Multiple Linear Regression - Estimated Regression Equation |
Y_t[t] = + 543.179209911223 + 1.16860440434678X_1t[t] + 1.83917635776336X_2t[t] + 1.21611151450579X_3t[t] + 1.02513487046208X_4t[t] -3.36894732142928t + 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) | 543.179209911223 | 196.29568 | 2.7671 | 0.006431 | 0.003215 |
X_1t | 1.16860440434678 | 0.074693 | 15.6455 | 0 | 0 |
X_2t | 1.83917635776336 | 0.107896 | 17.0459 | 0 | 0 |
X_3t | 1.21611151450579 | 0.041056 | 29.6211 | 0 | 0 |
X_4t | 1.02513487046208 | 0.046665 | 21.9681 | 0 | 0 |
t | -3.36894732142928 | 0.510045 | -6.6052 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.995896303894516 |
R-squared | 0.991809448110757 |
Adjusted R-squared | 0.991512688984335 |
F-TEST (value) | 3342.13629777612 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 138 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 81.9500414576458 |
Sum Squared Residuals | 926781.682697561 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 14915 | 14916.2680887553 | -1.2680887552735 |
2 | 11773 | 11857.0264700271 | -84.0264700271269 |
3 | 11608 | 11755.1567365281 | -147.15673652815 |
4 | 11468 | 11602.7374451341 | -134.737445134088 |
5 | 11511 | 11543.1558489896 | -32.1558489895916 |
6 | 11200 | 11249.7412139574 | -49.741213957414 |
7 | 11164 | 11252.1355839829 | -88.1355839828744 |
8 | 10960 | 11044.6904098699 | -84.6904098699172 |
9 | 10667 | 10781.6492191359 | -114.649219135902 |
10 | 11556 | 11712.3647835678 | -156.364783567842 |
11 | 11372 | 11480.1265667893 | -108.126566789294 |
12 | 12333 | 12027.6937412484 | 305.306258751603 |
13 | 13102 | 12949.2289955163 | 152.771004483703 |
14 | 11115 | 11076.3715220077 | 38.6284779923386 |
15 | 12572 | 12578.0686357972 | -6.0686357971692 |
16 | 11557 | 11559.5381615317 | -2.53816153169688 |
17 | 12059 | 12088.1691339455 | -29.1691339454685 |
18 | 11420 | 11410.7570843935 | 9.24291560648886 |
19 | 11185 | 11013.8260201519 | 171.173979848139 |
20 | 11113 | 10893.4260179672 | 219.573982032771 |
21 | 10706 | 10502.6115344097 | 203.388465590252 |
22 | 11523 | 11387.6138780156 | 135.38612198438 |
23 | 11391 | 11267.3770489365 | 123.622951063472 |
24 | 12634 | 12378.4289443979 | 255.57105560206 |
25 | 13469 | 13278.4080682729 | 190.591931727137 |
26 | 11735 | 11669.1743838601 | 65.8256161398678 |
27 | 13281 | 13223.2327128968 | 57.7672871031933 |
28 | 11968 | 12033.8878233498 | -65.8878233498179 |
29 | 11623 | 11623.6218378726 | -0.621837872594722 |
30 | 11084 | 11147.3631208461 | -63.3631208460878 |
31 | 11509 | 11451.2178575436 | 57.7821424564428 |
32 | 11134 | 11247.7411691982 | -113.74116919818 |
33 | 10438 | 10383.1535342963 | 54.8464657037024 |
34 | 11530 | 11574.787623508 | -44.7876235080021 |
35 | 11491 | 11478.124800932 | 12.8751990680394 |
36 | 13093 | 13088.2507911424 | 4.74920885761829 |
37 | 13106 | 13064.3052289821 | 41.6947710178924 |
