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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: Sun, 19 Dec 2010 15:27:49 +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/19/t12927724910mthvhny74w8y6e.htm/, Retrieved Sun, 19 Dec 2010 16:28:14 +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/19/t12927724910mthvhny74w8y6e.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 «

15 0 13,6 13,7 13 14,4 15 14,4 0 15,2 13,6 13,7 13 14,4 13 0 12,9 15,2 13,6 13,7 13 13,7 0 14 12,9 15,2 13,6 13,7 13,6 0 14,1 14 12,9 15,2 13,6 15,2 0 13,2 14,1 14 12,9 15,2 12,9 0 11,3 13,2 14,1 14 12,9 14 0 13,3 11,3 13,2 14,1 14 14,1 0 14,4 13,3 11,3 13,2 14,1 13,2 0 13,3 14,4 13,3 11,3 13,2 11,3 0 11,6 13,3 14,4 13,3 11,3 13,3 0 13,2 11,6 13,3 14,4 13,3 14,4 0 13,1 13,2 11,6 13,3 14,4 13,3 0 14,6 13,1 13,2 11,6 13,3 11,6 0 14 14,6 13,1 13,2 11,6 13,2 0 14,3 14 14,6 13,1 13,2 13,1 0 13,8 14,3 14 14,6 13,1 14,6 0 13,7 13,8 14,3 14 14,6 14 0 11 13,7 13,8 14,3 14 14,3 0 14,4 11 13,7 13,8 14,3 13,8 0 15,6 14,4 11 13,7 13,8 13,7 0 13,7 15,6 14,4 11 13,7 11 0 12,6 13,7 15,6 14,4 11 14,4 0 13,2 12,6 13,7 15,6 14,4 15,6 0 13,3 13,2 12,6 13,7 15,6 13,7 0 14,3 13,3 13,2 12,6 13,7 12,6 0 14 14,3 13,3 13,2 12,6 13,2 0 13,4 14 14,3 13,3 13,2 13,3 0 13,9 13,4 14 14,3 13,3 14,3 0 13,7 13,9 13,4 14 14,3 14 0 10,5 13,7 13,9 13,4 14 13,4 0 14,5 10,5 13,7 13,9 13,4 13,9 0 15 14,5 10,5 13,7 13, 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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Multiple Linear Regression - Estimated Regression Equation

uitvoercijfer[t] = + 2.67868885112499e-16 + 1.25611255456158e-16X[t] + 2.21995911620994e-17Y1[t] + 5.45430166641358e-17Y2[t] -2.94857131153639e-17Y3[t] + 4.46932466310697e-17Y4[t] + 1Y5[t] -7.60702659134785e-17M1[t] -3.57828127270844e-18M2[t] + 4.1212859638548e-17M3[t] + 1.0850439386405e-16M4[t] -4.33776525511453e-17M5[t] + 5.98989216374346e-17M6[t] + 4.21435215809026e-16M7[t] -6.42465345341248e-17M8[t] -2.41337263452827e-17M9[t] + 1.78461801535162e-16M10[t] + 2.47939467126275e-17M11[t] -2.26079895601757e-18t + 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)	2.67868885112499e-16	0	0.4908	0.624646	0.312323
X	1.25611255456158e-16	0	0.5987	0.550773	0.275387
Y1	2.21995911620994e-17	0	0.5156	0.607319	0.30366
Y2	5.45430166641358e-17	0	1.2546	0.212616	0.106308
Y3	-2.94857131153639e-17	0	-0.6677	0.505899	0.252949
Y4	4.46932466310697e-17	0	0.9684	0.335242	0.167621
Y5	1	0	22725891407733848	0	0
M1	-7.60702659134785e-17	0	-0.4436	0.658338	0.329169
M2	-3.57828127270844e-18	0	-0.0166	0.986818	0.493409
M3	4.1212859638548e-17	0	0.188	0.851288	0.425644
M4	1.0850439386405e-16	0	0.5572	0.578645	0.289323
M5	-4.33776525511453e-17	0	-0.2505	0.802705	0.401353
M6	5.98989216374346e-17	0	0.3219	0.748215	0.374107
M7	4.21435215809026e-16	0	2.1015	0.038163	0.019081
M8	-6.42465345341248e-17	0	-0.3558	0.722738	0.361369
M9	-2.41337263452827e-17	0	-0.0978	0.922262	0.461131
M10	1.78461801535162e-16	0	0.6977	0.487022	0.243511
M11	2.47939467126275e-17	0	0.099	0.921303	0.460651
t	-2.26079895601757e-18	0	-0.6746	0.501534	0.250767

