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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: Thu, 30 Dec 2010 01:00:37 +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/30/t1293670688mg2de0euqhz2msc.htm/, Retrieved Thu, 30 Dec 2010 01:58:20 +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/30/t1293670688mg2de0euqhz2msc.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 «

13 360 3821 73 0 0 15 390 3850 70 0 0 17 304 3672 72 0 0 19.4 232 3210 78 0 0 24.3 151 3003 80 0 0 18.1 258 3410 78 0 0 20.2 232 3265 79 0 0 18 232 2789 73 0 0 19 232 2634 71 0 0 20 232 2914 75 0 0 21 199 2648 70 0 0 18 199 2774 70 0 0 18 232 2945 73 0 0 19 232 2901 74 0 0 22.5 232 3085 76 0 0 18 258 2962 71 0 0 14 304 3672 73 0 0 15 258 3730 75 0 0 15.5 304 3962 76 0 0 16 258 3632 74 0 0 18 232 3288 71 0 0 14 304 4257 74 0 0 15 304 3892 72 0 0 19 232 3211 75 0 0 17.5 258 3193 76 0 0 16 304 3433 70 0 0 27.4 121 2670 79 0 0 24 107 2430 70 0 1 20 114 2582 73 0 1 23 115 2694 75 0 1 34.3 97 2188 80 0 1 20.3 131 2830 78 0 1 36.4 121 2950 80 0 1 29 98 2219 74 0 1 26 121 2234 70 0 1 21.5 121 2600 77 0 1 17 231 3907 75 0 0 22.4 231 3415 81 0 0 13 350 4100 73 0 0 25 181 2945 82 0 0 13 350 4699 74 0 0 20.6 231 3380 78 0 0 12 455 4951 73 0 0 14 455 3086 70 0 0 16.9 350 4360 79 0 0 13 350 4502 72 0 0 30 111 2155 77 0 0 17.7 231 3445 78 0 0 21 231 3039 75 0 0 20.5 231 3425 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	15 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

Multiple Linear Regression - Estimated Regression Equation

MPG[t] = -19.5949213012208 + 0.00932120264360868Displ[t] -0.00681998045690182Weight[t] + 0.797990841371979Year[t] + 2.43807959073668OriginJapan[t] + 2.38304851707346OriginEurope[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)	-19.5949213012208	4.063657	-4.822	2e-06	1e-06
Displ	0.00932120264360868	0.005001	1.8638	0.063109	0.031555
Weight	-0.00681998045690182	0.000564	-12.0993	0	0
Year	0.797990841371979	0.050811	15.7051	0	0
OriginJapan	2.43807959073668	0.530893	4.5924	6e-06	3e-06
OriginEurope	2.38304851707346	0.56055	4.2513	2.7e-05	1.3e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.905896689865256
R-squared	0.820648812708828
Adjusted R-squared	0.818325610800911
F-TEST (value)	353.240417852756
F-TEST (DF numerator)	5
F-TEST (DF denominator)	386
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.32675009800069
Sum Squared Residuals	4271.96475881537

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	13	15.9548977448107	-2.95489774481071
2	15	13.642781866753	1.357218133247
3	17	15.6510966434752	1.34890335652482
4	19.4	22.9187460724559	-3.5187460724559
5	24.3	25.1714462956462	-0.87144629564624
6	18.1	21.7971012498094	-3.69710124980935
7	20.2	23.3416379886983	-3.14163798869828
8	18	21.8000036379517	-3.80000363795167
9	19	21.2611189260275	-2.26111892602749
10	20	22.5434877635829	-2.5434877635829
11	21	20.0600486710198	0.939951328980195
12	18	19.2007311334502	-1.20073113345018
13	18	20.736086686675	-2.73608668667498
14	19	21.8341566681506	-2.83415666815064
15	22.5	22.1752619468247	0.324738053175334
16	18	19.2665166048975	-1.26651660489752
17	14	16.4490874848472	-2.44908748484718
18	15	17.2207349794848	-2.22073497948484
19	15.5	16.8652656764616	-1.36526567646159
20	16	17.0911022228892	-1.09110222288924
21	18	16.8008517072137	1.1991482927863
22	14	13.2573897589316	0.742610241068404
23	15	14.1507009429568	0.849299057043198
24	19	20.5179535678831	-1.51795356788306
25	17.5	21.6810553262131	-4.1810553262131
26	16	15.6850902899308	0.314909710069219
27	27.4	26.3648728671143	1.0351271328857
28	24	23.0723022844859	0.927697715514132
29	20	24.494886197658	-4.49488619765799
30	23	25.3363512718726	-2.33635127187255
31	34.3	32.6094339423398	1.69056605766019
32	20.3	26.9519456961476	-6.65194569614758
33	36.4	27.6363176976272	8.76368230237277
34	29	27.6193907025876	1.38060929741241
35	26	24.5395152910491	1.46048470895085
36	21.5	27.6293383334269	-6.12933833342693
37	17	15.7619259672358	1.23807403276422
38	22.4	23.9053014002634	-1.50530140026335
39	13	13.9589111708992	-0.9589111708992
40	25	27.4426229241988	-2.44262292419875
41	13	10.671733718587	2.32826628141301
42	20.6	21.750028192139	-1.15002819213898
43	12	9.13383407965465	2.86616592034534
44	14	19.4591251076606	-5.45912510766062
45	16.9	16.9736613003366	-0.0736613003366014
46	13	10.4192881858527	2.58071181414731
47	30	28.1879690932387	1.81203090676131
48	17.7	21.3067294624404	-3.60672946244036
49	21	21.6816690038266	-0.681669003826563
50	20.5	20.6451382302064	-0.145138230206418
51	26.6	28.4791899451581	-1.87918994515808
52	15	14.3406706927423	0.659329307257695
53	28.4	26.6445089464226	1.75549105357744
54	23	20.1108523105114	2.88914768948856
55	16.5	14.4432891670826	2.05671083291737
56	25	24.8163612780033	0.183638721996693
57	16	16.0072286220334	-0.00722862203336408
58	15	13.2360994982965	1.76390050170346
59	27	27.128886942606	-0.128886942605986
