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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, 15 Dec 2010 17:40:40 +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/Dec/15/t1292435014psxl7bn8wnvdncv.htm/, Retrieved Wed, 15 Dec 2010 18:43:34 +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/Dec/15/t1292435014psxl7bn8wnvdncv.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 «

5 0 4 0 5 0 6 0 6 0 6 0 7 0 8 0 7 0 8 0 7 0 8 0 8 0 9 0 9 0 8 0 9 0 9 0 10 0 11 0 12 0 13 0 13 0 13 0 14 0 14 0 15 0 15 0 16 0 16 0 17 0 18 0 19 0 20 0 22 0 20 0 22 0 25 0 24 0 25 0 28 0 26 0 27 0 26 0 25 0 27 0 28 0 30 0 31 0 32 0 34 0 34 0 33 0 32 0 34 0 36 0 37 0 40 0 38 0 38 0 36 0 40 0 40 0 42 0 44 0 45 0 47 0 49 0 47 0 49 0 52 0 50 0 50 0 57 0 58 0 58 0 58 0 61 0 61 0 64 0 68 0 40 0 34 0 46 0 36 0 34 0 45 0 55 0 50 0 56 0 72 0 76 0 78 0 77 0 90 0 88 0 97 0 93 0 84 0 67 0 72 0 75 0 71 0 75 0 90 0 78 0 73 0 62 0 65 0 61 0 58 0 33 0 39 0 56 0 79 0 82 0 79 0 73 0 87 0 85 0 83 0 82 0 83 0 92 0 95 0 97 0 87 0 84 0 84 0 89 0 103 0 106 0 109 0 106 0 105 0 115 0 120 0 124 0 121 0 131 0 139 0 133 0 119 0 123 0 120 0 128 0 134 0 126 0 115 0 106 0 99 0 100 0 99 0 99 0 100 0 100 0 108 0 109 0 115 0 114 0 108 0 113 0 118 0 122 0 118 0 121 0 118 0 121 0 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	7 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

CO2-uitstoot[t] = -4.14151777712791 -19.0254747328007`Kyoto-protocol`[t] + 0.755971303781826t + 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)	-4.14151777712791	1.750778	-2.3655	0.019111	0.009556
`Kyoto-protocol`	-19.0254747328007	5.984213	-3.1793	0.00175	0.000875
t	0.755971303781826	0.017554	43.0657	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.95782498600972
R-squared	0.91742870382452
Adjusted R-squared	0.916474122365844
F-TEST (value)	961.079534371974
F-TEST (DF numerator)	2
F-TEST (DF denominator)	173
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	11.4306480477221
Sum Squared Residuals	22604.1306588244

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	5	-3.38554647334607	8.38554647334607
2	4	-2.62957516956427	6.62957516956427
3	5	-1.8736038657825	6.8736038657825
4	6	-1.11763256200062	7.11763256200062
5	6	-0.361661258218797	6.3616612582188
6	6	0.394310045563028	5.60568995443697
7	7	1.15028134934485	5.84971865065515
8	8	1.90625265312668	6.09374734687332
9	7	2.66222395690851	4.33777604309149
10	8	3.41819526069033	4.58180473930967
11	7	4.17416656447216	2.82583343552784
12	8	4.93013786825398	3.06986213174602
13	8	5.68610917203581	2.31389082796419
14	9	6.44208047581763	2.55791952418237
15	9	7.19805177959946	1.80194822040054
16	8	7.95402308338129	0.0459769166187149
17	9	8.70999438716311	0.290005612836889
18	9	9.46596569094494	-0.465965690944936
19	10	10.2219369947268	-0.221936994726762
20	11	10.9779082985086	0.0220917014914120
21	12	11.7338796022904	0.266120397709586
22	13	12.4898509060722	0.510149093927761
23	13	13.2458222098541	-0.245822209854065
24	13	14.0017935136359	-1.00179351363589
25	14	14.7577648174177	-0.757764817417717
26	14	15.5137361211995	-1.51373612119954
27	15	16.2697074249814	-1.26970742498137
28	15	17.0256787287632	-2.02567872876319
29	16	17.7816500325450	-1.78165003254502
30	16	18.5376213363268	-2.53762133632685
31	17	19.2935926401087	-2.29359264010867
32	18	20.0495639438905	-2.04956394389050
