Multiple Linear Regression - Estimated Regression Equation |
Y1[t] = + 9975.2865695666 + 0.399373740130443X1[t] + 0.829081886969305X2[t] -263.961831618897X3[t] + 351.1105913586X4[t] + 282.1501377318X5[t] -0.0726533526117337X6[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) | 9975.2865695666 | 7338.710441 | 1.3593 | 0.176231 | 0.088116 |
X1 | 0.399373740130443 | 0.093475 | 4.2725 | 3.5e-05 | 1.8e-05 |
X2 | 0.829081886969305 | 0.36592 | 2.2657 | 0.02499 | 0.012495 |
X3 | -263.961831618897 | 613.350328 | -0.4304 | 0.66759 | 0.333795 |
X4 | 351.1105913586 | 636.371629 | 0.5517 | 0.582001 | 0.291001 |
X5 | 282.1501377318 | 68.425718 | 4.1235 | 6.3e-05 | 3.2e-05 |
X6 | -0.0726533526117337 | 0.040572 | -1.7907 | 0.075485 | 0.037743 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.798523959241787 |
R-squared | 0.637640513483179 |
Adjusted R-squared | 0.622220960865442 |
F-TEST (value) | 41.3527246406425 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 141 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 28974.7475546615 |
Sum Squared Residuals | 118374575415.747 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 140824 | 141641.102268507 | -817.102268507171 |
2 | 110459 | 108196.50883672 | 2262.49116327959 |
3 | 105079 | 90217.636913442 | 14861.363086558 |
4 | 112098 | 119073.037454421 | -6975.03745442069 |
5 | 43929 | 72231.728853686 | -28302.728853686 |
6 | 76173 | 60809.0364186994 | 15363.9635813006 |
7 | 187326 | 156829.183322644 | 30496.816677356 |
8 | 22807 | 17997.9305580436 | 4809.06944195637 |
9 | 144408 | 115892.927670175 | 28515.0723298249 |
10 | 66485 | 86012.995366264 | -19527.995366264 |
11 | 79089 | 124900.911500947 | -45811.9115009473 |
12 | 81625 | 109785.130946324 | -28160.1309463243 |
13 | 68788 | 71987.0518701783 | -3199.05187017828 |
14 | 103297 | 102938.396314613 | 358.603685386712 |
15 | 69446 | 78222.4910504812 | -8776.49105048116 |
16 | 114948 | 143818.524754736 | -28870.5247547364 |
17 | 167949 | 140247.190542335 | 27701.809457665 |
18 | 125081 | 88343.3157586121 | 36737.6842413879 |
19 | 125818 | 106306.616897531 | 19511.383102469 |
20 | 136588 | 130454.989968982 | 6133.01003101796 |
21 | 112431 | 136631.914743867 | -24200.9147438666 |
22 | 103037 | 101470.011123056 | 1566.98887694428 |
23 | 82317 | 82217.4772692933 | 99.5227307066657 |
24 | 118906 | 130278.115212286 | -11372.1152122855 |
25 | 83515 | 109568.231105926 | -26053.2311059255 |
26 | 104581 | 116046.487456789 | -11465.4874567887 |
27 | 103129 | 120347.427050616 | -17218.4270506156 |
28 | 83243 | 121231.858146693 | -37988.8581466928 |
29 | 37110 | 65855.329177109 | -28745.329177109 |
30 | 113344 | 142108.744604834 | -28764.7446048336 |
31 | 139165 | 161130.537592256 | -21965.5375922559 |
32 | 86652 | 99430.9626540302 | -12778.9626540302 |
33 | 112302 | 156007.134621809 | -43705.1346218094 |
34 | 69652 | 62358.682724705 | 7293.31727529496 |
35 | 119442 | 145198.961069617 | -25756.9610696165 |
36 | 69867 | 77080.4160912034 | -7213.41609120343 |
