Multiple Linear Regression - Estimated Regression Equation |
Y[t] = + 6115.58568755992 + 715.087147974851X1[t] + 856.154686534896X2[t] + 198.22582540084X3[t] + 0.459192074858798X4[t] + 2.79279819005493X5[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) | 6115.58568755992 | 7508.320188 | 0.8145 | 0.416757 | 0.208379 |
X1 | 715.087147974851 | 124.47306 | 5.7449 | 0 | 0 |
X2 | 856.154686534896 | 468.854031 | 1.8261 | 0.070003 | 0.035002 |
X3 | 198.22582540084 | 75.04617 | 2.6414 | 0.009209 | 0.004605 |
X4 | 0.459192074858798 | 0.178951 | 2.566 | 0.011354 | 0.005677 |
X5 | 2.79279819005493 | 0.832169 | 3.356 | 0.001022 | 0.000511 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.86406719386569 |
R-squared | 0.746612115514928 |
Adjusted R-squared | 0.73743139506257 |
F-TEST (value) | 81.3239134542205 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 138 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 34805.7767349601 |
Sum Squared Residuals | 167179008989.096 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 449290 | 406352.67847105 | 42937.3215289504 |
2 | 312831 | 210174.171216254 | 102656.828783746 |
3 | 275326 | 192919.827891711 | 82406.1721082885 |
4 | 266451 | 179319.545205099 | 87131.454794901 |
5 | 244190 | 126132.504700903 | 118057.495299097 |
6 | 233497 | 205092.532465537 | 28404.4675344634 |
7 | 229437 | 140281.632284036 | 89155.3677159637 |
8 | 221399 | 230181.798765078 | -8782.79876507783 |
9 | 218900 | 301244.136699301 | -82344.136699301 |
10 | 215480 | 211203.663262346 | 4276.33673765381 |
11 | 214975 | 209906.42015276 | 5068.57984723967 |
12 | 204812 | 157597.205438396 | 47214.7945616043 |
13 | 200652 | 208003.457900403 | -7351.45790040288 |
14 | 200609 | 137002.511702702 | 63606.4882972978 |
15 | 191923 | 129133.368706343 | 62789.6312936565 |
16 | 191463 | 207957.050260456 | -16494.050260456 |
17 | 189007 | 167311.78307692 | 21695.21692308 |
18 | 186704 | 123040.960711163 | 63663.0392888368 |
19 | 184024 | 133658.870464835 | 50365.1295351653 |
20 | 183873 | 168039.111715287 | 15833.8882847126 |
21 | 182328 | 153823.532418144 | 28504.4675818556 |
22 | 178613 | 190412.764945678 | -11799.7649456784 |
23 | 178228 | 153702.815825366 | 24525.1841746343 |
24 | 176034 | 127048.909911865 | 48985.0900881346 |
25 | 174876 | 123562.99241866 | 51313.0075813399 |
26 | 174181 | 222512.952356736 | -48331.9523567356 |
27 | 173779 | 202126.759122944 | -28347.7591229442 |
28 | 172071 | 181127.8237015 | -9056.82370149983 |
29 | 168465 | 119202.165898953 | 49262.8341010474 |
30 | 166226 | 159929.262235304 | 6296.73776469637 |
31 | 164516 | 118763.513835361 | 45752.4861646386 |
32 | 161553 | 137099.681765152 | 24453.3182348479 |
33 | 156916 | 130628.107182068 | 26287.8928179323 |
34 | 155934 | 159371.746796417 | -3437.74679641721 |
35 | 154806 | 109372.879776662 | 45433.1202233383 |
36 | 153278 | 119283.788473821 | 33994.2115261793 |
37 | 152455 | 136027.984471802 | 16427.0155281979 |
