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*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: Wed, 24 Nov 2010 01:04:45 +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/24/t1290560721rxsba8erxx1qgsb.htm/, Retrieved Wed, 24 Nov 2010 02:05:31 +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/24/t1290560721rxsba8erxx1qgsb.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 4 3 3 3 4 3 2 4 3 3 4 3 4 3 1 3 3 2 2 3 4 2 2 3 4 4 3 2 4 2 2 3 4 3 2 3 2 2 2 3 2 4 4 3 4 3 3 3 4 3 4 2 4 2 2 3 4 3 3 3 3 2 3 2 4 3 3 3 4 3 4 2 3 2 2 1 2 3 2 2 2 2 2 3 4 3 3 3 3 3 4 3 4 2 2 3 4 3 3 3 3 3 4 2 3 4 3 3 2 3 3 3 3 3 3 4 4 2 2 3 3 2 2 3 3 4 4 3 4 4 3 3 4 3 3 2 3 3 2 3 4 4 4 3 2 3 3 3 3 2 2 3 4 3 3 4 4 4 4 3 3 3 4 3 5 3 2 1 3 2 1 2 3 2 2 3 4 3 3 4 4 4 3 4 5 4 4 2 3 2 2 1 4 3 3 3 4 3 4 3 2 3 2 1 4 2 2 3 4 4 3 2 4 3 2 3 3 4 4 3 3 3 3 2 3 3 3 4 2 4 4 1 4 1 4 3 4 4 4 2 4 2 2 4 3 3 4 3 4 3 4 4 3 3 4 3 4 3 2 3 4 4 3 3 4 2 3 3 4 2 2 3 4 4 4 1 4 1 1 3 4 4 3 3 4 4 3 3 2 3 2 2 3 2 2 3 4 3 3 3 4 3 3 3 3 3 3 2 4 3 3 3 4 4 3 2 4 2 2 2 3 3 2 3 3 3 3 3 3 3 3 2 3 2 2 2 4 2 2 3 4 3 3 2 2 2 2 3 4 3 3 4 3 3 3 2 4 3 2 3 3 3 3 2 4 4 3 4 3 4 4 3 3 4 4 3 4 3 3 3 3 2 2 3 4 3 1 2 2 2 2 3 4 3 3 4 4 3 3 4 4 4 5 4 4 3 4 3 4 3 5 3 3 2 2 1 4 1 1 4 3 3 3 1 4 3 3 3 3 4 4 2 3 2 2 2 2 3 2 3 4 4 3 3 4 3 4 2 4 4 2 3 1 4 3 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	'George Udny Yule' @ 72.249.76.132
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

Poular[t] = + 1.35086028455801 + 0.0042491286076238Friends[t] + 0.15135129972613Considerfriends[t] + 0.341801603945097FriendStudents[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)	1.35086028455801	0.363066	3.7207	0.000279	0.00014
Friends	0.0042491286076238	0.079078	0.0537	0.957218	0.478609
Considerfriends	0.15135129972613	0.083278	1.8174	0.07112	0.03556
FriendStudents	0.341801603945097	0.072283	4.7287	5e-06	3e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.460942309224963
R-squared	0.212467812433641
Adjusted R-squared	0.196924413994832
F-TEST (value)	13.6693280604027
F-TEST (DF numerator)	3
F-TEST (DF denominator)	152
p-value	6.09727346390088e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.698728939181563
Sum Squared Residuals	74.2097638283684

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3	2.84731551000220	0.152684489997804
2	3	2.50551390605709	0.494486093942914
3	4	3.18486798533965	0.815132014660347
4	3	2.16371230211199	0.83628769788801
5	3	2.34991347772333	0.650086522276666
6	3	2.35416260633096	0.645837393669042
7	3	2.99866680972831	0.00133319027168608
8	2	2.35416260633096	-0.354162606330958
9	3	2.50551390605709	0.494486093942913
10	3	2.34566434911571	0.65433565088429
11	3	3.33197015645816	-0.331970156458163
12	3	2.84731551000218	0.152684489997816
13	3	3.18911711394728	-0.189117113947281
14	2	2.35416260633096	-0.354162606330958
15	3	2.84731551000218	0.152684489997816
16	3	2.69171508166843	0.308284918331569
17	2	2.84731551000218	-0.847315510002184
18	3	3.18911711394728	-0.189117113947281
19	2	2.34991347772333	-0.349913477723334
20	1	2.49701564884184	-1.49701564884184
21	2	2.34566434911571	-0.345664349115711
22	3	2.84731551000218	0.152684489997816
23	3	3.18486798533966	-0.184867985339657
24	3	2.35416260633096	0.645837393669042
25	3	2.84731551000218	0.152684489997816
26	3	3.18486798533966	-0.184867985339657
27	2	2.99441768112069	-0.99441768112069
28	3	2.83881725278694	0.161182747213063
29	3	2.84306638139456	0.156933618605439
30	4	2.35416260633096	1.64583739366904
31	3	2.34991347772333	0.650086522276666
32	3	3.33621928506579	-0.336219285065787
33	3	2.99866680972831	0.00133319027168608
34	3	2.84731551000218	0.152684489997816
35	2	2.50126477744946	-0.501264777449464
36	3	3.34046841367341	-0.340468413673411
