Multiple Linear Regression - Estimated Regression Equation
Banknotes[t] = + 402943.640784314 -59077.5699709514M1[t] -58286.3821205519M2[t] -53674.6942701525M3[t] -45337.4508641975M4[t] -69183.151902687M5[t] -56813.797385621M6[t] -63913.7762018882M7[t] -70055.9216848221M8[t] -72600.8449455338M9[t] -70229.7126506899M10[t] -67890.8581336239M11[t] + 2385.14548293391t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)402943.6407843149789.5269741.160700
M1-59077.569970951412260.44047-4.81863e-061e-06
M2-58286.382120551912259.85678-4.75424e-062e-06
M3-53674.694270152512259.40278-4.37821.9e-051e-05
M4-45337.450864197512259.078484-3.69830.000280.00014
M5-69183.15190268712258.883902-5.643500
M6-56813.79738562112258.819041-4.63456e-063e-06
M7-63913.776201888212258.883902-5.213700
M8-70055.921684822112259.078484-5.714600
M9-72600.844945533812259.40278-5.922100
M10-70229.712650689912259.85678-5.728400
M11-67890.858133623912260.44047-5.537400
t2385.1454829339139.87794159.811100


Multiple Linear Regression - Regression Statistics
Multiple R0.973284918016012
R-squared0.947283531637436
Adjusted R-squared0.94415186024956
F-TEST (value)302.484971860405
F-TEST (DF numerator)12
F-TEST (DF denominator)202
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation36247.2718766881
Sum Squared Residuals265400673137.513


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1347553346251.2162962961301.78370370392
2353245349427.549629633817.45037037029
3347966356424.382962963-8458.38296296292
4364343367146.771851852-2803.77185185165
5341713345686.216296296-3973.21629629632
6361162360440.716296296721.283703703775
7354400355725.882962963-1325.88296296284
8345183351968.882962963-6785.88296296282
9341807351809.105185185-10002.105185185
10348712356565.382962963-7853.38296296293
11349011361289.382962963-12278.3829629630
12416259431565.386579521-15306.3865795207
13360289374872.962091504-14583.9620915036
14367557378049.295424837-10492.2954248366
15364611385046.12875817-20435.1287581699
16378688395768.517647059-17080.5176470588
17351763374307.962091503-22544.9620915032
18377765389062.462091503-11297.4620915032
19373212384347.62875817-11135.6287581699
20365819380590.62875817-14771.6287581699
21364686380430.850980392-15744.8509803922
22363333385187.12875817-21854.1287581699
23362536389911.12875817-27375.1287581699
24428803460187.132374728-31384.1323747276
25375361403494.70788671-28133.7078867102
26377205406671.041220044-29466.0412200435
27381266413667.874553377-32401.8745533769
28390516424390.263442266-33874.2634422658
29366117402929.70788671-36812.7078867102
30393928417684.20788671-23756.2078867103
31387784412969.374553377-25185.3745533769
32385656409212.374553377-23556.3745533769
33385320409052.596775599-23732.5967755992
34389053413808.874553377-24755.8745533769
35390595418532.874553377-27937.8745533769
36462440488808.878169935-26368.8781699346
37402532432116.453681917-29584.4536819172
38409070435292.787015251-26222.7870152505
39421329442289.620348584-20960.6203485839
40428841453012.009237473-24171.0092374728
41404864431551.453681917-26687.4536819172
42432633446305.953681917-13672.9536819172
43416886441591.120348584-24705.1203485839
44414893437834.120348584-22941.1203485839
45417914437674.342570806-19760.3425708061
46417518442430.620348584-24912.6203485839
47423137447154.620348584-24017.6203485839
48506710517430.623965142-10720.6239651416
49436264460738.199477124-24474.1994771242
50443712463914.532810457-20202.5328104575
51452849470911.366143791-18062.3661437909
52453009481633.75503268-28624.7550326798
53437876460173.199477124-22297.1994771242
54460041474927.699477124-14886.6994771242
55450426470212.866143791-19786.8661437909
56447873466455.866143791-18582.8661437908
57444955466296.088366013-21341.0883660130
58452043471052.366143791-19009.3661437908
59480877475776.3661437915100.63385620915
60546696546052.369760349643.630239651392
61483668489359.945272331-5691.94527233116
62489627492536.278605664-2909.27860566448
