Multiple Linear Regression - Estimated Regression Equation
Gold[t] = + 314.125322655855 + 4.45579919198396Oil[t] + 117.538980489271ETF[t] + 335.677304242437Crisis[t] -0.0148989271676622Dow[t] + 18.2333614796751Bonds[t] -2932.84128226089Inflation[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)314.12532265585545.0083376.979300
Oil4.455799191983960.5408858.23800
ETF117.53898048927118.9043166.217600
Crisis335.67730424243725.17368713.334500
Dow-0.01489892716766220.002441-6.104200
Bonds18.23336147967516.0856412.99610.0029690.001484
Inflation-2932.84128226089510.038096-5.750200


Multiple Linear Regression - Regression Statistics
Multiple R0.945251705974231
R-squared0.893500787647195
Adjusted R-squared0.891312447667343
F-TEST (value)408.300719208885
F-TEST (DF numerator)6
F-TEST (DF denominator)292
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation73.5219597847205
Sum Squared Residuals1578399.74261113


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1321.61467.705461860838-146.095461860838
2345.85443.802983256713-97.9529832567128
3338.6428.973332018486-90.3733320184864
4345.64419.633073739576-73.9930737395758
5340.71426.988099839084-86.2780998390838
6342.49443.12085778867-100.630857788670
7342.65429.60488273986-86.9548827398601
8348.68418.55118505228-69.8711850522796
9377.36430.206414587293-52.8464145872931
10418.05434.690064193239-16.6400641932395
11423.13440.879248860502-17.7492488605019
12397.69444.603369899266-46.9133698992659
13390.8452.114925888377-61.3149258883773
14408.29448.898605631507-40.6086056315073
15401.02428.462708276029-27.4427082760288
16409.24402.0698026522727.17019734772817
17439.28395.9963380791843.2836619208204
18459.95405.89315284699854.0568471530017
19449.66407.48351659262142.1764834073793
20451.14402.12932838187449.0106716181256
21460.66392.64545695342668.0145430465743
22460.23401.08642362251659.1435763774837
23465.69408.06852543557657.6214745644237
24468.01395.15187633393872.8581236660616
25486.74393.82674301592192.9132569840789
26475.89397.86780417285278.0221958271484
27441.52388.17052781103153.3494721889685
28443.63388.21496890792455.4150310920761
29451.62401.50108048758550.1189195124147
30451.14408.40283608237142.7371639176291
31450.88397.59691306432653.2830869356738
32437.56390.95006993071646.6099300692839
33431.18399.68843983423331.4915601657673
34412.02382.87276856852429.1472314314757
35407.14372.42100811191034.7189918880896
36420.48377.29225020720143.1877497927988
37418.92383.71917274707635.200827252924
38403.57381.3850007944722.1849992055297
39387.55379.7017651967197.84823480328137
40390.02385.2557199021434.76428009785688
41384.37381.5952297074882.77477029251212
42370.62362.6559903871367.96400961286414
43367.9356.44342400294811.4565759970519
44374.91353.42678827407821.4832117259224
45365.15358.3684013439196.78159865608111
46361.91374.856752116421-12.9467521164213
47367.03371.039211343538-4.0092113435382
48395.19362.67533432356132.5146656764391
49409.25366.06619680599143.1838031940095
50410.49364.39480594423546.0951940557653
51416.58362.74766270702353.8323372929769
52392.21357.67901919600634.5309808039944
53374.29369.3487382676864.94126173231367
54369.05375.291471392075-6.24147139207527
55352.19355.278065417452-3.08806541745165
56362.85358.7228638617254.12713613827471
57395.47388.2061126800717.26388731992851
58388.82408.821680146520-20.0016801465195
59380.39407.547037827492-27.1570378274922
60381.73385.473317270762-3.74331727076152
61377.69361.69305315651215.9969468434877
62383.04356.75134520555926.2886547944414
63363.89341.07473526383622.8152647361638
64363.23356.1592350066027.07076499339775
65358.37356.740642531321.62935746868015
66356.97354.2935319018712.67646809812868
67366.87363.2910640120203.57893598798029
68367.57374.148251444604-6.57825144460421
69355.88387.389205334133-31.5092053341331
70348.88398.101663610384-49.2216636103835
71358.77416.074256286289-57.3042562862888
72360.42409.554958705830-49.1349587058305
73361.08384.872521501677-23.7925215016766
74354.57396.083879985201-41.5138799852008
75353.73395.241627559569-41.5116275595692
76344.2387.291240777068-43.0912407770685
77338.34390.285369233852-51.9453692338519
78337.21396.559956479724-59.3499564797236
79340.96399.522370852982-58.5623708529815
80353.29385.603278695013-32.3132786950132
81342.67380.852172809036-38.1821728090355
82345.71384.759917935641-39.0499179356408
83344.17381.591052479218-37.4210524792181
84334.92384.969862179491-50.0498621794911
85334.81383.201883837816-48.3918838378162
86329.05366.401106405537-37.3511064055375