37	3	2.83881725278694	0.161182747213063
38	3	2.34991347772333	0.650086522276666
39	3	2.84731551000218	0.152684489997816
40	4	3.34046841367341	0.659531586326589
41	3	3.18486798533966	-0.184867985339657
42	3	2.50976303466471	0.490236965335289
43	1	2.00811187377824	-1.00811187377824
44	2	2.34991347772333	-0.349913477723334
45	3	2.84731551000218	0.152684489997816
46	4	2.99866680972831	1.00133319027169
47	4	3.34471754228103	0.655282457718966
48	2	2.34991347772333	-0.349913477723334
49	1	2.84731551000218	-1.84731551000218
50	3	3.18911711394728	-0.189117113947281
51	3	2.49701564884184	0.50298435115816
52	1	2.35416260633096	-1.35416260633096
53	3	2.99866680972831	0.00133319027168608
54	2	2.50551390605709	-0.505513906057087
55	3	3.33621928506579	-0.336219285065787
56	3	2.84306638139456	0.156933618605439
57	2	2.84306638139456	-0.84306638139456
58	4	3.33197015645816	0.668029843541837
59	1	2.88641451449502	-1.88641451449502
60	3	3.34046841367341	-0.340468413673411
61	2	2.35416260633096	-0.354162606330958
62	4	3.18486798533966	0.815132014660343
63	3	3.18911711394728	-0.189117113947281
64	4	3.18486798533966	0.815132014660343
65	3	2.50551390605709	0.494486093942913
66	3	2.99866680972831	0.00133319027168608
67	3	2.69596421027605	0.304035789723945
68	3	2.35416260633096	0.645837393669042
69	3	3.34046841367341	-0.340468413673411
70	1	1.86100970265973	-0.861009702659732
71	3	2.99866680972831	0.00133319027168608
72	3	2.99866680972831	0.00133319027168608
73	3	2.49701564884184	0.50298435115816
74	2	2.34991347772333	-0.349913477723334
75	3	2.84731551000218	0.152684489997816
76	3	2.84731551000218	0.152684489997816
77	3	2.84306638139456	0.156933618605439
78	2	2.84731551000218	-0.847315510002184
79	3	2.99866680972831	0.00133319027168608
80	2	2.35416260633096	-0.354162606330958
81	2	2.50126477744946	-0.501264777449464
82	3	2.84306638139456	0.156933618605439
83	3	2.84306638139456	0.156933618605439
84	2	2.34991347772333	-0.349913477723334
85	2	2.35416260633096	-0.354162606330958
86	3	2.84731551000218	0.152684489997816
87	2	2.34566434911571	-0.345664349115711
88	3	2.84731551000218	0.152684489997816
89	4	2.84306638139456	1.15693361860544
90	2	2.50551390605709	-0.505513906057087
91	3	2.84306638139456	0.156933618605439
92	2	2.99866680972831	-0.998666809728314
93	4	3.33621928506579	0.663780714934213
94	3	3.33621928506579	-0.336219285065787
95	3	2.84731551000218	0.152684489997816
96	3	2.34991347772333	0.650086522276666
97	3	2.16371230211199	0.83628769788801
98	2	2.34566434911571	-0.345664349115711
99	3	2.84731551000218	0.152684489997816
100	4	2.84731551000218	1.15268448999782
101	4	3.68227001761851	0.317729982381492
102	4	3.18911711394728	0.810882886052719
103	3	3.53091871789238	-0.530918717892378
104	3	2.34991347772333	0.650086522276666
105	1	1.86100970265973	-0.861009702659732
106	4	2.84306638139456	1.15693361860544
107	1	2.84731551000218	-1.84731551000218
108	3	3.33621928506579	-0.336219285065787
109	2	2.34991347772333	-0.349913477723334
110	2	2.49701564884184	-0.49701564884184
111	3	2.99866680972831	0.00133319027168608
112	3	3.18911711394728	-0.189117113947281
113	2	2.65686520578322	-0.656865205783217
114	3	2.98591942390544	0.014080576094557
115	3	2.84731551000218	0.152684489997816
116	4	3.18911711394728	0.810882886052719
117	4	3.18911711394728	0.810882886052719
118	3	2.50126477744946	0.498735222550536
119	3	2.84731551000218	0.152684489997816
120	3	2.50551390605709	0.494486093942913
121	3	2.84306638139456	0.156933618605439
122	3	3.18911711394728	-0.189117113947281
123	1	2.65686520578322	-1.65686520578322
124	2	3.18911711394728	-1.18911711394728
125	4	3.03776581422115	0.962234185778848
126	3	2.65686520578322	0.343134794216783
127	4	2.84306638139456	1.15693361860544
128	3	2.84306638139456	0.156933618605439
