Home » date » 2008 » Dec » 13 »

paper

*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: Sat, 13 Dec 2008 06:49:32 -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/13/t122917628679y53ggqsc9how0.htm/, Retrieved Sat, 13 Dec 2008 14:51:36 +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/13/t122917628679y53ggqsc9how0.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 «

6340,5 0 7901,5 0 8191,1 0 7181,7 0 7594,4 0 7384,7 0 7876,7 0 8463,4 0 8317,2 0 7778,7 0 8532,8 0 7272,2 0 6680,1 0 8427,6 0 8752,8 0 7952,7 0 8694,3 0 7787 0 8474,2 0 9154,7 0 8557,2 0 7951,1 0 9156,7 0 7865,7 0 7337,4 0 9131,7 0 8814,6 0 8598,8 0 8439,6 0 7451,8 0 8016,2 0 9544,1 0 8270,7 0 8102,2 0 9369 0 7657,7 0 7816,6 0 9391,3 0 9445,4 0 9533,1 0 10068,7 0 8955,5 0 10423,9 0 11617,2 0 9391,1 0 10872 0 10230,4 0 9221 0 9428,6 0 10934,5 0 10986 0 11724,6 0 11180,9 0 11163,2 0 11240,9 0 12107,1 0 10762,3 0 11340,4 0 11266,8 0 9542,7 0 9227,7 0 10571,9 0 10774,4 0 10392,8 0 9920,2 0 9884,9 1 10174,5 1 11395,4 1 10760,2 1 10570,1 1 10536 1 9902,6 1 8889 1 10837,3 1 11624,1 1 10509 1 10984,9 1 10649,1 1 10855,7 1 11677,4 1 10760,2 1 10046,2 1 10772,8 1 9987,7 1 8638,7 1 11063,7 1 11855,7 1 10684,5 1 11337,4 1 10478 1 11123,9 1 12909,3 1 11339,9 1 10462,2 1 12733,5 1 10519,2 1 10414,9 1 12476,8 1 12384,6 1 12266,7 1 12919,9 1 11497,3 1 12142 1 13919,4 1 12656,8 1 12034,1 1 13199,7 1 10881,3 1 11301,2 1 13643,9 1 12517 1 13981,1 1 14275,7 1 13435 1 13565,7 1 16216,3 1 12970 1 14079,9 1 14235 1 12213,4 1 12581 1

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 5906.22198597221 -1277.30401026107x[t] -274.589574772598M1[t] + 1446.17899581606M2[t] + 1478.50505613185M3[t] + 1162.21111644763M4[t] + 1357.08717676341M5[t] + 747.643638105304M6[t] + 1204.13969842109M7[t] + 2450.97575873687M8[t] + 1064.88181905265M9[t] + 945.787879368435M10[t] + 1561.14393968422M11[t] + 64.2239396842171t + 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)	5906.22198597221	224.51576	26.3065	0	0
x	-1277.30401026107	216.050221	-5.9121	0	0
M1	-274.589574772598	259.807241	-1.0569	0.292939	0.146469
M2	1446.17899581606	266.27891	5.4311	0	0
M3	1478.50505613185	266.155941	5.555	0	0
M4	1162.21111644763	266.068631	4.3681	2.9e-05	1.5e-05
M5	1357.08717676341	266.017015	5.1015	1e-06	1e-06
M6	747.643638105304	266.421156	2.8062	0.005956	0.002978
M7	1204.13969842109	266.22492	4.523	1.6e-05	8e-06
M8	2450.97575873687	266.064255	9.212	0	0
M9	1064.88181905265	265.939226	4.0042	0.000115	5.8e-05
M10	945.787879368435	265.849884	3.5576	0.000559	0.00028
M11	1561.14393968422	265.796264	5.8735	0	0
t	64.2239396842171	3.082571	20.8345	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.95690842309601
R-squared	0.91567373019209
Adjusted R-squared	0.90542848245842
F-TEST (value)	89.3754601152988
F-TEST (DF numerator)	13
F-TEST (DF denominator)	107
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	594.298543635704
Sum Squared Residuals	37791411.2095245

