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workshop 7

*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, 23 Nov 2010 14:21:20 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk.htm/, Retrieved Tue, 23 Nov 2010 15:20:43 +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/2010/Nov/23/t1290522038ws66008p4asg5wk.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

3 3 3 3 3 3 5 5 5 1 5 5 4 4 4 3 3 4 4 4 4 3 4 4 5 4 4 1 4 4 5 3 5 1 5 5 2 1 3 5 3 2 5 4 4 2 4 4 4 4 4 2 4 4 4 4 4 2 5 4 5 4 5 4 5 4 3 3 3 3 3 3 5 4 4 2 4 4 3 3 3 3 3 3 5 4 5 1 5 4 3 3 3 3 3 3 4 5 4 2 4 4 5 4 5 1 5 5 4 3 3 3 4 3 3 3 3 3 3 3 4 4 3 2 4 3 4 3 4 2 4 3 3 3 3 3 3 3 3 3 3 3 4 3 4 5 5 1 4 4 5 5 5 1 4 4 4 4 4 1 4 4 4 4 4 1 4 4 4 5 4 1 4 4 4 4 4 3 4 4 4 4 5 1 4 4 3 3 3 3 3 3 4 4 4 1 4 4 5 4 5 2 5 5 4 4 4 1 4 4 4 4 4 2 4 4 3 4 4 2 4 4 4 4 4 2 3 4 4 3 4 1 5 4 4 4 4 3 4 4 5 2 4 1 5 3 4 4 4 1 4 4 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 1 3 4 4 3 4 2 4 3 4 4 4 4 4 4 5 4 4 2 4 4 4 4 4 1 4 3 5 4 4 1 4 4 4 4 4 2 4 4 4 4 4 2 4 4 4 3 3 3 4 4 4 4 5 5 4 5 4 3 4 2 3 3 5 4 4 1 4 4 4 4 4 1 4 4 4 3 5 1 4 4 4 4 4 1 4 4 4 4 4 2 4 4 3 3 2 2 3 3 4 4 4 2 4 4 5 4 1 4 4 1 3 2 3 3 3 3 3 3 3 3 3 5 4 5 1 4 4 4 4 3 2 4 4 4 4 4 1 4 4 3 4 3 3 3 4 4 3 4 2 4 4 4 4 4 2 4 4 3 3 3 3 3 3 5 3 4 1 4 4 4 3 3 1 4 3 5 5 4 1 5 5 4 4 5 2 5 5 4 4 4 2 4 4 4 2 4 1 4 4 4 4 4 1 4 4 etc...

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	9 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Multiple Linear Regression - Estimated Regression Equation

Part_of_team[t] = + 5.81048931666183 -0.156605514625096Respect_of_coach[t] -0.295803656235203Respect_of_team[t] -0.423699767643735Be_on_different_team[t] + 0.29183798031099Be_liked[t] -0.156382636161066Proudness[t] + 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)	5.81048931666183	0.648255	8.9633	0	0
Respect_of_coach	-0.156605514625096	0.101821	-1.538	0.126076	0.063038
Respect_of_team	-0.295803656235203	0.070444	-4.1991	4.5e-05	2.3e-05
Be_on_different_team	-0.423699767643735	0.06709	-6.3154	0	0
Be_liked	0.29183798031099	0.133002	2.1942	0.029706	0.014853
Proudness	-0.156382636161066	0.125873	-1.2424	0.215972	0.107986

Multiple Linear Regression - Regression Statistics
Multiple R	0.518329919577727
R-squared	0.268665905529453
Adjusted R-squared	0.245074483127177
F-TEST (value)	11.3882876983092
F-TEST (DF numerator)	5
F-TEST (DF denominator)	155
p-value	2.26940699565858e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.05384274249476
Sum Squared Residuals	172.140601515875

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3	3.5885285335995	-0.588528533599502
2	5	3.80202041546622	1.19797958453378
3	4	2.97973672657813	1.02026327342187
4	4	3.27157470688912	0.728425293110878
5	5	4.11897424217659	0.881025757823407
6	5	4.11523144471641	0.884768555283591
7	2	3.21072266372329	-1.21072266372329
8	5	3.69527447453286	1.30472552546714
9	4	3.69527447453286	0.304725525467142
10	4	3.98711245484385	0.0128875451561523
11	5	2.84390926332117	2.15609073667883
12	3	3.5885285335995	-0.588528533599499
13	5	3.69527447453286	1.30472552546714
14	3	3.5885285335995	-0.588528533599499
15	5	4.11500856625238	0.884991433747621
16	3	3.5885285335995	-0.588528533599499
17	4	3.53866895990776	0.461331040092238
18	5	3.95862593009131	1.04137406990869