129	2	2.54461291054993	-0.544612910549925
130	1	2.99866680972831	-1.99866680972831
131	4	3.18911711394728	0.810882886052719
132	3	2.69596421027605	0.304035789723945
133	3	2.35416260633096	0.645837393669042
134	3	2.99866680972831	0.00133319027168608
135	4	2.84731551000218	1.15268448999782
136	3	2.99866680972831	0.00133319027168608
137	3	3.03776581422115	-0.0377658142211516
138	1	2.99441768112069	-1.99441768112069
139	4	3.33621928506579	0.663780714934213
140	2	3.18911711394728	-1.18911711394728
141	2	3.18911711394728	-1.18911711394728
142	3	2.83881725278694	0.161182747213063
143	3	2.69596421027605	0.304035789723945
144	2	2.50551390605709	-0.505513906057087
145	3	2.84731551000218	0.152684489997816
146	3	2.16796143071961	0.832038569280386
147	2	2.65686520578322	-0.656865205783217
148	3	3.34046841367341	-0.340468413673411
149	4	3.18911711394728	0.810882886052719
150	4	2.84731551000218	1.15268448999782
151	4	2.99866680972831	1.00133319027169
152	2	3.03776581422115	-1.03776581422115
153	3	2.50551390605709	0.494486093942913
154	3	3.34046841367341	-0.340468413673411
155	3	2.83881725278694	0.161182747213063
156	3	2.84731551000218	0.152684489997816

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.0997077201981054	0.199415440396211	0.900292279801895
8	0.184142139262694	0.368284278525388	0.815857860737306
9	0.0972248604934743	0.194449720986949	0.902775139506526
10	0.0837658950309369	0.167531790061874	0.916234104969063
11	0.120747972569395	0.241495945138790	0.879252027430605
12	0.069600621745846	0.139201243491692	0.930399378254154
13	0.0407570976566292	0.0815141953132583	0.95924290234337
14	0.0595865857432683	0.119173171486537	0.940413414256732
15	0.0343135974349097	0.0686271948698193	0.96568640256509
16	0.0192565188736376	0.0385130377472752	0.980743481126362
17	0.0466764180855753	0.0933528361711505	0.953323581914425
18	0.0282662942727469	0.0565325885454937	0.971733705727253
19	0.0380036463569691	0.0760072927139381	0.96199635364303
20	0.280344394183375	0.56068878836675	0.719655605816625
21	0.229403280068110	0.458806560136219	0.77059671993189
22	0.176252536968684	0.352505073937368	0.823747463031316
23	0.132468062866502	0.264936125733004	0.867531937133498
24	0.109851137094607	0.219702274189214	0.890148862905393
25	0.0797527641977912	0.159505528395582	0.920247235802209
26	0.0567459837377677	0.113491967475535	0.943254016262232
27	0.062669653517619	0.125339307035238	0.937330346482381
28	0.0538503222202304	0.107700644440461	0.94614967777977
29	0.0399357270362183	0.0798714540724366	0.960064272963782
30	0.108999833333925	0.217999666667851	0.891000166666075
31	0.0933940921865981	0.186788184373196	0.906605907813402
32	0.0714613734202051	0.142922746840410	0.928538626579795
33	0.0535129392528578	0.107025878505716	0.946487060747142
34	0.0387710811561712	0.0775421623123424	0.961228918843829
35	0.0330800542089557	0.0661601084179114	0.966919945791044
36	0.0240956247095152	0.0481912494190303	0.975904375290485
37	0.0197599559820310	0.0395199119640619	0.980240044017969
38	0.0162255966016325	0.0324511932032650	0.983774403398368
39	0.0111769177282006	0.0223538354564013	0.9888230822718
40	0.0146494307969997	0.0292988615939993	0.985350569203
41	0.0103318435500736	0.0206636871001471	0.989668156449926
42	0.00753757971402405	0.0150751594280481	0.992462420285976
43	0.0188767164876127	0.0377534329752255	0.981123283512387
44	0.0164235212985376	0.0328470425970752	0.983576478701462
45	0.0116247438152610	0.0232494876305221	0.988375256184739
46	0.0209552544855553	0.0419105089711106	0.979044745514445
47	0.017757680899154	0.035515361798308	0.982242319100846
48	0.0147704070227463	0.0295408140454926	0.985229592977254
49	0.134356518325722	0.268713036651445	0.865643481674278
