 0.79875711851511 | 0.131148 | 6.0905 | 0 | 0 |
X2 | 0.233450466257558 | 0.134333 | 1.7379 | 0.084276 | 0.042138 |
X3 | 0.207082749570129 | 0.170009 | 1.2181 | 0.225097 | 0.112548 |
X4 | 0.571862761699044 | 0.096247 | 5.9416 | 0 | 0 |
`X5 ` | -0.0999815995143383 | 0.105485 | -0.9478 | 0.344732 | 0.172366 |
t | 0.00354783249216934 | 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 | 23.3005712933063 | 0.699428706693719 |
2 | 25 | 20.0175224671839 | 4.98247753281608 |
3 | 17 | 21.0211399791426 | -4.02113997914265 |
4 | 18 | 18.0925500792618 | -0.0925500792618023 |
5 | 18 | 17.6905678029332 | 0.309432197066762 |
6 | 16 | 17.877648378172 | -1.87764837817201 |
7 | 20 | 20.7303968936034 | -0.7303968936034 |
8 | 16 | 22.2384819662608 | -6.23848196626085 |
9 | 18 | 22.1097766895970 | -4.10977668959702 |
10 | 17 | 20.3404956440243 | -3.34049564402435 |
11 | 23 | 22.1666780037712 | 0.833321996228807 |
12 | 30 | 22.0240937482091 | 7.97590625179086 |
13 | 23 | 14.9779833304995 | 8.02201666950045 |
14 | 18 | 18.8006776299538 | -0.800677629953757 |
15 | 15 | 21.5420869454813 | -6.54208694548131 |
16 | 12 | 17.7473672648276 | -5.74736726482756 |
17 | 21 | 19.3199506278201 | 1.68004937217993 |
18 | 15 | 15.0095102272645 | -0.00951022726447562 |
19 | 20 | 19.5818010071522 | 0.41819899284785 |
20 | 31 | 26.1780117087719 | 4.8219882912281 |
21 | 27 | 25.0654667635792 | 1.93453323642076 |
22 | 34 | 26.8723465536459 | 7.12765344635407 |
23 | 21 | 19.5212510677299 | 1.47874893227008 |
24 | 31 | 20.7775429191891 | 10.2224570808109 |
25 | 19 | 19.2620873882198 | -0.262087388219842 |
26 | 16 | 20.1257631629215 | -4.12576316292152 |
27 | 20 | 21.4505453886165 | -1.45054538861650 |
28 | 21 | 18.1772639671097 | 2.82273603289032 |
29 | 22 | 21.8404586063841 | 0.15954139361592 |
30 | 17 | 19.3786812679951 | -2.37868126799510 |
31 | 24 | 20.3628830419833 | 3.63711695801675 |
32 | 25 | 30.4026260368561 | -5.40262603685613 |
33 | 26 | 26.4499559136845 | -0.449955913684488 |
34 | 25 | 24.086412180723 | 0.913587819277002 |
35 | 17 | 22.8670220283224 | -5.86702202832238 |
36 | 32 | 27.7605607608740 | 4.23943923912604 |
37 | 33 | 23.5983866371489 | 9.40161336285112 |
38 | 13 | 21.7984983327297 | -8.79849833272967 |
39 | 32 | 27.7477901143871 | 4.25220988561288 |
40 | 25 | 25.787102563668 | -0.787102563668005 |
41 | 29 | 26.9946561977486 | 2.00534380225137 |
42 | 22 | 21.9915422579662 | 0.00845774203379076 |
43 | 18 | 17.1296141440575 | 0.87038585594253 |
44 | 17 | 21.6372078571851 | -4.63720785718515 |
45 | 20 | 22.2319210210565 | -2.23192102105651 |
46 | 15 | 20.4352937876135 | -5.43529378761353 |
47 | 20 | 22.1071288311651 | -2.1071288311651 |
48 | 33 | 28.1211719978756 | 4.87882800212443 |
49 | 29 | 22.1411505218413 | 6.85884947815874 |
50 | 23 | 26.4998596091402 | -3.49985960914021 |
51 | 26 | 23.2345975129204 | 2.76540248707958 |
52 | 18 | 18.9656042544921 | -0.965604254492147 |
53 | 20 | 18.7961200457430 | 1.20387995425697 |
54 | 11 | 11.7160709940257 | -0.716070994025735 |
55 | 28 | 29.0105804767345 | -1.01058047673453 |
56 | 26 | 23.3905043460467 | 2.60949565395329 |
57 | 22 | 22.3414695454203 | -0.341469545420307 |
58 | 17 | 20.1564210484307 | -3.15642104843071 |
59 | 12 | 15.5692778789805 | -3.56927787898050 |
60 | 14 | 20.8167935559991 | -6.81679355599913 |
61 | 17 | 20.8202241820746 | -3.82022418207459 |