38 | 11305 | 11375.1012162013 | -70.1012162013339 |
39 | 13113 | 13144.6294495056 | -31.6294495056006 |
40 | 12203 | 12150.5495410625 | 52.4504589375398 |
41 | 11309 | 11427.3885038344 | -118.388503834381 |
42 | 11088 | 11084.4053340255 | 3.59466597448785 |
43 | 11234 | 11140.6474343226 | 93.3525656774188 |
44 | 11619 | 11539.926518727 | 79.0734812730107 |
45 | 10942 | 10957.173178101 | -15.1731781009696 |
46 | 11445 | 11386.5611637318 | 58.4388362682217 |
47 | 11291 | 11363.0807557447 | -72.0807557447392 |
48 | 13281 | 13271.1359386931 | 9.86406130689028 |
49 | 13726 | 13724.7260443517 | 1.2739556483387 |
50 | 11300 | 11318.8132103628 | -18.8132103627832 |
51 | 11983 | 12021.8743749971 | -38.8743749970956 |
52 | 11092 | 11141.055109203 | -49.0551092029949 |
53 | 11093 | 11214.5001257251 | -121.500125725083 |
54 | 10692 | 10863.4400772341 | -171.440077234077 |
55 | 10786 | 10817.7201363308 | -31.7201363307651 |
56 | 11166 | 11202.1666911467 | -36.166691146726 |
57 | 10553 | 10587.1952876145 | -34.1952876145317 |
58 | 11103 | 11106.4564644271 | -3.45646442706535 |
59 | 10969 | 11016.4263952093 | -47.4263952093036 |
60 | 12090 | 12075.6593062269 | 14.3406937730788 |
61 | 12544 | 12582.4409066394 | -38.4409066394401 |
62 | 12264 | 12279.0392193146 | -15.0392193145671 |
63 | 13783 | 13933.3853226723 | -150.385322672287 |
64 | 11214 | 11267.6757683801 | -53.6757683800812 |
65 | 11453 | 11416.0339157845 | 36.9660842154957 |
66 | 10883 | 10946.8160072616 | -63.8160072615728 |
67 | 10381 | 10356.8888576417 | 24.1111423583492 |
68 | 10348 | 10311.9958382015 | 36.0041617985144 |
69 | 10024 | 9965.97979296767 | 58.0202070323282 |
70 | 10805 | 10824.7928928887 | -19.7928928887295 |
71 | 10796 | 10894.9456600143 | -98.945660014263 |
72 | 11907 | 11998.2528062645 | -91.2528062645424 |
73 | 12261 | 12205.0577223929 | 55.9422776070702 |
74 | 11377 | 11411.5811190114 | -34.5811190113686 |
75 | 12689 | 12678.4901782589 | 10.509821741095 |
76 | 11474 | 11580.7151318706 | -106.715131870618 |
77 | 10992 | 10975.3549117938 | 16.6450882061717 |
78 | 10764 | 10844.2334924165 | -80.2334924165347 |
79 | 12164 | 12169.6712605155 | -5.67126051547433 |
80 | 10409 | 10254.1406064621 | 154.859393537863 |
81 | 10398 | 10383.5682088576 | 14.4317911424124 |
82 | 10349 | 10455.0245448773 | -106.024544877268 |
83 | 10865 | 10861.3404356471 | 3.65956435293107 |
84 | 11630 | 11650.7475242053 | -20.7475242052648 |
85 | 12221 | 12239.441035063 | -18.441035063015 |
86 | 10884 | 10931.9936345979 | -47.9936345978577 |
87 | 12019 | 11955.2094030185 | 63.790596981476 |
88 | 11021 | 11105.7646202771 | -84.7646202771221 |
89 | 10799 | 10801.8286731016 | -2.82867310157428 |
90 | 10423 | 10492.8009888879 | -69.8009888879449 |
91 | 10484 | 10425.3905770331 | 58.6094229668937 |
92 | 10450 | 10458.5938440908 | -8.59384409084922 |
93 | 9906 | 9902.01488509032 | 3.9851149096803 |
94 | 11049 | 11005.3799222459 | 43.6200777541166 |