50	0.113730990282218	0.227461980564436	0.886269009717782
51	0.115440018814416	0.230880037628831	0.884559981185584
52	0.237122355699519	0.474244711399037	0.762877644300481
53	0.200080847315928	0.400161694631856	0.799919152684072
54	0.188557813670264	0.377115627340528	0.811442186329736
55	0.161450094800665	0.322900189601331	0.838549905199335
56	0.135063355262932	0.270126710525865	0.864936644737068
57	0.145690184131426	0.291380368262851	0.854309815868574
58	0.157520478548005	0.315040957096009	0.842479521451995
59	0.368002495860407	0.736004991720814	0.631997504139593
60	0.334184411278982	0.668368822557964	0.665815588721018
61	0.301291341032095	0.60258268206419	0.698708658967905
62	0.332207429013259	0.664414858026518	0.667792570986741
63	0.291883996658072	0.583767993316143	0.708116003341928
64	0.316157892642315	0.63231578528463	0.683842107357685
65	0.291693523190468	0.583387046380937	0.708306476809532
66	0.253841542708134	0.507683085416269	0.746158457291866
67	0.227225028796191	0.454450057592382	0.772774971203809
68	0.222187210118659	0.444374420237318	0.777812789881341
69	0.197089190294300	0.394178380588601	0.8029108097057
70	0.212758089861184	0.425516179722367	0.787241910138816
71	0.181261365238067	0.362522730476133	0.818738634761933
72	0.152823869818969	0.305647739637939	0.84717613018103
73	0.137759225531377	0.275518451062753	0.862240774468623
74	0.119343487163615	0.238686974327231	0.880656512836385
75	0.098502503256754	0.197005006513508	0.901497496743246
76	0.0804658994578013	0.160931798915603	0.919534100542199
77	0.0650720056054062	0.130144011210812	0.934927994394594
78	0.0723674781228154	0.144734956245631	0.927632521877185
79	0.0580018478189396	0.116003695637879	0.94199815218106
80	0.0486030293810799	0.0972060587621597	0.95139697061892
81	0.0440477845731427	0.0880955691462854	0.955952215426857
82	0.0346391989240108	0.0692783978480216	0.96536080107599
83	0.0269417091806120	0.0538834183612241	0.973058290819388
84	0.0221311164018527	0.0442622328037053	0.977868883598147
85	0.0180896292900084	0.0361792585800169	0.981910370709992
86	0.0136813580661717	0.0273627161323433	0.986318641933828
87	0.0112393484612302	0.0224786969224605	0.98876065153877
88	0.00833714630466	0.01667429260932	0.99166285369534
89	0.0139406014249339	0.0278812028498678	0.986059398575066
90	0.0123325054172013	0.0246650108344026	0.987667494582799
91	0.00915576404333714	0.0183115280866743	0.990844235956663
92	0.0127437632071105	0.0254875264142210	0.98725623679289
93	0.0124596024120148	0.0249192048240296	0.987540397587985
94	0.00977168325470277	0.0195433665094055	0.990228316745297
95	0.0071886754290659	0.0143773508581318	0.992811324570934
96	0.00664965852224185	0.0132993170444837	0.993350341477758
97	0.0071692770393711	0.0143385540787422	0.992830722960629
98	0.00571877785940844	0.0114375557188169	0.994281222140592
99	0.0041144772462355	0.008228954492471	0.995885522753765
100	0.00715618910625302	0.0143123782125060	0.992843810893747
101	0.00562901604410624	0.0112580320882125	0.994370983955894
102	0.0063996817551195	0.012799363510239	0.99360031824488
103	0.00528663442241695	0.0105732688448339	0.994713365577583
104	0.00478400645235927	0.00956801290471854	0.99521599354764
105	0.00665535125353362	0.0133107025070672	0.993344648746466
106	0.0109518134048810	0.0219036268097619	0.989048186595119
107	0.0545922181716176	0.109184436343235	0.945407781828382
108	0.0438336264125004	0.0876672528250008	0.9561663735875
109	0.0392129632904552	0.0784259265809104	0.960787036709545
110	0.0370762462014605	0.074152492402921	0.96292375379854
111	0.0285484500106334	0.0570969000212669	0.971451549989367
112	0.0214193006675377	0.0428386013350754	0.978580699332462
113	0.0200155535268614	0.0400311070537228	0.979984446473139
114	0.0146173493018105	0.0292346986036211	0.98538265069819