62 | 21 | 21.3347129501434 | -0.334712950143380 |
63 | 19 | 22.9763818374361 | -3.97638183743611 |
64 | 18 | 23.1920758880957 | -5.19207588809565 |
65 | 10 | 17.9120405565538 | -7.91204055655377 |
66 | 29 | 24.4099265188341 | 4.59007348116592 |
67 | 31 | 18.5584769188011 | 12.4415230811989 |
68 | 19 | 22.9869414093617 | -3.98694140936169 |
69 | 9 | 20.0961723263517 | -11.0961723263517 |
70 | 20 | 22.5809984574057 | -2.58099845740569 |
71 | 28 | 17.6552736410878 | 10.3447263589122 |
72 | 19 | 18.2291083555071 | 0.770891644492931 |
73 | 30 | 23.1787562563361 | 6.82124374366391 |
74 | 29 | 27.1018574495787 | 1.89814255042130 |
75 | 26 | 21.5208597487263 | 4.47914025127371 |
76 | 23 | 19.5775913896633 | 3.42240861033671 |
77 | 13 | 22.7673890269749 | -9.7673890269749 |
78 | 21 | 22.6999656986182 | -1.69996569861817 |
79 | 19 | 21.6345836806373 | -2.63458368063733 |
80 | 28 | 22.9691570142453 | 5.03084298575474 |
81 | 23 | 25.6973992029916 | -2.69739920299159 |
82 | 18 | 13.9549031616295 | 4.04509683837052 |
83 | 21 | 20.7615465591829 | 0.238453440817124 |
84 | 20 | 21.9157961866931 | -1.91579618669312 |
85 | 23 | 20.0777478836276 | 2.92225211637243 |
86 | 21 | 20.8386011500172 | 0.161398849982816 |
87 | 21 | 21.8931506037605 | -0.893150603760456 |
88 | 15 | 23.0305779438395 | -8.03057794383952 |
89 | 28 | 27.3005835439217 | 0.699416456078311 |
90 | 19 | 17.7045900098864 | 1.29540999011360 |
91 | 26 | 21.2772051999812 | 4.72279480001875 |
92 | 10 | 13.4207961925499 | -3.4207961925499 |
93 | 16 | 17.1995105289364 | -1.19951052893642 |
94 | 22 | 21.1713453970672 | 0.82865460293282 |
95 | 19 | 18.9989312859951 | 0.00106871400488703 |
96 | 31 | 28.9403783769220 | 2.05962162307796 |
97 | 31 | 25.2905586288165 | 5.70944137118355 |
98 | 29 | 24.8528116175613 | 4.14718838243874 |
99 | 19 | 17.5096261454999 | 1.49037385450014 |
100 | 22 | 18.9524275113635 | 3.04757248863650 |
101 | 23 | 22.4963923849776 | 0.503607615022413 |
102 | 15 | 16.2875354180751 | -1.28753541807506 |
103 | 20 | 21.4228525089516 | -1.42285250895161 |
104 | 18 | 19.6658145225114 | -1.66581452251145 |
105 | 23 | 22.2563692427646 | 0.743630757235358 |
106 | 25 | 20.9086574355098 | 4.09134256449023 |
107 | 21 | 16.6722771524643 | 4.32772284753566 |
108 | 24 | 19.5680077116824 | 4.4319922883176 |
109 | 25 | 25.3550235068465 | -0.355023506846472 |
110 | 17 | 19.619766860822 | -2.61976686082202 |
111 | 13 | 14.6659551691233 | -1.66595516912329 |
112 | 28 | 18.4262616637208 | 9.57373833627919 |
113 | 21 | 20.4196764510916 | 0.580323548908437 |
114 | 25 | 28.3159565386191 | -3.31595653861913 |
115 | 9 | 21.1551764227403 | -12.1551764227403 |
116 | 16 | 18.0061106330230 | -2.00611063302304 |
117 | 19 | 21.2544613841652 | -2.25446138416516 |
118 | 17 | 19.6108037739653 | -2.61080377396526 |
119 | 25 | 24.6763915340849 | 0.323608465915107 |
120 | 20 | 15.5671337387445 | 4.43286626125549 |
121 | 29 | 21.8716126114376 | 7.12838738856236 |
122 | 14 | 19.1167857657226 | -5.11678576572263 |
123 | 22 | 27.0867941796051 | -5.08679417960509 |
124 | 15 | 15.9355784175142 | -0.935578417514242 |
125 | 19 | 25.6263325925739 | -6.62633259257395 |
126 | 20 | 22.0928920267450 | -2.09289202674503 |
127 | 15 | 17.7095654037931 | -2.70956540379315 |
128 | 20 | 22.1149283807381 | -2.11492838073813 |
129 | 18 | 20.5115649579609 | -2.51156495796086 |
