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Multiple Linear Regression

*The author of this computation has been verified*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 16 Dec 2008 12:51:28 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy.htm/, Retrieved Tue, 16 Dec 2008 20:52:17 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

205597 0 205471 0 211064 0 212856 0 217036 0 219302 0 219759 0 221388 0 220834 0 221788 0 222358 0 222972 0 224164 0 224915 0 226294 0 224690 0 227021 0 229284 0 229189 0 230032 0 229389 0 231053 0 232560 0 232681 0 231555 0 231428 0 232141 0 234939 0 235424 0 235471 0 236355 0 238693 0 236958 0 237060 0 239282 0 238252 0 241552 0 236230 0 238909 0 240723 0 242120 0 242100 0 243276 0 244677 0 243494 0 244902 0 245247 0 245578 0 243052 0 238121 0 241863 0 241203 0 243634 0 242351 0 245180 0 246126 0 244424 0 245166 0 247258 0 245094 0 246020 0 243082 0 245555 0 243685 0 247277 0 245029 0 246169 0 246778 0 244577 0 246048 0 245775 0 245328 0 245477 0 241903 0 243219 0 248088 0 248521 0 247389 0 249057 0 248916 0 249193 0 250768 1 253106 1 249829 1 249447 1 246755 1 250785 1 250140 1 255755 1 254671 1 253919 1 253741 1 252729 1 253810 1 256653 1 255231 1 258405 1 251061 1 254811 1 254895 1 258325 1 257608 1 258759 1 258621 1 257852 1 260560 1 262358 1 260812 1 261165 1 257164 1 260720 1 259581 1 264743 1 261845 1 262262 1 261631 1 258953 1 259966 1 262850 1 262204 1 263418 1 262752 1 266433 1 267722 1 266003 1 262971 1 265521 1 264676 1 270223 1 269508 1 268457 1 265814 1 266680 1 263018 1 269285 1 269829 1 270911 1 266844 1 271244 1 269907 1 271296 1 270157 1 271322 1 267179 1 264101 1 265518 1 269419 1 268714 1 272482 1 268351 1 268175 1 270674 1 272764 1 272599 1 270333 1 270846 1 270491 1 269160 1 274027 1 273784 1 276663 1 274525 1 271344 1 271115 1 270798 1 273911 1 273985 1 271917 1 273338 1 270601 1 273547 1 275363 1 281229 1 277793 1 279913 1 282500 1 280041 1 282166 1 290304 1 283519 1 287816 1 285226 1 287595 1 289741 1 289148 1 288301 0 290155 0 289648 0 288225 0 289351 0 294735 0 305333 0

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

Brutoschuld[t] = + 223036.069848789 -3280.17593296528Dummy[t] -1711.30752207312M1[t] -4560.92729279379M2[t] -1589.60956351440M3[t] -1304.29183423502M4[t] + 859.338395044333M5[t] -1106.79237148660M6[t] -436.724642207233M7[t] -241.406912927854M8[t] -1059.77668364848M9[t] -145.88545855878M10[t] + 1232.1822707206M11[t] + 357.557270720626t + 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)	223036.069848789	1125.608167	198.1472	0	0
Dummy	-3280.17593296528	840.026763	-3.9048	0.000134	6.7e-05
M1	-1711.30752207312	1403.219202	-1.2196	0.224246	0.112123
M2	-4560.92729279379	1402.792242	-3.2513	0.001374	0.000687
M3	-1589.60956351440	1402.405833	-1.1335	0.258534	0.129267
M4	-1304.29183423502	1402.060008	-0.9303	0.353492	0.176746
M5	859.338395044333	1401.754798	0.613	0.540629	0.270315
M6	-1106.79237148660	1401.235681	-0.7899	0.430655	0.215328
M7	-436.724642207233	1401.218109	-0.3117	0.755652	0.377826
M8	-241.406912927854	1401.241252	-0.1723	0.863413	0.431706
M9	-1059.77668364848	1401.305108	-0.7563	0.450482	0.225241
M10	-145.88545855878	1400.838768	-0.1041	0.917174	0.458587
M11	1232.1822707206	1400.777678	0.8796	0.38024	0.19012
t	357.557270720626	7.553159	47.3388	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.97999376366391
R-squared	0.960387776820155
Adjusted R-squared	0.957494749284548
F-TEST (value)	331.966344944853
F-TEST (DF numerator)	13
F-TEST (DF denominator)	178
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3961.9399831563
Sum Squared Residuals	2794060380.56360