38 | 151621 | 117098.648322558 | 34522.3516774417 |
39 | 150416 | 118465.268876776 | 31950.7311232245 |
40 | 148950 | 117880.61633397 | 31069.3836660297 |
41 | 148531 | 89117.8387535077 | 59413.1612464923 |
42 | 147766 | 151710.535490323 | -3944.5354903234 |
43 | 146552 | 150328.837085743 | -3776.83708574315 |
44 | 146020 | 134939.392802408 | 11080.6071975919 |
45 | 144677 | 137933.817440418 | 6743.18255958247 |
46 | 144193 | 174637.411051241 | -30444.4110512414 |
47 | 143910 | 122291.096332011 | 21618.9036679889 |
48 | 143546 | 120853.151463579 | 22692.8485364209 |
49 | 141868 | 123556.648933614 | 18311.3510663862 |
50 | 140935 | 93866.0505967364 | 47068.9494032636 |
51 | 140303 | 169711.603861433 | -29408.6038614331 |
52 | 139901 | 149819.467697954 | -9918.46769795387 |
53 | 139780 | 107739.983115081 | 32040.0168849187 |
54 | 139075 | 164344.777840386 | -25269.7778403863 |
55 | 136333 | 171115.620741584 | -34782.6207415835 |
56 | 136220 | 113226.963810552 | 22993.0361894485 |
57 | 134379 | 125022.780978938 | 9356.2190210625 |
58 | 134153 | 194100.911378332 | -59947.9113783316 |
59 | 131263 | 133616.523992446 | -2353.52399244575 |
60 | 130414 | 134898.665999024 | -4484.66599902423 |
61 | 129419 | 179625.441437799 | -50206.4414377991 |
62 | 128907 | 144060.610072711 | -15153.6100727107 |
63 | 126905 | 137913.333710213 | -11008.3337102134 |
64 | 126602 | 149240.444161632 | -22638.4441616316 |
65 | 125760 | 110112.326371904 | 15647.6736280964 |
66 | 125728 | 137621.715790978 | -11893.7157909775 |
67 | 124626 | 118687.683558707 | 5938.31644129293 |
68 | 124401 | 102583.864552865 | 21817.1354471355 |
69 | 122294 | 191594.423632718 | -69300.4236327181 |
70 | 122259 | 160527.239940012 | -38268.2399400115 |
71 | 121593 | 154855.162137596 | -33262.1621375959 |
72 | 121391 | 115523.579645201 | 5867.42035479895 |
73 | 120414 | 160194.348130077 | -39780.3481300773 |
74 | 120111 | 124035.830993694 | -3924.8309936943 |
75 | 119070 | 99955.1766113552 | 19114.8233886448 |
76 | 115944 | 111844.74399166 | 4099.25600834002 |
77 | 115572 | 132327.216919172 | -16755.2169191715 |
78 | 115343 | 135620.881484266 | -20277.8814842657 |
79 | 113870 | 126621.289709813 | -12751.2897098129 |
80 | 113245 | 100290.322145925 | 12954.6778540753 |
81 | 111940 | 129982.985136186 | -18042.9851361859 |
82 | 111924 | 108690.169993257 | 3233.83000674272 |
83 | 109807 | 121540.873301169 | -11733.8733011694 |
84 | 108685 | 86164.370670475 | 22520.629329525 |
85 | 106742 | 114159.849250696 | -7417.84925069588 |
86 | 104972 | 113948.517866818 | -8976.51786681784 |
87 | 102378 | 125974.531091834 | -23596.5310918338 |
88 | 102194 | 92385.7620821462 | 9808.23791785375 |
89 | 102141 | 123701.63541268 | -21560.6354126803 |
90 | 101560 | 103808.20075725 | -2248.20075724979 |
91 | 100798 | 103930.274004462 | -3132.27400446194 |
92 | 98629 | 132708.889457318 | -34079.8894573181 |
93 | 97181 | 118105.350442274 | -20924.3504422743 |
