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*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 01 Dec 2010 21:14:12 +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/01/t1291238073mnx5ywq7leejjnv.htm/, Retrieved Wed, 01 Dec 2010 22:14:33 +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/01/t1291238073mnx5ywq7leejjnv.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 «

2502,66 10169,02 10433,44 24977 -7,9 -15 2,85 0,3 2466,92 9633,83 10238,83 24320 -8,8 -10 2,98 -0,1 2513,17 10066,24 9857,34 22680 -14,2 -12 3,06 -1 2443,27 10302,87 9634,97 22052 -17,8 -11 3,08 -1,2 2293,41 10430,35 9374,63 21467 -18,2 -11 3,3 -0,8 2070,83 9691,12 8679,75 21383 -22,8 -17 3,47 -1,7 2029,6 9810,31 8593 21777 -23,6 -18 3,72 -1,1 2052,02 9304,43 8398,37 21928 -27,6 -19 3,67 -0,4 1864,44 8767,96 7992,12 21814 -29,4 -22 3,82 0,6 1670,07 7764,58 7235,47 22937 -31,8 -24 3,85 0,6 1810,99 7694,78 7690,5 23595 -31,4 -24 3,9 1,9 1905,41 8331,49 8396,2 20830 -27,6 -20 3,99 2,3 1862,83 8460,94 8595,56 19650 -28,8 -25 4,35 2,6 2014,45 8531,45 8614,55 19195 -21,9 -22 4,98 3,1 2197,82 9117,03 9181,73 19644 -13,9 -17 5,46 4,7 2962,34 12123,53 11114,08 18483 -8 -9 5,19 5,5 3047,03 12989,35 11530,75 18079 -2,8 -11 5,03 5,4 3032,6 13168,91 11322,38 19178 -3,3 -13 5,38 5,9 3504,37 14084,6 12056,67 18391 -1,3 -11 5,37 5,8 3801,06 13995,33 12812,48 18441 0,5 -9 4,87 5,2 3857,62 13357,7 12656,63 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

BEL_20[t] = -1550.70804561538 + 0.086528028444836Nikkei[t] + 0.376273521438822DJ_Indust[t] + 0.0122770847008117Goudprijs[t] -7.74003093034112Conjunct_Seizoenzuiver[t] + 6.90342219860368Cons_vertrouw[t] -184.570093209091Rend_oblig_EUR[t] + 33.8362739714698Alg_consumptie_index_BE[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)	-1550.70804561538	354.791303	-4.3708	2.6e-05	1.3e-05
Nikkei	0.086528028444836	0.015381	5.6258	0	0
DJ_Indust	0.376273521438822	0.036089	10.4263	0	0
Goudprijs	0.0122770847008117	0.008021	1.5306	0.128412	0.064206
Conjunct_Seizoenzuiver	-7.74003093034112	7.007133	-1.1046	0.271475	0.135737
Cons_vertrouw	6.90342219860368	6.308425	1.0943	0.275937	0.137968
Rend_oblig_EUR	-184.570093209091	45.948764	-4.0169	0.000102	5.1e-05
Alg_consumptie_index_BE	33.8362739714698	25.209669	1.3422	0.181985	0.090993

Multiple Linear Regression - Regression Statistics
Multiple R	0.935715907429102
R-squared	0.875564259415868
Adjusted R-squared	0.868539661157086
F-TEST (value)	124.642609749433
F-TEST (DF numerator)	7
F-TEST (DF denominator)	124
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	273.003433972532
Sum Squared Residuals	9241828.49513854