37 | 101629 | 132659.15107857 | -31030.1510785697 |
38 | 70168 | 86255.1331910242 | -16087.1331910242 |
39 | 31081 | 51514.8308108997 | -20433.8308108997 |
40 | 103925 | 131956.800588094 | -28031.8005880938 |
41 | 92622 | 106825.765161477 | -14203.7651614767 |
42 | 79011 | 80390.2398926568 | -1379.23989265677 |
43 | 93487 | 109732.070694231 | -16245.070694231 |
44 | 64520 | 79792.6901063083 | -15272.6901063083 |
45 | 93473 | 77289.659743119 | 16183.340256881 |
46 | 114360 | 61836.0726967973 | 52523.9273032027 |
47 | 33032 | 54032.5234294471 | -21000.5234294471 |
48 | 96125 | 122987.319094174 | -26862.3190941744 |
49 | 151911 | 143287.749953836 | 8623.25004616382 |
50 | 89256 | 111041.964475959 | -21785.9644759588 |
51 | 95676 | 134741.041364414 | -39065.0413644137 |
52 | 5950 | 19046.7615776129 | -13096.7615776129 |
53 | 149695 | 135856.395629831 | 13838.6043701693 |
54 | 32551 | 37302.0768471156 | -4751.07684711561 |
55 | 31701 | 39940.3327595984 | -8239.33275959841 |
56 | 100087 | 114976.478929464 | -14889.4789294642 |
57 | 169707 | 177045.952901418 | -7338.95290141825 |
58 | 150491 | 158018.306777546 | -7527.30677754586 |
59 | 120192 | 151655.799809454 | -31463.7998094541 |
60 | 95893 | 89586.0926879577 | 6306.90731204225 |
61 | 151715 | 147949.398619262 | 3765.60138073796 |
62 | 176225 | 158322.622381743 | 17902.3776182571 |
63 | 59900 | 71178.933094198 | -11278.933094198 |
64 | 104767 | 110300.441126718 | -5533.44112671752 |
65 | 114799 | 131699.320506644 | -16900.3205066443 |
66 | 72128 | 103813.345647731 | -31685.3456477313 |
67 | 143592 | 112702.093684693 | 30889.906315307 |
68 | 89626 | 125658.359317489 | -36032.3593174892 |
69 | 131072 | 111081.19340439 | 19990.8065956104 |
70 | 126817 | 87694.9028898012 | 39122.0971101988 |
71 | 81351 | 101019.551311646 | -19668.5513116456 |
72 | 22618 | 37457.0156402204 | -14839.0156402204 |
73 | 88977 | 111202.895619082 | -22225.8956190821 |
74 | 92059 | 86347.1192077296 | 5711.88079227044 |
75 | 81897 | 98802.955668672 | -16905.955668672 |
76 | 108146 | 95061.358725891 | 13084.641274109 |
77 | 126372 | 127514.993474579 | -1142.993474579 |
78 | 249771 | 123838.026312793 | 125932.973687207 |
79 | 71154 | 90306.0458569506 | -19152.0458569506 |
80 | 71571 | 81548.2141417226 | -9977.21414172256 |
81 | 55918 | 79727.530216048 | -23809.530216048 |
82 | 160141 | 129908.654818141 | 30232.3451818594 |
83 | 38692 | 66004.5879785349 | -27312.5879785349 |
84 | 102812 | 105042.720481724 | -2230.72048172411 |
85 | 56622 | 45338.2516934814 | 11283.7483065186 |
86 | 15986 | 32060.4861665097 | -16074.4861665097 |
87 | 123534 | 119738.567922662 | 3795.43207733847 |
88 | 108535 | 93393.0767342202 | 15141.9232657798 |
89 | 93879 | 121892.061480648 | -28013.0614806476 |
90 | 144551 | 119420.601313879 | 25130.3986861208 |
91 | 56750 | 82253.5981959157 | -25503.5981959157 |
92 | 127654 | 104608.310115226 | 23045.6898847735 |
93 | 65594 | 76106.567480747 | -10512.5674807471 |