19	4	3.88036651391049	0.119633486089512
20	3	3.5885285335995	-0.588528533599499
21	4	4.14746076692913	-0.147460766929127
22	4	4.00826262531902	-0.00826262531901992
23	3	3.5885285335995	-0.588528533599499
24	3	3.88036651391049	-0.880366513910488
25	4	3.66656507131629	0.333434928683707
26	5	3.66656507131629	1.33343492868371
27	4	4.11897424217659	-0.118974242176593
28	4	4.11897424217659	-0.118974242176593
29	4	3.9623687275515	0.0376312724485033
30	4	3.27157470688912	0.728425293110877
31	4	3.82317058594139	0.176829414058611
32	3	3.5885285335995	-0.588528533599499
33	4	4.11897424217659	-0.118974242176593
34	5	3.53492616244758	1.46507383755242
35	4	4.11897424217659	-0.118974242176593
36	4	3.69527447453286	0.304725525467142
37	3	3.69527447453286	-0.695274474532858
38	4	3.40343649422187	0.596563505778132
39	4	4.56741773711268	-0.567417737112678
40	4	3.27157470688912	0.728425293110877
41	5	4.88040588789884	0.11959411210116
42	4	4.11897424217659	-0.118974242176593
43	3	3.5885285335995	-0.588528533599499
44	3	3.5885285335995	-0.588528533599499
45	4	3.8271362618656	0.172863738134397
46	4	4.00826262531902	-0.00826262531901992
47	4	2.84787493924539	1.15212506075461
48	5	3.69527447453286	1.30472552546714
49	4	4.27535687833766	-0.275356878337659
50	5	4.11897424217659	0.881025757823407
51	4	3.69527447453286	0.304725525467142
52	4	3.69527447453286	0.304725525467142
53	4	3.72398387774942	0.276016122250578
54	4	1.97198887920539	2.02801112079461
55	4	3.71642464500803	0.28357535499197
56	5	4.11897424217659	0.881025757823407
57	4	4.11897424217659	-0.118974242176593
58	4	3.97977610056649	0.020223899433515
59	4	4.11897424217659	-0.118974242176593
60	4	3.69527447453286	0.304725525467142
61	3	4.30803195747844	-1.30803195747844
62	4	3.69527447453286	0.304725525467142
63	5	4.2044338164342	0.795566183565803
64	3	3.74513404822459	-0.745134048224594
65	3	3.27576326127737	-0.275763261277366
66	4	3.5786803933259	0.421319606674098
67	4	3.59608776634089	0.403912233659109
68	4	3.89166854411206	0.108331455887936
69	4	3.72398387774942	0.276016122250578
70	3	3.43948225171579	-0.439482251715795
71	4	3.59586488787686	0.404135112123139
72	3	3.27576326127737	-0.275763261277366
73	3	3.735285907951	-0.735285907950998
74	3	3.44367080610404	-0.443670806104038
75	5	3.60342412061825	1.39657587938175
76	4	3.15101494975795	0.848985050242046
77	4	3.43948225171579	0.560517748284205
78	2	3.735285907951	-1.735285907951
79	4	3.89166854411206	0.108331455887936
80	3	3.27576326127737	-0.275763261277366
81	4	3.1552035041462	0.844796495853803
82	4	3.1476442714048	0.852355728595195
83	4	4.18372940288708	-0.183729402887084
84	4	3.28309961555473	0.716900384445271
85	4	3.15498062568217	0.845019374317832
86	4	3.735285907951	0.264714092049002
87	4	3.59586488787686	0.404135112123139
88	3	3.43214589743843	-0.432145897438432
89	4	3.43948225171579	0.560517748284205
90	3	3.17216512023313	-0.172165120233127
91	3	3.27576326127737	-0.275763261277366
92	5	3.28309961555473	1.71690038444527
93	4	3.57890327178993	0.421096728210068
94	5	4.02712388826199	0.972876111738012
95	4	3.735285907951	0.264714092049002
96	3	3.43948225171579	-0.439482251715795
97	3	3.735285907951	-0.735285907950998
98	4	4.02712388826199	-0.0271238882619879
99	4	4.02712388826199	-0.0271238882619879