63490007499533.111938998-9526.11193899786
64496590510255.500827887-13665.5008278867
65480846488794.945272331-7948.94527233115
66497677503549.445272331-5872.44527233116
67492795498834.611938998-6039.61193899784
68488495495077.611938998-6582.61193899785
69486769494917.83416122-8148.83416122002
70494455499674.111938998-5219.1119389978
71498054504398.111938998-6344.11193899782
72558648574674.115555556-16026.1155555556
73506424517981.691067538-11557.6910675381
74512528521158.024400871-8630.0244008715
75512866528154.857734205-15288.8577342048
76529324538877.246623094-9553.24662309369
77508431517416.691067538-8985.69106753812
78523026532171.191067538-9145.19106753815
79521355527456.357734205-6101.35773420485
80514103523699.357734205-9596.35773420482
81513885523539.579956427-9654.57995642702
82522150528295.857734205-6145.85773420479
83527384533019.857734205-5635.8577342048
84654047603295.86135076350751.1386492375
85543115546603.436862745-3488.43686274509
86543200549779.770196078-6579.77019607847
87571201556776.60352941214424.3964705882
88568892567498.9924183011393.00758169935
89537223546038.436862745-8815.43686274512
90553186560792.936862745-7606.93686274511
91550954556078.103529412-5124.10352941181
92543433552321.103529412-8888.1035294118
93557195552161.3257516345033.67424836602
94565522556917.6035294128604.39647058825
95571691561641.60352941210049.3964705882
96633972631917.607145972054.39285403049
97575265575225.18265795239.8173420479491
98572364578401.515991285-6037.51599128543
99586744585398.3493246191345.65067538124
100600389596120.7382135084268.26178649237
101578540574660.1826579523879.81734204791
102610778589414.68265795221363.3173420479
103596577584699.84932461911877.1506753812
104590558580942.8493246199615.15067538123
105597294580783.07154684116510.9284531591
106602384585539.34932461916844.6506753813
107614190590263.34932461923926.6506753813
108690042660539.35294117729502.6470588234
109639497603846.92845315935650.071546841
110649304607023.26178649242280.7382135076
111678762614020.09511982664741.9048801743
112691885624742.48400871567142.5159912854
113667973603281.92845315964691.071546841
114682032618036.42845315963995.571546841
115672651613321.59511982659329.4048801743
116671865609564.59511982662300.4048801743
117671463609404.81734204862058.1826579521
118675917614161.09511982661755.9048801742
119680952618885.09511982662066.9048801743
120754718689161.09873638365556.9012636165
121694413632468.67424836661944.325751634
122699390635645.007581763744.9924183006
123710573642641.84091503367931.1590849673
124714217653364.22980392260852.7701960784
125702996631903.67424836671092.325751634
126712370646658.17424836665711.825751634
127708445641943.34091503366501.6590849673
128707083638186.34091503368896.6590849673
129700632638026.56313725562605.436862745
130706309642782.84091503363526.1590849672
131709523647506.84091503362016.1590849672
132769096717782.8445315951313.1554684095
133715100661090.42004357354009.579956427
134713872664266.75337690649605.2466230937
135714032671263.5867102442768.4132897603
136732269681985.97559912950283.0244008715
137711137660525.42004357350611.579956427
138715284675279.92004357340004.079956427
139716888670565.0867102446322.9132897603
140716426666808.0867102449617.9132897603
141714726666648.30893246248077.691067538
142718016671404.5867102446611.4132897603
143725932676128.5867102449803.4132897603
144779564746404.59032679733159.4096732026
145732144689712.1658387842431.8341612201
146730816692888.49917211337927.5008278867
147746719699885.33250544746833.6674945534
148760065710607.72139433649457.2786056645
149734516689147.1658387845368.83416122
150740167703901.6658387836265.33416122
151740976699186.83250544741789.1674945533
152735764695429.83250544740334.1674945533
153734711695270.05472766939440.9452723311
154737916700026.33250544737889.6674945533
155739132704750.33250544734381.6674945534
156792705775026.33612200417678.6638779957
157747488718333.91163398729154.0883660131