115	0.0105685528863733	0.0211371057727466	0.989431447113627
116	0.0121136623474940	0.0242273246949880	0.987886337652506
117	0.0143442184862325	0.0286884369724651	0.985655781513767
118	0.0110001121545370	0.0220002243090739	0.988999887845463
119	0.00779950682316354	0.0155990136463271	0.992200493176836
120	0.00595279371435628	0.0119055874287126	0.994047206285644
121	0.00406507702728397	0.00813015405456795	0.995934922972716
122	0.00272283912847722	0.00544567825695444	0.997277160871523
123	0.0121535461332177	0.0243070922664353	0.987846453866782
124	0.0179366175445403	0.0358732350890807	0.98206338245546
125	0.0219635671802370	0.0439271343604741	0.978036432819763
126	0.0161574806681968	0.0323149613363936	0.983842519331803
127	0.0250729387337287	0.0501458774674574	0.974927061266271
128	0.0179424277960161	0.0358848555920321	0.982057572203984
129	0.0198863701503634	0.0397727403007269	0.980113629849637
130	0.110662057605004	0.221324115210007	0.889337942394996
131	0.126129656862796	0.252259313725592	0.873870343137204
132	0.0967792373539926	0.193558474707985	0.903220762646007
133	0.0766458511958595	0.153291702391719	0.92335414880414
134	0.0552538168648388	0.110507633729678	0.94474618313516
135	0.0814371528435614	0.162874305687123	0.918562847156439
136	0.0582041234208045	0.116408246841609	0.941795876579196
137	0.0405168619454216	0.0810337238908432	0.959483138054578
138	0.286707146718020	0.573414293436039	0.71329285328198
139	0.289746661466465	0.57949332293293	0.710253338533535
140	0.341146988148944	0.682293976297889	0.658853011851056
141	0.450307508455385	0.90061501691077	0.549692491544615
142	0.363274125722073	0.726548251444146	0.636725874277927
143	0.284862182285023	0.569724364570045	0.715137817714977
144	0.305020075416075	0.610040150832151	0.694979924583925
145	0.219713365063883	0.439426730127766	0.780286634936117
146	0.155540620159322	0.311081240318644	0.844459379840678
147	0.364695391717337	0.729390783434673	0.635304608282663
148	0.306309818380505	0.61261963676101	0.693690181619495
149	0.463510206974237	0.927020413948475	0.536489793025763

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	4	0.0279720279720280	NOK
5% type I error level	54	0.377622377622378	NOK
10% type I error level	72	0.503496503496504	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/105vr01290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/105vr01290560674.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/1gcu61290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/1gcu61290560674.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/2gcu61290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/2gcu61290560674.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/394b91290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/394b91290560674.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/494b91290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/494b91290560674.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/52dtu1290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/52dtu1290560674.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/62dtu1290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/62dtu1290560674.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/7v4ax1290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/7v4ax1290560674.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/8v4ax1290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/8v4ax1290560674.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/95vr01290560674.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290560721rxsba8erxx1qgsb/95vr01290560674.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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