95 | 11281 | 11284.9303789549 | -3.9303789549026 |
96 | 12485 | 12512.2888027185 | -27.2888027184667 |
97 | 12849 | 12796.8974913906 | 52.1025086093708 |
98 | 11380 | 11443.4698585758 | -63.4698585757659 |
99 | 12079 | 12066.4956575347 | 12.5043424652911 |
100 | 11366 | 11397.3666909499 | -31.3666909498944 |
101 | 11328 | 11315.3565193778 | 12.643480622186 |
102 | 10444 | 10480.3230962593 | -36.3230962593505 |
103 | 10854 | 10736.8355765072 | 117.164423492774 |
104 | 10434 | 10355.7127062058 | 78.2872937942147 |
105 | 10137 | 10204.7446952981 | -67.7446952980938 |
106 | 10992 | 11010.5214424436 | -18.5214424436253 |
107 | 10906 | 10942.7122512628 | -36.7122512627499 |
108 | 12367 | 12351.2337468288 | 15.7662531712066 |
109 | 14371 | 14372.9851966995 | -1.98519669953394 |
110 | 11695 | 11653.373617447 | 41.6263825530174 |
111 | 11546 | 11546.173750331 | -0.173750331042818 |
112 | 10922 | 10954.0835785842 | -32.0835785841988 |
113 | 10670 | 10701.6693920559 | -31.6693920559257 |
114 | 10254 | 10251.2467324309 | 2.75326756909892 |
115 | 10573 | 10562.7280242342 | 10.2719757658242 |
116 | 10239 | 10274.5957296726 | -35.5957296726312 |
117 | 10253 | 10198.3184584151 | 54.681541584866 |
118 | 11176 | 11237.5564115563 | -61.5564115562869 |
119 | 10719 | 10697.2697970635 | 21.7302029365275 |
120 | 11817 | 11871.3049325007 | -54.3049325006818 |
121 | 12487 | 12498.2085249836 | -11.208524983599 |
122 | 11519 | 11528.043457392 | -9.04345739204921 |
123 | 12025 | 11990.4951402514 | 34.5048597486472 |
124 | 10976 | 10797.7091809859 | 178.290819014091 |
125 | 11276 | 11109.6459615189 | 166.354038481074 |
126 | 10657 | 10665.848875379 | -8.84887537898897 |
127 | 11141 | 11099.761447865 | 41.2385521350101 |
128 | 10423 | 10406.7424534961 | 16.2575465039248 |
129 | 10640 | 10555.6698269802 | 84.3301730198412 |
130 | 11426 | 11466.8892797423 | -40.8892797423077 |
131 | 10948 | 10925.1388108614 | 22.8611891385534 |
132 | 12540 | 12655.8662323966 | -115.866232396596 |
133 | 12200 | 12226.60648228 | -26.6064822799891 |
134 | 10644 | 10638.276939435 | 5.72306056496531 |
135 | 12044 | 11929.3920281867 | 114.607971813331 |
136 | 11338 | 11371.1929824499 | -33.1929824498633 |
137 | 11292 | 11274.4044540141 | 17.5955459858633 |
138 | 10612 | 10572.3172719275 | 39.6827280725319 |
139 | 10995 | 11022.210032476 | -27.2100324759534 |
140 | 10686 | 10749.0796281693 | -63.0796281693284 |
141 | 10635 | 10630.8294603631 | 4.17053963694008 |
142 | 11285 | 11272.2252615649 | 12.774738435087 |
143 | 11475 | 11464.0461590974 | 10.9538409025592 |
144 | 12535 | 12554.5515706031 | -19.5515706031395 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.19303705451862 | 0.38607410903724 | 0.80696294548138 |
10 | 0.131586381857562 | 0.263172763715124 | 0.868413618142438 |
11 | 0.072703727319985 | 0.14540745463997 | 0.927296272680015 |
12 | 0.854502267129104 | 0.290995465741792 | 0.145497732870896 |