158746616721510.2449673225105.7550326797
159749781728507.07830065421273.9216993464
160760911739229.46718954221681.5328104575
161739543717768.91163398721774.0883660131
162745626732523.41163398713102.5883660131
163746246727808.57830065418437.4216993464
164744769724051.57830065420717.4216993464
165741388723891.80052287617496.1994771241
166744469728648.07830065415820.9216993464
167745566733372.07830065312193.9216993465
168798367803648.081917211-5281.08191721128
169752440746955.6574291945484.34257080612
170756627750131.9907625276495.00923747278
171758941757128.824095861812.17590413944
172771287767851.212984753435.78701525056
173749858746390.6574291943467.34257080612
174758370761145.157429194-2775.15742919387
175755407756430.32409586-1023.32409586052
176752063752673.32409586-610.324095860527
177756298752513.5463180833784.45368191721
178755892757269.82409586-1377.82409586053
179758486761993.82409586-3507.82409586049
180812777832269.827712418-19492.8277124182
181762561775577.403224401-13016.4032244009
182763579778753.736557734-15174.7365577342
183764615785750.569891067-21135.5698910675
184773312796472.958779956-23160.9587799565
185755697775012.403224401-19315.4032244009
186762909789766.903224401-26857.9032244009
187760337785052.069891067-24715.0698910675
188759270781295.069891067-22025.0698910675
189754929781135.29211329-26206.2921132898
190766116785891.569891067-19775.5698910675
191765945790615.569891067-24670.5698910675
192814783860891.573507625-46108.5735076252
193768494804199.149019608-35705.1490196079
194769222807375.482352941-38153.4823529412
195768977814372.315686275-45395.3156862745
196783341825094.704575163-41753.7045751634
197764061803634.149019608-39573.1490196078
198767394818388.649019608-50994.6490196078
199763910813673.815686274-49763.8156862744
200761677809916.815686274-48239.8156862745
201759173809757.037908497-50584.0379084968
202762486814513.315686274-52027.3156862745
203762690819237.315686275-56547.3156862745
204809542889513.319302832-79971.3193028323
205769041832820.894814815-63779.8948148148
206770889835997.228148148-65108.2281481482
207773527842994.061481481-69467.0614814814
208789890853716.45037037-63826.4503703704
209768325832255.894814815-63930.8948148148
210772712847010.394814815-74298.3948148148
211772944842295.561481481-69351.5614814814
212769637838538.561481481-68901.5614814815
213768546838378.783703704-69832.7837037037
214775013843135.061481481-68122.0614814815
215776635847859.061481482-71224.0614814815


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
163.83790855038461e-057.67581710076923e-050.999961620914496
178.76619450722308e-061.75323890144462e-050.999991233805493
186.71577170790007e-071.34315434158001e-060.99999932842283
191.13658129067719e-072.27316258135439e-070.99999988634187
202.81812295181948e-085.63624590363895e-080.99999997181877
211.05595302593293e-082.11190605186587e-080.99999998944047
227.9614575254638e-101.59229150509276e-090.999999999203854
236.71098407005523e-111.34219681401105e-100.99999999993289
246.60316918203436e-121.32063383640687e-110.999999999993397
255.13226890727989e-131.02645378145598e-120.999999999999487
261.67529927115709e-133.35059854231419e-130.999999999999832
271.68596852592284e-143.37193705184568e-140.999999999999983
281.94518844167676e-153.89037688335352e-150.999999999999998
291.88457847622883e-163.76915695245766e-161
301.81769165660247e-173.63538331320495e-171
311.50564369221822e-183.01128738443644e-181
321.44445275115071e-182.88890550230142e-181
331.87334150971721e-183.74668301943443e-181
341.85298545377578e-183.70597090755157e-181
352.26488915941791e-184.52977831883582e-181
361.2575905586267e-172.5151811172534e-171
373.49500550493867e-186.99001100987733e-181
381.16505973053886e-182.33011946107771e-181
393.37214229251294e-176.74428458502588e-171
403.0176405272693e-176.0352810545386e-171
412.31128777662654e-174.62257555325307e-171
422.67389541438526e-175.34779082877051e-171
435.76157305849672e-181.15231461169934e-171