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	205597	221682.319597436	-16085.3195974361
2	205471	219190.257097437	-13719.2570974367
3	211064	222519.132097437	-11455.1320974366
4	212856	223162.007097437	-10306.0070974366
5	217036	225683.194597437	-8647.19459743666
6	219302	224074.621101626	-4772.62110162627
7	219759	225102.246101626	-5343.24610162624
8	221388	225655.121101626	-4267.1211016263
9	220834	225194.308601626	-4360.30860162628
10	221788	226465.757097437	-4677.75709743664
11	222358	228201.382097437	-5843.38209743662
12	222972	227326.757097437	-4354.75709743664
13	224164	225973.006846084	-1809.00684608416
14	224915	223480.944346084	1434.05565391593
15	226294	226809.819346084	-515.819346084138
16	224690	227452.694346084	-2762.69434608415
17	227021	229973.881846084	-2952.88184608414
18	229284	228365.308350274	918.691649726187
19	229189	229392.933350274	-203.933350273815
20	230032	229945.808350274	86.191649726191
21	229389	229484.995850274	-95.9958502738156
22	231053	230756.444346084	296.555653915858
23	232560	232492.069346084	67.930653915857
24	232681	231617.444346084	1063.55565391583
25	231555	230263.694094732	1291.30590526832
26	231428	227771.631594732	3656.36840526835
27	232141	231100.506594732	1040.49340526835
28	234939	231743.381594732	3195.61840526834
29	235424	234264.569094732	1159.43090526835
30	235471	232655.995598921	2815.00440107867
31	236355	233683.620598921	2671.37940107867
32	238693	234236.495598921	4456.50440107868
33	236958	233775.683098921	3182.31690107867
34	237060	235047.131594732	2012.86840526835
35	239282	236782.756594732	2499.24340526834
36	238252	235908.131594732	2343.86840526832
37	241552	234554.381343379	6997.6186566208
38	236230	232062.318843379	4167.68115662084
39	238909	235391.193843379	3517.80615662084
40	240723	236034.068843379	4688.93115662082
41	242120	238555.256343379	3564.74365662083
42	242100	236946.682847569	5153.31715243116
43	243276	237974.307847569	5301.69215243116
44	244677	238527.182847569	6149.81715243116
45	243494	238066.370347569	5427.62965243116
46	244902	239337.818843379	5564.18115662083
47	245247	241073.443843379	4173.55615662083
48	245578	240198.818843379	5379.1811566208
49	243052	238845.068592027	4206.93140797329
50	238121	236353.006092027	1767.99390797332
51	241863	239681.881092027	2181.11890797333
52	241203	240324.756092027	878.24390797331
53	243634	242845.943592027	788.056407973321
54	242351	241237.370096216	1113.62990378365
55	245180	242264.995096216	2915.00490378365
56	246126	242817.870096216	3308.12990378365
57	244424	242357.057596216	2066.94240378364
58	245166	243628.506092027	1537.49390797332
59	247258	245364.131092027	1893.86890797332
60	245094	244489.506092027	604.493907973291
61	246020	243135.755840674	2884.24415932577
62	243082	240643.693340674	2438.30665932581
63	245555	243972.568340674	1582.43165932581
64	243685	244615.443340674	-930.443340674203
65	247277	247136.630840674	140.369159325806
66	245029	245528.057344864	-499.057344863868
67	246169	246555.682344864	-386.682344863869
68	246778	247108.557344864	-330.557344863865
69	244577	246647.744844864	-2070.74484486387
70	246048	247919.193340674	-1871.19334067420
71	245775	249654.818340674	-3879.8183406742
72	245328	248780.193340674	-3452.19334067422
73	245477	247426.443089322	-1949.44308932174
74	241903	244934.380589322	-3031.38058932171
75	243219	248263.255589322	-5044.2555893217
76	248088	248906.130589322	-818.130589321715
77	248521	251427.318089322	-2906.31808932171
78	247389	249818.744593511	-2429.74459351138
79	249057	250846.369593511	-1789.36959351138
80	248916	251399.244593511	-2483.24459351138
81	249193	250938.432093511	-1745.43209351138
82	250768	248929.704656356	1838.29534364359
83	253106	250665.329656356	2440.67034364359
84	249829	249790.704656356	38.2953436435610
85	249447	248436.954405004	1010.04559499605
86	246755	245944.891905004	810.108094996088
87	250785	249273.766905004	1511.23309499608
88	250140	249916.641905004	223.358094996073
89	255755	252437.829405004	3317.17059499608
90	254671	250829.255909194	3841.7440908064
91	253919	251856.880909194	2062.1190908064
92	253741	252409.755909194	1331.24409080640
93	252729	251948.943409194	780.056590806406
94	253810	253220.391905004	589.608094996074
95	256653	254956.016905004	1696.98309499607
96	255231	254081.391905004	1149.60809499605
97	258405	252727.641653651	5677.35834634854