100	4	3.43948225171579	0.560517748284205
101	5	3.57890327178993	1.42109672821007
102	5	3.15498062568217	1.84501937431783
103	3	3.14367859548059	-0.143678595480592
104	5	3.46796877646833	1.53203122353167
105	4	3.28309961555473	0.716900384445271
106	4	3.14367859548059	0.856321404519408
107	4	3.30402690756587	0.695973092434129
108	3	3.74491116976056	-0.744911169760565
109	4	3.2470538580608	0.752946141939198
110	5	2.59818805924174	2.40181194075826
111	4	3.4531468272706	0.546853172729401
112	5	2.03521651216687	2.96478348783313
113	1	5.61165709890741	-4.61165709890741
114	4	3.2965413126455	0.703458687354497
115	5	2.46273271509181	2.53726728490819
116	3	3.72398387774942	-0.723983877749422
117	4	2.42417517160165	1.57582482839835
118	3	2.85543417198678	0.144565828013219
119	1	2.6837101918789	-1.6837101918789
120	3	3.0084461297947	-0.0084461297946977
121	1	2.85543417198678	-1.85543417198678
122	1	2.3994314443093	-1.3994314443093
123	1	2.98310740493128	-1.98310740493128
124	3	2.84787493924539	0.152125060754612
125	2	2.40302500112648	-0.403025001126482
126	1	2.39546576838509	-1.39546576838509
127	2	2.26779253544059	-0.267792535440587
128	4	2.69126942462029	1.30873057537971
129	2	2.84787493924539	-0.847874939245388
130	1	2.84787493924539	-1.84787493924539
131	2	2.84787493924539	-0.847874939245388
132	1	2.68789874626714	-1.68789874626714
133	2	2.84787493924539	-0.847874939245388
134	2	2.26382685951637	-0.263826859516374
135	1	2.840315706504	-1.840315706504
136	3	3.0084461297947	-0.0084461297946977
137	3	3.2927248773643	-0.292724877364295
138	4	2.71660814948371	1.28339185051629
139	2	3.41077284849923	-1.41077284849923
140	1	3.1361193627392	-2.1361193627392
141	3	3.01203968661188	-0.0120396866118764
142	1	1.81538336458029	-0.815383364580288
143	1	1.97176600074135	-0.971766000741355
144	1	2.26779253544059	-1.26779253544059
145	1	1.97176600074135	-0.971766000741355
146	3	2.85161773670557	0.148382263294428
147	2	3.43573945425561	-1.43573945425561
148	2	2.84787493924539	-0.847874939245388
149	1	1.97198887920538	-0.971988879205385
150	1	2.26360398105234	-1.26360398105234
151	2	2.84787493924539	-0.847874939245388
152	1	2.84787493924539	-1.84787493924539
153	2	3.13971291955638	-1.13971291955638
154	2	2.55963051575158	-0.559630515751577
155	2	2.9795138481141	-0.979513848114104
156	3	3.30028411010569	-0.300284110105687
157	1	2.26779253544059	-1.26779253544059
158	4	2.26756965697656	1.73243034302344
159	1	2.10722134489128	-1.10722134489128
160	1	2.26360398105234	-1.26360398105234
161	3	2.840315706504	0.159684293496004

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.138457923814003	0.276915847628005	0.861542076185998
10	0.0555855291271995	0.111171058254399	0.9444144708728
11	0.0436099988779568	0.0872199977559135	0.956390001122043
12	0.0173312258687455	0.034662451737491	0.982668774131255
13	0.0166879292621213	0.0333758585242426	0.983312070737879
14	0.00687077550777815	0.0137415510155563	0.993129224492222
15	0.00529047212735104	0.0105809442547021	0.994709527872649
16	0.0021795150850995	0.004359030170199	0.9978204849149
17	0.0016265249381938	0.0032530498763876	0.998373475061806
18	0.00081042703748266	0.00162085407496532	0.999189572962517
19	0.00119733129938544	0.00239466259877088	0.998802668700615
20	0.00053380675209737	0.00106761350419474	0.999466193247903