60	13	11.9424984167674	1.05750158323263
61	17	20.1005970189632	-3.10059701896316
62	17.5	18.2318161179431	-0.731816117943128
63	28	29.1182532971364	-1.11825329713638
64	34	30.5504491930858	3.44955080691424
65	27	28.8795539811448	-1.87955398114481
66	13	12.7737485767659	0.226251423234147
67	17	16.6890141560657	0.310985843934316
68	18	15.2288352854216	2.77116471457842
69	16	16.000355513662	-0.000355513661996265
70	17.5	15.149131823509	2.35086817649096
71	29	27.9660246379611	1.03397536203889
72	30	28.8647843002438	1.13521569975624
73	30.5	28.7760714263896	1.72392857361043
74	32.1	30.6994652989793	1.40053470102072
75	23.5	28.0704581621963	-4.57045816219631
76	28	27.3879399441393	0.612060055860675
77	28.8	27.3610739388496	1.43892606115041
78	17.5	20.1743429370293	-2.67434293702931
79	11	8.3074488332387	2.6925511667613
80	13	11.9742437300263	1.02575626997369
81	14	11.6195516183529	2.38044838164706
82	14	10.8020686856655	3.1979313143345
83	13	14.7227489820722	-1.7227489820722
84	20.5	22.99556651299	-2.49556651299002
85	19.2	21.349086725878	-2.14908672587796
86	15	14.3429721538534	0.657027846146587
87	15.5	16.7075758066885	-1.2075758066885
88	19.2	22.1328980672054	-2.93289806720544
89	15	14.0816708191234	0.918329180876566
90	20	20.7293898426223	-0.729389842622299
91	15	19.0352468169833	-4.03524681698331
92	18	18.9943800621564	-0.994380062156362
93	22	20.5152888319599	1.48471116804007
94	16	18.6328148421116	-2.63281484211163
95	20	22.7428747074473	-2.74287470744729
96	21	23.5886054120176	-2.58860541201758
97	25	23.4249790089664	1.5750209910336
98	22	21.9448838660753	0.0551161339246882
99	28	22.9269610518692	5.07303894813083
100	24.5	27.2074227933877	-2.70742279338769
101	13	16.6597828155757	-3.65978281557572
102	10	9.28181232700319	0.718187672996812
103	31	28.3992039630979	2.60079603690207
104	15.5	16.0824390657646	-0.582439065764638
105	26	29.6647858225932	-3.66478582259319
106	17.6	23.5083751615566	-5.90837516155661
107	18.5	19.9312651186715	-1.43126511867145
108	13	10.4671318186913	2.53286818130868
109	13	11.4309467545853	1.56905324541473
110	35	29.1710061402836	5.82899385971645
111	23.9	29.7936140322708	-5.89361403227077
112	32.9	30.7553906604373	2.14460933956268
113	31.8	32.9003764596673	-1.10037645966726
114	40.8	33.0845690599181	7.71543094008193
115	37	34.8032572629718	2.1967427370282
116	32.7	28.4022445138161	4.29775548618387
117	37.2	33.7145084841397	3.48549151586026
118	38	35.5207757110674	2.47922428893261
119	27.2	30.5097119802455	-3.30971198024546
120	28	25.598540239337	2.40145976066298
121	37	31.1918162817646	5.80818371823543
122	22	25.8784460882106	-3.87844608821063
123	24	26.4448442441886	-2.44484424418858
124	32	29.0077195152875	2.99228048471252
125	22	26.4511036749465	-4.45110367494648
126	24.2	28.8587692878907	-4.65876928789068
127	32	30.7110033492584	1.28899665074163
128	31	29.3318936689288	1.66810633107116
129	39.4	31.7613865954502	7.63861340454981
130	33.5	31.8158933111909	1.68410668880907
131	27	25.0801154687835	1.91988453121645
132	27	25.8781063101555	1.12189368984447
133	29	29.8782393944915	-0.878239394491522
134	25.8	28.6280956652297	-2.82809566522965
135	18.6	20.0573056666209	-1.45730566662089
136	19.1	23.2832626785644	-4.18326267856438
137	20.6	22.6284914267873	-2.02849142678734
138	20	18.249904589713	1.75009541028703
139	15	15.5348678393786	-0.534867839378627
140	36	30.9353363653113	5.06466363468869
141	26	26.5868045718096	-0.586804571809622
142	27.9	26.6025083416153	1.29749165838465
143	28	25.802850727314	2.19714927268597
144	28	24.0154594278998	3.98454057210023
145	25	24.2699580839402	0.730041916059763
146	35.7	31.2995704512722	4.40042954872783
147	33.5	28.6123918954239	4.88760810457607
148	16	15.4408069692985	0.559193030701504
149	15	15.863486373883	-0.863486373883012
150	14	12.0238905045618	1.97610949543825
151	13	18.4074984680508	-5.40749846805079
152	11	9.34342567334147	1.65657432665853
153	15	18.4414389865919	-3.4414389865919
154	19.4	20.1398797599328	-0.739879759932783
155	17.5	17.7869865023017	-0.286986502301654
156	12	6.83944588474327	5.16055411525673
157	15.5	16.5797968335156	-1.07979683351557
158	30.9	28.4185341844814	2.48146581551861
159	32	31.4468348995789	0.553165100421058
160	18.2	20.2899724578991	-2.08997245789909
161	26	26.5076807601981	-0.507680760198128
162	26	27.6030328778362	-1.6030328778362
163	30	26.1824831423984	3.81751685760155
164	24	28.3018389121548	-4.30183891215482
165	29	28.9423969027368	0.057603097263206
166	28	27.6283679971831	0.37163200281692
167	37.3	32.1510747516065	5.14892524839351
168	31	28.9358635724205	2.06413642757947
169	12	8.92806705481676	3.07193294518324
170	13	8.4232822451771	4.5767177548229
171	15.5	19.0698965227922	-3.56989652279217
172	29.9	29.7242612215568	0.17573877844321
173	34.4	32.0089546746189	2.3910453253811
174	13	17.4740614732093	-4.47406147320934
175	10	8.1458607379149	1.85413926208509
176	26.4	25.9759704673345	0.424029532665519