Multiple Linear Regression - Regression Statistics
Multiple R	1
R-squared	1
Adjusted R-squared	1
F-TEST (value)	3.19975962880079e+32
F-TEST (DF numerator)	18
F-TEST (DF denominator)	98
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.26900285120209e-16
Sum Squared Residuals	1.04726520483441e-29

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	15	15	-2.89296795448131e-16
2	14.4	14.4	-2.57901354069519e-16
3	13	13	-6.74979900756436e-16
4	13.7	13.7	-5.99532317973799e-17
5	13.6	13.6	1.19375966974017e-16
6	15.2	15.2	1.76246915351944e-16
7	12.9	12.9	2.86085812889703e-15
8	14	14	-6.18645742387088e-17
9	14.1	14.1	-7.4461608657557e-17
10	13.2	13.2	-1.10493330503759e-16
11	11.3	11.3	6.08080803806897e-18
12	13.3	13.3	-1.1815875102057e-16
13	14.4	14.4	3.69914892012958e-18
14	13.3	13.3	2.66069956729712e-17
15	11.6	11.6	-1.32121368677276e-16
16	13.2	13.2	-6.76248333803364e-17
17	13.1	13.1	-6.31738092303693e-17
18	14.6	14.6	-1.24684451230098e-16
19	14	14	-4.51966447946513e-16
20	14.3	14.3	3.76756307634271e-17
21	13.8	13.8	-7.06613987846437e-17
22	13.7	13.7	-2.32681453430692e-17
23	11	11	-1.71997573888969e-17
24	14.4	14.4	-1.24266653161158e-16
25	15.6	15.6	-6.86351439679292e-17
26	13.7	13.7	2.46877428755157e-17
27	12.6	12.6	8.92254042244412e-17
28	13.2	13.2	-6.11380785941764e-17
29	13.3	13.3	2.95146079605198e-17
30	14.3	14.3	-7.76536297158759e-17
31	14	14	-3.62775832681693e-16
32	13.4	13.4	-1.39314095149291e-17
33	13.9	13.9	-6.77557766024397e-17
34	13.7	13.7	9.63564371041354e-18
35	10.5	10.5	-7.25107076860199e-17
36	14.5	14.5	-5.98920229497522e-17
37	15	15	1.739712445657e-17
38	13.5	13.5	2.64018155009445e-18
39	13.5	13.5	1.23390119246382e-16
40	13.2	13.2	5.30304495003798e-17
41	13.8	13.8	-1.16322040956552e-16
42	16.2	16.2	-8.83220749074289e-17
43	14.7	14.7	-2.81157382641636e-16
44	13.9	13.9	-2.91859322944952e-17
45	16	16	2.37501759892062e-17
46	14.4	14.4	-1.30911500757679e-17
47	12.3	12.3	2.58468368412539e-17
48	15.9	15.9	-1.06845734128434e-17
49	15.9	15.9	4.83336180301154e-17
50	15.5	15.5	-1.23932134928787e-17
51	15.1	15.1	1.05807742029812e-16
52	14.5	14.5	6.04747476917268e-17
53	15.1	15.1	1.01605082441038e-17
54	17.4	17.4	-2.7030544884209e-17
