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Task 6 - Q1

*The author of this computation has been verified*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 25 Nov 2008 00:14:27 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/25/t1227597344dhgvv8gp7ix3jte.htm/, Retrieved Fri, 24 May 2013 18:56:21 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t1226831811qp4g74kkt1g3rr3 (pk = 24947)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Correlation Matrix « » Notched Boxplots «

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	8 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

Aantal_slachtoffers[t] = + 1717.75147928994 -396.055827116028Dummy_factor[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)	1717.75147928994	20.000334	85.8861	0	0
Dummy_factor	-396.055827116028	57.786173	-6.8538	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.445226892939612
R-squared	0.198226986196661
Adjusted R-squared	0.194007128229275
F-TEST (value)	46.9748005095662
F-TEST (DF numerator)	1
F-TEST (DF denominator)	190
p-value	9.762957109416e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	260.004336317031
Sum Squared Residuals	12844428.4316954

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1687	1717.75147928994	-30.7514792899354
2	1508	1717.75147928994	-209.751479289941
3	1507	1717.75147928994	-210.751479289941
4	1385	1717.75147928994	-332.751479289941
5	1632	1717.75147928994	-85.7514792899409
6	1511	1717.75147928994	-206.751479289941
7	1559	1717.75147928994	-158.751479289941
8	1630	1717.75147928994	-87.7514792899409
9	1579	1717.75147928994	-138.751479289941
10	1653	1717.75147928994	-64.7514792899408
11	2152	1717.75147928994	434.248520710059
12	2148	1717.75147928994	430.248520710059
13	1752	1717.75147928994	34.2485207100591
14	1765	1717.75147928994	47.2485207100591
15	1717	1717.75147928994	-0.751479289940856
16	1558	1717.75147928994	-159.751479289941
17	1575	1717.75147928994	-142.751479289941
18	1520	1717.75147928994	-197.751479289941
19	1805	1717.75147928994	87.2485207100591
20	1800	1717.75147928994	82.2485207100591
21	1719	1717.75147928994	1.24852071005914
22	2008	1717.75147928994	290.248520710059
23	2242	1717.75147928994	524.248520710059
24	2478	1717.75147928994	760.248520710059
25	2030	1717.75147928994	312.248520710059
26	1655	1717.75147928994	-62.7514792899409
27	1693	1717.75147928994	-24.7514792899409
28	1623	1717.75147928994	-94.7514792899409
29	1805	1717.75147928994	87.2485207100591
30	1746	1717.75147928994	28.2485207100591
31	1795	1717.75147928994	77.2485207100591
32	1926	1717.75147928994	208.248520710059
33	1619	1717.75147928994	-98.7514792899409
34	1992	1717.75147928994	274.248520710059
35	2233	1717.75147928994	515.248520710059
36	2192	1717.75147928994	474.248520710059
37	2080	1717.75147928994	362.248520710059
38	1768	1717.75147928994	50.2485207100591
39	1835	1717.75147928994	117.248520710059
40	1569	1717.75147928994	-148.751479289941
41	1976	1717.75147928994	258.248520710059
42	1853	1717.75147928994	135.248520710059
43	1965	1717.75147928994	247.248520710059
44	1689	1717.75147928994	-28.7514792899409
45	1778	1717.75147928994	60.2485207100591
46	1976	1717.75147928994	258.248520710059
47	2397	1717.75147928994	679.248520710059
48	2654	1717.75147928994	936.24852071006
49	2097	1717.75147928994	379.248520710059
50	1963	1717.75147928994	245.248520710059
51	1677	1717.75147928994	-40.7514792899409
52	1941	1717.75147928994	223.248520710059