130 | 33 | 25.7620025241802 | 7.23799747581977 |
131 | 22 | 24.0135738555549 | -2.01357385555485 |
132 | 16 | 16.6900618439135 | -0.690061843913491 |
133 | 17 | 19.3420422957593 | -2.34204229575933 |
134 | 16 | 15.3134803176989 | 0.68651968230106 |
135 | 21 | 17.2994992608764 | 3.70050073912357 |
136 | 26 | 27.7996968946194 | -1.79969689461943 |
137 | 18 | 21.304233865906 | -3.30423386590599 |
138 | 18 | 23.2073200148495 | -5.20732001484945 |
139 | 17 | 18.6825913123659 | -1.68259131236590 |
140 | 22 | 24.9799528930422 | -2.97995289304222 |
141 | 30 | 24.9254198082097 | 5.0745801917903 |
142 | 30 | 27.5705627248667 | 2.42943727513332 |
143 | 24 | 29.9683835869881 | -5.96838358698809 |
144 | 21 | 22.2960469748642 | -1.29604697486422 |
145 | 21 | 25.6227704527493 | -4.62277045274928 |
146 | 29 | 27.6739609431583 | 1.32603905684171 |
147 | 31 | 23.464342466474 | 7.53565753352598 |
148 | 20 | 19.2655893559701 | 0.734410644029932 |
149 | 16 | 14.3261339717709 | 1.67386602822906 |
150 | 22 | 19.2236647882233 | 2.77633521177669 |
151 | 20 | 20.7522347250232 | -0.752234725023154 |
152 | 28 | 27.5610774834422 | 0.438922516557781 |
153 | 38 | 26.890415116 | 11.1095848840000 |
154 | 22 | 19.4362722728422 | 2.56372772715775 |
155 | 20 | 25.9470773992814 | -5.9470773992814 |
156 | 17 | 18.31008307594 | -1.31008307593998 |
157 | 28 | 24.8140500775851 | 3.18594992241494 |
158 | 22 | 24.4230458313632 | -2.42304583136319 |
159 | 31 | 26.3398127723852 | 4.66018722761484 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
11 | 0.482919301614959 | 0.965838603229918 | 0.517080698385041 |
12 | 0.554073239343645 | 0.89185352131271 | 0.445926760656355 |
13 | 0.778571207452893 | 0.442857585094213 | 0.221428792547107 |
14 | 0.804401377897167 | 0.391197244205666 | 0.195598622102833 |
15 | 0.744773564280576 | 0.510452871438847 | 0.255226435719424 |
16 | 0.66423254463189 | 0.67153491073622 | 0.33576745536811 |
17 | 0.623527767746131 | 0.752944464507739 | 0.376472232253869 |
18 | 0.581415909333898 | 0.837168181332203 | 0.418584090666102 |
19 | 0.541563815283281 | 0.916872369433438 | 0.458436184716719 |
20 | 0.562150479533601 | 0.875699040932797 | 0.437849520466399 |
21 | 0.485348761129402 | 0.970697522258804 | 0.514651238870598 |
22 | 0.455924906437963 | 0.911849812875926 | 0.544075093562037 |
23 | 0.418029313423604 | 0.836058626847208 | 0.581970686576396 |
24 | 0.525131871059443 | 0.949736257881114 | 0.474868128940557 |
25 | 0.496594569472841 | 0.993189138945682 | 0.503405430527159 |
26 | 0.528430312047999 | 0.943139375904001 | 0.471569687952001 |
27 | 0.462456469163947 | 0.924912938327894 | 0.537543530836053 |
28 | 0.399432869722768 | 0.798865739445536 | 0.600567130277232 |
29 | 0.337499119939794 | 0.674998239879589 | 0.662500880060206 |
30 | 0.303449426252635 | 0.606898852505269 | 0.696550573747365 |
31 | 0.292068810897149 | 0.584137621794297 | 0.707931189102851 |
32 | 0.427890514331057 | 0.855781028662114 | 0.572109485668943 |
33 | 0.367770972580548 | 0.735541945161096 | 0.632229027419452 |
34 | 0.338921624250193 | 0.677843248500386 | 0.661078375749807 |
35 | 0.389911976046697 | 0.779823952093394 | 0.610088023953303 |
36 | 0.35418446066544 | 0.70836892133088 | 0.64581553933456 |
37 | 0.465426892273875 | 0.93085378454775 | 0.534573107726125 |
38 | 0.761514402351724 | 0.476971195296551 | 0.238485597648276 |