94 | 95704 | 123190.010422038 | -27486.0104220383 |
95 | 95276 | 140615.618408613 | -45339.6184086132 |
96 | 94982 | 108128.010089754 | -13146.010089754 |
97 | 94341 | 106541.127893073 | -12200.1278930733 |
98 | 94332 | 117797.901899112 | -23465.9018991121 |
99 | 94127 | 81369.9893244889 | 12757.0106755111 |
100 | 93107 | 113416.115393032 | -20309.1153930322 |
101 | 90385 | 118177.482537727 | -27792.4825377269 |
102 | 89920 | 52936.1005400421 | 36983.8994599579 |
103 | 88874 | 82457.5193083283 | 6416.48069167167 |
104 | 86249 | 139622.840278837 | -53373.8402788368 |
105 | 85610 | 135934.247817767 | -50324.2478177671 |
106 | 84971 | 151955.07416493 | -66984.0741649305 |
107 | 84315 | 95880.0896138218 | -11565.0896138218 |
108 | 82209 | 136736.301212771 | -54527.3012127709 |
109 | 81293 | 99195.6255363624 | -17902.6255363624 |
110 | 80420 | 144188.36855618 | -63768.3685561799 |
111 | 72904 | 67995.9878169228 | 4908.01218307721 |
112 | 72559 | 91787.6639863725 | -19228.6639863725 |
113 | 71921 | 90422.3383848073 | -18501.3383848073 |
114 | 71894 | 100097.94192992 | -28203.9419299204 |
115 | 64149 | 76807.9084168091 | -12658.9084168091 |
116 | 63952 | 58916.1390549769 | 5035.86094502312 |
117 | 60373 | 66274.1289668758 | -5901.12896687575 |
118 | 60138 | 79035.2639174511 | -18897.2639174511 |
119 | 58280 | 79166.6712190745 | -20886.6712190745 |
120 | 56252 | 72465.3050467325 | -16213.3050467325 |
121 | 52197 | 77791.2863917276 | -25594.2863917276 |
122 | 51201 | 33751.792409179 | 17449.207590821 |
123 | 50913 | 82254.6165644365 | -31341.6165644365 |
124 | 49176 | 93018.4200590576 | -43842.4200590576 |
125 | 48188 | 68439.3523747446 | -20251.3523747446 |
126 | 43410 | 34334.8075388124 | 9075.19246118761 |
127 | 40248 | 32385.5371177495 | 7862.4628822505 |
128 | 31970 | 48242.1958734775 | -16272.1958734775 |
129 | 27918 | 83683.5172164147 | -55765.5172164147 |
130 | 27676 | 51381.7423827482 | -23705.7423827482 |
131 | 19764 | 29563.9047607044 | -9799.90476070436 |
132 | 19349 | 22509.8660397638 | -3160.86603976378 |
133 | 11796 | 18624.6475512218 | -6828.64755122182 |
134 | 10674 | 13938.9507971394 | -3264.95079713944 |
135 | 8812 | 24935.4351538551 | -16123.4351538551 |
136 | 7215 | 21522.8678076353 | -14307.8678076352 |
137 | 7131 | 8975.9342794593 | -1844.93427945931 |
138 | 6836 | 10108.1309450236 | -3272.13094502355 |
139 | 5118 | 8459.0729568853 | -3341.0729568853 |
140 | 3616 | 10682.1505544384 | -7066.15055443835 |
141 | 0 | 6830.67283553475 | -6830.67283553475 |
142 | 0 | 6115.5856875599 | -6115.5856875599 |
143 | 0 | 6115.5856875599 | -6115.5856875599 |
144 | 0 | 6115.5856875599 | -6115.5856875599 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.0493938304898398 | 0.0987876609796797 | 0.95060616951016 |
10 | 0.117178537168504 | 0.234357074337008 | 0.882821462831496 |
11 | 0.935149426900283 | 0.129701146199434 | 0.0648505730997172 |
12 | 0.902246887802773 | 0.195506224394454 | 0.0977531121972271 |