177	20.2	24.2913627998014	-4.09136279980137
178	25.1	25.4029858531258	-0.302985853125794
179	22.3	25.0415800168245	-2.74158001682446
180	24	27.6060520523629	-3.60605205236295
181	36.1	31.2858773624439	4.81412263755609
182	18.1	23.605330159793	-5.50533015979301
183	14	12.9724620989207	1.02753790107932
184	14	12.0039717461262	1.99602825387385
185	15	10.657698365515	4.34230163448499
186	14	13.9070523105063	0.092947689493709
187	14.5	15.577907145115	-1.07790714511504
188	16	14.029865086645	1.97013491335501
189	13	11.3904263939951	1.60957360600495
190	14	10.6403347995648	3.35966520043522
191	18.5	20.1402430347448	-1.6402430347448
192	18	19.0080731509846	-1.00807315098463
193	20.2	26.0374371805116	-5.83743718051163
194	22	28.668202109282	-6.66820210928199
195	13	12.1745775133776	0.82542248662237
196	14	11.7654849417925	2.23451505820755
197	17.6	20.856931163576	-3.25693116357604
198	15	21.0471941796838	-6.04719417968381
199	18	20.3855498195354	-2.3855498195354
200	21	20.4853886815344	0.514611318465575
201	24	22.374842035583	1.62515796441698
202	18	17.984810442877	0.0151895571229702
203	27	28.1175505866306	-1.11755058663058
204	13	21.4568769321255	-8.45687693212554
205	25.5	24.3662956957623	1.13370430423775
206	18	21.4974957703396	-3.49749577033965
207	19	24.0414419860107	-5.04144198601069
208	23	23.5614317460189	-0.561431746018907
209	26	23.8778155829595	2.12218441704049
210	26.5	24.8641011412016	1.63589885879838
211	22	22.6637528058021	-0.663752805802058
212	21	23.8163295030185	-2.81632950301847
213	28	29.0564233091472	-1.05642330914721
214	16	15.5575003316588	0.442499668341203
215	17	15.5573281973331	1.44267180266687
216	19	16.873153628402	2.12684637159797
217	9	6.82593567641531	2.17406432358469
218	32.4	32.0620390358351	0.337960964164866
219	36	34.2377190574157	1.76228094258425
220	31.5	31.2550708998677	0.244929100132335
221	29.5	31.4392635001185	-1.93926350011848
222	24	26.0380935110467	-2.03809351104671
223	33	32.0968267542159	0.903173245784119
224	38	35.7253751247744	2.27462487522556
225	32	35.7253751247744	-3.72537512477444
226	35.1	36.2322682506313	-1.13226825063125
227	44.6	34.9136911945742	9.6863088054258
228	33	31.2988359128439	1.7011640871561
229	36.1	33.6587085346753	2.44129146532467
230	33.7	33.4056283137593	0.294371686240746
231	34.1	33.2165967828714	0.883403217128556
232	18	27.2633354042635	-9.26333540426346
233	31.3	30.4645795950628	0.835420404937216
234	31.6	30.6283122539429	0.971687746057106
235	46.6	33.0938902625617	13.5061097374383
236	34.1	34.7909846742644	-0.690984674264428
237	31	35.6912752224899	-4.69127522248993
238	37	35.3161762973603	1.68382370263967
239	32.8	32.2758365157816	0.524163484218416
240	21.5	26.483802443874	-4.98380244387398
241	23.7	30.8305570786244	-7.13055707862438
242	19	25.0604285887697	-6.06042858876971
243	25.4	23.4606527551559	1.93934724484407
244	30	25.8233536266469	4.1766463733531
245	16.5	18.9490678588843	-2.44906785888434
246	23	23.0592585443879	-0.0592585443878986
247	21	23.2442048392317	-2.24420483923168
248	15	15.373560620398	-0.373560620398045
249	16.5	19.7450745880254	-3.24507458802545
250	36	32.2613470794387	3.73865292056127
251	11	10.2622457548436	0.737754245156368
252	12	8.88466283046393	3.11533716953607
253	15	19.1785195344927	-4.17851953449271
254	20.2	21.1160372930238	-0.916037293023845
255	20.8	23.5752648518267	-2.77526485182667
256	19.8	24.9188541297508	-5.1188541297508
257	36	34.6657938123432	1.33420618765676
258	38	27.7202417063479	10.2797582936521
259	26.6	22.9003305732132	3.69966942678679
260	19.9	22.1226427756572	-2.22264277565716
261	23.9	22.5455346918995	1.35446530810046
262	17	16.5847655167384	0.415234483261589
263	12	10.7330072868702	1.26699271312983
264	11	16.9324226501084	-5.9324226501084
265	26.8	26.6449759908749	0.155024009125105
266	23.8	24.5848217205237	-0.784821720523743
267	12	11.2377389685954	0.762261031404626
268	25	29.3763340524596	-4.3763340524596
269	28	26.0479179499192	1.95208205008082
270	24	27.4052003166716	-3.40520031667158
271	26	27.0576510829349	-1.05765108293493
272	30	26.0372124944939	3.96278750550615
273	19	22.2526393832871	-3.25263938328712
274	23	23.5893024249254	-0.589302424925415
275	25	21.4498306218465	3.55016937815355
276	27.2	25.387955599471	1.81204440052901
277	21	21.0452903307576	-0.0452903307576384
278	28.1	26.7111380639389	1.38886193606113
279	16.2	23.29463551574	-7.09463551574
280	14	14.820337024686	-0.820337024685971
281	25.5	27.3016051560676	-1.80160515606763
282	39	33.0564969205689	5.94350307943109
283	26	24.577596083515	1.42240391648499
284	13	10.2738540242117	2.72614597578832
285	20	20.1464197064307	-0.146419706430684
286	22	18.7890310838494	3.21096891615064
287	23	20.6987849955253	2.30121500447473
288	18	16.5380363671162	1.46196363288385
289	14	12.7262953637082	1.27370463629183
290	14	12.0919309253874	1.90806907461263
291	14	10.9580110278449	3.04198897215514
292	15	12.6239425289402	2.37605747105982