94 | 59938 | 82257.2549250543 | -22319.2549250543 |
95 | 146975 | 125014.017119056 | 21960.9828809436 |
96 | 165904 | 129465.564676397 | 36438.4353236028 |
97 | 169265 | 138933.696317271 | 30331.3036827292 |
98 | 183500 | 156189.266757155 | 27310.7332428446 |
99 | 165986 | 174181.583484306 | -8195.58348430622 |
100 | 184923 | 167609.235812352 | 17313.7641876479 |
101 | 140358 | 129289.814408065 | 11068.1855919346 |
102 | 149959 | 148350.732757626 | 1608.26724237419 |
103 | 57224 | 57277.1251201434 | -53.1251201434266 |
104 | 43750 | 43140.6131564593 | 609.386843540694 |
105 | 48029 | 61607.6867976128 | -13578.6867976128 |
106 | 104978 | 129758.348277069 | -24780.3482770688 |
107 | 100046 | 121233.432417949 | -21187.4324179485 |
108 | 101047 | 113126.395133896 | -12079.3951338961 |
109 | 197426 | 119930.124058418 | 77495.8759415824 |
110 | 160902 | 92413.757134752 | 68488.242865248 |
111 | 147172 | 130151.990174772 | 17020.0098252282 |
112 | 109432 | 98350.2607767331 | 11081.7392232669 |
113 | 1168 | 11744.4268822894 | -10576.4268822894 |
114 | 83248 | 102316.085699168 | -19068.0856991677 |
115 | 25162 | 28666.7372151927 | -3504.73721519267 |
116 | 45724 | 69319.6748924629 | -23595.6748924629 |
117 | 110529 | 140515.745706648 | -29986.7457066484 |
118 | 855 | 11719.1205075774 | -10864.1205075774 |
119 | 101382 | 82274.8863796744 | 19107.1136203256 |
120 | 14116 | 22151.5057528272 | -8035.50575282715 |
121 | 89506 | 119183.396213403 | -29677.3962134029 |
122 | 135356 | 106173.295297498 | 29182.7047025022 |
123 | 116066 | 54493.4498912668 | 61572.5501087332 |
124 | 144244 | 81303.3277504436 | 62940.6722495564 |
125 | 8773 | 21668.1940119069 | -12895.1940119069 |
126 | 102153 | 85858.74099612 | 16294.25900388 |
127 | 117440 | 143495.999554349 | -26055.9995543491 |
128 | 104128 | 122452.913446352 | -18324.9134463522 |
129 | 134238 | 144362.218623266 | -10124.2186232664 |
130 | 134047 | 148606.850430257 | -14559.8504302568 |
131 | 279488 | 197507.840435259 | 81980.1595647407 |
132 | 79756 | 111609.657767436 | -31853.6577674365 |
133 | 66089 | 68160.2360002771 | -2071.23600027706 |
134 | 102070 | 95442.8817670392 | 6627.11823296078 |
135 | 146760 | 141331.230799556 | 5428.76920044449 |
136 | 154771 | 50910.4317712199 | 103860.56822878 |
137 | 165933 | 133913.751594381 | 32019.2484056191 |
138 | 64593 | 80939.5445837735 | -16346.5445837735 |
139 | 92280 | 129641.25424569 | -37361.2542456898 |
140 | 67150 | 95623.4779707979 | -28473.4779707979 |
141 | 128692 | 72678.1134091442 | 56013.8865908558 |
142 | 124089 | 98304.0831290266 | 25784.9168709734 |
143 | 125386 | 127895.204833847 | -2509.2048338471 |
144 | 37238 | 27117.4948377255 | 10120.5051622745 |
145 | 140015 | 131235.66328982 | 8779.33671018038 |
146 | 150047 | 108593.546564195 | 41453.4534358048 |
147 | 154451 | 122219.029282234 | 32231.9707177663 |
148 | 156349 | 145439.079820662 | 10909.9201793379 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.517006125361534 | 0.965987749276932 | 0.482993874638466 |