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	6340.5	5695.85635088381	644.643649116188
2	7901.5	7480.8488611567	420.651138843303
3	8191.1	7577.3988611567	613.701138843297
4	7181.7	7325.3288611567	-143.628861156701
5	7594.4	7584.4288611567	9.97113884329899
6	7384.7	7039.2092621828	345.490737817196
7	7876.7	7559.92926218281	316.770737817188
8	8463.4	8870.98926218281	-407.589262182813
9	8317.2	7549.11926218281	768.080737817188
10	7778.7	7494.24926218281	284.450737817190
11	8532.8	8173.82926218281	358.970737817188
12	7272.2	6676.90926218281	595.29073781719
13	6680.1	6466.54362709443	213.556372905570
14	8427.6	8251.53613736731	176.063862632692
15	8752.8	8348.08613736731	404.71386263269
16	7952.7	8096.01613736731	-143.31613736731
17	8694.3	8355.11613736731	339.18386263269
18	7787	7809.89653839342	-22.8965383934169
19	8474.2	8330.61653839342	143.583461606584
20	9154.7	9641.67653839342	-486.976538393415
21	8557.2	8319.80653839342	237.393461606584
22	7951.1	8264.93653839342	-313.836538393416
23	9156.7	8944.51653839342	212.183461606584
24	7865.7	7447.59653839342	418.103461606584
25	7337.4	7237.23090330504	100.169096694964
26	9131.7	9022.22341357792	109.476586422085
27	8814.6	9118.77341357792	-304.173413577915
28	8598.8	8866.70341357791	-267.903413577916
29	8439.6	9125.80341357791	-686.203413577915
30	7451.8	8580.58381460402	-1128.78381460402
31	8016.2	9101.30381460402	-1085.10381460402
32	9544.1	10412.3638146040	-868.263814604021
33	8270.7	9090.49381460402	-819.793814604021
34	8102.2	9035.62381460402	-933.423814604022
35	9369	9715.20381460402	-346.203814604022
36	7657.7	8218.28381460402	-560.583814604021
37	7816.6	8007.91817951564	-191.318179515641
38	9391.3	9792.91068978852	-401.610689788522
39	9445.4	9889.46068978852	-444.060689788521
40	9533.1	9637.39068978852	-104.290689788520
41	10068.7	9896.49068978852	172.209310211480
42	8955.5	9351.27109081463	-395.771090814628
43	10423.9	9871.99109081463	551.908909185372
44	11617.2	11183.0510908146	434.148909185373
45	9391.1	9861.18109081463	-470.081090814627
46	10872	9806.31109081463	1065.68890918537
47	10230.4	10485.8910908146	-255.491090814628
48	9221	8988.97109081463	232.028909185373
49	9428.6	8778.60545572625	649.994544273754
50	10934.5	10563.5979659991	370.902034000873
51	10986	10660.1479659991	325.852034000874
52	11724.6	10408.0779659991	1316.52203400087
53	11180.9	10667.1779659991	513.722034000873
54	11163.2	10121.9583670252	1041.24163297477
55	11240.9	10642.6783670252	598.221632974766
56	12107.1	11953.7383670252	153.361632974767
57	10762.3	10631.8683670252	130.431632974765
58	11340.4	10576.9983670252	763.401632974766
59	11266.8	11256.5783670252	10.2216329747667
60	9542.7	9759.65836702523	-216.958367025232
61	9227.7	9549.29273193685	-321.592731936852