293	16	12.5422621472008	3.45773785279924
294	34.2	29.4211244395604	4.77887556043958
295	34.7	30.9148064154508	3.78519358454915
296	38	32.326595497944	5.67340450205601
297	34.5	29.7621234624055	4.73787653759449
298	27.2	29.3189478691111	-2.11894786911111
299	30	30.0350458170858	-0.0350458170857983
300	23.2	25.381625584001	-2.18162558400099
301	18	15.7951271855706	2.2048728144294
302	16	15.7057862397163	0.294213760283733
303	14	13.0195013954405	0.980498604559514
304	18	16.9130821643313	1.08691783566871
305	18	19.470521707755	-1.470521707755
306	22	21.1006564206979	0.899343579302063
307	19	20.091246185162	-1.091246185162
308	20.5	21.3531019534322	-0.853101953432235
309	19	19.1911150206799	-0.191115020679893
310	13	17.145802083524	-4.14580208352395
311	23	23.8819708274933	-0.881970827493291
312	14	11.6832860314906	2.31671396850937
313	14	10.3271712758691	3.67282872413092
314	16	12.1472040863034	3.85279591369664
315	14	10.3465167340234	3.65348326597659
316	19	17.0095532375401	1.99044676245993
317	16	13.2110147817511	2.78898521824889
318	16	16.7985370137393	-0.79853701373933
319	31	29.3228527108434	1.67714728915657
320	21.5	23.4687163951927	-1.9687163951927
321	27	28.5951827408399	-1.59518274083988
322	33.5	27.4219867185094	6.07801328149063
323	19.2	20.6929312213192	-1.4929312213192
324	13	5.73620994515778	7.26379005484222
325	24.5	24.5711286316955	-0.0711286316954749
326	18.5	18.5238545385446	-0.0238545385446018
327	26	26.2093660282635	-0.20936602826347
328	27	29.3592756610297	-2.3592756610297
329	36	32.5233326764943	3.47666732350572
330	25	23.4194376016846	1.58056239831536
331	21.6	27.0974329857031	-5.49743298570305
332	24	24.0281761405249	-0.0281761405249066
333	25	25.5491380382429	-0.549138038242944
334	26	26.5945971640998	-0.594597164099785
335	32.3	34.3013134535739	-2.00131345357394
336	30	31.6549485246382	-1.65494852463816
337	33.8	32.9577241756498	0.842275824350186
338	20	26.4579109048211	-6.45791090482112
339	32	31.4454125450544	0.554587454945572
340	21.1	29.1832342216657	-8.0832342216657
341	28	29.6975610055929	-1.69756100559288
342	29	28.7904504769105	0.209549523089532
343	32.2	32.2418597499013	-0.0418597499012848
344	32.4	32.4601522524366	-0.0601522524366136
345	34	33.9742410417833	0.0257589582167182
346	31	28.0704880645357	2.92951193546435
347	32	30.0348018198668	1.96519818013322
348	27	26.8806965652346	0.119303434765439
349	26	29.7453539967057	-3.74535399670565
350	38.1	34.0902910953726	4.00970890462744
351	24	25.5139253521091	-1.51392535210912
352	25	25.3588874676769	-0.358887467676887
353	27.5	28.8763351011051	-1.37633510110512
354	31	31.3567441785255	-0.35674417852546
355	24	25.8158792862038	-1.81587928620377
356	29.8	29.4424997348569	0.357500265143102
357	24	23.578819440511	0.421180559488953
358	25.4	29.2684351597571	-3.86843515975713
359	19	24.9620271074669	-5.96202710746688
360	20	23.4069121795499	-3.40691217954986
361	39.1	36.2477257476285	2.85227425237146
362	37.7	34.3290435392786	3.37095646072141
363	23	24.3261721605354	-1.32617216053542
364	35	30.7146301058767	4.28536989412334
365	29.8	34.8741176179083	-5.07411761790827
366	26	27.0369786299064	-1.03697862990637
367	22	24.2463623872313	-2.2463623872313
368	25	28.3155320009831	-3.31553200098309
369	26	29.1882028493259	-3.18820284932589
370	30.5	30.2018214573101	0.29817854268993
371	33	33.4683544439469	-0.468354443946855
372	27	27.8417894517352	-0.841789451735246
373	29	30.266046411657	-1.26604641165701
374	29.5	31.8931234827073	-2.39312348270726
375	29	31.9068165715355	-2.90681657153553
376	43.1	32.3326598738417	10.7673401261583
377	36	35.6985411812682	0.301458818731784
378	31.5	32.2892387689135	-0.789238768913546
379	26	28.6466534014786	-2.64665340147859
380	23	25.7753885012085	-2.77538850120846
381	19	22.6096202054893	-3.60962020548933
382	18	21.3683306344187	-3.36833063441873
383	22	23.6804633930518	-1.68046339305185
384	20	23.1642490645514	-3.16424906455143
385	17	25.1360302391035	-8.13603023910349
386	30.7	27.2258215064964	3.47417849350357
387	43.4	31.54164839667	11.85835160333
388	44	34.6009744915841	9.39902550841592
389	29	31.064037253029	-2.06403725302899
390	41.5	32.9188342850871	8.5811657149129
391	44.3	33.2466435108954	11.0533564891046
392	31.9	33.5305283399841	-1.63052833998414

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.130057985254309	0.260115970508619	0.86994201474569
10	0.0600805644877129	0.120161128975426	0.939919435512287
11	0.0222375916274835	0.0444751832549671	0.977762408372516
12	0.0322944086408054	0.0645888172816108	0.967705591359195
13	0.0164194613626907	0.0328389227253813	0.98358053863731
14	0.00670741269122846	0.0134148253824569	0.993292587308772
15	0.0125172797423999	0.0250345594847997	0.9874827202576
16	0.00564985125563449	0.011299702511269	0.994350148744366
17	0.00638147201035473	0.0127629440207095	0.993618527989645
18	0.00575075287296963	0.0115015057459393	0.99424924712703
