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Multiple Regression

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 29 Dec 2010 09:50:36 +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/29/t1293616114h5a2fi2ztsrd0ea.htm/, Retrieved Wed, 29 Dec 2010 10:48:37 +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/29/t1293616114h5a2fi2ztsrd0ea.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 «

1775 2197 2920 4240 5415 6136 6719 6234 7152 3646 2165 2803 1615 2350 3350 3536 5834 6767 5993 7276 5641 3477 2247 2466 1567 2237 2598 3729 5715 5776 5852 6878 5488 3583 2054 2282 1552 2261 2446 3519 5161 5085 5711 6057 5224 3363 1899 2115 1491 2061 2419 3430 4778 4862 6176 5664 5529 3418 1941 2402 1579 2146 2462 3695 4831 5134 6250 5760 6249 2917 1741 2359 1511 2059 2635 2867 4403 5720 4502 5749 5627 2846 1762 2429 1169 2154 2249 2687 4359 5382 4459 6398 4596 3024 1887 2070 1351 2218 2461 3028 4784 4975 4607 6249 4809 3157 1910 2228 1594 2467 2222 3607 4685 4962 5770 5480 5000 3228 1993 2288 1588 2105 2191 3591 4668 4885 5822 5599 5340 3082 2010 2301

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

marriages[t] = + 2340.27272727273 -813.727272727272M1[t] -135.272727272727M2[t] + 200.909090909091M3[t] + 1107.81818181818M4[t] + 2626.36363636364M5[t] + 3085.54545454545M6[t] + 3283.45454545455M7[t] + 3781.90909090909M8[t] + 3173.81818181818M9[t] + 908.90909090909M10[t] -375.818181818182M11[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)	2340.27272727273	137.634085	17.0036	0	0
M1	-813.727272727272	194.64399	-4.1806	5.6e-05	2.8e-05
M2	-135.272727272727	194.64399	-0.695	0.488414	0.244207
M3	200.909090909091	194.64399	1.0322	0.30406	0.15203
M4	1107.81818181818	194.64399	5.6915	0	0
M5	2626.36363636364	194.64399	13.4932	0	0
M6	3085.54545454545	194.64399	15.8523	0	0
M7	3283.45454545455	194.64399	16.869	0	0
M8	3781.90909090909	194.64399	19.4299	0	0
M9	3173.81818181818	194.64399	16.3058	0	0
M10	908.90909090909	194.64399	4.6696	8e-06	4e-06
M11	-375.818181818182	194.64399	-1.9308	0.055867	0.027933

Multiple Linear Regression - Regression Statistics
Multiple R	0.96507373665963
R-squared	0.93136731719018
Adjusted R-squared	0.925075987932613
F-TEST (value)	148.039830544551
F-TEST (DF numerator)	11
F-TEST (DF denominator)	120
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	456.480619589273
Sum Squared Residuals	25004946.7272727