33	19	20.8055352476723	-1.80553524767232
34	20	21.5615065514541	-1.56150655145415
35	22	22.3174778552360	-0.317477855235974
36	20	23.0734491590178	-3.0734491590178
37	22	23.8294204627996	-1.82942046279963
38	25	24.5853917665815	0.414608233418546
39	24	25.3413630703633	-1.34136307036328
40	25	26.0973343741451	-1.09733437414511
41	28	26.8533056779269	1.14669432207307
42	26	27.6092769817088	-1.60927698170876
43	27	28.3652482854906	-1.36524828549058
44	26	29.1212195892724	-3.12121958927241
45	25	29.8771908930542	-4.87719089305423
46	27	30.6331621968361	-3.63316219683606
47	28	31.3891335006179	-3.38913350061788
48	30	32.1451048043997	-2.14510480439971
49	31	32.9010761081815	-1.90107610818153
50	32	33.6570474119634	-1.65704741196336
51	34	34.4130187157452	-0.413018715745189
52	34	35.168990019527	-1.16899001952701
53	33	35.9249613233088	-2.92496132330884
54	32	36.6809326270907	-4.68093262709067
55	34	37.4369039308725	-3.43690393087249
56	36	38.1928752346543	-2.19287523465432
57	37	38.9488465384361	-1.94884653843614
58	40	39.704817842218	0.295182157782031
59	38	40.4607891459998	-2.46078914599979
60	38	41.2167604497816	-3.21676044978162
61	36	41.9727317535634	-5.97273175356345
62	40	42.7287030573453	-2.72870305734527
63	40	43.4846743611271	-3.4846743611271
64	42	44.2406456649089	-2.24064566490892
65	44	44.9966169686908	-0.996616968690749
66	45	45.7525882724726	-0.752588272472574
67	47	46.5085595762544	0.4914404237456
68	49	47.2645308800362	1.73546911996377
69	47	48.0205021838181	-1.02050218381805
70	49	48.7764734875999	0.223526512400124
71	52	49.5324447913817	2.46755520861830
72	50	50.2884160951635	-0.288416095163528
73	50	51.0443873989454	-1.04438739894535
74	57	51.8003587027272	5.19964129727282
75	58	52.556330006509	5.44366999349099
76	58	53.3123013102908	4.68769868970917
77	58	54.0682726140727	3.93172738592734
78	61	54.8242439178545	6.17575608214552
79	61	55.5802152216363	5.41978477836369
80	64	56.3361865254181	7.66381347458186
81	68	57.0921578292	10.9078421708000
82	40	57.8481291329818	-17.8481291329818
83	34	58.6041004367636	-24.6041004367636
84	46	59.3600717405454	-13.3600717405454
85	36	60.1160430443273	-24.1160430443273
86	34	60.8720143481091	-26.8720143481091
87	45	61.6279856518909	-16.6279856518909
88	55	62.3839569556727	-7.38395695567274
89	50	63.1399282594546	-13.1399282594546
90	56	63.8958995632364	-7.8958995632364
91	72	64.6518708670182	7.34812913298178
92	76	65.4078421708	10.5921578292000
93	78	66.1638134745819	11.8361865254181
94	77	66.9197847783637	10.0802152216363
95	90	67.6757560821455	22.3242439178545
96	88	68.4317273859273	19.5682726140727
97	97	69.1876986897092	27.8123013102908
98	93	69.943669993491	23.056330006509
99	84	70.6996412972728	13.3003587027272
100	67	71.4556126010547	-4.45561260105465
101	72	72.2115839048365	-0.211583904836474
102	75	72.9675552086183	2.0324447913817
103	71	73.7235265124001	-2.72352651240013
104	75	74.479497816182	0.520502183818048
105	90	75.2354691199638	14.7645308800362
106	78	75.9914404237456	2.00855957625440
107	73	76.7474117275274	-3.74741172752743
108	62	77.5033830313093	-15.5033830313093
109	65	78.259354335091	-13.2593543350911
110	61	79.0153256388729	-18.0153256388729
111	58	79.7712969426547	-21.7712969426547
112	33	80.5272682464365	-47.5272682464365
113	39	81.2832395502184	-42.2832395502184
114	56	82.0392108540002	-26.0392108540002