53	2003	1717.75147928994	285.248520710059
54	1813	1717.75147928994	95.2485207100591
55	2012	1717.75147928994	294.248520710059
56	1912	1717.75147928994	194.248520710059
57	2084	1717.75147928994	366.248520710059
58	2080	1717.75147928994	362.248520710059
59	2118	1717.75147928994	400.248520710059
60	2150	1717.75147928994	432.248520710059
61	1608	1717.75147928994	-109.751479289941
62	1503	1717.75147928994	-214.751479289941
63	1548	1717.75147928994	-169.751479289941
64	1382	1717.75147928994	-335.751479289941
65	1731	1717.75147928994	13.2485207100591
66	1798	1717.75147928994	80.2485207100591
67	1779	1717.75147928994	61.2485207100591
68	1887	1717.75147928994	169.248520710059
69	2004	1717.75147928994	286.248520710059
70	2077	1717.75147928994	359.248520710059
71	2092	1717.75147928994	374.248520710059
72	2051	1717.75147928994	333.248520710059
73	1577	1717.75147928994	-140.751479289941
74	1356	1717.75147928994	-361.751479289941
75	1652	1717.75147928994	-65.7514792899408
76	1382	1717.75147928994	-335.751479289941
77	1519	1717.75147928994	-198.751479289941
78	1421	1717.75147928994	-296.751479289941
79	1442	1717.75147928994	-275.751479289941
80	1543	1717.75147928994	-174.751479289941
81	1656	1717.75147928994	-61.7514792899409
82	1561	1717.75147928994	-156.751479289941
83	1905	1717.75147928994	187.248520710059
84	2199	1717.75147928994	481.248520710059
85	1473	1717.75147928994	-244.751479289941
86	1655	1717.75147928994	-62.7514792899409
87	1407	1717.75147928994	-310.751479289941
88	1395	1717.75147928994	-322.751479289941
89	1530	1717.75147928994	-187.751479289941
90	1309	1717.75147928994	-408.751479289941
91	1526	1717.75147928994	-191.751479289941
92	1327	1717.75147928994	-390.751479289941
93	1627	1717.75147928994	-90.7514792899409
94	1748	1717.75147928994	30.2485207100591
95	1958	1717.75147928994	240.248520710059
96	2274	1717.75147928994	556.248520710059
97	1648	1717.75147928994	-69.7514792899408
98	1401	1717.75147928994	-316.751479289941
99	1411	1717.75147928994	-306.751479289941
100	1403	1717.75147928994	-314.751479289941
101	1394	1717.75147928994	-323.751479289941
102	1520	1717.75147928994	-197.751479289941
103	1528	1717.75147928994	-189.751479289941
104	1643	1717.75147928994	-74.7514792899409
105	1515	1717.75147928994	-202.751479289941
106	1685	1717.75147928994	-32.7514792899409
107	2000	1717.75147928994	282.248520710059
108	2215	1717.75147928994	497.248520710059
109	1956	1717.75147928994	238.248520710059
110	1462	1717.75147928994	-255.751479289941
111	1563	1717.75147928994	-154.751479289941
112	1459	1717.75147928994	-258.751479289941
113	1446	1717.75147928994	-271.751479289941
114	1622	1717.75147928994	-95.7514792899409
115	1657	1717.75147928994	-60.7514792899409
116	1638	1717.75147928994	-79.7514792899409
117	1643	1717.75147928994	-74.7514792899409
118	1683	1717.75147928994	-34.7514792899409
119	2050	1717.75147928994	332.248520710059
120	2262	1717.75147928994	544.248520710059
121	1813	1717.75147928994	95.2485207100591
122	1445	1717.75147928994	-272.751479289941
123	1762	1717.75147928994	44.2485207100591
124	1461	1717.75147928994	-256.751479289941
125	1556	1717.75147928994	-161.751479289941
126	1431	1717.75147928994	-286.751479289941
127	1427	1717.75147928994	-290.751479289941
128	1554	1717.75147928994	-163.751479289941
129	1645	1717.75147928994	-72.7514792899409
130	1653	1717.75147928994	-64.7514792899408
131	2016	1717.75147928994	298.248520710059
132	2207	1717.75147928994	489.248520710059