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1775	1526.54545454545	248.454545454546
2	2197	2205	-8.00000000000081
3	2920	2541.18181818182	378.818181818182
4	4240	3448.09090909091	791.90909090909
5	5415	4966.63636363636	448.363636363636
6	6136	5425.81818181818	710.181818181818
7	6719	5623.72727272727	1095.27272727273
8	6234	6122.18181818182	111.818181818183
9	7152	5514.09090909091	1637.90909090909
10	3646	3249.18181818182	396.818181818179
11	2165	1964.45454545455	200.545454545455
12	2803	2340.27272727273	462.727272727273
13	1615	1526.54545454545	88.4545454545454
14	2350	2205	145
15	3350	2541.18181818182	808.818181818182
16	3536	3448.09090909091	87.909090909091
17	5834	4966.63636363636	867.363636363637
18	6767	5425.81818181818	1341.18181818182
19	5993	5623.72727272727	369.272727272727
20	7276	6122.18181818182	1153.81818181818
21	5641	5514.09090909091	126.909090909091
22	3477	3249.18181818182	227.818181818182
23	2247	1964.45454545455	282.545454545455
24	2466	2340.27272727273	125.727272727273
25	1567	1526.54545454545	40.4545454545454
26	2237	2205	32.0000000000001
27	2598	2541.18181818182	56.8181818181819
28	3729	3448.09090909091	280.909090909091
29	5715	4966.63636363636	748.363636363637
30	5776	5425.81818181818	350.181818181818
31	5852	5623.72727272727	228.272727272727
32	6878	6122.18181818182	755.818181818182
33	5488	5514.09090909091	-26.0909090909091
34	3583	3249.18181818182	333.818181818182
35	2054	1964.45454545455	89.5454545454544
36	2282	2340.27272727273	-58.2727272727272
37	1552	1526.54545454545	25.4545454545454
38	2261	2205	56
39	2446	2541.18181818182	-95.1818181818181
40	3519	3448.09090909091	70.9090909090911
41	5161	4966.63636363636	194.363636363636
42	5085	5425.81818181818	-340.818181818182
43	5711	5623.72727272727	87.2727272727273
44	6057	6122.18181818182	-65.1818181818184
45	5224	5514.09090909091	-290.090909090909
46	3363	3249.18181818182	113.818181818182
47	1899	1964.45454545455	-65.4545454545456
48	2115	2340.27272727273	-225.272727272727
49	1491	1526.54545454545	-35.5454545454546
50	2061	2205	-144
51	2419	2541.18181818182	-122.181818181818
52	3430	3448.09090909091	-18.0909090909089
53	4778	4966.63636363636	-188.636363636364
54	4862	5425.81818181818	-563.818181818182
55	6176	5623.72727272727	552.272727272727
56	5664	6122.18181818182	-458.181818181818
57	5529	5514.09090909091	14.9090909090909
58	3418	3249.18181818182	168.818181818182
59	1941	1964.45454545455	-23.4545454545456
60	2402	2340.27272727273	61.7272727272728
61	1579	1526.54545454545	52.4545454545454
62	2146	2205	-59
63	2462	2541.18181818182	-79.1818181818182
64	3695	3448.09090909091	246.909090909091
65	4831	4966.63636363636	-135.636363636364
66	5134	5425.81818181818	-291.818181818182
67	6250	5623.72727272727	626.272727272727
68	5760	6122.18181818182	-362.181818181818
69	6249	5514.09090909091	734.909090909091
70	2917	3249.18181818182	-332.181818181818
71	1741	1964.45454545455	-223.454545454545
72	2359	2340.27272727273	18.7272727272728
73	1511	1526.54545454545	-15.5454545454546
74	2059	2205	-146
75	2635	2541.18181818182	93.8181818181818
76	2867	3448.09090909091	-581.090909090909
77	4403	4966.63636363636	-563.636363636364
78	5720	5425.81818181818	294.181818181818
79	4502	5623.72727272727	-1121.72727272727
80	5749	6122.18181818182	-373.181818181818
81	5627	5514.09090909091	112.909090909091
82	2846	3249.18181818182	-403.181818181818
83	1762	1964.45454545455	-202.454545454546
84	2429	2340.27272727273	88.7272727272728
85	1169	1526.54545454545	-357.545454545455
86	2154	2205	-51
87	2249	2541.18181818182	-292.181818181818
88	2687	3448.09090909091	-761.090909090909
89	4359	4966.63636363636	-607.636363636364
90	5382	5425.81818181818	-43.8181818181818
91	4459	5623.72727272727	-1164.72727272727
92	6398	6122.18181818182	275.818181818182
93	4596	5514.09090909091	-918.09090909091
94	3024	3249.18181818182	-225.181818181818
95	1887	1964.45454545455	-77.4545454545455
96	2070	2340.27272727273	-270.272727272727
97	1351	1526.54545454545	-175.545454545455
98	2218	2205	13.0000000000001
99	2461	2541.18181818182	-80.1818181818182
100	3028	3448.09090909091	-420.090909090909
101	4784	4966.63636363636	-182.636363636364
102	4975	5425.81818181818	-450.818181818182
103	4607	5623.72727272727	-1016.72727272727
104	6249	6122.18181818182	126.818181818182
105	4809	5514.09090909091	-705.090909090909
106	3157	3249.18181818182	-92.181818181818
107	1910	1964.45454545455	-54.4545454545456
108	2228	2340.27272727273	-112.272727272727
109	1594	1526.54545454545	67.4545454545454
110	2467	2205	262
111	2222	2541.18181818182	-319.181818181818
112	3607	3448.09090909091	158.909090909091
113	4685	4966.63636363636	-281.636363636364
114	4962	5425.81818181818	-463.818181818182
115	5770	5623.72727272727	146.272727272727
116	5480	6122.18181818182	-642.181818181818
117	5000	5514.09090909091	-514.090909090909
118	3228	3249.18181818182	-21.181818181818
119	1993	1964.45454545455	28.5454545454544
120	2288	2340.27272727273	-52.2727272727272
121	1588	1526.54545454545	61.4545454545454
122	2105	2205	-100
123	2191	2541.18181818182	-350.181818181818
124	3591	3448.09090909091	142.909090909091
125	4668	4966.63636363636	-298.636363636364
126	4885	5425.81818181818	-540.818181818182
127	5822	5623.72727272727	198.272727272727
128	5599	6122.18181818182	-523.181818181818
129	5340	5514.09090909091	-174.090909090909
130	3082	3249.18181818182	-167.181818181818
131	2010	1964.45454545455	45.5454545454544
132	2301	2340.27272727273	-39.2727272727272