21	0.000236006833714512	0.000472013667429025	0.999763993166286
22	9.31553046880573e-05	0.000186310609376115	0.999906844695312
23	3.85479030081104e-05	7.70958060162209e-05	0.999961452096992
24	2.12113549525971e-05	4.24227099051942e-05	0.999978788645047
25	4.36179374800895e-05	8.72358749601789e-05	0.99995638206252
26	2.6910927356922e-05	5.3821854713844e-05	0.999973089072643
27	1.39815597638153e-05	2.79631195276306e-05	0.999986018440236
28	6.82806764000936e-06	1.36561352800187e-05	0.99999317193236
29	4.08228554803687e-06	8.16457109607373e-06	0.999995917714452
30	1.75858740647556e-06	3.51717481295112e-06	0.999998241412594
31	1.1343502168857e-06	2.2687004337714e-06	0.999998865649783
32	4.61912580586599e-07	9.23825161173198e-07	0.99999953808742
33	1.96925241299266e-07	3.93850482598531e-07	0.99999980307476
34	1.15385255028441e-07	2.30770510056882e-07	0.999999884614745
35	4.82954019449333e-08	9.65908038898666e-08	0.999999951704598
36	1.99899248288793e-08	3.99798496577587e-08	0.999999980010075
37	1.63112135531683e-07	3.26224271063365e-07	0.999999836887864
38	8.4017714042613e-08	1.68035428085226e-07	0.999999915982286
39	4.21997390220572e-08	8.43994780441144e-08	0.99999995780026
40	1.89821803452293e-08	3.79643606904587e-08	0.99999998101782
41	4.41787807935692e-08	8.83575615871384e-08	0.999999955821219
42	1.99271884182202e-08	3.98543768364403e-08	0.999999980072812
43	8.51894974184499e-09	1.703789948369e-08	0.99999999148105
44	3.61655398639625e-09	7.2331079727925e-09	0.999999996383446
45	1.72759404651243e-09	3.45518809302485e-09	0.999999998272406
46	6.87704361906833e-10	1.37540872381367e-09	0.999999999312296
47	3.32187863027781e-10	6.64375726055562e-10	0.999999999667812
48	1.33415834446109e-09	2.66831668892218e-09	0.999999998665842
49	5.57279767305451e-10	1.1145595346109e-09	0.99999999944272
50	1.44333345974335e-09	2.88666691948671e-09	0.999999998556667
51	7.63491432965051e-10	1.5269828659301e-09	0.99999999923651
52	4.14699961446615e-10	8.2939992289323e-10	0.9999999995853
53	2.17367552480427e-10	4.34735104960853e-10	0.999999999782632
54	2.2400494587421e-10	4.4800989174842e-10	0.999999999775995
55	1.73390295780629e-10	3.46780591561258e-10	0.99999999982661
56	6.24642812454306e-10	1.24928562490861e-09	0.999999999375357
57	5.50323815312538e-10	1.10064763062508e-09	0.999999999449676
58	8.48059547194976e-10	1.69611909438995e-09	0.99999999915194
59	1.35089087086061e-09	2.70178174172122e-09	0.99999999864911
60	2.1710167733875e-09	4.342033546775e-09	0.999999997828983
61	1.02930252322964e-09	2.05860504645928e-09	0.999999998970697
62	2.55061532830212e-09	5.10123065660424e-09	0.999999997449385
63	6.5281946595955e-08	1.3056389319191e-07	0.999999934718053
64	3.88024264524142e-08	7.76048529048284e-08	0.999999961197574
65	1.9024507708362e-08	3.80490154167241e-08	0.999999980975492
66	9.70213665618036e-09	1.94042733123607e-08	0.999999990297863
67	6.2398833545439e-09	1.24797667090878e-08	0.999999993760117
68	3.027541124361e-09	6.05508224872199e-09	0.99999999697246
69	2.31082807347657e-09	4.62165614695313e-09	0.999999997689172
70	3.96287424965667e-09	7.92574849931335e-09	0.999999996037126
71	1.94774165729567e-09	3.89548331459134e-09	0.999999998052258
72	9.2054009445336e-10	1.84108018890672e-09	0.99999999907946
73	1.20130528334178e-09	2.40261056668356e-09	0.999999998798695