98	251061	250235.579153651	825.420846348572
99	254811	253564.454153651	1246.54584634857
100	254895	254207.329153651	687.670846348554
101	258325	256728.516653651	1596.48334634857
102	257608	255119.943157841	2488.05684215889
103	258759	256147.568157841	2611.43184215889
104	258621	256700.443157841	1920.55684215890
105	257852	256239.630657841	1612.36934215889
106	260560	257511.079153651	3048.92084634856
107	262358	259246.704153651	3111.29584634856
108	260812	258372.079153651	2439.92084634853
109	261165	257018.328902299	4146.67109770102
110	257164	254526.266402299	2637.73359770105
111	260720	257855.141402299	2864.85859770106
112	259581	258498.016402299	1082.98359770104
113	264743	261019.203902299	3723.79609770105
114	261845	259410.630406489	2434.36959351138
115	262262	260438.255406489	1823.74459351138
116	261631	260991.130406489	639.869593511381
117	258953	260530.317906489	-1577.31790648862
118	259966	261801.766402299	-1835.76640229895
119	262850	263537.391402299	-687.391402298951
120	262204	262662.766402299	-458.766402298977
121	263418	261309.016150946	2108.98384905351
122	262752	258816.953650946	3935.04634905354
123	266433	262145.828650946	4287.17134905354
124	267722	262788.703650946	4933.29634905353
125	266003	265309.891150946	693.10884905354
126	262971	263701.317655136	-730.317655136134
127	265521	264728.942655136	792.057344863864
128	264676	265281.817655136	-605.817655136132
129	270223	264821.005155136	5401.99484486387
130	269508	266092.453650946	3415.54634905354
131	268457	267828.078650946	628.921349053534
132	265814	266953.453650946	-1139.45365094649
133	266680	265599.703399594	1080.29660040599
134	263018	263107.640899594	-89.6408995939712
135	269285	266436.515899594	2848.48410040603
136	269829	267079.390899594	2749.60910040602
137	270911	269600.578399594	1310.42160040603
138	266844	267992.004903784	-1148.00490378365
139	271244	269019.629903784	2224.37009621635
140	269907	269572.504903784	334.495096216354
141	271296	269111.692403784	2184.30759621635
142	270157	270383.140899594	-226.140899593977
143	271322	272118.765899594	-796.765899593979
144	267179	271244.140899594	-4065.14089959400
145	264101	269890.390648242	-5789.39064824152
146	265518	267398.328148242	-1880.32814824148
147	269419	270727.203148242	-1308.20314824148
148	268714	271370.078148242	-2656.0781482415
149	272482	273891.265648242	-1409.26564824149
150	268351	272282.692152431	-3931.69215243116
151	268175	273310.317152431	-5135.31715243116
152	270674	273863.192152431	-3189.19215243116
153	272764	273402.379652431	-638.379652431164
154	272599	274673.828148242	-2074.82814824149
155	270333	276409.453148242	-6076.45314824149
156	270846	275534.828148242	-4688.82814824152
157	270491	274181.077896889	-3690.07789688903
158	269160	271689.015396889	-2529.015396889
159	274027	275017.890396889	-990.890396888999
160	273784	275660.765396889	-1876.76539688901
161	276663	278181.952896889	-1518.95289688900
162	274525	276573.379401079	-2048.37940107868
163	271344	277601.004401079	-6257.00440107868
164	271115	278153.879401079	-7038.87940107868
165	270798	277693.066901079	-6895.06690107868
166	273911	278964.515396889	-5053.51539688901
167	273985	280700.140396889	-6715.14039688901
168	271917	279825.515396889	-7908.51539688904
169	273338	278471.765145537	-5133.76514553655
170	270601	275979.702645537	-5378.70264553651
171	273547	279308.577645537	-5761.57764553651
172	275363	279951.452645537	-4588.45264553653
173	281229	282472.640145537	-1243.64014553652
174	277793	280864.066649726	-3071.06664972619
175	279913	281891.691649726	-1978.69164972619
176	282500	282444.566649726	55.4333502738082
177	280041	281983.754149726	-1942.75414972619
178	282166	283255.202645537	-1089.20264553652
179	290304	284990.827645537	5313.17235446348
180	283519	284116.202645537	-597.202645536546
181	287816	282762.452394184	5053.54760581594
182	285226	280270.389894184	4955.61010581598
183	287595	283599.264894184	3995.73510581597
184	289741	284242.139894184	5498.86010581596
185	289148	286763.327394184	2384.67260581598
186	288301	288434.929831339	-133.929831339018
187	290155	289462.554831339	692.445168661002
188	289648	290015.429831339	-367.429831339003
189	288225	289554.617331339	-1329.61733133899
190	289351	290826.065827149	-1475.06582714933
191	294735	292561.690827149	2173.30917285067
192	305333	291687.065827149	13645.9341728506