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
15	0.125186214052768	0.250372428105537	0.874813785947232
16	0.290044551783452	0.580089103566904	0.709955448216548
17	0.266075993663952	0.532151987327905	0.733924006336048
18	0.397212308109574	0.794424616219148	0.602787691890426
19	0.507404180772738	0.985191638454525	0.492595819227262
20	0.803860940506534	0.392278118986932	0.196139059493466
21	0.975254098605245	0.0494918027895096	0.0247459013947548
22	0.961737968863222	0.0765240622735565	0.0382620311367782
23	0.942868937116171	0.114262125767658	0.0571310628838291
24	0.923969591061827	0.152060817876347	0.0760304089381734
25	0.892550007213193	0.214899985573614	0.107449992786807
26	0.851274899085846	0.297450201828307	0.148725100914154
27	0.85158781872514	0.296824362549721	0.148412181274861
28	0.817344819679293	0.365310360641415	0.182655180320707
29	0.826083611253977	0.347832777492045	0.173916388746023
30	0.873745921326218	0.252508157347563	0.126254078673782
31	0.878624583509699	0.242750832980602	0.121375416490301
32	0.897845931974527	0.204308136050945	0.102154068025473
33	0.943156738363684	0.113686523272631	0.0568432616363156
34	0.930089873711269	0.139820252577463	0.0699101262887314
35	0.908827447494956	0.182345105010088	0.091172552505044
36	0.892393103050096	0.215213793899809	0.107606896949904
37	0.861689189288479	0.276621621423042	0.138310810711521
38	0.824378187606643	0.351243624786714	0.175621812393357
39	0.824337848891395	0.35132430221721	0.175662151108605
40	0.80334849670631	0.39330300658738	0.19665150329369
41	0.821650925123414	0.356698149753172	0.178349074876586
42	0.9254233941103	0.149153211779399	0.0745766058896996
43	0.924819766779374	0.150360466441251	0.0751802332206255
44	0.939552831904577	0.120894336190847	0.0604471680954235
45	0.957604809319111	0.0847903813617771	0.0423951906808886
46	0.947368432909245	0.105263134181509	0.0526315670907547
47	0.933477536947278	0.133044926105444	0.0665224630527219
48	0.924238795801254	0.151522408397491	0.0757612041987457
49	0.903133714306886	0.193732571386228	0.0968662856931139
50	0.881023265362185	0.23795346927563	0.118976734637815
51	0.866276721126022	0.267446557747956	0.133723278873978
52	0.846847324668222	0.306305350663556	0.153152675331778
53	0.867615626211578	0.264768747576844	0.132384373788422
54	0.9239554312441	0.152089137511801	0.0760445687559003
55	0.947180368400501	0.105639263198998	0.052819631599499
56	0.963489894976213	0.0730202100475749	0.0365101050237874
57	0.95713682531555	0.0857263493689002	0.0428631746844501
58	0.949318048084666	0.101363903830668	0.0506819519153342
59	0.93434833740928	0.131303325181439	0.0656516625907195
60	0.915810287784243	0.168379424431514	0.0841897122157569
61	0.89384825336169	0.212303493276619	0.10615174663831
62	0.867131398871073	0.265737202257854	0.132868601128927
63	0.842956637005812	0.314086725988377	0.157043362994188
64	0.836939206160205	0.32612158767959	0.163060793839795
65	0.833001174985884	0.333997650028232	0.166998825014116
66	0.825945007146323	0.348109985707353	0.174054992853677
67	0.925757858047528	0.148484283904944	0.0742421419524721
68	0.925822889168973	0.148354221662053	0.0741771108310265
69	0.980606314124542	0.0387873717509156	0.0193936858754578
70	0.97898884022883	0.0420223195423419	0.021011159771171
71	0.973690882942118	0.0526182341157638	0.0263091170578819
72	0.964393909775953	0.071212180448094	0.035606090224047
73	0.952529899459966	0.0949402010800687	0.0474701005400343
74	0.939714905755292	0.120570188489417	0.0602850942447084
75	0.930645330161638	0.138709339676724	0.0693546698383621
76	0.944275960196329	0.111448079607343	0.0557240398036715
77	0.952752878746522	0.0944942425069562	0.0472471212534781
78	0.962919915670134	0.0741601686597325	0.0370800843298663
79	0.993151179293998	0.0136976414120034	0.00684882070600172
80	0.99177776924463	0.0164444615107411	0.00822223075537054