441.84272363439577e-183.68544726879154e-181
451.1459183641795e-182.291836728359e-181
463.79097696884853e-197.58195393769706e-191
472.75389934921445e-195.50779869842891e-191
487.22608240720008e-181.44521648144002e-171
492.7268408936989e-185.4536817873978e-181
501.18361905241646e-182.36723810483292e-181
511.37048224058783e-182.74096448117566e-181
524.10664267814014e-198.21328535628029e-191
532.80130923164540e-195.60261846329081e-191
541.10200550953722e-192.20401101907443e-191
553.95166895622161e-207.90333791244322e-201
561.77555199278612e-203.55110398557224e-201
576.4677569699005e-211.2935513939801e-201
583.75873086405444e-217.51746172810889e-211
599.39041459157537e-191.87808291831507e-181
607.96252877369845e-181.59250575473969e-171
611.35210518818755e-172.70421037637509e-171
621.81663501061937e-173.63327002123874e-171
631.58079555949079e-173.16159111898158e-171
641.05116386859423e-172.10232773718846e-171
651.24164712423928e-172.48329424847855e-171
666.30384158742949e-181.26076831748590e-171
674.22117489923534e-188.44234979847069e-181
682.87544680990545e-185.75089361981089e-181
691.86862003465749e-183.73724006931499e-181
701.70096161009550e-183.40192322019101e-181
711.13206736271165e-182.26413472542329e-181
725.8505118662716e-191.17010237325432e-181
733.27782002340312e-196.55564004680625e-191
741.76435584569845e-193.52871169139691e-191
751.10933606122213e-192.21867212244427e-191
769.06479379692025e-201.81295875938405e-191
777.86749976763869e-201.57349995352774e-191
784.64213960190722e-209.28427920381443e-201
793.35463248682862e-206.70926497365724e-201
802.56669080991704e-205.13338161983407e-201
812.22784226666886e-204.45568453333773e-201
822.38089938834447e-204.76179877668894e-201
832.44620398104890e-204.89240796209779e-201
849.43381991833917e-161.88676398366783e-151
859.92529348911813e-161.98505869782363e-151
861.056462184477e-152.112924368954e-150.999999999999999
873.4770281763808e-156.9540563527616e-150.999999999999997
885.52516568180426e-151.10503313636085e-140.999999999999994
891.01722165231766e-142.03444330463532e-140.99999999999999
901.73098525336803e-143.46197050673605e-140.999999999999983
913.25013690522308e-146.50027381044616e-140.999999999999967
929.31047690917752e-141.86209538183550e-130.999999999999907
932.47493645865701e-134.94987291731401e-130.999999999999753
948.0508156316227e-131.61016312632454e-120.999999999999195
952.57099194936154e-125.14198389872308e-120.99999999999743
965.1253489283139e-121.02506978566278e-110.999999999994875
972.17438661857043e-114.34877323714087e-110.999999999978256
981.65163906175564e-103.30327812351128e-100.999999999834836
991.17109437451478e-092.34218874902956e-090.999999998828906
1001.24999182994707e-082.49998365989413e-080.999999987500082
1012.25064433149005e-074.5012886629801e-070.999999774935567
1021.56732818635419e-063.13465637270837e-060.999998432671814
1031.91757355558608e-053.83514711117216e-050.999980824264444
1040.0004114757532902070.0008229515065804140.99958852424671
1050.006282125976508370.01256425195301670.993717874023492
1060.0819957163658610.1639914327317220.918004283634139
1070.4294520071896130.8589040143792250.570547992810387
1080.736674261397390.5266514772052190.263325738602609
1090.9703303827600180.05933923447996480.0296696172399824
1100.9989869980579060.002026003884188490.00101300194209425
1110.999968249598986.3500802039752e-053.1750401019876e-05
1120.9999993145363361.37092732757962e-066.8546366378981e-07
1130.9999999902807841.94384324375031e-089.71921621875153e-09
1140.999999999147411.70517829106575e-098.52589145532877e-10
1150.9999999999801333.97338234928499e-111.98669117464249e-11
1160.999999999999725.60325719632949e-132.80162859816474e-13
1170.9999999999999968.15843193453494e-154.07921596726747e-15
11816.08199790384112e-173.04099895192056e-17
11915.76248689442578e-192.88124344721289e-19
12014.56330049781327e-192.28165024890664e-19
12113.42503594784741e-201.71251797392371e-20
12217.01255155444594e-213.50627577722297e-21