74	1.47295813983883e-09	2.94591627967766e-09	0.999999998527042
75	1.84928341831919e-09	3.69856683663837e-09	0.999999998150717
76	2.09273400526747e-09	4.18546801053494e-09	0.999999997907266
77	1.18059599168589e-09	2.36119198337179e-09	0.999999998819404
78	9.28214130574e-08	1.856428261148e-07	0.999999907178587
79	5.66270360427121e-08	1.13254072085424e-07	0.999999943372964
80	2.91271386099873e-08	5.82542772199747e-08	0.999999970872861
81	2.37888589912363e-08	4.75777179824725e-08	0.99999997621114
82	2.94851951783875e-08	5.8970390356775e-08	0.999999970514805
83	1.54031615373647e-08	3.08063230747294e-08	0.999999984596838
84	1.02777740102044e-08	2.05555480204088e-08	0.999999989722226
85	5.29189653987717e-09	1.05837930797543e-08	0.999999994708103
86	2.93050753597014e-09	5.86101507194028e-09	0.999999997069492
87	1.50070454883133e-09	3.00140909766267e-09	0.999999998499295
88	7.4252532309393e-10	1.48505064618786e-09	0.999999999257475
89	4.10033113117508e-10	8.20066226235017e-10	0.999999999589967
90	8.55995595384935e-10	1.71199119076987e-09	0.999999999144004
91	4.16711119300215e-10	8.33422238600431e-10	0.999999999583289
92	4.76231898765135e-09	9.5246379753027e-09	0.999999995237681
93	2.58931280444449e-09	5.17862560888898e-09	0.999999997410687
94	3.72998119022445e-09	7.4599623804489e-09	0.999999996270019
95	1.91286464894737e-09	3.82572929789474e-09	0.999999998087135
96	2.3498881270694e-09	4.6997762541388e-09	0.999999997650112
97	3.7072747367728e-09	7.4145494735456e-09	0.999999996292725
98	2.16550498787329e-09	4.33100997574657e-09	0.999999997834495
99	1.23560982944979e-09	2.47121965889958e-09	0.99999999876439
100	7.2496319490336e-10	1.44992638980672e-09	0.999999999275037
101	4.49960713104946e-09	8.99921426209892e-09	0.999999995500393
102	1.3921777116148e-08	2.7843554232296e-08	0.999999986078223
103	1.66147195774867e-08	3.32294391549735e-08	0.99999998338528
104	4.48885844182819e-08	8.97771688365639e-08	0.999999955111416
105	6.23192615057864e-08	1.24638523011573e-07	0.999999937680738
106	1.08608725838518e-07	2.17217451677036e-07	0.999999891391274
107	1.20970253093394e-07	2.41940506186788e-07	0.999999879029747
108	6.91901292863704e-08	1.38380258572741e-07	0.99999993080987
109	1.6634533048903e-05	3.32690660978059e-05	0.99998336546695
110	6.93013258465729e-05	0.000138602651693146	0.999930698674153
111	8.27767596671496e-05	0.000165553519334299	0.999917223240333
112	0.00141067531742495	0.0028213506348499	0.998589324682575
113	0.00566265832443253	0.0113253166488651	0.994337341675567
114	0.0131378085678173	0.0262756171356346	0.986862191432183
115	0.0170115765148281	0.0340231530296561	0.982988423485172
116	0.0163480603265147	0.0326961206530295	0.983651939673485
117	0.0271767323710377	0.0543534647420754	0.972823267628962
118	0.0387832118384793	0.0775664236769586	0.96121678816152
119	0.165549691953263	0.331099383906527	0.834450308046736
120	0.136779141417075	0.27355828283415	0.863220858582925
121	0.416709527176955	0.83341905435391	0.583290472823045
122	0.567365644023255	0.865268711953491	0.432634355976745
123	0.736019692714317	0.527960614571366	0.263980307285683
124	0.750645431015563	0.498709137968873	0.249354568984437
125	0.757669165072781	0.484661669854438	0.242330834927219
126	0.788698938260905	0.42260212347819	0.211301061739095