11 | 0.641638067843522 | 0.716723864312956 | 0.358361932156478 |
12 | 0.566984013829031 | 0.866031972341939 | 0.433015986170969 |
13 | 0.435939988691428 | 0.871879977382857 | 0.564060011308572 |
14 | 0.318686577032864 | 0.637373154065728 | 0.681313422967136 |
15 | 0.222360126582016 | 0.444720253164033 | 0.777639873417984 |
16 | 0.159799946392886 | 0.319599892785772 | 0.840200053607114 |
17 | 0.1343085109232 | 0.2686170218464 | 0.8656914890768 |
18 | 0.106683153776339 | 0.213366307552677 | 0.893316846223661 |
19 | 0.0690556835195019 | 0.138111367039004 | 0.930944316480498 |
20 | 0.0771068890392582 | 0.154213778078516 | 0.922893110960742 |
21 | 0.0792839206038001 | 0.1585678412076 | 0.9207160793962 |
22 | 0.0531634179948527 | 0.106326835989705 | 0.946836582005147 |
23 | 0.035514143537813 | 0.071028287075626 | 0.964485856462187 |
24 | 0.0317397793220259 | 0.0634795586440517 | 0.968260220677974 |
25 | 0.0447472517727246 | 0.0894945035454493 | 0.955252748227275 |
26 | 0.0298778641366007 | 0.0597557282732013 | 0.970122135863399 |
27 | 0.0205688524712189 | 0.0411377049424378 | 0.979431147528781 |
28 | 0.0231083367152121 | 0.0462166734304242 | 0.976891663284788 |
29 | 0.019649558391409 | 0.039299116782818 | 0.980350441608591 |
30 | 0.0133807424585667 | 0.0267614849171334 | 0.986619257541433 |
31 | 0.0089923712066662 | 0.0179847424133324 | 0.991007628793334 |
32 | 0.00639952463681201 | 0.012799049273624 | 0.993600475363188 |
33 | 0.00697052060389325 | 0.0139410412077865 | 0.993029479396107 |
34 | 0.0103046104219752 | 0.0206092208439504 | 0.989695389578025 |
35 | 0.00861884651127477 | 0.0172376930225495 | 0.991381153488725 |
36 | 0.00554043608068787 | 0.0110808721613757 | 0.994459563919312 |
37 | 0.00421122000084308 | 0.00842244000168616 | 0.995788779999157 |
38 | 0.00341405050270165 | 0.0068281010054033 | 0.996585949497298 |
39 | 0.00288839743753553 | 0.00577679487507106 | 0.997111602562464 |
40 | 0.00230901332263627 | 0.00461802664527253 | 0.997690986677364 |
41 | 0.00165374674590116 | 0.00330749349180231 | 0.998346253254099 |
42 | 0.00100820371364484 | 0.00201640742728967 | 0.998991796286355 |
43 | 0.000684129326703382 | 0.00136825865340676 | 0.999315870673297 |
44 | 0.000425993105898642 | 0.000851986211797284 | 0.999574006894101 |
45 | 0.000566504265336934 | 0.00113300853067387 | 0.999433495734663 |
46 | 0.00221319583088158 | 0.00442639166176315 | 0.997786804169118 |
47 | 0.00162220538337443 | 0.00324441076674887 | 0.998377794616626 |
48 | 0.00137516487483245 | 0.00275032974966491 | 0.998624835125168 |
49 | 0.00120557457574801 | 0.00241114915149602 | 0.998794425424252 |
50 | 0.000940075418078627 | 0.00188015083615725 | 0.999059924581921 |
51 | 0.000988027227097514 | 0.00197605445419503 | 0.999011972772902 |
52 | 0.000746731670130587 | 0.00149346334026117 | 0.999253268329869 |
53 | 0.000783721151648982 | 0.00156744230329796 | 0.999216278848351 |
54 | 0.000494206961912482 | 0.000988413923824964 | 0.999505793038088 |