13 | 0.847647910249879 | 0.304704179500242 | 0.152352089750121 |
14 | 0.808396181170485 | 0.38320763765903 | 0.191603818829515 |
15 | 0.774100950852723 | 0.451798098294554 | 0.225899049147277 |
16 | 0.972294606978336 | 0.0554107860433285 | 0.0277053930216642 |
17 | 0.964091163873044 | 0.071817672253912 | 0.035908836126956 |
18 | 0.968472324504632 | 0.0630553509907352 | 0.0315276754953676 |
19 | 0.96581982427461 | 0.0683603514507813 | 0.0341801757253907 |
20 | 0.96740008533563 | 0.0651998293287411 | 0.0325999146643705 |
21 | 0.993491766636405 | 0.0130164667271908 | 0.00650823336359542 |
22 | 0.99697678968241 | 0.00604642063518044 | 0.00302321031759022 |
23 | 0.996695386511515 | 0.00660922697697067 | 0.00330461348848534 |
24 | 0.997266698925598 | 0.00546660214880411 | 0.00273330107440206 |
25 | 0.997065985050933 | 0.00586802989813465 | 0.00293401494906732 |
26 | 0.998872380640977 | 0.00225523871804619 | 0.00112761935902309 |
27 | 0.99904246804441 | 0.00191506391118126 | 0.000957531955590632 |
28 | 0.998536990786766 | 0.00292601842646695 | 0.00146300921323347 |
29 | 0.998707246001247 | 0.00258550799750562 | 0.00129275399875281 |
30 | 0.999148235875677 | 0.00170352824864675 | 0.000851764124323377 |
31 | 0.999291657973423 | 0.00141668405315368 | 0.000708342026576838 |
32 | 0.99972766663702 | 0.000544666725961135 | 0.000272333362980567 |
33 | 0.999681162987284 | 0.00063767402543152 | 0.00031883701271576 |
34 | 0.999592910117074 | 0.00081417976585159 | 0.000407089882925795 |
35 | 0.999676722994733 | 0.000646554010534903 | 0.000323277005267451 |
36 | 0.999832293018503 | 0.000335413962993168 | 0.000167706981496584 |
37 | 0.999826174637518 | 0.000347650724963343 | 0.000173825362481671 |
38 | 0.999837009682472 | 0.000325980635056415 | 0.000162990317528207 |
39 | 0.999832480668425 | 0.000335038663149611 | 0.000167519331574805 |
40 | 0.999855266787209 | 0.00028946642558239 | 0.000144733212791195 |
41 | 0.999946014030762 | 0.000107971938476905 | 5.39859692384523e-05 |
42 | 0.99992816274244 | 0.000143674515120822 | 7.1837257560411e-05 |
43 | 0.99993343660168 | 0.000133126796639191 | 6.65633983195957e-05 |
44 | 0.999917185656 | 0.000165628688000424 | 8.28143440002122e-05 |
45 | 0.9999617084482 | 7.65831036004955e-05 | 3.82915518002477e-05 |
46 | 0.999992288183763 | 1.5423632473727e-05 | 7.71181623686348e-06 |
47 | 0.9999938783653 | 1.22432693999632e-05 | 6.12163469998159e-06 |
48 | 0.999995521158122 | 8.95768375518852e-06 | 4.47884187759426e-06 |
49 | 0.999996099476026 | 7.8010479474087e-06 | 3.90052397370435e-06 |
50 | 0.999999026485944 | 1.9470281113705e-06 | 9.73514055685248e-07 |
51 | 0.999999489089172 | 1.02182165626493e-06 | 5.10910828132466e-07 |
52 | 0.99999944788989 | 1.10422022118798e-06 | 5.52110110593988e-07 |
53 | 0.999999753049355 | 4.93901290727007e-07 | 2.46950645363504e-07 |
54 | 0.999999864679204 | 2.70641591743679e-07 | 1.3532079587184e-07 |
55 | 0.9999999027014 | 1.94597198741146e-07 | 9.72985993705732e-08 |