39 | 0.748042922363758 | 0.503914155272483 | 0.251957077636242 |
40 | 0.711410768934749 | 0.577178462130503 | 0.288589231065251 |
41 | 0.676447198133766 | 0.647105603732469 | 0.323552801866234 |
42 | 0.62816507684451 | 0.74366984631098 | 0.37183492315549 |
43 | 0.576422723698907 | 0.847154552602186 | 0.423577276301093 |
44 | 0.564043835542671 | 0.871912328914659 | 0.435956164457329 |
45 | 0.547145831190928 | 0.905708337618143 | 0.452854168809072 |
46 | 0.579192685522074 | 0.841614628955852 | 0.420807314477926 |
47 | 0.535476535517343 | 0.929046928965313 | 0.464523464482657 |
48 | 0.525984911848510 | 0.948030176302979 | 0.474015088151489 |
49 | 0.5862103539833 | 0.8275792920334 | 0.4137896460167 |
50 | 0.5573213315437 | 0.8853573369126 | 0.4426786684563 |
51 | 0.526419736329641 | 0.947160527340718 | 0.473580263670359 |
52 | 0.476679027266429 | 0.953358054532857 | 0.523320972733571 |
53 | 0.433008721292444 | 0.866017442584889 | 0.566991278707556 |
54 | 0.388214689123759 | 0.776429378247518 | 0.611785310876241 |
55 | 0.347336244766196 | 0.694672489532392 | 0.652663755233804 |
56 | 0.318722802009980 | 0.637445604019959 | 0.68127719799002 |
57 | 0.275855712367904 | 0.551711424735809 | 0.724144287632096 |
58 | 0.247829977005935 | 0.495659954011869 | 0.752170022994066 |
59 | 0.229544224760974 | 0.459088449521947 | 0.770455775239026 |
60 | 0.264607003917427 | 0.529214007834855 | 0.735392996082573 |
61 | 0.24812764027652 | 0.49625528055304 | 0.75187235972348 |
62 | 0.214130181035499 | 0.428260362070998 | 0.785869818964501 |
63 | 0.196907532926841 | 0.393815065853682 | 0.803092467073159 |
64 | 0.217946681722193 | 0.435893363444386 | 0.782053318277807 |
65 | 0.266979412065807 | 0.533958824131614 | 0.733020587934193 |
66 | 0.275929127254054 | 0.551858254508108 | 0.724070872745946 |
67 | 0.63776942013587 | 0.72446115972826 | 0.36223057986413 |
68 | 0.621918172530883 | 0.756163654938234 | 0.378081827469117 |
69 | 0.795195289203809 | 0.409609421592383 | 0.204804710796191 |
70 | 0.767814750635933 | 0.464370498728134 | 0.232185249364067 |
71 | 0.912753156491534 | 0.174493687016932 | 0.0872468435084658 |
72 | 0.893727121804516 | 0.212545756390967 | 0.106272878195484 |
73 | 0.924292609592878 | 0.151414780814245 | 0.0757073904071223 |
74 | 0.912497020729957 | 0.175005958540086 | 0.0875029792700431 |
75 | 0.916330968011296 | 0.167338063977408 | 0.0836690319887039 |
76 | 0.910662472173308 | 0.178675055653384 | 0.089337527826692 |
77 | 0.962094085816427 | 0.0758118283671457 | 0.0379059141835728 |
78 | 0.952685243442333 | 0.0946295131153332 | 0.0473147565576666 |
79 | 0.94347392980676 | 0.113052140386480 | 0.0565260701932398 |
80 | 0.947942852549188 | 0.104114294901625 | 0.0520571474508123 |
81 | 0.938265238808533 | 0.123469522382935 | 0.0617347611914673 |
82 | 0.937582724026703 | 0.124834551946594 | 0.0624172759732972 |
83 | 0.922053336251284 | 0.155893327497433 | 0.0779466637487164 |
84 | 0.906574250002529 | 0.186851499994942 | 0.0934257499974709 |
85 | 0.896763278206496 | 0.206473443587007 | 0.103236721793503 |
86 | 0.878080050015044 | 0.243839899969911 | 0.121919949984956 |
87 | 0.853375575666524 | 0.293248848666953 | 0.146624424333476 |
88 | 0.905330192016902 | 0.189339615966196 | 0.0946698079830979 |
89 | 0.886155588871522 | 0.227688822256956 | 0.113844411128478 |
90 | 0.863647711730098 | 0.272704576539804 | 0.136352288269902 |