13 | 0.853170602019266 | 0.293658795961469 | 0.146829397980734 |
14 | 0.86579695047756 | 0.26840609904488 | 0.13420304952244 |
15 | 0.839711414388218 | 0.320577171223563 | 0.160288585611782 |
16 | 0.904160748981371 | 0.191678502037258 | 0.095839251018629 |
17 | 0.963173849760031 | 0.0736523004799389 | 0.0368261502399695 |
18 | 0.947285875794809 | 0.105428248410382 | 0.052714124205191 |
19 | 0.951590636480976 | 0.0968187270380489 | 0.0484093635190245 |
20 | 0.985241865493692 | 0.0295162690126171 | 0.0147581345063085 |
21 | 0.988250108362814 | 0.0234997832743723 | 0.0117498916371861 |
22 | 0.985343290070758 | 0.0293134198584831 | 0.0146567099292415 |
23 | 0.983590937054092 | 0.0328181258918157 | 0.0164090629459079 |
24 | 0.994063894709429 | 0.0118722105811415 | 0.00593610529057076 |
25 | 0.99703773778038 | 0.00592452443923989 | 0.00296226221961994 |
26 | 0.999620506964081 | 0.000758986071838859 | 0.000379493035919429 |
27 | 0.999942205454147 | 0.000115589091705916 | 5.77945458529578e-05 |
28 | 0.999997956497583 | 4.08700483368542e-06 | 2.04350241684271e-06 |
29 | 0.999998714178804 | 2.57164239165047e-06 | 1.28582119582523e-06 |
30 | 0.999999681244117 | 6.37511765531777e-07 | 3.18755882765888e-07 |
31 | 0.999999572155504 | 8.55688991877352e-07 | 4.27844495938676e-07 |
32 | 0.999999892317242 | 2.15365515498961e-07 | 1.0768275774948e-07 |
33 | 0.999999857835003 | 2.84329994855052e-07 | 1.42164997427526e-07 |
34 | 0.99999991154574 | 1.76908519993808e-07 | 8.84542599969042e-08 |
35 | 0.999999893574199 | 2.12851600989999e-07 | 1.06425800494999e-07 |
36 | 0.999999875895277 | 2.48209446810428e-07 | 1.24104723405214e-07 |
37 | 0.999999872943915 | 2.54112170147989e-07 | 1.27056085073995e-07 |
38 | 0.999999960625476 | 7.8749048418322e-08 | 3.9374524209161e-08 |
39 | 0.99999995845205 | 8.30959005624224e-08 | 4.15479502812112e-08 |
40 | 0.999999949706923 | 1.0058615432611e-07 | 5.02930771630549e-08 |
41 | 0.99999998243912 | 3.51217602446366e-08 | 1.75608801223183e-08 |
42 | 0.999999966714388 | 6.65712233414961e-08 | 3.32856116707481e-08 |
43 | 0.99999997484793 | 5.03041399475913e-08 | 2.51520699737956e-08 |
44 | 0.999999983656274 | 3.26874516082403e-08 | 1.63437258041202e-08 |
45 | 0.999999972276805 | 5.54463902408326e-08 | 2.77231951204163e-08 |
46 | 0.999999974558036 | 5.08839274411269e-08 | 2.54419637205634e-08 |
47 | 0.99999997240526 | 5.51894799737363e-08 | 2.75947399868682e-08 |
48 | 0.999999958937983 | 8.21240335677408e-08 | 4.10620167838704e-08 |
49 | 0.999999941476952 | 1.17046095960067e-07 | 5.85230479800336e-08 |
50 | 0.999999899590962 | 2.00818076037649e-07 | 1.00409038018825e-07 |
51 | 0.99999983295033 | 3.34099339070451e-07 | 1.67049669535226e-07 |
52 | 0.999999715796519 | 5.68406962319328e-07 | 2.84203481159664e-07 |
53 | 0.999999786783191 | 4.26433618047185e-07 | 2.13216809023593e-07 |
54 | 0.999999960054449 | 7.98911019934677e-08 | 3.99455509967339e-08 |