19	0.00272769071445002	0.00545538142890003	0.99727230928555
20	0.00130221677381672	0.00260443354763345	0.998697783226183
21	0.000674729588239515	0.00134945917647903	0.99932527041176
22	0.000295174279497103	0.000590348558994207	0.999704825720503
23	0.000131492225641703	0.000262984451283406	0.999868507774358
24	5.46717347902289e-05	0.000109343469580458	0.99994532826521
25	3.30385966657336e-05	6.60771933314673e-05	0.999966961403334
26	1.43529286318126e-05	2.87058572636252e-05	0.999985647071368
27	4.48058575885238e-05	8.96117151770476e-05	0.999955194142411
28	1.94153161257431e-05	3.88306322514862e-05	0.999980584683874
29	4.23230618242872e-05	8.46461236485744e-05	0.999957676938176
30	2.01849903895264e-05	4.03699807790528e-05	0.99997981500961
31	0.000890621430743805	0.00178124286148761	0.999109378569256
32	0.00267754438530073	0.00535508877060147	0.9973224556147
33	0.160934435948829	0.321868871897658	0.83906556405117
34	0.139793347968323	0.279586695936646	0.860206652031677
35	0.115741513373837	0.231483026747675	0.884258486626162
36	0.188340484671283	0.376680969342567	0.811659515328717
37	0.154341203135411	0.308682406270821	0.84565879686459
38	0.125003493463909	0.250006986927819	0.87499650653609
39	0.0991463219606353	0.198292643921271	0.900853678039365
40	0.0783314881288735	0.156662976257747	0.921668511871127
41	0.0653039126883868	0.130607825376774	0.934696087311613
42	0.0502119526653305	0.100423905330661	0.94978804733467
43	0.0485238948930537	0.0970477897861075	0.951476105106946
44	0.0403354153352442	0.0806708306704885	0.959664584664756
45	0.0306715042025874	0.0613430084051748	0.969328495797413
46	0.0241266241809094	0.0482532483618187	0.97587337581909
47	0.0318112786738145	0.063622557347629	0.968188721326185
48	0.0305763764871881	0.0611527529743763	0.969423623512812
49	0.0236082639658033	0.0472165279316066	0.976391736034197
50	0.0177922768937283	0.0355845537874566	0.982207723106272
51	0.0133721287375428	0.0267442574750856	0.986627871262457
52	0.0106141945067472	0.0212283890134944	0.989385805493253
53	0.0116753727762676	0.0233507455525352	0.988324627223732
54	0.0178965994622011	0.0357931989244022	0.9821034005378
55	0.0148123365614013	0.0296246731228026	0.985187663438599
56	0.0116201962515955	0.023240392503191	0.988379803748405
57	0.00877371088149343	0.0175474217629869	0.991226289118507
58	0.00673183153675026	0.0134636630735005	0.99326816846325
59	0.00501256544229776	0.0100251308845955	0.994987434557702
60	0.00370602065703697	0.00741204131407395	0.996293979342963
61	0.00332050357966309	0.00664100715932618	0.996679496420337
62	0.00237340150148982	0.00474680300297963	0.99762659849851
63	0.00168393402045813	0.00336786804091626	0.998316065979542
64	0.0032842349902198	0.00656846998043961	0.99671576500978
65	0.00248028832333056	0.00496057664666113	0.99751971167667
66	0.00178199351411365	0.0035639870282273	0.998218006485886
67	0.00126952196279785	0.00253904392559571	0.998730478037202
68	0.00137989043365175	0.0027597808673035	0.998620109566348
69	0.000990722255882249	0.0019814445117645	0.999009277744118
70	0.000790701463823593	0.00158140292764719	0.999209298536176
71	0.000664977461548181	0.00132995492309636	0.999335022538452
72	0.000569619618987669	0.00113923923797534	0.999430380381012
73	0.000543365160664825	0.00108673032132965	0.999456634839335
74	0.00048879425300658	0.00097758850601316	0.999511205746993
75	0.00056575658746674	0.00113151317493348	0.999434243412533
76	0.000428711289092044	0.000857422578184087	0.999571288710908
77	0.00039805947067199	0.000796118941343979	0.999601940529328
78	0.000359021277241981	0.000718042554483961	0.999640978722758
79	0.000288445198120478	0.000576890396240957	0.99971155480188
80	0.000202647349318801	0.000405294698637602	0.999797352650681
81	0.000164926501018985	0.00032985300203797	0.99983507349898
82	0.000225807570848716	0.000451615141697433	0.999774192429151
83	0.000173476012196855	0.000346952024393711	0.999826523987803
84	0.000147956731178358	0.000295913462356715	0.999852043268822
85	0.000113743603057394	0.000227487206114788	0.999886256396943
86	8.81519482070292e-05	0.000176303896414058	0.999911848051793
87	6.18240945030591e-05	0.000123648189006118	0.999938175905497
88	4.77612291328166e-05	9.55224582656332e-05	0.999952238770867
89	3.33518150987324e-05	6.67036301974648e-05	0.999966648184901
90	2.24263689294307e-05	4.48527378588614e-05	0.99997757363107
91	3.1284933147858e-05	6.2569866295716e-05	0.999968715066852
92	2.18332913135466e-05	4.36665826270932e-05	0.999978166708686
93	1.74322410343387e-05	3.48644820686775e-05	0.999982567758966
94	1.57412773009112e-05	3.14825546018224e-05	0.9999842587227
95	1.42737795454578e-05	2.85475590909157e-05	0.999985726220455
96	1.18126269097232e-05	2.36252538194464e-05	0.99998818737309
97	9.4242581155718e-06	1.88485162311436e-05	0.999990575741884
98	6.24954248974225e-06	1.24990849794845e-05	0.99999375045751
99	1.67974260462905e-05	3.3594852092581e-05	0.999983202573954