133	1665	1717.75147928994	-52.7514792899409
134	1361	1717.75147928994	-356.751479289941
135	1506	1717.75147928994	-211.751479289941
136	1360	1717.75147928994	-357.751479289941
137	1453	1717.75147928994	-264.751479289941
138	1522	1717.75147928994	-195.751479289941
139	1460	1717.75147928994	-257.751479289941
140	1552	1717.75147928994	-165.751479289941
141	1548	1717.75147928994	-169.751479289941
142	1827	1717.75147928994	109.248520710059
143	1737	1717.75147928994	19.2485207100591
144	1941	1717.75147928994	223.248520710059
145	1474	1717.75147928994	-243.751479289941
146	1458	1717.75147928994	-259.751479289941
147	1542	1717.75147928994	-175.751479289941
148	1404	1717.75147928994	-313.751479289941
149	1522	1717.75147928994	-195.751479289941
150	1385	1717.75147928994	-332.751479289941
151	1641	1717.75147928994	-76.7514792899409
152	1510	1717.75147928994	-207.751479289941
153	1681	1717.75147928994	-36.7514792899409
154	1938	1717.75147928994	220.248520710059
155	1868	1717.75147928994	150.248520710059
156	1726	1717.75147928994	8.24852071005914
157	1456	1717.75147928994	-261.751479289941
158	1445	1717.75147928994	-272.751479289941
159	1456	1717.75147928994	-261.751479289941
160	1365	1717.75147928994	-352.751479289941
161	1487	1717.75147928994	-230.751479289941
162	1558	1717.75147928994	-159.751479289941
163	1488	1717.75147928994	-229.751479289941
164	1684	1717.75147928994	-33.7514792899409
165	1594	1717.75147928994	-123.751479289941
166	1850	1717.75147928994	132.248520710059
167	1998	1717.75147928994	280.248520710059
168	2079	1717.75147928994	361.248520710059
169	1494	1717.75147928994	-223.751479289941
170	1057	1321.69565217391	-264.695652173913
171	1218	1321.69565217391	-103.695652173913
172	1168	1321.69565217391	-153.695652173913
173	1236	1321.69565217391	-85.695652173913
174	1076	1321.69565217391	-245.695652173913
175	1174	1321.69565217391	-147.695652173913
176	1139	1321.69565217391	-182.695652173913
177	1427	1321.69565217391	105.304347826087
178	1487	1321.69565217391	165.304347826087
179	1483	1321.69565217391	161.304347826087
180	1513	1321.69565217391	191.304347826087
181	1357	1321.69565217391	35.3043478260869
182	1165	1321.69565217391	-156.695652173913
183	1282	1321.69565217391	-39.6956521739131
184	1110	1321.69565217391	-211.695652173913
185	1297	1321.69565217391	-24.6956521739131
186	1185	1321.69565217391	-136.695652173913
187	1222	1321.69565217391	-99.695652173913
188	1284	1321.69565217391	-37.6956521739131
189	1444	1321.69565217391	122.304347826087
190	1575	1321.69565217391	253.304347826087
191	1737	1321.69565217391	415.304347826087
192	1763	1321.69565217391	441.304347826087

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.155930802918944	0.311861605837888	0.844069197081056
6	0.0664935273773447	0.132987054754689	0.933506472622655
7	0.0256738331429404	0.0513476662858808	0.97432616685706
8	0.0122173968073303	0.0244347936146606	0.98778260319267
9	0.00437997810460292	0.00875995620920583	0.995620021895397
10	0.00224015981786413	0.00448031963572825	0.997759840182136
11	0.223580158345551	0.447160316691101	0.77641984165445
12	0.503981354000825	0.99203729199835	0.496018645999175
13	0.420841205312304	0.841682410624607	0.579158794687696
14	0.345365652564086	0.690731305128172	0.654634347435914
15	0.270018209378630	0.540036418757261	0.72998179062137
16	0.219064424415852	0.438128848831704	0.780935575584148
17	0.171075044874818	0.342150089749637	0.828924955125182