55	16.2	16.2	-2.82677379293975e-16
56	15.6	15.6	-5.63846947730492e-17
57	17.2	17.2	1.45383358439572e-17
58	14.9	14.9	8.39707768018205e-17
59	13.8	13.8	-1.71215932246123e-16
60	17.5	17.5	6.17088890378218e-17
61	16.2	16.2	6.99292671256961e-17
62	17.5	17.5	4.399592581324e-19
63	16.6	16.6	1.37195859457235e-16
64	16.2	16.2	2.88417670813949e-17
65	16.6	16.6	-1.24676138789622e-16
66	19.6	19.6	1.11401944620687e-16
67	15.9	15.9	-3.29726925643704e-16
68	18	18	1.24086179939321e-17
69	18.3	18.3	1.09831892180842e-16
70	16.3	16.3	-4.53693916462838e-18
71	14.9	14.9	-8.63377341698488e-17
72	18.2	18.2	-1.25917464527822e-17
73	18.4	18.4	1.50250330807415e-17
74	18.5	18.5	9.10776006556092e-18
75	16	16	1.80952817728626e-16
76	17.4	17.4	1.54663357875496e-17
77	17.2	17.2	1.02360655488643e-16
78	19.6	19.6	-1.77785889214598e-17
79	17.2	17.2	-2.91943580338292e-16
80	18.3	18.3	6.70206189704102e-17
81	19.3	19.3	6.12348762080334e-17
82	18.1	18.1	2.77652331965105e-17
83	16.2	16.2	2.94629547582709e-16
84	18.4	18.4	-4.18321427506925e-17
85	20.5	20.5	1.20604404388515e-17
86	19	19	1.62458117465963e-16
87	16.5	16.5	-6.6699792415586e-17
88	18.7	18.7	2.48556162729576e-17
89	19	19	1.3161757279558e-16
90	19.2	19.2	4.53570097117462e-19
91	20.5	20.5	-3.39057005183814e-16
92	19.3	19.3	8.49741910060189e-17
93	20.6	20.6	-2.7239555401431e-18
94	20.1	20.1	-1.74652269959715e-17
95	16.1	16.1	-2.87837186831201e-17
96	20.4	20.4	2.84299234820946e-16
97	19.7	19.7	2.90363891613402e-17
98	15.6	15.6	9.01680099153656e-18
99	14.4	14.4	6.10915174221326e-17
100	13.7	13.7	-1.3540638913855e-17
101	14.1	14.1	3.48896599531176e-17
102	15	15	-1.48632837906236e-17
103	14.2	14.2	-2.86291300456655e-16
104	13.6	13.6	2.32717049038207e-17
105	15.4	15.4	4.74745275543349e-17
106	14.8	14.8	4.74831383744517e-17
107	12.5	12.5	4.9490657711978e-17
108	16.2	16.2	2.14177658890305e-17
109	16.1	16.1	1.62450918202615e-16
110	16	16	3.53370096826234e-17
111	15.8	15.8	1.76137601740669e-16
112	15.2	15.2	1.9587866351739e-17
113	15.7	15.7	-1.23746982439437e-16
114	18.9	18.9	6.22301433799458e-17
115	17.4	17.4	-2.35262274710747e-16
116	17	17	-6.39841528164268e-17
117	19.8	19.8	-4.1227068191591e-17