100	1.42485713530544e-05	2.84971427061088e-05	0.999985751428647
101	1.52037634462116e-05	3.04075268924231e-05	0.999984796236554
102	1.08295409717373e-05	2.16590819434745e-05	0.999989170459028
103	1.18360880895458e-05	2.36721761790915e-05	0.99998816391191
104	8.09562629960194e-06	1.61912525992039e-05	0.9999919043737
105	7.17205020317145e-06	1.43441004063429e-05	0.999992827949797
106	1.74058395158116e-05	3.48116790316232e-05	0.999982594160484
107	1.22831042637065e-05	2.4566208527413e-05	0.999987716895736
108	1.14201738951943e-05	2.28403477903885e-05	0.999988579826105
109	8.51375144236002e-06	1.702750288472e-05	0.999991486248558
110	7.29947994149277e-06	1.45989598829855e-05	0.999992700520059
111	6.11744940739954e-05	0.000122348988147991	0.999938825505926
112	5.21616701577746e-05	0.000104323340315549	0.999947838329842
113	3.82282805842277e-05	7.64565611684553e-05	0.999961771719416
114	0.000193006395035349	0.000386012790070698	0.999806993604965
115	0.000149697341512276	0.000299394683024552	0.999850302658488
116	0.000141083825190908	0.000282167650381815	0.99985891617481
117	0.000119761899950587	0.000239523799901175	0.99988023810005
118	9.2350003531587e-05	0.000184700007063174	0.999907649996468
119	0.00017355915975524	0.00034711831951048	0.999826440840245
120	0.000136837803572936	0.000273675607145872	0.999863162196427
121	0.000194553911482972	0.000389107822965943	0.999805446088517
122	0.000534198150493864	0.00106839630098773	0.999465801849506
123	0.000708870239517336	0.00141774047903467	0.999291129760483
124	0.000593002040641175	0.00118600408128235	0.99940699795936
125	0.00122223486328357	0.00244446972656714	0.998777765136716
126	0.00208322826560607	0.00416645653121213	0.997916771734394
127	0.00163893047788791	0.00327786095577582	0.998361069522112
128	0.00129875772240208	0.00259751544480417	0.998701242277598
129	0.00360801546717985	0.00721603093435969	0.99639198453282
130	0.00292584329782116	0.00585168659564232	0.997074156702179
131	0.00239249923085232	0.00478499846170465	0.997607500769148
132	0.00193419852085747	0.00386839704171494	0.998065801479143
133	0.0015227861118939	0.0030455722237878	0.998477213888106
134	0.00133413251192008	0.00266826502384017	0.99866586748808
135	0.00108090065420319	0.00216180130840637	0.998919099345797
136	0.00120822914641057	0.00241645829282114	0.99879177085359
137	0.00100155549710212	0.00200311099420423	0.998998444502898
138	0.000825942133046622	0.00165188426609324	0.999174057866953
139	0.00063696389843448	0.00127392779686896	0.999363036101566
140	0.00133272028822805	0.00266544057645609	0.998667279711772
141	0.00103423208546445	0.0020684641709289	0.998965767914536
142	0.000868279482681855	0.00173655896536371	0.999131720517318
143	0.000760873702648032	0.00152174740529606	0.999239126297352
144	0.000858380340783423	0.00171676068156685	0.999141619659217
145	0.000662229288989813	0.00132445857797963	0.99933777071101
146	0.00097392753253266	0.00194785506506532	0.999026072467467
147	0.00143148740014868	0.00286297480029736	0.998568512599851
148	0.00112551679701057	0.00225103359402114	0.99887448320299
149	0.00088353250858821	0.00176706501717642	0.999116467491412
150	0.000735983337908114	0.00147196667581623	0.999264016662092
151	0.00111158971717959	0.00222317943435918	0.99888841028282
152	0.000891914215944055	0.00178382843188811	0.999108085784056
153	0.000891194209418128	0.00178238841883626	0.999108805790582
154	0.000702777653275213	0.00140555530655043	0.999297222346725
155	0.000544022939269491	0.00108804587853898	0.99945597706073
156	0.000746919454303249	0.0014938389086065	0.999253080545697
157	0.000589602607495167	0.00117920521499033	0.999410397392505
158	0.000542223531284619	0.00108444706256924	0.999457776468715
159	0.000438293928604724	0.000876587857209448	0.999561706071395
160	0.000365688631258702	0.000731377262517404	0.999634311368741
161	0.000277446721923512	0.000554893443847024	0.999722553278076
162	0.000217134352548545	0.00043426870509709	0.999782865647451
163	0.00025627832875681	0.00051255665751362	0.999743721671243
164	0.000300042669646384	0.000600085339292769	0.999699957330354
165	0.000228302990974044	0.000456605981948089	0.999771697009026
166	0.000175770791465242	0.000351541582930483	0.999824229208535
167	0.000349210020886534	0.000698420041773069	0.999650789979113
168	0.000301272173686474	0.000602544347372949	0.999698727826314
169	0.000288096682543919	0.000576193365087838	0.999711903317456
170	0.000362624111859163	0.000725248223718325	0.99963737588814
171	0.0003679816826281	0.0007359633652562	0.999632018317372
172	0.000281352924185748	0.000562705848371495	0.999718647075814
173	0.000266786939441924	0.000533573878883849	0.999733213060558
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183	0.000352621780311431	0.000705243560622861	0.999647378219689
184	0.000292928770061061	0.000585857540122121	0.99970707122994
185	0.000374687330248405	0.00074937466049681	0.999625312669752