62	10571.9	11334.2852422097	-762.385242209734
63	10774.4	11430.8352422097	-656.435242209732
64	10392.8	11178.7652422097	-785.965242209731
65	9920.2	11437.8652422097	-1517.66524220973
66	9884.9	9615.34163297477	269.558367025232
67	10174.5	10136.0616329748	38.4383670252339
68	11395.4	11447.1216329748	-51.7216329747669
69	10760.2	10125.2516329748	634.948367025234
70	10570.1	10070.3816329748	499.718367025233
71	10536	10749.9616329748	-213.961632974767
72	9902.6	9253.04163297477	649.558367025234
73	8889	9042.67599788639	-153.675997886386
74	10837.3	10827.6685081593	9.6314918407335
75	11624.1	10924.2185081593	699.881491840735
76	10509	10672.1485081593	-163.148508159265
77	10984.9	10931.2485081593	53.651491840734
78	10649.1	10386.0289091854	263.071090814627
79	10855.7	10906.7489091854	-51.0489091853717
80	11677.4	12217.8089091854	-540.408909185372
81	10760.2	10895.9389091854	-135.738909185372
82	10046.2	10841.0689091854	-794.868909185372
83	10772.8	11520.6489091854	-747.848909185373
84	9987.7	10023.7289091854	-36.0289091853711
85	8638.7	9813.363274097	-1174.66327409699
86	11063.7	11598.3557843699	-534.655784369871
87	11855.7	11694.9057843699	160.794215630129
88	10684.5	11442.8357843699	-758.335784369871
89	11337.4	11701.9357843699	-364.535784369871
90	10478	11156.7161853960	-678.716185395979
91	11123.9	11677.4361853960	-553.536185395978
92	12909.3	12988.4961853960	-79.1961853959782
93	11339.9	11666.6261853960	-326.726185395978
94	10462.2	11611.7561853960	-1149.55618539598
95	12733.5	12291.3361853960	442.163814604022
96	10519.2	10794.4161853960	-275.216185395977
97	10414.9	10584.0505503076	-169.150550307598
98	12476.8	12369.0430605805	107.756939419522
99	12384.6	12465.5930605805	-80.9930605804765
100	12266.7	12213.5230605805	53.1769394195241
101	12919.9	12472.6230605805	447.276939419523
102	11497.3	11927.4034616066	-430.103461606585
103	12142	12448.1234616066	-306.123461606583
104	13919.4	13759.1834616066	160.216538393416
105	12656.8	12437.3134616066	219.486538393416
106	12034.1	12382.4434616066	-348.343461606583
107	13199.7	13062.0234616066	137.676538393417
108	10881.3	11565.1034616066	-683.803461606584
109	11301.2	11354.7378265182	-53.5378265182022
110	13643.9	13139.7303367911	504.169663208917
111	12517	13236.2803367911	-719.280336791083
112	13981.1	12984.2103367911	996.889663208918
113	14275.7	13243.3103367911	1032.38966320892
114	13435	12698.0907378172	736.90926218281
115	13565.7	13218.8107378172	346.889262182812
116	16216.3	14529.8707378172	1686.42926218281
117	12970	13208.0007378172	-238.000737817189
118	14079.9	13153.1307378172	926.76926218281
119	14235	13832.7107378172	402.289262182811
120	12213.4	12335.7907378172	-122.390737817189
121	12581	12125.4251027288	455.574897271191