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.67795343799609	0.644093124007821	0.322046562003911
18	0.663668903439818	0.672662193120363	0.336331096560182
19	0.645444959083835	0.70911008183233	0.354555040916165
20	0.636972913206412	0.726054173587177	0.363027086793588
21	0.611776170814498	0.776447658371003	0.388223829185502
22	0.550908806349468	0.898182387301064	0.449091193650532
23	0.466748166382345	0.933496332764691	0.533251833617655
24	0.392150652011139	0.784301304022278	0.607849347988861
25	0.309797109008952	0.619594218017903	0.690202890991048
26	0.239516549068432	0.479033098136863	0.760483450931568
27	0.234166767241384	0.468333534482768	0.765833232758616
28	0.174092396349680	0.348184792699359	0.82590760365032
29	0.159826463444398	0.319652926888796	0.840173536555602
30	0.198481958810776	0.396963917621552	0.801518041189224
31	0.197220770520160	0.394441541040319	0.80277922947984
32	0.168251460087846	0.336502920175693	0.831748539912154
33	0.156856697674257	0.313713395348514	0.843143302325743
34	0.166305571098633	0.332611142197265	0.833694428901367
35	0.145665825700352	0.291331651400705	0.854334174299648
36	0.147568003048285	0.29513600609657	0.852431996951715
37	0.129414905223924	0.258829810447847	0.870585094776076
38	0.126537749107982	0.253075498215964	0.873462250892018
39	0.115737600580725	0.231475201161451	0.884262399419275
40	0.0964088416447913	0.192817683289583	0.903591158355209
41	0.0849022272746459	0.169804454549292	0.915097772725354
42	0.0940821632079993	0.188164326415999	0.905917836792
43	0.0900859962308346	0.180171992461669	0.909914003769165
44	0.0903452073294756	0.180690414658951	0.909654792670524
45	0.0886177164093198	0.177235432818640	0.91138228359068
46	0.0818497788351401	0.163699557670280	0.91815022116486
47	0.0804540998530717	0.160908199706143	0.919545900146928
48	0.0778173412534812	0.155634682506962	0.922182658746519
49	0.081381226235065	0.16276245247013	0.918618773764935
50	0.152130266070253	0.304260532140506	0.847869733929747
51	0.187807461310657	0.375614922621314	0.812192538689343
52	0.272706307194625	0.545412614389251	0.727293692805375
53	0.333508055274033	0.667016110548065	0.666491944725967
54	0.476427197928405	0.95285439585681	0.523572802071595
55	0.5176262238164	0.9647475523672	0.4823737761836
56	0.571133109290752	0.857733781418496	0.428866890709248
57	0.622512751033941	0.754974497932118	0.377487248966059
58	0.666082960424493	0.667834079151014	0.333917039575507
59	0.677939784802139	0.644120430395722	0.322060215197861
60	0.73002352117108	0.539952957657839	0.269976478828920
61	0.71802011927944	0.563959761441121	0.281979880720561
62	0.716482248962338	0.567035502075323	0.283517751037662
63	0.712209488720995	0.575581022558009	0.287790511279005
64	0.75423305861023	0.49153388277954	0.24576694138977
65	0.757481602171284	0.485036795657431	0.242518397828716
66	0.80715394526372	0.385692109472561	0.192846054736281
67	0.839561468229986	0.320877063540028	0.160438531770014
68	0.873027728165721	0.253944543668558	0.126972271834279
69	0.908341413447988	0.183317173104024	0.091658586552012