55 | 0.00031981065648317 | 0.00063962131296634 | 0.999680189343517 |
56 | 0.000214125288391751 | 0.000428250576783502 | 0.999785874711608 |
57 | 0.000213790387723686 | 0.000427580775447371 | 0.999786209612276 |
58 | 0.000155821212056753 | 0.000311642424113506 | 0.999844178787943 |
59 | 0.000137566674952933 | 0.000275133349905866 | 0.999862433325047 |
60 | 8.70379484732806e-05 | 0.000174075896946561 | 0.999912962051527 |
61 | 5.5011128354494e-05 | 0.000110022256708988 | 0.999944988871646 |
62 | 4.48665804013997e-05 | 8.97331608027994e-05 | 0.999955133419599 |
63 | 2.93675528450876e-05 | 5.87351056901752e-05 | 0.999970632447155 |
64 | 1.72849175908789e-05 | 3.45698351817579e-05 | 0.999982715082409 |
65 | 1.17601441832686e-05 | 2.35202883665371e-05 | 0.999988239855817 |
66 | 1.40632504300407e-05 | 2.81265008600814e-05 | 0.99998593674957 |
67 | 2.04175227519586e-05 | 4.08350455039172e-05 | 0.999979582477248 |
68 | 2.77740332742339e-05 | 5.55480665484679e-05 | 0.999972225966726 |
69 | 1.87407784216182e-05 | 3.74815568432364e-05 | 0.999981259221578 |
70 | 6.84894571451229e-05 | 0.000136978914290246 | 0.999931510542855 |
71 | 5.39573357435921e-05 | 0.000107914671487184 | 0.999946042664256 |
72 | 3.72981643686717e-05 | 7.45963287373433e-05 | 0.999962701835631 |
73 | 3.2709998602275e-05 | 6.54199972045501e-05 | 0.999967290001398 |
74 | 1.96140688987218e-05 | 3.92281377974437e-05 | 0.999980385931101 |
75 | 1.55251325528172e-05 | 3.10502651056344e-05 | 0.999984474867447 |
76 | 9.97692442096015e-06 | 1.99538488419203e-05 | 0.999990023075579 |
77 | 5.72280004127928e-06 | 1.14456000825586e-05 | 0.999994277199959 |
78 | 0.0765398096719202 | 0.15307961934384 | 0.92346019032808 |
79 | 0.0692374282173809 | 0.138474856434762 | 0.930762571782619 |
80 | 0.0568430464599177 | 0.113686092919835 | 0.943156953540082 |
81 | 0.0540066506535953 | 0.108013301307191 | 0.945993349346405 |
82 | 0.0618160029968713 | 0.123632005993743 | 0.938183997003129 |
83 | 0.0655427994018209 | 0.131085598803642 | 0.934457200598179 |
84 | 0.0513639976119863 | 0.102727995223973 | 0.948636002388014 |
85 | 0.0408333341767535 | 0.081666668353507 | 0.959166665823247 |
86 | 0.0334827461784595 | 0.0669654923569189 | 0.966517253821541 |
87 | 0.027538578501445 | 0.0550771570028901 | 0.972461421498555 |
88 | 0.0232659377588611 | 0.0465318755177222 | 0.976734062241139 |
89 | 0.0229176324652095 | 0.0458352649304189 | 0.97708236753479 |
90 | 0.0228092579236333 | 0.0456185158472666 | 0.977190742076367 |
91 | 0.0219086695373247 | 0.0438173390746495 | 0.978091330462675 |
92 | 0.0201803634241213 | 0.0403607268482426 | 0.979819636575879 |
93 | 0.0161342599785505 | 0.032268519957101 | 0.983865740021449 |
94 | 0.0151887108601315 | 0.030377421720263 | 0.984811289139868 |
95 | 0.0133184840407222 | 0.0266369680814445 | 0.986681515959278 |
96 | 0.0150928827856892 | 0.0301857655713784 | 0.984907117214311 |
97 | 0.0149589243254452 | 0.0299178486508903 | 0.985041075674555 |