18	0.140711526546593	0.281423053093185	0.859288473453407
19	0.114092242558859	0.228184485117717	0.885907757441141
20	0.0900792873398669	0.180158574679734	0.909920712660133
21	0.063884764368076	0.127769528736152	0.936115235631924
22	0.0882860430336207	0.176572086067241	0.91171395696638
23	0.254036608717035	0.50807321743407	0.745963391282965
24	0.704134515940508	0.591730968118983	0.295865484059492
25	0.709949406325989	0.580101187348023	0.290050593674011
26	0.661732750333152	0.676534499333696	0.338267249666848
27	0.606522270477901	0.786955459044198	0.393477729522099
28	0.559718943813697	0.880562112372606	0.440281056186303
29	0.503737541569718	0.992524916860564	0.496262458430282
30	0.444960834898958	0.889921669797916	0.555039165101042
31	0.390182856040329	0.780365712080657	0.609817143959671
32	0.362128112746561	0.724256225493123	0.637871887253439
33	0.322724826525609	0.645449653051218	0.677275173474391
34	0.318469939735743	0.636939879471486	0.681530060264257
35	0.447502775999533	0.895005551999066	0.552497224000467
36	0.540190518349439	0.919618963301122	0.459809481650561
37	0.562294509844802	0.875410980310396	0.437705490155198
38	0.510686000293268	0.978627999413463	0.489313999706732
39	0.462277789155232	0.924555578310465	0.537722210844768
40	0.443241446768204	0.886482893536409	0.556758553231796
41	0.425738673525253	0.851477347050505	0.574261326474747
42	0.382073906721554	0.764147813443107	0.617926093278446
43	0.362011567326384	0.724023134652767	0.637988432673616
44	0.321992731747725	0.643985463495451	0.678007268252275
45	0.279428290514558	0.558856581029116	0.720571709485442
46	0.265648617004253	0.531297234008506	0.734351382995747
47	0.493782232847649	0.987564465695298	0.506217767152351
48	0.889937540791619	0.220124918416762	0.110062459208381
49	0.901113662368407	0.197772675263187	0.0988863376315933
50	0.891931280284285	0.216137439431430	0.108068719715715
51	0.874958770476828	0.250082459046344	0.125041229523172
52	0.861924268804623	0.276151462390755	0.138075731195377
53	0.857741867660571	0.284516264678857	0.142258132339429
54	0.83378722062345	0.332425558753099	0.166212779376550
55	0.831683517129929	0.336632965740142	0.168316482870071
56	0.813452152132249	0.373095695735503	0.186547847867751
57	0.829990046479602	0.340019907040796	0.170009953520398
58	0.845293937668114	0.309412124663772	0.154706062331886
59	0.86988655679995	0.260226886400100	0.130113443200050
60	0.899973180621902	0.200053638756195	0.100026819378098
61	0.892911538118977	0.214176923762045	0.107088461881023
62	0.89981365764821	0.200372684703580	0.100186342351790
63	0.898719123289092	0.202561753421815	0.101280876710908
64	0.924221577235453	0.151556845529094	0.0757784227645468
65	0.910274154620367	0.179451690759265	0.0897258453796325
66	0.894792536598393	0.210414926803214	0.105207463401607
67	0.877169794617804	0.245660410764392	0.122830205382196
68	0.864097265370824	0.271805469258351	0.135902734629176
69	0.867873641028726	0.264252717942549	0.132126358971274
70	0.887176441345612	0.225647117308775	0.112823558654388
71	0.908449632411517	0.183100735176966	0.0915503675884829
72	0.920869504333542	0.158260991332917	0.0791304956664583
73	0.916010299414107	0.167979401171786	0.0839897005858932
74	0.940402539413845	0.119194921172311	0.0595974605861555
75	0.931292247693514	0.137415504612973	0.0687077523064863
76	0.946956055853137	0.106087888293726	0.0530439441468632
77	0.945881642017068	0.108236715965863	0.0541183579829316