56 | 0.99999994800403 | 1.03991940396972e-07 | 5.19959701984862e-08 |
57 | 0.99999995573867 | 8.85226587350042e-08 | 4.42613293675021e-08 |
58 | 0.999999988355976 | 2.32880484461963e-08 | 1.16440242230981e-08 |
59 | 0.999999992529457 | 1.49410854102197e-08 | 7.47054270510987e-09 |
60 | 0.999999989144474 | 2.1711051737473e-08 | 1.08555258687365e-08 |
61 | 0.999999995039404 | 9.92119190633695e-09 | 4.96059595316848e-09 |
62 | 0.999999993139962 | 1.37200761105279e-08 | 6.86003805526397e-09 |
63 | 0.99999998970915 | 2.05816971298635e-08 | 1.02908485649317e-08 |
64 | 0.99999998337886 | 3.32422779774463e-08 | 1.66211389887232e-08 |
65 | 0.99999998746227 | 2.50754608267686e-08 | 1.25377304133843e-08 |
66 | 0.999999978962166 | 4.20756675572446e-08 | 2.10378337786223e-08 |
67 | 0.99999998697684 | 2.60463188343318e-08 | 1.30231594171659e-08 |
68 | 0.999999993270649 | 1.34587022185736e-08 | 6.72935110928682e-09 |
69 | 0.99999999839705 | 3.2058975044392e-09 | 1.6029487522196e-09 |
70 | 0.999999998227399 | 3.54520232809263e-09 | 1.77260116404631e-09 |
71 | 0.999999997895745 | 4.20850922076518e-09 | 2.10425461038259e-09 |
72 | 0.999999997224644 | 5.55071236051496e-09 | 2.77535618025748e-09 |
73 | 0.999999998080102 | 3.83979594669382e-09 | 1.91989797334691e-09 |
74 | 0.999999997335761 | 5.3284777718181e-09 | 2.66423888590905e-09 |
75 | 0.999999998774758 | 2.4504835889685e-09 | 1.22524179448425e-09 |
76 | 0.999999998695688 | 2.60862416698474e-09 | 1.30431208349237e-09 |
77 | 0.999999998020885 | 3.95823077110239e-09 | 1.9791153855512e-09 |
78 | 0.999999997442304 | 5.11539204016737e-09 | 2.55769602008369e-09 |
79 | 0.99999999639369 | 7.21261939996434e-09 | 3.60630969998217e-09 |
80 | 0.999999997732215 | 4.53557058216728e-09 | 2.26778529108364e-09 |
81 | 0.999999996691787 | 6.61642554454069e-09 | 3.30821277227034e-09 |
82 | 0.99999999667473 | 6.65054008566215e-09 | 3.32527004283107e-09 |
83 | 0.99999999556178 | 8.87644099965172e-09 | 4.43822049982586e-09 |
84 | 0.9999999982748 | 3.45040075127241e-09 | 1.7252003756362e-09 |
85 | 0.999999998147974 | 3.70405095790591e-09 | 1.85202547895295e-09 |
86 | 0.999999998441582 | 3.11683512940069e-09 | 1.55841756470035e-09 |
87 | 0.999999997673495 | 4.65300900801243e-09 | 2.32650450400621e-09 |
88 | 0.99999999848278 | 3.03444187799141e-09 | 1.51722093899571e-09 |
89 | 0.99999999778811 | 4.42378165688185e-09 | 2.21189082844093e-09 |
90 | 0.999999997729976 | 4.54004785084065e-09 | 2.27002392542032e-09 |
91 | 0.999999997722091 | 4.55581701053341e-09 | 2.27790850526671e-09 |
92 | 0.999999996251043 | 7.49791401146833e-09 | 3.74895700573416e-09 |
93 | 0.99999999232554 | 1.53489195680674e-08 | 7.67445978403372e-09 |
94 | 0.999999988483384 | 2.30332326993523e-08 | 1.15166163496762e-08 |
95 | 0.999999982404583 | 3.51908349646145e-08 | 1.75954174823072e-08 |
96 | 0.999999974674304 | 5.06513923044599e-08 | 2.532569615223e-08 |