91 | 0.865827478842622 | 0.268345042314756 | 0.134172521157378 |
92 | 0.854384780881698 | 0.291230438236603 | 0.145615219118302 |
93 | 0.829831700773176 | 0.340336598453648 | 0.170168299226824 |
94 | 0.79955374740597 | 0.400892505188061 | 0.200446252594031 |
95 | 0.763688446644035 | 0.47262310671193 | 0.236311553355965 |
96 | 0.731055574998138 | 0.537888850003723 | 0.268944425001862 |
97 | 0.75174192733153 | 0.49651614533694 | 0.24825807266847 |
98 | 0.749346506853056 | 0.501306986293889 | 0.250653493146944 |
99 | 0.712234696431953 | 0.575530607136093 | 0.287765303568047 |
100 | 0.689744864923868 | 0.620510270152265 | 0.310255135076132 |
101 | 0.649434922236285 | 0.70113015552743 | 0.350565077763715 |
102 | 0.606634845790477 | 0.786730308419046 | 0.393365154209523 |
103 | 0.56324421674873 | 0.873511566502539 | 0.436755783251269 |
104 | 0.518654156668534 | 0.962691686662932 | 0.481345843331466 |
105 | 0.475880650474408 | 0.951761300948816 | 0.524119349525592 |
106 | 0.463612141119946 | 0.927224282239892 | 0.536387858880054 |
107 | 0.470779049273711 | 0.941558098547422 | 0.529220950726289 |
108 | 0.509532807449635 | 0.98093438510073 | 0.490467192550365 |
109 | 0.47097175676288 | 0.94194351352576 | 0.52902824323712 |
110 | 0.428611691000273 | 0.857223382000546 | 0.571388308999727 |
111 | 0.381451505416848 | 0.762903010833696 | 0.618548494583152 |
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 | 0.822716200104193 | 0.354567599791615 | 0.177283799895807 |
117 | 0.789598373374736 | 0.420803253250528 | 0.210401626625264 |
118 | 0.752405016530784 | 0.495189966938432 | 0.247594983469216 |
119 | 0.721776844050078 | 0.556446311899844 | 0.278223155949922 |
120 | 0.773892573829069 | 0.452214852341862 | 0.226107426170931 |
121 | 0.86094268064034 | 0.278114638719321 | 0.139057319359660 |
122 | 0.83849371344511 | 0.323012573109779 | 0.161506286554890 |
123 | 0.8144281484347 | 0.3711437031306 | 0.1855718515653 |
124 | 0.77154929585405 | 0.456901408291901 | 0.228450704145950 |
125 | 0.77469827761769 | 0.450603444764621 | 0.225301722382310 |
126 | 0.725912210291747 | 0.548175579416506 | 0.274087789708253 |
127 | 0.69067688627089 | 0.618646227458221 | 0.309323113729111 |
128 | 0.639778003698588 | 0.720443992602823 | 0.360221996301412 |
129 | 0.590736886156087 | 0.818526227687827 | 0.409263113843913 |
130 | 0.718503215808757 | 0.562993568382487 | 0.281496784191244 |
131 | 0.660323778713816 | 0.679352442572369 | 0.339676221286184 |
132 | 0.595126930986174 | 0.809746138027651 | 0.404873069013826 |
133 | 0.553718763961046 | 0.892562472077909 | 0.446281236038954 |
134 | 0.481445774757762 | 0.962891549515525 | 0.518554225242238 |
135 | 0.504899838699719 | 0.990200322600562 | 0.495100161300281 |
136 | 0.432400563387952 | 0.864801126775904 | 0.567599436612048 |
137 | 0.383851090629990 | 0.767702181259979 | 0.61614890937001 |
138 | 0.396248754615259 | 0.792497509230519 | 0.603751245384741 |
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 | 0.226445586897251 | 0.452891173794503 | 0.773554413102749 |
144 | 0.159698858380339 | 0.319397716760677 | 0.840301141619661 |
145 | 0.239930077553042 | 0.479860155106083 | 0.760069922446958 |
146 | 0.169348307271413 | 0.338696614542827 | 0.830651692728587 |
147 | 0.160521283906014 | 0.321042567812028 | 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 |