186	0.000286846932800158	0.000573693865600316	0.9997131530672
187	0.000226726994071998	0.000453453988143997	0.999773273005928
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191	0.000114667262788164	0.000229334525576328	0.999885332737212
192	8.8846600192852e-05	0.000177693200385704	0.999911153399807
193	0.000164174363272165	0.000328348726544329	0.999835825636728
194	0.000380542723954616	0.000761085447909233	0.999619457276045
195	0.00029380494797655	0.000587609895953099	0.999706195052023
196	0.000249077823916199	0.000498155647832398	0.999750922176084
197	0.000255743309914103	0.000511486619828206	0.999744256690086
198	0.000528040994824192	0.00105608198964838	0.999471959005176
199	0.000482203780460427	0.000964407560920854	0.99951779621954
200	0.000371497569107663	0.000742995138215326	0.999628502430892
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209	0.000938678861727119	0.00187735772345424	0.999061321138273
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219	0.000152198709927976	0.000304397419855951	0.999847801290072
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223	7.51677055359884e-05	0.000150335411071977	0.999924832294464
224	6.4538301447028e-05	0.000129076602894056	0.999935461698553
225	7.46912776497657e-05	0.000149382555299531	0.99992530872235
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232	0.00176112294838553	0.00352224589677106	0.998238877051614
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247	0.0639754283961737	0.127950856792347	0.936024571603826
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249	0.0614849473412655	0.122969894682531	0.938515052658734
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255	0.0561416266736028	0.112283253347206	0.943858373326397
256	0.0793452182516294	0.158690436503259	0.92065478174837
257	0.0700337842220561	0.140067568444112	0.929966215777944
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267	0.137230767204971	0.274461534409941	0.86276923279503
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271	0.129483010450545	0.25896602090109	0.870516989549455
272	0.141206546433512	0.282413092867023	0.858793453566488
273	0.134014338726655	0.26802867745331	0.865985661273345
274	0.118251277976328	0.236502555952655	0.881748722023672
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279	0.149058861202036	0.298117722404073	0.850941138797964
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281	0.137090766454543	0.274181532909086	0.862909233545457
282	0.154961560093778	0.309923120187557	0.845038439906222
283	0.138102109759393	0.276204219518785	0.861897890240607
284	0.129267454267758	0.258534908535516	0.870732545732242
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289	0.075946864494994	0.151893728989988	0.924053135505006
290	0.0673973590448093	0.134794718089619	0.93260264095519
291	0.0603375113196672	0.120675022639334	0.939662488680333
292	0.0546027963083976	0.109205592616795	0.945397203691602
293	0.0558350466866502	0.1116700933733	0.94416495331335
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295	0.0571380489795277	0.114276097959055	0.942861951020472
296	0.0663810579683776	0.132762115936755	0.933618942031622
297	0.0731127214647829	0.146225442929566	0.926887278535217
298	0.0696846900879747	0.139369380175949	0.930315309912025
299	0.0607008740219916	0.121401748043983	0.939299125978008
300	0.0570836092792165	0.114167218558433	0.942916390720783
301	0.0492549215192221	0.0985098430384442	0.950745078480778
302	0.041693768731373	0.083387537462746	0.958306231268627
303	0.035004055261112	0.070008110522224	0.964995944738888
304	0.0301359193452402	0.0602718386904804	0.96986408065476
305	0.0261596419493003	0.0523192838986006	0.9738403580507
306	0.021436047543154	0.042872095086308	0.978563952456846
307	0.0181199286837924	0.0362398573675847	0.981880071316208
308	0.0152216163048321	0.0304432326096641	0.984778383695168
309	0.0122043524422931	0.0244087048845862	0.987795647557707
310	0.0169516622023251	0.0339033244046502	0.983048337797675
311	0.0141776323289271	0.0283552646578543	0.985822367671073
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314	0.0094217837330237	0.0188435674660474	0.990578216266976
315	0.0091364928908174	0.0182729857816348	0.990863507109183
316	0.0076031336822491	0.0152062673644982	0.992396866317751
317	0.00680420002883994	0.0136084000576799	0.99319579997116
318	0.00573485513270961	0.0114697102654192	0.99426514486729
319	0.00452600120692268	0.00905200241384536	0.995473998793077
320	0.00479799496661095	0.0095959899332219	0.99520200503339
321	0.00599310983273179	0.0119862196654636	0.994006890167268
322	0.00614110349138239	0.0122822069827648	0.993858896508618
323	0.00648942991211769	0.0129788598242354	0.993510570087882
324	0.0710867292536726	0.142173458507345	0.928913270746327
325	0.0916324868533088	0.183264973706618	0.908367513146691
326	0.076717327059686	0.153434654119372	0.923282672940314