87329.31364.050590339286-34.7405903392861
88330.25363.879927100267-33.6299271002673
89341.89359.469164882279-17.5791648822786
90367.74358.1892402574989.55075974250191
91371.93359.94859190038811.9814080996118
92392.79358.85862055969333.931379440307
93377.97355.32192390135222.6480760986484
94354.93350.417541853394.51245814660983
95364.4349.06091807668215.3390819233183
96374.05352.28564082201321.7643591779869
97383.63342.3233212952541.3066787047499
98386.56348.79310064625437.7668993537458
99381.9353.37140354570428.5285964542959
100384.08365.57931080086818.5006891991321
101377.29384.616812237647-7.3268122376467
102381.54395.136034149823-13.596034149823
103385.6393.229077194968-7.62907719496818
104385.47390.281980187572-4.81198018757194
105380.4378.4187252481301.98127475187021
106391.74377.84422994891513.8957700510853
107389.57393.965031456577-4.39503145657704
108384.29401.74168823313-17.4516882331302
109379.26392.820452020123-13.560452020123
110378.44391.676923215273-13.2369232152735
111376.63384.310232079519-7.68023207951888
112382.48377.0859094772415.39409052275864
113390.89372.56935601722518.3206439827749
114385.04357.15518709226027.8848129077396
115387.58346.7782025850740.8017974149301
116386.19349.01142621332237.1785737866779
117383.78360.4795309623.3004690399999
118383.1355.94709313427027.1529068657304
119383.25343.10301275755340.1469872424472
120385.19345.18500962027940.0049903797209
121387.35347.44360390924639.9063960907544
122400.49336.02347254420364.4665274557973
123404.53339.41077998859265.1192200114078
124396.15348.61755036439147.5324496356089
125392.79357.49016419438535.2998358056152
126391.96353.35037212598238.6096278740182
127385.04357.79633018807927.2436698119213
128383.58357.62698924218725.953010757813
129387.46357.08370022840730.3762997715926
130382.9361.61120990285921.2887900971409
131381.04359.98332979392621.0566702060741
132377.69333.67766211125644.012337888744
133368.95340.23553128008328.7144687199168
134353.87347.0931330339466.77686696605424
135347.03331.24655022351415.7834497764859
136351.49343.5552135305227.93478646947847
137344.23342.2619145081131.96808549188703
138344.09348.452103759925-4.36210375992481
139340.51331.058054086349.4519459136598
140323.9321.8565769172772.04342308272335
141324.02333.898516832822-9.8785168328216
142323.11329.244916964035-6.13491696403537
143324.36341.706303844359-17.3463038443585
144305.55336.527502724735-30.9775027247351
145288.59329.126149148968-40.5361491489682
146289.15318.405085346438-29.2550853464382
147297.49309.281292035353-11.7912920353534
148295.94304.704449396806-8.76444939680565
149308.29299.4834897581658.80651024183498
150299.1297.3323364874241.76766351257625
151292.32287.2439939987245.07600600127625
152292.87288.6696442767744.20035572322621
153284.11307.399388319688-23.2893883196877
154288.98302.807204017791-13.8272040177912
155295.93284.22573030262911.7042696973708
156294.17273.90030447297720.2696955270228
157291.68261.22754662041730.4524533795834
158287.07262.18814599390424.8818540060957
159287.33267.4355646054819.8944353945198
160285.96270.35460564598215.6053943540179
161282.62251.14102107495931.4789789250413
162276.44268.384589867848.05541013216008
163261.31273.033793028695-11.7237930286947
164256.08281.594851512262-25.5148515122615
165256.69284.727428510656-28.0374285106558
166264.74290.646934080773-25.9069340807731
167310.72289.43202645815221.2879735418481
168293.18293.0253004428710.154699557129412
169283.07290.040708947556-6.9707089475565
170284.32304.560607204211-20.2406072042113
171299.86308.587770260304-8.72777026030408
172286.39277.8268996622638.56310033773686
173279.69277.9108870587051.77911294129464
174275.19302.582927617833-27.3929276178326
175285.73292.260685378503-6.53068537850281
176281.59285.824939122058-4.23493912205791
177274.47284.323848119625-9.85384811962496
178273.68302.821655703070-29.1416557030704
179270294.10567942433-24.10567942433
180266.01306.239982918088-40.2299829180882
181271.45262.2689283058709.18107169413049
182265.49252.16811988757413.3218801124261
183261.87268.48829330692-6.6182933069198
184263.03281.930918849107-18.9009188491067
185260.48266.363706381535-5.88370638153529
186272.36266.5562804055385.8037195944624
187269.82278.828548408282-9.00854840828226
188267.53283.623175934465-16.0931759344647
189272.39291.738504721557-19.3485047215567
190283.42302.411270330994-18.9912703309938
191283.06292.246863934736-9.18686393473557
192276.16279.819807990686-3.65980799068642
193275.85294.636185824647-18.7861858246466
194281.51310.053599421445-28.5435994214455