78	0.953436314940004	0.0931273701199919	0.0465636850599959
79	0.957766908324575	0.0844661833508502	0.0422330916754251
80	0.95441175157656	0.091176496846881	0.0455882484234405
81	0.945791198150969	0.108417603698063	0.0542088018490313
82	0.940175035777144	0.119649928445711	0.0598249642228557
83	0.936131061979697	0.127737876040607	0.0638689380203034
84	0.966338566371464	0.067322867257073	0.0336614336285365
85	0.96691607478516	0.066167850429681	0.0330839252148405
86	0.960164119344155	0.0796717613116905	0.0398358806558452
87	0.965277069335224	0.069445861329553	0.0347229306647765
88	0.970379455025867	0.0592410899482654	0.0296205449741327
89	0.967464051159065	0.0650718976818692	0.0325359488409346
90	0.977737303238431	0.044525393523138	0.022262696761569
91	0.9753226480452	0.0493547039096	0.0246773519548
92	0.982127603682625	0.0357447926347509	0.0178723963173755
93	0.977903931631157	0.0441921367376859	0.0220960683688429
94	0.972580035455955	0.0548399290880909	0.0274199645440455
95	0.973652199286683	0.0526956014266346	0.0263478007133173
96	0.992147866748658	0.0157042665026847	0.00785213325134237
97	0.989944177220263	0.0201116455594737	0.0100558227797368
98	0.99108047497721	0.0178390500455795	0.00891952502278976
99	0.99185205302911	0.0162958939417815	0.00814794697089075
100	0.992689155839436	0.0146216883211272	0.00731084416056362
101	0.993587965644624	0.0128240687107510	0.00641203435537552
102	0.992587470675183	0.0148250586496335	0.00741252932481676
103	0.991334311192622	0.0173313776147553	0.00866568880737766
104	0.988786623466502	0.0224267530669964	0.0112133765334982
105	0.987197426903214	0.0256051461935712	0.0128025730967856
106	0.983488734830613	0.0330225303387732	0.0165112651693866
107	0.986210074067875	0.0275798518642497	0.0137899259321249
108	0.995481225694707	0.00903754861058545	0.00451877430529273
109	0.996074339401285	0.00785132119742921	0.00392566059871461
110	0.995808213551387	0.00838357289722578	0.00419178644861289
111	0.994712555294524	0.0105748894109525	0.00528744470547626
112	0.99438371667621	0.0112325666475790	0.00561628332378949
113	0.994202765554047	0.0115944688919066	0.0057972344459533
114	0.992371888869807	0.0152562222603854	0.0076281111301927
115	0.98993717879755	0.0201256424048992	0.0100628212024496
116	0.986889938231705	0.0262201235365897	0.0131100617682949
117	0.983038753707429	0.0339224925851423	0.0169612462925711
118	0.97820102961212	0.0435979407757616	0.0217989703878808
119	0.985499028598025	0.0290019428039499	0.0145009714019749
120	0.997273737946519	0.00545252410696247	0.00272626205348123
121	0.996840500171403	0.00631899965719486	0.00315949982859743
122	0.996604328712003	0.00679134257599476	0.00339567128799738
123	0.995731903492709	0.00853619301458283	0.00426809650729142
124	0.995231935474466	0.00953612905106843	0.00476806452553421
125	0.99383571956488	0.0123285608702407	0.00616428043512034
126	0.993579112677005	0.0128417746459893	0.00642088732299466
127	0.993393503511835	0.0132129929763303	0.00660649648816513
128	0.991524685107479	0.0169506297850422	0.00847531489252108
129	0.988655488303615	0.0226890233927702	0.0113445116963851
130	0.98495935978621	0.0300812804275793	0.0150406402137896
131	0.99022162695995	0.0195567460801009	0.00977837304005047
132	0.998279991070906	0.0034400178581885	0.00172000892909425
133	0.997591624783056	0.00481675043388758	0.00240837521694379
134	0.99789281272571	0.00421437454857823	0.00210718727428912