81	0.994861182828325	0.01027763434335	0.00513881717167498
82	0.994189275368446	0.0116214492631074	0.00581072463155371
83	0.991953150279963	0.0160936994400737	0.00804684972003683
84	0.988802111672032	0.022395776655936	0.011197888327968
85	0.987308288265266	0.0253834234694672	0.0126917117347336
86	0.981643042345557	0.0367139153088858	0.0183569576544429
87	0.975509323621777	0.0489813527564466	0.0244906763782233
88	0.988888501298392	0.0222229974032168	0.0111114987016084
89	0.989668403097329	0.0206631938053423	0.0103315969026711
90	0.989263211657018	0.0214735766859646	0.0107367883429823
91	0.999053132724169	0.00189373455166259	0.000946867275831297
92	0.99949112692883	0.00101774614234065	0.000508873071170326
93	0.999755867717568	0.000488264564863856	0.000244132282431928
94	0.999571968074408	0.000856063851184678	0.000428031925592339
95	0.99921060479531	0.0015787904093781	0.00078939520468905
96	0.998767694371546	0.0024646112569082	0.0012323056284541
97	0.998101340197	0.00379731960599944	0.00189865980299972
98	0.996625166880246	0.00674966623950798	0.00337483311975399
99	0.99500523090759	0.00998953818482158	0.00499476909241079
100	0.996515672525706	0.00696865494858736	0.00348432747429368
101	0.99404542527874	0.0119091494425204	0.00595457472126021
102	0.990594990172648	0.0188100196547039	0.00940500982735193
103	0.999976888507988	4.62229840248892e-05	2.31114920124446e-05
104	0.999999877681874	2.44636251704263e-07	1.22318125852132e-07
105	0.999999983068729	3.38625420164111e-08	1.69312710082056e-08
106	0.999999916722175	1.66555650718953e-07	8.32778253594767e-08
107	0.99999968456997	6.30860058285634e-07	3.15430029142817e-07
108	0.999998696015347	2.60796930561417e-06	1.30398465280709e-06
109	0.999994142784828	1.17144303438604e-05	5.85721517193022e-06
110	0.999998548639398	2.90272120405374e-06	1.45136060202687e-06
111	0.999992429093433	1.51418131343731e-05	7.57090656718655e-06
112	0.999960802218585	7.83955628300864e-05	3.91977814150432e-05
113	0.99981046011736	0.000379079765279564	0.000189539882639782
114	0.99923922693195	0.00152154613609814	0.000760773068049068
115	0.996788561468465	0.00642287706307106	0.00321143853153553
116	0.989547244545645	0.0209055109087108	0.0104527554543554
117	0.997255127706328	0.00548974458734464	0.00274487229367232

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	24	0.233009708737864	NOK
5% type I error level	42	0.407766990291262	NOK
10% type I error level	51	0.495145631067961	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/10mf6j1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/10mf6j1293616226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/1khye1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/1khye1293616226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/2khye1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/2khye1293616226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/3khye1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/3khye1293616226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/4vrfz1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/4vrfz1293616226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/5vrfz1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/5vrfz1293616226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/6vrfz1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/6vrfz1293616226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/7ifqw1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/7ifqw1293616226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/8t6pg1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/8t6pg1293616226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/9t6pg1293616226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293616114h5a2fi2ztsrd0ea/9t6pg1293616226.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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