55 | 0.999999921333875 | 1.57332248962259e-07 | 7.86661244811293e-08 |
56 | 0.999999852397056 | 2.95205887380542e-07 | 1.47602943690271e-07 |
57 | 0.999999721663603 | 5.56672793719032e-07 | 2.78336396859516e-07 |
58 | 0.999999505769719 | 9.88460562933245e-07 | 4.94230281466622e-07 |
59 | 0.999999110347959 | 1.77930408305735e-06 | 8.89652041528676e-07 |
60 | 0.999998734922451 | 2.53015509907404e-06 | 1.26507754953702e-06 |
61 | 0.99999778066253 | 4.43867494019273e-06 | 2.21933747009636e-06 |
62 | 0.999995997696191 | 8.00460761870213e-06 | 4.00230380935107e-06 |
63 | 0.99999844984197 | 3.10031606008196e-06 | 1.55015803004098e-06 |
64 | 0.999997825866216 | 4.34826756878054e-06 | 2.17413378439027e-06 |
65 | 0.999997305171505 | 5.38965698998157e-06 | 2.69482849499078e-06 |
66 | 0.999996432719622 | 7.13456075578553e-06 | 3.56728037789277e-06 |
67 | 0.99999464978329 | 1.07004334209377e-05 | 5.35021671046884e-06 |
68 | 0.999993192059329 | 1.36158813424105e-05 | 6.80794067120525e-06 |
69 | 0.99999262331797 | 1.47533640607804e-05 | 7.37668203039022e-06 |
70 | 0.999987296301895 | 2.54073962107189e-05 | 1.27036981053594e-05 |
71 | 0.999986793740134 | 2.64125197312698e-05 | 1.32062598656349e-05 |
72 | 0.999983553309769 | 3.28933804622483e-05 | 1.64466902311241e-05 |
73 | 0.999984156357025 | 3.168728594937e-05 | 1.5843642974685e-05 |
74 | 0.999973403195599 | 5.31936088012472e-05 | 2.65968044006236e-05 |
75 | 0.999960499117628 | 7.90017647444254e-05 | 3.95008823722127e-05 |
76 | 0.999966956820504 | 6.60863589912784e-05 | 3.30431794956392e-05 |
77 | 0.999948844027222 | 0.00010231194555648 | 5.11559727782401e-05 |
78 | 0.999946222371776 | 0.000107555256447709 | 5.37776282238547e-05 |
79 | 0.99991224042235 | 0.00017551915530079 | 8.77595776503948e-05 |
80 | 0.999992711932865 | 1.45761342693515e-05 | 7.28806713467576e-06 |
81 | 0.999989155401362 | 2.16891972762327e-05 | 1.08445986381163e-05 |
82 | 0.999993397838505 | 1.32043229894936e-05 | 6.6021614947468e-06 |
83 | 0.999988584362646 | 2.28312747081782e-05 | 1.14156373540891e-05 |
84 | 0.999979818587767 | 4.03628244660794e-05 | 2.01814122330397e-05 |
85 | 0.999966472437763 | 6.70551244733256e-05 | 3.35275622366628e-05 |
86 | 0.999963845500389 | 7.2308999222361e-05 | 3.61544996111805e-05 |
87 | 0.999963478459562 | 7.30430808769406e-05 | 3.65215404384703e-05 |
88 | 0.999962999196393 | 7.40016072139159e-05 | 3.70008036069579e-05 |
89 | 0.999936555802895 | 0.000126888394209288 | 6.3444197104644e-05 |
90 | 0.999946202779102 | 0.000107594441795636 | 5.37972208978178e-05 |
91 | 0.999928834863825 | 0.00014233027235056 | 7.116513617528e-05 |
92 | 0.999877006752528 | 0.000245986494944433 | 0.000122993247472216 |
93 | 0.999793452540349 | 0.000413094919301353 | 0.000206547459650677 |
94 | 0.999727388409513 | 0.000545223180974315 | 0.000272611590487158 |
95 | 0.99954766386237 | 0.000904672275259917 | 0.000452336137629959 |