70	0.926796975635881	0.146406048728237	0.0732030243641187
71	0.954642858538154	0.0907142829236912	0.0453571414618456
72	0.970371000971018	0.0592579980579632	0.0296289990289816
73	0.973138333081964	0.0537233338360716	0.0268616669180358
74	0.979885269384482	0.0402294612310367	0.0201147306155184
75	0.990670333826788	0.0186593323464245	0.00932966617321227
76	0.989946045158357	0.0201079096832853	0.0100539548416427
77	0.99301986683786	0.0139602663242827	0.00698013316214135
78	0.995145322893445	0.00970935421310912	0.00485467710655456
79	0.996384304564537	0.00723139087092515	0.00361569543546257
80	0.998099845083832	0.0038003098323366	0.0019001549161683
81	0.999099640007212	0.00180071998557647	0.000900359992788233
82	0.99869234785358	0.00261530429284080	0.00130765214642040
83	0.998137971188357	0.00372405762328566	0.00186202881164283
84	0.997587282105774	0.00482543578845164	0.00241271789422582
85	0.996800539334724	0.00639892133055241	0.00319946066527621
86	0.995828874811153	0.00834225037769319	0.00417112518884659
87	0.994643438097483	0.0107131238050337	0.00535656190251683
88	0.9936696715392	0.0126606569215995	0.00633032846079976
89	0.991904912137026	0.0161901757259474	0.00809508786297372
90	0.989858193623103	0.0202836127537941	0.0101418063768970
91	0.986498580642036	0.0270028387159288	0.0135014193579644
92	0.982513325944012	0.0349733481119769	0.0174866740559885
93	0.977731044966802	0.0445379100663952	0.0222689550331976
94	0.972195800485506	0.0556083990289874	0.0278041995144937
95	0.964343631903372	0.0713127361932556	0.0356563680966278
96	0.95522315047802	0.089553699043959	0.0447768495219795
97	0.953156759499799	0.0936864810004028	0.0468432405002014
98	0.94375018839384	0.112499623212319	0.0562498116061597
99	0.933099696628335	0.13380060674333	0.0669003033716649
100	0.923025982401445	0.153948035197110	0.0769740175985552
101	0.908236024762381	0.183527950475238	0.0917639752376192
102	0.890578855667242	0.218842288665515	0.109421144332758
103	0.870674238090315	0.258651523819370	0.129325761909685
104	0.84848370548858	0.303032589022838	0.151516294511419
105	0.821342417007721	0.357315165984557	0.178657582992279
106	0.797022794566714	0.405954410866572	0.202977205433286
107	0.770064641925646	0.459870716148709	0.229935358074354
108	0.737310605295096	0.525378789409807	0.262689394704904
109	0.714520189613493	0.570959620773014	0.285479810386507
110	0.675782070540043	0.648435858919914	0.324217929459957
111	0.635143551003895	0.72971289799221	0.364856448996105
112	0.597681537715196	0.804636924569608	0.402318462284804
113	0.560091738026204	0.879816523947592	0.439908261973796
114	0.53379920848168	0.93240158303664	0.46620079151832
115	0.501758568749357	0.996482862501286	0.498241431250643
116	0.470550047602434	0.941100095204867	0.529449952397566
117	0.454483710044094	0.908967420088189	0.545516289955906
118	0.443574654008602	0.887149308017205	0.556425345991398
119	0.41401150552178	0.82802301104356	0.58598849447822
120	0.381524303102757	0.763048606205513	0.618475696897243
121	0.34606891605957	0.69213783211914	0.65393108394043
122	0.323152772002291	0.646305544004582	0.676847227997709