135	0.99729389880209	0.00541220239582078	0.00270610119791039
136	0.997677692215397	0.00464461556920594	0.00232230778460297
137	0.99735459133933	0.00529081732134144	0.00264540866067072
138	0.996546553843356	0.00690689231328844	0.00345344615664422
139	0.9960452898774	0.00790942024520082	0.00395471012260041
140	0.994686970830008	0.0106260583399844	0.00531302916999218
141	0.992957425200093	0.0140851495998132	0.00704257479990659
142	0.992033009605433	0.0159339807891335	0.00796699039456673
143	0.989583771235881	0.020832457528237	0.0104162287641185
144	0.992081659149131	0.0158366817017377	0.00791834085086885
145	0.990449484404383	0.019101031191235	0.0095505155956175
146	0.988949707339056	0.0221005853218887	0.0110502926609444
147	0.985456060894265	0.0290878782114692	0.0145439391057346
148	0.985571134514045	0.0288577309719094	0.0144288654859547
149	0.981780174692575	0.0364396506148505	0.0182198253074253
150	0.983522709663428	0.0329545806731444	0.0164772903365722
151	0.977248897775252	0.0455022044494958	0.0227511022247479
152	0.972640095312507	0.0547198093749852	0.0273599046874926
153	0.962925549083712	0.0741489018325764	0.0370744509162882
154	0.967302522490983	0.0653949550180346	0.0326974775090173
155	0.966685544248089	0.0666289115038225	0.0333144557519112
156	0.957191721243764	0.0856165575124728	0.0428082787562364
157	0.951103839795078	0.097792320409845	0.0488961602049225
158	0.946573335209496	0.106853329581007	0.0534266647905037
159	0.94198975976146	0.116020480477081	0.0580102402385407
160	0.953946388633883	0.0921072227322349	0.0460536113661174
161	0.951782015166047	0.0964359696679061	0.0482179848339531
162	0.943781675674247	0.112436648651507	0.0562183243257533
163	0.948852829830086	0.102294340339827	0.0511471701699137
164	0.93386958805322	0.132260823893559	0.0661304119467795
165	0.93201799159513	0.13596401680974	0.06798200840487
166	0.908408408610311	0.183183182779377	0.0915915913896886
167	0.896695571660102	0.206608856679795	0.103304428339898
168	0.946324945345166	0.107350109309668	0.0536750546548339
169	0.92576197839223	0.148476043215541	0.0742380216077705
170	0.932074147271306	0.135851705457388	0.0679258527286941
171	0.912198628384566	0.175602743230867	0.0878013716154336
172	0.897139750110684	0.205720499778631	0.102860249889316
173	0.867972375515691	0.264055248968618	0.132027624484309
174	0.884055444197872	0.231889111604255	0.115944555802128
175	0.871741028095492	0.256517943809015	0.128258971904507
176	0.875980463407352	0.248039073185296	0.124019536592648
177	0.829472349328393	0.341055301343215	0.170527650671607
178	0.781248854895941	0.437502290208118	0.218751145104059
179	0.723085429655236	0.553829140689528	0.276914570344764
180	0.668097907094829	0.663804185810341	0.331902092905171
181	0.573634400111419	0.852731199777162	0.426365599888581
182	0.540064085792425	0.91987182841515	0.459935914207575
183	0.449856183719487	0.899712367438975	0.550143816280513
184	0.49102948923368	0.98205897846736	0.50897051076632
185	0.403462687220028	0.806925374440056	0.596537312779972
186	0.428895543286732	0.857791086573464	0.571104456713268
187	0.488140962852545	0.97628192570509	0.511859037147455

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	18	0.098360655737705	NOK
5% type I error level	63	0.344262295081967	NOK
10% type I error level	83	0.453551912568306	NOK

Charts produced by software:

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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')
}