115	79	82.795182157782	-3.79518215778203
116	82	83.5511534615639	-1.55115346156386
117	79	84.3071247653457	-5.30712476534568
118	73	85.0630960691275	-12.0630960691275
119	87	85.8190673729093	1.18093262709067
120	85	86.5750386766912	-1.57503867669116
121	83	87.331009980473	-4.33100998047299
122	82	88.0869812842548	-6.08698128425481
123	83	88.8429525880366	-5.84295258803664
124	92	89.5989238918185	2.40107610818154
125	95	90.3548951956003	4.64510480439971
126	97	91.1108664993821	5.88913350061789
127	87	91.866837803164	-4.86683780316394
128	84	92.6228091069458	-8.62280910694576
129	84	93.3787804107276	-9.3787804107276
130	89	94.1347517145094	-5.13475171450942
131	103	94.8907230182912	8.10927698170876
132	106	95.646694322073	10.3533056779269
133	109	96.4026656258549	12.5973343741451
134	106	97.1586369296367	8.84136307036328
135	105	97.9146082334185	7.08539176658145
136	115	98.6705795372004	16.3294204627996
137	120	99.4265508409822	20.5734491590178
138	124	100.182522144764	23.817477855236
139	121	100.938493448546	20.0615065514542
140	131	101.694464752328	29.3055352476723
141	139	102.450436056109	36.5495639438905
142	133	103.206407359891	29.7935926401087
143	119	103.962378663673	15.0376213363268
144	123	104.718349967455	18.2816500325450
145	120	105.474321271237	14.5256787287632
146	128	106.230292575019	21.7697074249814
147	134	106.986263878800	27.0137361211995
148	126	107.742235182582	18.2577648174177
149	115	108.498206486364	6.5017935136359
150	106	109.254177790146	-3.25417779014593
151	99	110.010149093928	-11.0101490939278
152	100	110.766120397710	-10.7661203977096
153	99	111.522091701491	-12.5220917014914
154	99	112.278063005273	-13.2780630052732
155	100	113.034034309055	-13.0340343090551
156	100	113.790005612837	-13.7900056128369
157	108	114.545976916619	-6.54597691661871
158	109	115.301948220401	-6.30194822040054
159	115	116.057919524182	-1.05791952418236
160	114	116.813890827964	-2.81389082796419
161	108	117.569862131746	-9.56986213174602
162	113	118.325833435528	-5.32583343552785
163	118	119.081804739310	-1.08180473930967
164	122	119.837776043091	2.1622239569085
165	118	120.593747346873	-2.59374734687332
166	121	121.349718650655	-0.349718650655150
167	118	122.105689954437	-4.10568995443698
168	121	122.861661258219	-1.8616612582188
169	121	123.617632562001	-2.61763256200063
170	112	124.373603865782	-12.3736038657825
171	119	125.129575169564	-6.12957516956428
172	116	125.885546473346	-9.8855464733461
173	110	107.616043044327	2.38395695567274
174	111	108.372014348109	2.62798565189091
175	106	109.127985651891	-3.12798565189091
176	108	109.883956955673	-1.88395695567274

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.000249257898267695	0.00049851579653539	0.999750742101732
7	1.36382402959156e-05	2.72764805918313e-05	0.999986361759704
8	1.15759564259917e-06	2.31519128519833e-06	0.999998842404357
9	1.20504208821981e-07	2.41008417643963e-07	0.999999879495791
10	5.86643214753693e-09	1.17328642950739e-08	0.999999994133568
11	1.56276469318397e-09	3.12552938636795e-09	0.999999998437235
12	9.00482382075089e-11	1.80096476415018e-10	0.999999999909952
13	5.9956137896972e-12	1.19912275793944e-11	0.999999999994004
14	3.31369945910701e-13	6.62739891821402e-13	0.999999999999669
15	1.6184105187675e-14	3.236821037535e-14	0.999999999999984
16	5.54284075733313e-15	1.10856815146663e-14	0.999999999999994