127	0.760883256144154	0.478233487711691	0.239116743855846
128	0.94091512237711	0.118169755245781	0.0590848776228905
129	0.929466055413356	0.141067889173288	0.0705339445866438
130	0.952624241284921	0.0947515174301577	0.0473757587150788
131	0.940253996071197	0.119492007857606	0.0597460039288029
132	0.938597382950177	0.122805234099646	0.0614026170498229
133	0.9214818920763	0.157036215847398	0.078518107923699
134	0.937176732408175	0.125646535183651	0.0628232675918254
135	0.936951014406776	0.126097971186449	0.0630489855932245
136	0.91235568014574	0.175288639708521	0.0876443198542605
137	0.883103284290392	0.233793431419215	0.116896715709608
138	0.882842588242529	0.234314823514942	0.117157411757471
139	0.850299137071288	0.299401725857425	0.149700862928712
140	0.917318562889604	0.165362874220791	0.0826814371103956
141	0.900913323538414	0.198173352923172	0.0990866764615862
142	0.871605972111652	0.256788055776696	0.128394027888348
143	0.84339790137888	0.313204197242239	0.15660209862112
144	0.814446918635563	0.371106162728873	0.185553081364437
145	0.788801281185116	0.422397437629769	0.211198718814884
146	0.740672767809729	0.518654464380542	0.259327232190271
147	0.679234610562825	0.641530778874351	0.320765389437176
148	0.576400633737127	0.847198732525746	0.423599366262873
149	0.467162493203227	0.934324986406454	0.532837506796773
150	0.424833737055876	0.849667474111752	0.575166262944124
151	0.296477901303685	0.59295580260737	0.703522098696315
152	0.301292351795734	0.602584703591467	0.698707648204266

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	97	0.673611111111111	NOK
5% type I error level	105	0.729166666666667	NOK
10% type I error level	109	0.756944444444444	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/103l021290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/103l021290522067.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/1w23q1290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/1w23q1290522067.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/2pt3t1290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/2pt3t1290522067.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/3pt3t1290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/3pt3t1290522067.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/4pt3t1290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/4pt3t1290522067.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/5h22w1290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/5h22w1290522067.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/6h22w1290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/6h22w1290522067.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/7aujz1290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/7aujz1290522067.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/8aujz1290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/8aujz1290522067.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/93l021290522067.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290522038ws66008p4asg5wk/93l021290522067.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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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.

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