96 | 0.999261211659089 | 0.0014775766818227 | 0.00073878834091135 |
97 | 0.999272358840396 | 0.00145528231920874 | 0.00072764115960437 |
98 | 0.999140636977123 | 0.00171872604575345 | 0.000859363022876723 |
99 | 0.998707532305409 | 0.0025849353891825 | 0.00129246769459125 |
100 | 0.998043842353072 | 0.00391231529385633 | 0.00195615764692817 |
101 | 0.997090251851024 | 0.00581949629795109 | 0.00290974814897555 |
102 | 0.995929645363423 | 0.00814070927315419 | 0.0040703546365771 |
103 | 0.997733607998233 | 0.0045327840035331 | 0.00226639200176655 |
104 | 0.998041159684654 | 0.00391768063069297 | 0.00195884031534649 |
105 | 0.99775386977387 | 0.00449226045226049 | 0.00224613022613024 |
106 | 0.99649438096237 | 0.00701123807525921 | 0.0035056190376296 |
107 | 0.995354452565832 | 0.00929109486833528 | 0.00464554743416764 |
108 | 0.992992061210722 | 0.014015877578555 | 0.00700793878927749 |
109 | 0.990098221092636 | 0.0198035578147281 | 0.00990177890736407 |
110 | 0.98592409125333 | 0.0281518174933406 | 0.0140759087466703 |
111 | 0.978977207433082 | 0.0420455851338369 | 0.0210227925669185 |
112 | 0.975522346871768 | 0.0489553062564642 | 0.0244776531282321 |
113 | 0.971397209254496 | 0.0572055814910078 | 0.0286027907455039 |
114 | 0.960300452850019 | 0.0793990942999625 | 0.0396995471499812 |
115 | 0.943677622439543 | 0.112644755120914 | 0.0563223775604568 |
116 | 0.934252847052578 | 0.131494305894844 | 0.0657471529474221 |
117 | 0.910645904037229 | 0.178708191925543 | 0.0893540959627713 |
118 | 0.927823789722896 | 0.144352420554208 | 0.072176210277104 |
119 | 0.912441035920824 | 0.175117928158353 | 0.0875589640791764 |
120 | 0.917828806774991 | 0.164342386450019 | 0.0821711932250094 |
121 | 0.893668230643032 | 0.212663538713937 | 0.106331769356968 |
122 | 0.900735055604335 | 0.198529888791329 | 0.0992649443956646 |
123 | 0.862051883388496 | 0.275896233223008 | 0.137948116611504 |
124 | 0.912303891540081 | 0.175392216919838 | 0.0876961084599192 |
125 | 0.984030091890608 | 0.0319398162187831 | 0.0159699081093916 |
126 | 0.975469188398592 | 0.0490616232028155 | 0.0245308116014077 |
127 | 0.984010101335122 | 0.0319797973297552 | 0.0159898986648776 |
128 | 0.971872097425991 | 0.0562558051480175 | 0.0281279025740087 |
129 | 0.990015716735462 | 0.0199685665290769 | 0.00998428326453845 |
130 | 0.986364091182023 | 0.0272718176359548 | 0.0136359088179774 |
131 | 0.97026664984774 | 0.0594667003045201 | 0.0297333501522601 |
132 | 0.956939636739632 | 0.0861207265207357 | 0.0430603632603679 |
133 | 0.911963032623451 | 0.176073934753098 | 0.088036967376549 |
134 | 0.833719664688429 | 0.332560670623142 | 0.166280335311571 |
135 | 0.904187220146024 | 0.191625559707951 | 0.0958127798539757 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 83 | 0.653543307086614 | NOK |
5% type I error level | 98 | 0.771653543307087 | NOK |
10% type I error level | 105 | 0.826771653543307 | NOK |