17	3.25377807893474e-16	6.50755615786948e-16	1
18	2.25344075079091e-17	4.50688150158181e-17	1
19	1.23628991731868e-18	2.47257983463736e-18	1
20	1.66122039183249e-19	3.32244078366499e-19	1
21	7.39886624170266e-20	1.47977324834053e-19	1
22	7.49692528802564e-20	1.49938505760513e-19	1
23	1.39710232090540e-20	2.79420464181080e-20	1
24	1.26690002807663e-21	2.53380005615327e-21	1
25	2.29009380750139e-22	4.58018761500278e-22	1
26	2.06156718317198e-23	4.12313436634396e-23	1
27	3.57660880091938e-24	7.15321760183876e-24	1
28	3.17052395893258e-25	6.34104791786516e-25	1
29	5.25937375975203e-26	1.05187475195041e-25	1
30	4.57084414613945e-27	9.1416882922789e-27	1
31	7.24681868013422e-28	1.44936373602684e-27	1
32	2.40890985987076e-28	4.81781971974153e-28	1
33	1.58337738848071e-28	3.16675477696142e-28	1
34	1.73444532544484e-28	3.46889065088968e-28	1
35	2.468137758833e-27	4.936275517666e-27	1
36	2.76484972305770e-28	5.52969944611539e-28	1
37	1.34716416443245e-28	2.69432832886491e-28	1
38	3.71055089252259e-27	7.42110178504519e-27	1
39	1.90232180351005e-27	3.8046436070201e-27	1
40	1.21625833178627e-27	2.43251666357253e-27	1
41	1.63103660688180e-26	3.26207321376359e-26	1
42	4.18659599825152e-27	8.37319199650305e-27	1
43	1.30339638700306e-27	2.60679277400613e-27	1
44	1.75592878549514e-28	3.51185757099028e-28	1
45	2.57120629904929e-29	5.14241259809858e-29	1
46	3.3593195525268e-30	6.7186391050536e-30	1
47	4.8446609616405e-31	9.689321923281e-31	1
48	1.52782105180880e-31	3.05564210361760e-31	1
49	5.90718321010035e-32	1.18143664202007e-31	1
50	2.75546957805599e-32	5.51093915611197e-32	1
51	4.38461052394556e-32	8.76922104789113e-32	1
52	2.47323076205896e-32	4.94646152411793e-32	1
53	4.28082723567737e-33	8.56165447135474e-33	1
54	5.69212365450691e-34	1.13842473090138e-33	1
55	8.92705361816418e-35	1.78541072363284e-34	1
56	2.81227270965848e-35	5.62454541931695e-35	1
57	1.04786543713228e-35	2.09573087426456e-35	1
58	3.64165621353425e-35	7.2833124270685e-35	1
59	8.3066703811261e-36	1.66133407622522e-35	1
60	1.38940123982163e-36	2.77880247964326e-36	1
61	2.44041127366140e-37	4.88082254732279e-37	1
62	5.71181109508085e-38	1.14236221901617e-37	1
63	9.64099965809368e-39	1.92819993161874e-38	1
64	3.17591145228337e-39	6.35182290456674e-39	1
65	2.79906124669582e-39	5.59812249339165e-39	1
66	2.65156751285962e-39	5.30313502571925e-39	1
67	7.36159442800386e-39	1.47231888560077e-38	1
68	5.56947029863132e-38	1.11389405972626e-37	1
69	2.27206399045775e-38	4.5441279809155e-38	1
70	2.08809594236772e-38	4.17619188473544e-38	1
71	1.27673041498184e-37	2.55346082996368e-37	1
72	5.5524623865718e-38	1.11049247731436e-37	1
73	1.5694799596314e-38	3.1389599192628e-38	1
74	8.94161147946263e-37	1.78832229589253e-36	1
75	2.11953965972773e-35	4.23907931945546e-35	1
76	1.10574249679397e-34	2.21148499358794e-34	1
77	2.11007749654016e-34	4.22015499308033e-34	1
78	1.60424191287760e-33	3.20848382575520e-33	1
79	4.256374009234e-33	8.512748018468e-33	1
80	4.03121226746757e-32	8.06242453493514e-32	1
81	2.88873064580402e-30	5.77746129160804e-30	1
82	6.96629267911383e-27	1.39325853582277e-26	1
83	4.50463680677019e-22	9.00927361354038e-22	1
84	1.28333809476269e-21	2.56667618952537e-21	1
85	7.41214918185849e-19	1.48242983637170e-18	1
86	3.98214099125216e-16	7.96428198250432e-16	1
87	9.59295929122672e-16	1.91859185824534e-15	1