195295.5308.740714280962-13.2407142809625
196294.06317.448013889271-23.3880138892709
197302.68326.166034903466-23.4860349034661
198314.58340.143053988448-25.5630539884477
199321.18344.118511583722-22.9385115837220
200313.29340.521205523647-27.2312055236474
201310.25329.17562676696-18.9256267669603
202319.14353.174805062237-34.0348050622374
203316.56324.109748709095-7.5497487090951
204319.07301.4119188816317.6580811183702
205331.92317.88596661573314.0340333842671
206356.86328.90462970825127.9553702917486
207358.97326.74841788191032.2215821180905
208340.55428.762571501272-88.2125715012719
209328.18425.855572716632-97.675572716632
210355.68420.664143509429-64.9841435094295
211356.35420.918929786121-64.568929786121
212350.99432.170648837873-81.1806488378726
213359.77441.46575194891-81.6957519489102
214378.95423.050546414589-44.1005464145888
215378.92433.268560522489-54.3485605224892
216389.91442.307822285828-52.3978222858283
217406.11432.096997866598-25.9869978665976
218413.79434.488535234540-20.6985352345395
219404.95438.267059696816-33.3170596968156
220406.67446.256899726451-39.5868997264506
221403.26441.816037524717-38.5560375247168
222383.78444.096068170143-60.316068170143
223392.48424.997287786298-32.5172877862983
224398.09443.936675294541-45.8466752945407
225400.51467.773288190865-67.2632881908655
226405.28467.937267780729-62.6572677807288
227420.46472.3316739603-51.8716739603
228439.38437.5401787654711.83982123452876
229442.08426.83175119534615.2482488046541
230424.03456.329943479817-32.2999434798165
231423.35457.63735430588-34.2873543058802
232434.32491.818885335384-57.4988853353838
233429.23481.620972848264-52.390972848264
234421.87482.029214272847-60.1592142728472
235430.66517.425054874881-86.7650548748804
236424.48507.605532513912-83.1255325139124
237437.93522.063507286338-84.1335072863376
238456.05488.02867761298-31.9786776129797
239469.9489.208134500589-19.3081345005893
240476.67497.083403216378-20.4134032163778
241510.1504.9300977330035.16990226699715
242549.86511.3621170486238.4978829513802
243555511.74755481701843.2524451829816
244557.09525.08094357721732.0090564227828
245610.65552.2951776738758.3548223261303
246675.39541.950627884447133.439372115553
247596.15536.33344214515659.8165578548436
248633.71559.33241117309374.3775888269075
249632.33559.05071216237373.2792878376269
250598.06559.35911333506138.7008866649389
251585.78557.85230530119927.9276946988013
252627.83534.5742396754193.25576032459
253629.42526.409919615414103.010080384586
254631.17507.471086942905123.698913057095
255664.75520.667279337468144.082720662532
256654.9519.265508121399135.634491878601
257679.37537.145266124411142.224733875589
258666.92526.38825568026140.53174431974
259655.49549.915895539646105.574104460354
260665.3585.08309714880280.216902851198
261665.41908.180701345091-242.770701345091
262712.65904.619227644829-191.969227644829
263754.6904.729300653858-150.129300653858
264806.25924.1725560975-117.9225560975
265803.2923.250872868294-120.050872868294
266889.6926.198864248211-36.5988642482108
267922.3952.415715278387-30.115715278387
268968.43985.644315264598-17.2143152645984
269909.71013.87606792733-104.176067927328
270890.511074.36731978616-183.857319786161
271889.491111.74070332915-222.250703329146
272939.771097.31123387844-157.541233878438
273838.311019.23448542106-180.924485421061
274829.93970.584378694648-140.654378694648
275806.62914.568898513517-107.948898513517
276760.86909.58386747019-148.723867470191
277822863.076270274485-41.0762702744854
278859.19888.865603715584-29.6756037155845
279943.16893.58807832248449.5719216775158
280924.27925.845093078078-1.57509307807838
281889.5944.71882232822-55.2188223282203
282930.2997.14693032976-66.9469303297592
283945.671059.19365186386-113.523651863861
284934.231045.18018998834-110.950189988343
285949.671054.01605029028-104.346050290279
286996.591027.04223738682-30.4522373868188
2871043.161019.8902839406423.2697160593615
2881127.04966.885382735814160.154617264186
2891126.22931.27145133045194.94854866955
2901116.51951.84957542565164.660424574350
2911095.41950.776026958892144.633973041108
2921113.34959.078834703306154.261165296694
2931148.69983.067242013761165.622757986239
2941205.43956.082256184328249.347743815673
2951232.92982.156208398157250.763791601843
2961192.97961.978773932661230.991226067339
2971215.81972.01998138386243.790018616139
2981270.98960.651288810045310.328711189955
2991342.02977.75125818327364.268741816731


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
100.1436118959973420.2872237919946850.856388104002658