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.0722072391912238	0.144414478382448	0.927792760808776
18	0.0296893091522136	0.0593786183044273	0.970310690847786
19	0.0090979698414212	0.0181959396828424	0.990902030158579
20	0.00265665370494058	0.00531330740988116	0.99734334629506
21	0.00180332347318125	0.00360664694636251	0.998196676526819
22	0.00127363809630055	0.0025472761926011	0.9987263619037
23	0.00041037309421727	0.00082074618843454	0.999589626905783
24	0.000129916863852335	0.00025983372770467	0.999870083136148
25	3.72330480680559e-05	7.44660961361118e-05	0.999962766951932
26	1.21369722578842e-05	2.42739445157685e-05	0.999987863027742
27	2.49623970458331e-05	4.99247940916662e-05	0.999975037602954
28	1.15767391884147e-05	2.31534783768294e-05	0.999988423260812
29	1.95578608982100e-05	3.91157217964201e-05	0.999980442139102
30	0.000263175743543987	0.000526351487087973	0.999736824256456
31	0.000979289242744757	0.00195857848548951	0.999020710757255
32	0.000582454101199112	0.00116490820239822	0.9994175458988
33	0.00124872909246611	0.00249745818493222	0.998751270907534
34	0.000944072077744546	0.00188814415548909	0.999055927922256
35	0.000469738066223123	0.000939476132446245	0.999530261933777
36	0.000370577828333948	0.000741155656667895	0.999629422171666
37	0.000252668272069851	0.000505336544139702	0.99974733172793
38	0.000138403266235195	0.000276806532470390	0.999861596733765
39	7.13700318296091e-05	0.000142740063659218	0.99992862996817
40	0.000246002158687302	0.000492004317374605	0.999753997841313
41	0.000951992895828328	0.00190398579165666	0.999048007104172
42	0.000940856412088906	0.00188171282417781	0.999059143587911
43	0.00715661088537013	0.0143132217707403	0.99284338911463
44	0.0358534711286882	0.0717069422573765	0.964146528871312
45	0.0268967763185419	0.0537935526370838	0.973103223681458
46	0.139276672533538	0.278553345067076	0.860723327466462
47	0.10893258519538	0.21786517039076	0.89106741480462
48	0.0903770177342518	0.180754035468504	0.909622982265748
49	0.108652003024476	0.217304006048953	0.891347996975524
50	0.102276319482678	0.204552638965356	0.897723680517322
51	0.0918270478930808	0.183654095786162	0.908172952106919
52	0.287279584807987	0.574559169615974	0.712720415192013
53	0.290881208325663	0.581762416651325	0.709118791674337
54	0.450817510171593	0.901635020343186	0.549182489828407
55	0.47574913077944	0.95149826155888	0.52425086922056
56	0.436167342521899	0.872334685043797	0.563832657478101
57	0.39438379119182	0.78876758238364	0.60561620880818
58	0.500926699055934	0.998146601888132	0.499073300944066
59	0.473925313994905	0.94785062798981	0.526074686005095
60	0.460979854585485	0.92195970917097	0.539020145414515
61	0.485074427297048	0.970148854594096	0.514925572702952
62	0.487767384228685	0.97553476845737	0.512232615771315
63	0.484128752201638	0.968257504403275	0.515871247798362
64	0.505394583202012	0.989210833595976	0.494605416797988
65	0.573537015190505	0.85292596961899	0.426462984809495
66	0.536824094224816	0.926351811550368	0.463175905775184
67	0.497105705111935	0.99421141022387	0.502894294888065
68	0.438104943902965	0.87620988780593	0.561895056097035
69	0.47883035586953	0.95766071173906	0.52116964413047
70	0.544598915949228	0.910802168101543	0.455401084050772
71	0.498080476781760	0.996160953563521	0.501919523218240
72	0.627935399442982	0.744129201114035	0.372064600557018
73	0.625521607114327	0.748956785771346	0.374478392885673
74	0.588122238089005	0.82375552382199	0.411877761910995
75	0.74425174416973	0.511496511660542	0.255748255830271
76	0.706883836638129	0.586232326723742	0.293116163361871
77	0.659670563867266	0.680658872265467	0.340329436132734
78	0.717254668664688	0.565490662670625	0.282745331335312
79	0.740462904470769	0.519074191058463	0.259537095529231
80	0.70896228136807	0.582075437263861	0.291037718631931
81	0.717247788814828	0.565504422370345	0.282752211185172
82	0.709409569009257	0.581180861981487	0.290590430990743
83	0.678550246058418	0.642899507883164	0.321449753941582
84	0.782482406099013	0.435035187801974	0.217517593900987
85	0.791959181519944	0.416081636960112	0.208040818480056
86	0.74604594268131	0.50790811463738	0.25395405731869
87	0.851397904107404	0.297204191785193	0.148602095892596
88	0.847234494178458	0.305531011643084	0.152765505821542
89	0.81998599214336	0.36002801571328	0.18001400785664
90	0.776664396649887	0.446671206700227	0.223335603350113
91	0.71747926280309	0.565041474393821	0.282520737196910
92	0.673334522203723	0.653330955592553	0.326665477796277
93	0.607746923943916	0.784506152112168	0.392253076056084
94	0.684593085036964	0.630813829926072	0.315406914963036
95	0.708679864253289	0.582640271493422	0.291320135746711
96	0.742757278617457	0.514485442765086	0.257242721382543
97	0.693559651434648	0.612880697130705	0.306440348565352
98	0.607523249820329	0.784953500359342	0.392476750179671
99	0.783918319342081	0.432163361315838	0.216081680657919
100	0.702927744100214	0.594144511799572	0.297072255899786
101	0.602427334536039	0.795145330927923	0.397572665463961
102	0.527087572978808	0.945824854042383	0.472912427021192
103	0.382545114922416	0.765090229844832	0.617454885077584
104	0.466870865663728	0.933741731327455	0.533129134336272

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	23	0.261363636363636	NOK
5% type I error level	25	0.284090909090909	NOK
10% type I error level	28	0.318181818181818	NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/10910i1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/10910i1229176166.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/1ihxa1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/1ihxa1229176166.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/2snzw1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/2snzw1229176166.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/3ca5i1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/3ca5i1229176166.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/41z8e1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/41z8e1229176166.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/5mzdf1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/5mzdf1229176166.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/6wxmd1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/6wxmd1229176166.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/712kr1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/712kr1229176166.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/88z9x1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/88z9x1229176166.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/91iiq1229176166.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t122917628679y53ggqsc9how0/91iiq1229176166.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by