327	0.0640569545816719	0.128113909163344	0.935943045418328
328	0.0584514855903043	0.116902971180609	0.941548514409696
329	0.052009616671434	0.104019233342868	0.947990383328566
330	0.0524599805045036	0.104919961009007	0.947540019495496
331	0.0759191215978241	0.151838243195648	0.924080878402176
332	0.0664608959605627	0.132921791921125	0.933539104039437
333	0.0548073949106267	0.109614789821253	0.945192605089373
334	0.0453529601817962	0.0907059203635924	0.954647039818204
335	0.0479956966608346	0.0959913933216692	0.952004303339165
336	0.0411849096981135	0.082369819396227	0.958815090301886
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339	0.0471409151255135	0.094281830251027	0.952859084874486
340	0.0809460812803347	0.161892162560669	0.919053918719665
341	0.0731211613006362	0.146242322601272	0.926878838699364
342	0.0592007697770172	0.118401539554034	0.940799230222983
343	0.0497829336340861	0.0995658672681722	0.950217066365914
344	0.0446935148301067	0.0893870296602135	0.955306485169893
345	0.041430122878437	0.082860245756874	0.958569877121563
346	0.0361661488764742	0.0723322977529485	0.963833851123526
347	0.0282826263848625	0.056565252769725	0.971717373615137
348	0.0224883149128296	0.0449766298256592	0.97751168508717
349	0.0362831488421758	0.0725662976843516	0.963716851157824
350	0.0294302515791603	0.0588605031583206	0.97056974842084
351	0.0227376540940906	0.0454753081881813	0.97726234590591
352	0.020577017316354	0.041154034632708	0.979422982683646
353	0.0154275603963594	0.0308551207927189	0.98457243960364
354	0.0120399896342052	0.0240799792684104	0.987960010365795
355	0.0089754452419665	0.017950890483933	0.991024554758033
356	0.00641309331554766	0.0128261866310953	0.993586906684452
357	0.00702324971516823	0.0140464994303365	0.992976750284832
358	0.00527686304329019	0.0105537260865804	0.99472313695671
359	0.00465288648226573	0.00930577296453147	0.995347113517734
360	0.0045125932238027	0.0090251864476054	0.995487406776197
361	0.0037056313547682	0.00741126270953641	0.996294368645232
362	0.00369002254144851	0.00738004508289702	0.996309977458552
363	0.00245889630485985	0.00491779260971971	0.99754110369514
364	0.00248905407667556	0.00497810815335112	0.997510945923324
365	0.0133808092765861	0.0267616185531722	0.986619190723414
366	0.0204044080380958	0.0408088160761916	0.979595591961904
367	0.025101095556014	0.0502021911120279	0.974898904443986
368	0.0333008061112762	0.0666016122225524	0.966699193888724
369	0.0501756429375899	0.10035128587518	0.94982435706241
370	0.0391717248498435	0.078343449699687	0.960828275150156
371	0.0471739177148151	0.0943478354296301	0.952826082285185
372	0.137971525271822	0.275943050543644	0.862028474728178
373	0.101298247838741	0.202596495677481	0.89870175216126
374	0.0737909447539523	0.147581889507905	0.926209055246048
375	0.0582277959752248	0.11645559195045	0.941772204024775
376	0.205736118209017	0.411472236418034	0.794263881790983
377	0.192904438555374	0.385808877110747	0.807095561444626
378	0.266626831271754	0.533253662543508	0.733373168728246
379	0.274161345560689	0.548322691121379	0.72583865443931
380	0.2410894177507	0.4821788355014	0.7589105822493
381	0.175433822303512	0.350867644607023	0.824566177696488
382	0.216843471650891	0.433686943301781	0.78315652834911
383	0.136692022525004	0.273384045050007	0.863307977474996

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	197	0.525333333333333	NOK
5% type I error level	243	0.648	NOK
10% type I error level	276	0.736	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/10nmwl1293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/10nmwl1293670821.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/1ylh91293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/1ylh91293670821.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/2qchc1293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/2qchc1293670821.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/3qchc1293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/3qchc1293670821.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/4qchc1293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/4qchc1293670821.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/5qchc1293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/5qchc1293670821.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/6j4yx1293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/6j4yx1293670821.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/7udfi1293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/7udfi1293670821.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/8udfi1293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/8udfi1293670821.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/9udfi1293670821.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670688mg2de0euqhz2msc/9udfi1293670821.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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