123	0.301058941012405	0.60211788202481	0.698941058987595
124	0.290694198695611	0.581388397391221	0.709305801304389
125	0.254804015805301	0.509608031610602	0.745195984194699
126	0.235260502252238	0.470521004504475	0.764739497747762
127	0.215803804475911	0.431607608951823	0.784196195524089
128	0.196713651251547	0.393427302503094	0.803286348748453
129	0.241069990140848	0.482139980281695	0.758930009859152
130	0.258808561936984	0.517617123873968	0.741191438063016
131	0.237133876587704	0.474267753175409	0.762866123412296
132	0.213053066902757	0.426106133805514	0.786946933097243
133	0.200804466937012	0.401608933874025	0.799195533062988
134	0.176850040057223	0.353700080114446	0.823149959942777
135	0.170528454282763	0.341056908565527	0.829471545717237
136	0.165968960748849	0.331937921497699	0.83403103925115
137	0.147946543714983	0.295893087429966	0.852053456285017
138	0.143315320094847	0.286630640189693	0.856684679905153
139	0.194836415942487	0.389672831884975	0.805163584057513
140	0.219995168837042	0.439990337674083	0.780004831162958
141	0.311825282999358	0.623650565998715	0.688174717000642
142	0.361765785847424	0.723531571694849	0.638234214152576
143	0.383731299261834	0.767462598523667	0.616268700738166
144	0.366258230306289	0.732516460612578	0.633741769693711
145	0.373512695059956	0.747025390119912	0.626487304940044
146	0.350008375979755	0.70001675195951	0.649991624020245
147	0.333067478292206	0.666134956584413	0.666932521707794
148	0.303686600620254	0.607373201240508	0.696313399379746
149	0.280660343167937	0.561320686335874	0.719339656832063
150	0.270226418698661	0.540452837397323	0.729773581301339
151	0.266523729973263	0.533047459946526	0.733476270026737
152	0.276441519278908	0.552883038557815	0.723558480721092
153	0.407806510065357	0.815613020130714	0.592193489934643
154	0.505924169659017	0.988151660681965	0.494075830340983
155	0.477044732847899	0.954089465695799	0.522955267152101
156	0.431900214834423	0.863800429668846	0.568099785165577
157	0.392036705968747	0.784073411937494	0.607963294031253
158	0.372957064512095	0.74591412902419	0.627042935487905
159	0.43706508094961	0.87413016189922	0.56293491905039
160	0.467816947245558	0.935633894491115	0.532183052754442
161	0.569380092191107	0.861239815617786	0.430619907808893
162	0.699750000560878	0.600499998878243	0.300249999439122
163	0.681508421192954	0.636983157614093	0.318491578807046
164	0.645373155857227	0.709253688285546	0.354626844142773
165	0.652645481806656	0.694709036386687	0.347354518193344
166	0.745512704390097	0.508974591219806	0.254487295609903
167	0.678686191177471	0.642627617645057	0.321313808822529
168	0.66856268761612	0.66287462476776	0.33143731238388
169	0.586790896339435	0.82641820732113	0.413209103660565
170	0.504892307846482	0.990215384307036	0.495107692153518
171	0.421205672916922	0.842411345833844	0.578794327083078
172	0.381677337881934	0.763354675763868	0.618322662118066
173	0.268948301608981	0.537896603217961	0.73105169839102
174	0.171145228843345	0.342290457686689	0.828854771156655
175	0.0931537259968531	0.186307451993706	0.906846274003147