88	4.38849579474083e-16	8.77699158948166e-16	1
89	4.20116443112293e-16	8.40232886224586e-16	1
90	2.03269430916162e-16	4.06538861832325e-16	1
91	6.15553657675238e-16	1.23110731535048e-15	1
92	3.8668793616052e-15	7.7337587232104e-15	0.999999999999996
93	2.46456915590172e-14	4.92913831180343e-14	0.999999999999975
94	6.88013456098095e-14	1.37602691219619e-13	0.999999999999931
95	8.01006171464121e-12	1.60201234292824e-11	0.99999999999199
96	1.33331374137452e-10	2.66662748274904e-10	0.999999999866669
97	1.63701867048421e-08	3.27403734096842e-08	0.999999983629813
98	2.12118705238581e-07	4.24237410477162e-07	0.999999787881295
99	3.40368718289113e-07	6.80737436578227e-07	0.999999659631282
100	2.06027483762141e-07	4.12054967524283e-07	0.999999793972516
101	1.17596971737131e-07	2.35193943474263e-07	0.999999882403028
102	6.99999236412574e-08	1.39999847282515e-07	0.999999930000076
103	3.94203173207816e-08	7.88406346415632e-08	0.999999960579683
104	2.21692105925469e-08	4.43384211850939e-08	0.99999997783079
105	4.88139801104203e-08	9.76279602208405e-08	0.99999995118602
106	2.94471329761217e-08	5.88942659522435e-08	0.999999970552867
107	1.69898868902283e-08	3.39797737804565e-08	0.999999983010113
108	2.57505957586776e-08	5.15011915173553e-08	0.999999974249404
109	2.76838714717085e-08	5.5367742943417e-08	0.999999972316129
110	5.51060568864958e-08	1.10212113772992e-07	0.999999944893943
111	1.94888464613313e-07	3.89776929226626e-07	0.999999805111535
112	0.000326076088814931	0.000652152177629862	0.999673923911185
113	0.0190283580643136	0.0380567161286273	0.980971641935686
114	0.0594128708927263	0.118825741785453	0.940587129107274
115	0.0528602365787179	0.105720473157436	0.947139763421282
116	0.045820984258565	0.09164196851713	0.954179015741435
117	0.0431982965634394	0.0863965931268789	0.95680170343656
118	0.0560738182509703	0.112147636501941	0.94392618174903
119	0.0498710254382087	0.0997420508764175	0.950128974561791
120	0.0464181449991233	0.0928362899982465	0.953581855000877
121	0.0476394809828125	0.095278961965625	0.952360519017187
122	0.0546318462355632	0.109263692471126	0.945368153764437
123	0.0656070370424143	0.131214074084829	0.934392962957586
124	0.0638497849609018	0.127699569921804	0.936150215039098
125	0.0609346861909942	0.121869372381988	0.939065313809006
126	0.0576794335649466	0.115358867129893	0.942320566435053
127	0.0757562464817668	0.151512492963534	0.924243753518233
128	0.133870301195436	0.267740602390873	0.866129698804564
129	0.264687064343604	0.529374128687208	0.735312935656396
130	0.422543289699646	0.845086579399293	0.577456710300354
131	0.460473416834577	0.920946833669153	0.539526583165423
132	0.488436540706063	0.976873081412126	0.511563459293937
133	0.506325758957076	0.98734848208585	0.493674241042925
134	0.543841522922922	0.912316954154156	0.456158477077078
135	0.603548222156401	0.792903555687199	0.396451777843599
136	0.611475712484671	0.777048575030657	0.388524287515329
137	0.617012681396512	0.765974637206977	0.382987318603488
138	0.632729795410857	0.734540409178285	0.367270204589143
139	0.622849301039141	0.754301397921717	0.377150698960859
140	0.693057675906227	0.613884648187546	0.306942324093773
141	0.869614747688855	0.260770504622291	0.130385252311145
142	0.934537778007817	0.130924443984367	0.0654622219921835
143	0.923657700928383	0.152684598143234	0.0763422990716169