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
22	0.81277376673076	0.374452466538478	0.187226233269239
23	0.00458035365244824	0.00916070730489647	0.995419646347552
24	0.250145551500865	0.50029110300173	0.749854448499135
25	0.00514872168747404	0.0102974433749481	0.994851278312526
26	1.48026337390134e-07	2.96052674780269e-07	0.999999851973663
27	4.18991909481381e-06	8.37983818962763e-06	0.999995810080905
28	0.00126198955230274	0.00252397910460548	0.998738010447697
29	0.180070416060979	0.360140832121957	0.819929583939021
30	0.00106805424331387	0.00213610848662773	0.998931945756686
31	2.44811334985993e-10	4.89622669971986e-10	0.999999999755189
32	0.975853683937295	0.0482926321254091	0.0241463160627045
33	0.343061481160688	0.686122962321377	0.656938518839312
34	7.26122304504278e-08	1.45224460900856e-07	0.99999992738777
35	0.999999999792748	4.14503633384166e-10	2.07251816692083e-10
36	2.91457208265004e-15	5.82914416530008e-15	0.999999999999997
37	0.999999351591314	1.29681737251484e-06	6.48408686257421e-07
38	0.660342985713557	0.679314028572885	0.339657014286443
39	4.44929285073193e-08	8.89858570146385e-08	0.999999955507072
40	0.765957884939889	0.468084230120222	0.234042115060111
41	2.79616392277038e-10	5.59232784554075e-10	0.999999999720384
42	0.0585884705018824	0.117176941003765	0.941411529498118
43	1.65912474188311e-08	3.31824948376622e-08	0.999999983408753
44	0.769833124210053	0.460333751579894	0.230166875789947
45	0.000786809638208484	0.00157361927641697	0.999213190361792
46	0.366956553554797	0.733913107109594	0.633043446445203
47	3.47880202971822e-07	6.95760405943644e-07	0.999999652119797
48	1.36800381641299e-09	2.73600763282597e-09	0.999999998631996
49	0.99734191118218	0.00531617763563878	0.00265808881781939
50	0.00981258244112408	0.0196251648822482	0.990187417558876
51	0.999999596270463	8.07459074687847e-07	4.03729537343924e-07
52	0.999999374444706	1.25111058751734e-06	6.25555293758668e-07
53	0.0849283094862596	0.169856618972519	0.91507169051374
54	2.19921422398892e-11	4.39842844797783e-11	0.999999999978008
55	2.13694899955465e-18	4.2738979991093e-18	1
56	0.273921364243367	0.547842728486734	0.726078635756633
57	0.026004277242014	0.0520085544840281	0.973995722757986
58	0.99999718840945	5.62318110184393e-06	2.81159055092197e-06
59	0.000567592418201486	0.00113518483640297	0.999432407581799
60	1	9.6122802739859e-17	4.80614013699295e-17
61	0.955530080403278	0.0889398391934441	0.0444699195967221
62	3.42277750858199e-10	6.84555501716398e-10	0.999999999657722
63	0.999999816408129	3.67183742671529e-07	1.83591871335765e-07
64	1.17916167748806e-17	2.35832335497612e-17	1
65	0.99999999999999	1.9206155399927e-14	9.6030776999635e-15
66	0.0317546252615025	0.063509250523005	0.968245374738497
67	6.07443792874851e-14	1.2148875857497e-13	0.99999999999994
68	0.999970892506776	5.82149864490032e-05	2.91074932245016e-05
69	0.989241341696706	0.0215173166065889	0.0107586583032944
70	4.63389607470153e-18	9.26779214940306e-18	1
71	0.999999999997337	5.32609489661068e-12	2.66304744830534e-12
72	0.851759180831166	0.296481638337669	0.148240819168834
73	1.55138417772829e-06	3.10276835545658e-06	0.999998448615822
74	8.25515699881246e-23	1.65103139976249e-22	1
75	0.99999953232874	9.35342518458306e-07	4.67671259229153e-07
76	0.519822153290942	0.960355693418115	0.480177846709058
77	0.0912273868529886	0.182454773705977	0.908772613147011
78	0.999999537632536	9.24734928059614e-07	4.62367464029807e-07
79	0.999999712244489	5.75511022645216e-07	2.87755511322608e-07
80	0.00974742320907966	0.0194948464181593	0.99025257679092
81	0.999999956772453	8.64550946735569e-08	4.32275473367784e-08
82	0.997038354903	0.00592329019400029	0.00296164509700015
83	0.999999843239089	3.13521822631798e-07	1.56760911315899e-07
84	0.64767761482053	0.70464477035894	0.35232238517947
85	0.619959909453548	0.760080181092904	0.380040090546452
86	0.640741408597267	0.718517182805465	0.359258591402733
87	0.242213547101014	0.484427094202029	0.757786452898985
88	0.989766470332316	0.0204670593353689	0.0102335296676844
89	8.17553436501637e-08	1.63510687300327e-07	0.999999918244656
90	0.850454843633681	0.299090312732638	0.149545156366319
91	2.18650069460637e-15	4.37300138921275e-15	0.999999999999998
92	1.54004132081724e-25	3.08008264163447e-25	1
93	9.55374942309373e-05	0.000191074988461875	0.99990446250577
94	6.86923087307166e-09	1.37384617461433e-08	0.99999999313077
95	4.34987564184505e-06	8.6997512836901e-06	0.999995650124358

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	46	0.621621621621622	NOK
5% type I error level	52	0.702702702702703	NOK
10% type I error level	55	0.743243243243243	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/1017or1292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/1017or1292772458.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/1uorf1292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/1uorf1292772458.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/2uorf1292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/2uorf1292772458.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/35f901292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/35f901292772458.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/45f901292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/45f901292772458.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/55f901292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/55f901292772458.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/6y6ql1292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/6y6ql1292772458.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/7qfp61292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/7qfp61292772458.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/8qfp61292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/8qfp61292772458.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/9qfp61292772458.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927724910mthvhny74w8y6e/9qfp61292772458.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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

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