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	9	0.0566037735849057	NOK
5% type I error level	20	0.125786163522013	NOK
10% type I error level	27	0.169811320754717	NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/10ahyj1229457081.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/10ahyj1229457081.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/1trbo1229457081.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/3bll61229457081.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/4eklq1229457081.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/5qcqk1229457081.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/6patb1229457081.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/7b1gd1229457081.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/8kxtr1229457081.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/9azii1229457081.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229457127w46x33fw7m06epy/9azii1229457081.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)

library(lmtest)

n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test

par1 <- as.numeric(par1)

x <- t(y)

k <- length(x[1,])

n <- length(x[,1])

x1 <- cbind(x[,par1], x[,1:k!=par1])

mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])

colnames(x1) <- mycolnames #colnames(x)[par1]

x <- x1

if (par3 == 'First Differences'){

x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))

for (i in 1:n-1) {

for (j in 1:k) {

x2[i,j] <- x[i+1,j] - x[i,j]

}

}

x <- x2

}

if (par2 == 'Include Monthly Dummies'){

x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))

for (i in 1:11){

x2[seq(i,n,12),i] <- 1

}

x <- cbind(x, x2)

}

if (par2 == 'Include Quarterly Dummies'){

x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))

for (i in 1:3){

x2[seq(i,n,4),i] <- 1

}

x <- cbind(x, x2)

}

k <- length(x[1,])

if (par3 == 'Linear Trend'){

x <- cbind(x, c(1:n))

colnames(x)[k+1] <- 't'

}

x

k <- length(x[1,])

df <- as.data.frame(x)

(mylm <- lm(df))

(mysum <- summary(mylm))

if (n > n25) {

kp3 <- k + 3

nmkm3 <- n - k - 3

gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))

numgqtests <- 0

numsignificant1 <- 0

numsignificant5 <- 0

numsignificant10 <- 0

for (mypoint in kp3:nmkm3) {

j <- 0

numgqtests <- numgqtests + 1

for (myalt in c('greater', 'two.sided', 'less')) {

j <- j + 1

gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value

}

if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1

if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1

if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1

}

gqarr

}

bitmap(file='test0.png')

plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')

points(x[,1]-mysum$resid)

grid()

dev.off()

bitmap(file='test1.png')

plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')

grid()

dev.off()

bitmap(file='test2.png')

hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')

grid()

dev.off()

bitmap(file='test3.png')

densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')

dev.off()

bitmap(file='test4.png')

qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')

qqline(mysum$resid)

grid()

dev.off()