144	0.92836549932329	0.143269001353421	0.0716345006767105
145	0.92429283936319	0.151414321273619	0.0757071606368094
146	0.964753311698627	0.0704933766027463	0.0352466883013732
147	0.99884309515231	0.00231380969538052	0.00115690484769026
148	0.99999034139882	1.93172023594116e-05	9.65860117970579e-06
149	0.999999457126555	1.08574689022487e-06	5.42873445112437e-07
150	0.999999452749655	1.09450069054273e-06	5.47250345271363e-07
151	0.999998660318593	2.67936281445508e-06	1.33968140722754e-06
152	0.999996771032397	6.45793520629271e-06	3.22896760314635e-06
153	0.999994099299563	1.18014008740522e-05	5.90070043702609e-06
154	0.999992645191835	1.47096163305649e-05	7.35480816528247e-06
155	0.999993685494346	1.26290113071170e-05	6.31450565355848e-06
156	0.999998645191834	2.70961633206066e-06	1.35480816603033e-06
157	0.999997419680189	5.16063962209662e-06	2.58031981104831e-06
158	0.999995868121231	8.26375753744413e-06	4.13187876872206e-06
159	0.999986416547987	2.71669040254847e-05	1.35834520127424e-05
160	0.99995828420924	8.3431581518324e-05	4.1715790759162e-05
161	0.999992165147554	1.56697048928989e-05	7.83485244644946e-06
162	0.999997137386451	5.72522709790285e-06	2.86261354895143e-06
163	0.999993189130929	1.36217381426842e-05	6.81086907134212e-06
164	0.999970177123934	5.96457521311375e-05	2.98228760655687e-05
165	0.99991857182762	0.000162856344760604	8.14281723803022e-05
166	0.999637738476642	0.000724523046716433	0.000362261523358216
167	0.998884921659914	0.00223015668017171	0.00111507834008586
168	0.995694672301945	0.00861065539610924	0.00430532769805462
169	0.990267493279126	0.0194650134417473	0.00973250672087366
170	0.994427472901951	0.0111450541960977	0.00557252709804887

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	129	0.781818181818182	NOK
5% type I error level	132	0.8	NOK
10% type I error level	138	0.836363636363636	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/10slak1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/10slak1292434829.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/1l2dq1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/1l2dq1292434829.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/2l2dq1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/2l2dq1292434829.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/3vtub1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/3vtub1292434829.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/4vtub1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/4vtub1292434829.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/5vtub1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/5vtub1292434829.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/6okbw1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/6okbw1292434829.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/7hbbz1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/7hbbz1292434829.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/8hbbz1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/8hbbz1292434829.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/9hbbz1292434829.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292435014psxl7bn8wnvdncv/9hbbz1292434829.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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.

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