110.1331767295637620.2663534591275230.866823270436238
120.06219235117770990.1243847023554200.93780764882229
130.02858247442233520.05716494884467050.971417525577665
140.01252328836396560.02504657672793110.987476711636034
150.004882969765510140.009765939531020280.99511703023449
160.001803887007247320.003607774014494640.998196112992753
170.002013049295728750.00402609859145750.997986950704271
180.002320791062117870.004641582124235730.997679208937882
190.0009586077237807670.001917215447561530.99904139227622
200.0004126617169274250.000825323433854850.999587338283073
210.000164717828991870.000329435657983740.999835282171008
226.3047217025086e-050.0001260944340501720.999936952782975
230.0002768350526299250.0005536701052598490.99972316494737
240.0005575363351684710.001115072670336940.999442463664832
250.0007334818949221360.001466963789844270.999266518105078
260.0005927029648482540.001185405929696510.999407297035152
270.0002999110244044000.0005998220488087990.999700088975596
280.0001436595926982950.000287319185396590.999856340407302
297.40534891814681e-050.0001481069783629360.999925946510819
304.10206731989955e-058.2041346397991e-050.999958979326801
311.88909236193854e-053.77818472387707e-050.99998110907638
329.0910406743807e-061.81820813487614e-050.999990908959326
333.99220123218164e-067.98440246436329e-060.999996007798768
343.33401468082417e-066.66802936164834e-060.99999666598532
353.77826248012112e-067.55652496024223e-060.99999622173752
362.14882849837090e-064.29765699674179e-060.999997851171502
371.26049474103317e-062.52098948206634e-060.999998739505259
381.75115148752772e-063.50230297505544e-060.999998248848512
393.25843302042906e-066.51686604085812e-060.99999674156698
404.45004896472821e-068.90009792945642e-060.999995549951035
419.1779902794629e-061.83559805589258e-050.99999082200972
423.16796836223459e-056.33593672446918e-050.999968320316378
434.93168014668017e-059.86336029336033e-050.999950683198533
445.01045932332363e-050.0001002091864664730.999949895406767
455.6251868949957e-050.0001125037378999140.99994374813105
465.72605667407334e-050.0001145211334814670.99994273943326
474.16616283700752e-058.33232567401504e-050.99995833837163
482.38147791987208e-054.76295583974416e-050.999976185220801
491.37983104169209e-052.75966208338418e-050.999986201689583
508.05558650284883e-061.61111730056977e-050.999991944413497
514.68253378630163e-069.36506757260326e-060.999995317466214
523.0125146090866e-066.0250292181732e-060.99999698748539
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1971.47357714095912e-482.94715428191825e-481
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1993.13033398093488e-496.26066796186977e-491
2001.05493844429994e-492.10987688859988e-491
2013.48638220866432e-506.97276441732864e-501
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2161.95274193268911e-543.90548386537823e-541
2172.43498317487683e-544.86996634975367e-541
2183.84079554769954e-547.68159109539908e-541
2195.20196839935085e-541.04039367987017e-531
2201.44485867312092e-532.88971734624184e-531
2216.93203380616358e-541.38640676123272e-531
2221.79175080527695e-543.58350161055391e-541
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2321.04624763182972e-552.09249526365944e-551
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2521.57982245818818e-363.15964491637637e-361
2539.83383783156193e-361.96676756631239e-351
2541.19705440252119e-342.39410880504238e-341
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2738.55388530003498e-151.71077706000700e-140.999999999999991
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2760.4727390442392880.9454780884785750.527260955760712
2770.554981336325560.890037327348880.44501866367444
2780.8268977973112070.3462044053775850.173102202688793
2790.8632107792523650.2735784414952700.136789220747635
2800.8244175617908040.3511648764183930.175582438209196
2810.8479483147909880.3041033704180240.152051685209012
2820.8007075102508440.3985849794983130.199292489749156
2830.7220919739728660.5558160520542680.277908026027134
2840.6595835325239360.6808329349521290.340416467476064
2850.5684789826403060.8630420347193890.431521017359694
2860.4625408377581820.9250816755163640.537459162241818
2870.5352100399489540.9295799201020930.464789960051046
2880.5703438211596630.8593123576806730.429656178840337
2890.46356881965760.92713763931520.5364311803424


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level2600.928571428571429NOK
5% type I error level2610.932142857142857NOK
10% type I error level2620.935714285714286NOK