(myerror <- as.ts(mysum$resid))

bitmap(file='test5.png')

dum <- cbind(lag(myerror,k=1),myerror)

dum

dum1 <- dum[2:length(myerror),]

dum1

z <- as.data.frame(dum1)

z

plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')

lines(lowess(z))

abline(lm(z))

grid()

dev.off()

bitmap(file='test6.png')

acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')

grid()

dev.off()

bitmap(file='test7.png')

pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')

grid()

dev.off()

bitmap(file='test8.png')

opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))

plot(mylm, las = 1, sub='Residual Diagnostics')

par(opar)

dev.off()

if (n > n25) {

bitmap(file='test9.png')

plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')

grid()

dev.off()

}

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)

a<-table.row.end(a)

myeq <- colnames(x)[1]

myeq <- paste(myeq, '[t] = ', sep='')

for (i in 1:k){

if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')

myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')

if (rownames(mysum$coefficients)[i] != '(Intercept)') {

myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')

if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')

}

}

myeq <- paste(myeq, ' + e[t]')

a<-table.row.start(a)

a<-table.element(a, myeq)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable1.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Variable',header=TRUE)

a<-table.element(a,'Parameter',header=TRUE)

a<-table.element(a,'S.D.',header=TRUE)

a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)

a<-table.element(a,'2-tail p-value',header=TRUE)

a<-table.element(a,'1-tail p-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:k){

a<-table.row.start(a)

a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)

a<-table.element(a,mysum$coefficients[i,1])

a<-table.element(a, round(mysum$coefficients[i,2],6))

a<-table.element(a, round(mysum$coefficients[i,3],4))

a<-table.element(a, round(mysum$coefficients[i,4],6))

a<-table.element(a, round(mysum$coefficients[i,4]/2,6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple R',1,TRUE)

a<-table.element(a, sqrt(mysum$r.squared))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'R-squared',1,TRUE)

a<-table.element(a, mysum$r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Adjusted R-squared',1,TRUE)

a<-table.element(a, mysum$adj.r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (value)',1,TRUE)

a<-table.element(a, mysum$fstatistic[1])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[2])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[3])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'p-value',1,TRUE)

a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Residual Standard Deviation',1,TRUE)

a<-table.element(a, mysum$sigma)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Sum Squared Residuals',1,TRUE)

a<-table.element(a, sum(myerror*myerror))

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable3.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Time or Index', 1, TRUE)

a<-table.element(a, 'Actuals', 1, TRUE)

a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)

a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)

a<-table.row.end(a)

for (i in 1:n) {

a<-table.row.start(a)

a<-table.element(a,i, 1, TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i]-mysum$resid[i])

a<-table.element(a,mysum$resid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable4.tab')

if (n > n25) {

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'p-values',header=TRUE)

a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'breakpoint index',header=TRUE)

a<-table.element(a,'greater',header=TRUE)

a<-table.element(a,'2-sided',header=TRUE)

a<-table.element(a,'less',header=TRUE)

a<-table.row.end(a)

for (mypoint in kp3:nmkm3) {

a<-table.row.start(a)

a<-table.element(a,mypoint,header=TRUE)

a<-table.element(a,gqarr[mypoint-kp3+1,1])

a<-table.element(a,gqarr[mypoint-kp3+1,2])

a<-table.element(a,gqarr[mypoint-kp3+1,3])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable5.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Description',header=TRUE)

a<-table.element(a,'# significant tests',header=TRUE)

a<-table.element(a,'% significant tests',header=TRUE)

a<-table.element(a,'OK/NOK',header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'1% type I error level',header=TRUE)

a<-table.element(a,numsignificant1)

a<-table.element(a,numsignificant1/numgqtests)

if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'5% type I error level',header=TRUE)

a<-table.element(a,numsignificant5)

a<-table.element(a,numsignificant5/numgqtests)

if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'10% type I error level',header=TRUE)

a<-table.element(a,numsignificant10)

a<-table.element(a,numsignificant10/numgqtests)

if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable6.tab')

}

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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