97 | 0.99999996497213 | 7.00557383006526e-08 | 3.50278691503263e-08 |
98 | 0.999999955320652 | 8.93586961484828e-08 | 4.46793480742414e-08 |
99 | 0.999999987206917 | 2.5586166978983e-08 | 1.27930834894915e-08 |
100 | 0.999999980821581 | 3.83568373023657e-08 | 1.91784186511829e-08 |
101 | 0.99999996987523 | 6.02495383743203e-08 | 3.01247691871601e-08 |
102 | 0.999999999423566 | 1.15286809565699e-09 | 5.76434047828496e-10 |
103 | 0.999999999910809 | 1.78382414320985e-10 | 8.91912071604923e-11 |
104 | 0.999999999839369 | 3.21261703046093e-10 | 1.60630851523046e-10 |
105 | 0.999999999698381 | 6.03238147063515e-10 | 3.01619073531758e-10 |
106 | 0.999999999755828 | 4.88343539168655e-10 | 2.44171769584327e-10 |
107 | 0.999999999832395 | 3.35209488140964e-10 | 1.67604744070482e-10 |
108 | 0.99999999991025 | 1.7949877137707e-10 | 8.97493856885348e-11 |
109 | 0.999999999862136 | 2.75728424675346e-10 | 1.37864212337673e-10 |
110 | 0.999999999923288 | 1.5342406432626e-10 | 7.67120321631299e-11 |
111 | 0.9999999999538 | 9.24014189053486e-11 | 4.62007094526743e-11 |
112 | 0.999999999888627 | 2.227462403506e-10 | 1.113731201753e-10 |
113 | 0.999999999596502 | 8.06996229806778e-10 | 4.03498114903389e-10 |
114 | 0.999999998696446 | 2.60710710879634e-09 | 1.30355355439817e-09 |
115 | 0.999999996102225 | 7.7955492415273e-09 | 3.89777462076365e-09 |
116 | 0.999999997077401 | 5.84519797849753e-09 | 2.92259898924876e-09 |
117 | 0.999999998881817 | 2.23636688214627e-09 | 1.11818344107314e-09 |
118 | 0.999999995669732 | 8.66053688002638e-09 | 4.33026844001319e-09 |
119 | 0.999999995046486 | 9.90702741712456e-09 | 4.95351370856228e-09 |
120 | 0.999999990509639 | 1.89807222914835e-08 | 9.49036114574177e-09 |
121 | 0.99999998901218 | 2.19756403076599e-08 | 1.098782015383e-08 |
122 | 0.999999998388219 | 3.22356143962774e-09 | 1.61178071981387e-09 |
123 | 0.999999992900778 | 1.41984431920546e-08 | 7.0992215960273e-09 |
124 | 0.999999967320622 | 6.53587555085298e-08 | 3.26793777542649e-08 |
125 | 0.999999991720022 | 1.65599552786832e-08 | 8.27997763934162e-09 |
126 | 0.999999950041137 | 9.9917725621213e-08 | 4.99588628106065e-08 |
127 | 0.999999999232195 | 1.53561003182648e-09 | 7.67805015913239e-10 |
128 | 0.999999999119648 | 1.76070358416347e-09 | 8.80351792081736e-10 |
129 | 0.999999997826184 | 4.34763158414746e-09 | 2.17381579207373e-09 |
130 | 0.99999998247144 | 3.50571196447879e-08 | 1.75285598223939e-08 |
131 | 0.999999980562431 | 3.88751373722571e-08 | 1.94375686861285e-08 |
132 | 0.999999998680956 | 2.63808843020681e-09 | 1.31904421510341e-09 |
133 | 0.999999968088405 | 6.38231898538563e-08 | 3.19115949269282e-08 |
134 | 0.999999073569552 | 1.85286089551851e-06 | 9.26430447759257e-07 |
135 | 0.999962145916213 | 7.57081675729881e-05 | 3.78540837864941e-05 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 114 | 0.89763779527559 | NOK |
5% type I error level | 115 | 0.905511811023622 | NOK |
10% type I error level | 121 | 0.95275590551181 | NOK |