98 | 0.0140544649229212 | 0.0281089298458424 | 0.985945535077079 |
99 | 0.0118809923442276 | 0.0237619846884553 | 0.988119007655772 |
100 | 0.0122855241125108 | 0.0245710482250216 | 0.987714475887489 |
101 | 0.00917535602222119 | 0.0183507120444424 | 0.990824643977779 |
102 | 0.00641057734255434 | 0.0128211546851087 | 0.993589422657446 |
103 | 0.00440402455547924 | 0.00880804911095848 | 0.995595975444521 |
104 | 0.00304905385958126 | 0.00609810771916253 | 0.996950946140419 |
105 | 0.00218646362513382 | 0.00437292725026763 | 0.997813536374866 |
106 | 0.00185780151638843 | 0.00371560303277686 | 0.998142198483612 |
107 | 0.00175804941842704 | 0.00351609883685408 | 0.998241950581573 |
108 | 0.00130910215120066 | 0.00261820430240132 | 0.998690897848799 |
109 | 0.010236314998013 | 0.020472629996026 | 0.989763685001987 |
110 | 0.0326042494527923 | 0.0652084989055846 | 0.967395750547208 |
111 | 0.0266767326603244 | 0.0533534653206488 | 0.973323267339676 |
112 | 0.0194369359646746 | 0.0388738719293492 | 0.980563064035325 |
113 | 0.0139016713000778 | 0.0278033426001556 | 0.986098328699922 |
114 | 0.0115478610152805 | 0.0230957220305611 | 0.98845213898472 |
115 | 0.00783186226843142 | 0.0156637245368628 | 0.992168137731569 |
116 | 0.0133292862548152 | 0.0266585725096304 | 0.986670713745185 |
117 | 0.0115121134294839 | 0.0230242268589679 | 0.988487886570516 |
118 | 0.00789136076262145 | 0.0157827215252429 | 0.992108639237379 |
119 | 0.00622986587303376 | 0.0124597317460675 | 0.993770134126966 |
120 | 0.00407590544355298 | 0.00815181088710597 | 0.995924094556447 |
121 | 0.00457997737813602 | 0.00915995475627205 | 0.995420022621864 |
122 | 0.00350064038023069 | 0.00700128076046138 | 0.996499359619769 |
123 | 0.00598373698376544 | 0.0119674739675309 | 0.994016263016235 |
124 | 0.0175847139272834 | 0.0351694278545668 | 0.982415286072717 |
125 | 0.0115573850435304 | 0.0231147700870608 | 0.98844261495647 |
126 | 0.00750197118839318 | 0.0150039423767864 | 0.992498028811607 |
127 | 0.00811707835393373 | 0.0162341567078675 | 0.991882921646066 |
128 | 0.0171968458792253 | 0.0343936917584507 | 0.982803154120775 |
129 | 0.026719156220291 | 0.0534383124405819 | 0.973280843779709 |
130 | 0.0183433513285805 | 0.036686702657161 | 0.98165664867142 |
131 | 0.129474916816588 | 0.258949833633175 | 0.870525083183412 |
132 | 0.11014767226742 | 0.220295344534839 | 0.88985232773258 |
133 | 0.0761007515988342 | 0.152201503197668 | 0.923899248401166 |
134 | 0.126702842506185 | 0.25340568501237 | 0.873297157493815 |
135 | 0.0802313451709942 | 0.160462690341988 | 0.919768654829006 |
136 | 0.600751218188471 | 0.798497563623059 | 0.399248781811529 |
137 | 0.458681472789013 | 0.917362945578025 | 0.541318527210987 |
138 | 0.304421344280816 | 0.608842688561632 | 0.695578655719184 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 50 | 0.387596899224806 | NOK |
5% type I error level | 91 | 0.705426356589147 | NOK |
10% type I error level | 101 | 0.782945736434108 | NOK |