12315.31455297884162e-212.65727648942081e-21
12415.74310289460444e-222.87155144730222e-22
12513.41527370333571e-221.70763685166785e-22
12615.79369280637639e-222.89684640318819e-22
12716.22421647128229e-223.11210823564115e-22
12816.84307522586805e-223.42153761293403e-22
12913.84814902549256e-221.92407451274628e-22
13012.62470917749244e-221.31235458874622e-22
13112.3174888617783e-221.15874443088915e-22
13217.26882194510593e-223.63441097255297e-22
13316.3018903624916e-223.1509451812458e-22
13412.67358340028863e-221.33679170014432e-22
13511.56423641990453e-237.82118209952266e-24
13615.26518706924734e-242.63259353462367e-24
13711.22026697761239e-246.10133488806194e-25
13816.30218931403893e-263.15109465701946e-26
13917.27986567757056e-273.63993283878528e-27
14011.55569412075287e-277.77847060376433e-28
14111.43621901476462e-287.18109507382312e-29
14211.70153627007025e-308.50768135035126e-31
14319.5117923492287e-314.75589617461435e-31
14411.28928701549768e-306.44643507748841e-31
14517.49682941657668e-313.74841470828834e-31
14613.28487969316513e-321.64243984658257e-32
14711.45552072642734e-317.27760363213668e-32
14815.11199963023309e-312.55599981511655e-31
14912.82922452419087e-301.41461226209544e-30
15011.25425694235322e-296.27128471176609e-30
15117.09026047624687e-293.54513023812343e-29
15213.14677225559222e-281.57338612779611e-28
15311.43443272498357e-277.17216362491786e-28
15414.27748300673417e-272.13874150336708e-27
15511.15333173606597e-265.76665868032983e-27
15613.74097522038761e-261.87048761019381e-26
15711.76027874088891e-258.80139370444457e-26
15815.46255326041392e-252.73127663020696e-25
15911.98362931715242e-249.91814658576212e-25
16015.5168999834727e-242.75844999173635e-24
16119.92320511653318e-244.96160255826659e-24
16211.35687457118656e-236.78437285593278e-24
16314.65142716654806e-232.32571358327403e-23
16411.97171025115611e-229.85855125578055e-23
16514.64915954372569e-222.32457977186284e-22
16614.05881115057661e-222.02940557528831e-22
16712.29207908247659e-221.14603954123829e-22
16814.15212605974744e-222.07606302987372e-22
16919.22319341063707e-224.61159670531854e-22
17014.11062711571477e-212.05531355785738e-21
17111.81860103125834e-209.0930051562917e-21
17218.36545874256525e-204.18272937128262e-20
17312.90101224161924e-191.45050612080962e-19
17411.30644412908181e-186.53222064540906e-19
17516.24741825956472e-183.12370912978236e-18
17612.76586983844322e-171.38293491922161e-17
17716.54892069383706e-173.27446034691853e-17
17812.98285246990422e-161.49142623495211e-16
17911.58459508018239e-157.92297540091196e-16
18011.02804135936981e-155.14020679684907e-16
1810.9999999999999975.3532818693297e-152.67664093466485e-15
1820.9999999999999862.83923471649741e-141.41961735824870e-14
1830.9999999999999281.44826655181607e-137.24133275908035e-14
1840.9999999999998373.25024078427371e-131.62512039213685e-13
1850.9999999999992551.48989566563091e-127.44947832815457e-13
1860.9999999999956598.68276496691962e-124.34138248345981e-12
1870.999999999974175.1659139060297e-112.58295695301485e-11
1880.9999999998402033.19594646509123e-101.59797323254561e-10
1890.9999999990951351.80973014816685e-099.04865074083427e-10
1900.99999999647187.05640056881865e-093.52820028440932e-09
1910.9999999857312692.85374624951799e-081.42687312475899e-08
1920.9999999947884651.04230693995975e-085.21153469979876e-09
1930.9999999878690392.42619219350541e-081.21309609675270e-08
1940.9999999701615235.96769535948132e-082.98384767974066e-08
1950.9999998226720463.54655908089769e-071.77327954044884e-07
1960.9999983022342033.39553159461962e-061.69776579730981e-06
1970.9999930525576221.38948847565939e-056.94744237829696e-06
1980.9999742606822065.14786355878945e-052.57393177939473e-05
1990.9996347231913610.0007305536172777730.000365276808638887


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1790.972826086956522NOK
5% type I error level1800.978260869565217NOK
10% type I error level1810.983695652173913NOK