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	2502.66	3003.39018820974	-500.730188209737
2	2466.92	2879.74313513525	-412.823135135255
3	2513.17	2736.25078390764	-223.080783907643
4	2443.27	2689.65283601344	-246.38283601344
5	2293.41	2571.56738741295	-278.157387412954
6	2070.83	2177.46109992148	-106.631099921481
7	2029.6	2133.4176626454	-103.817662645401
8	2052.02	2075.23518589116	-23.2151858911566
9	1864.44	1873.92733779985	-9.48733779985038
10	1670.07	1515.41877778054	154.651222219463
11	1810.99	1720.33582271885	90.654177281152
12	1905.41	2002.14394105048	-96.7339410504801
13	1862.83	1992.34849837931	-129.518498379309
14	2014.45	1867.95198173867	146.498018261327
15	2197.82	2075.68954872001	122.130451279987
16	2962.34	3135.13864949752	-172.798649497525
17	3047.03	3333.97087532574	-286.940875325745
18	3032.6	3226.9780259678	-194.378025967801
19	3504.37	3569.63155080370	-65.2615508036956
20	3801.06	3918.7704091224	-117.710409122398
21	3857.62	3836.63449764519	20.9855023548056
22	3674.4	3675.48129357721	-1.08129357721300
23	3720.98	3823.44484027478	-102.464840274783
24	3844.49	3817.65162573115	26.8383742688539
25	4116.68	4246.37385899595	-129.693858995949
26	4105.18	4161.22899196693	-56.0489919669306
27	4435.23	4550.55943371415	-115.329433714150
28	4296.49	4312.55711359523	-16.0671135952274
29	4202.52	4181.76410073105	20.7558992689486
30	4562.84	4445.29523233311	117.544767666889
31	4621.4	4378.61759990765	242.782400092345
32	4696.96	4388.3867539917	308.573246008302
33	4591.27	4181.19208965739	410.07791034261
34	4356.98	4002.64630174071	354.333698259293
35	4502.64	4186.08222141898	316.557778581017
36	4443.91	4069.09529081717	374.814709182827
37	4290.89	3951.45637314425	339.433626855753
38	4199.75	3907.72610903661	292.023890963386
39	4138.52	3831.94423271205	306.575767287955
40	3970.1	3614.37185126701	355.728148732991
41	3862.27	3499.17669542812	363.09330457188
42	3701.61	3333.91184077139	367.698159228613
43	3570.12	3326.89435050467	243.22564949533
44	3801.06	3600.00479694653	201.055203053465
45	3895.51	3643.44755091068	252.062449089318
46	3917.96	3559.20292010767	358.75707989233
47	3813.06	3576.90500054989	236.154999450110
48	3667.03	3585.08856937863	81.9414306213735
49	3494.17	3511.36968520873	-17.1996852087344
50	3363.99	3304.57039378218	59.4196062178174
51	3295.32	3137.93699284063	157.383007159373
52	3277.01	3212.00465818399	65.0053418160117
53	3257.16	3176.67123910813	80.4887608918678
54	3161.69	3133.07957680062	28.6104231993798
55	3097.31	3077.23485179986	20.0751482001423
56	3061.26	2957.44747462901	103.81252537099
57	3119.31	2960.1802453105	159.129754689498
58	3106.22	3118.00868030601	-11.7886803060106
59	3080.58	3101.58732999367	-21.0073299936699
60	2981.85	2973.71620334155	8.13379665844577
61	2921.44	3000.09538834788	-78.6553883478807
62	2849.27	2851.77768219881	-2.50768219881385
63	2756.76	2677.97447790977	78.7855220902298
64	2645.64	2729.07123671718	-83.4312367171805
65	2497.84	2685.23746190292	-187.397461902915
66	2448.05	2698.42945212243	-250.379452122428
67	2454.62	2818.76176459596	-364.141764595956
68	2407.6	2655.19741010511	-247.597410105109
69	2472.81	2893.4737399117	-420.663739911701
70	2408.64	2839.65898710560	-431.018987105596
71	2440.25	2875.44491496144	-435.194914961435
72	2350.44	2894.43310420071	-543.99310420071
73	2196.72	2627.35878391799	-430.638783917994
74	2174.56	2480.03363689223	-305.473636892232
75	2120.88	2461.43759981296	-340.557599812959
76	2093.48	2485.35659070359	-391.876590703587
77	2061.41	2312.17252449898	-250.762524498983
78	1969.6	2295.00770267096	-325.407702670958
79	1959.67	2295.10063205556	-335.430632055561
80	1910.43	1968.62283911142	-58.1928391114226
81	1833.42	1785.79298492778	47.6270150722225
82	1635.25	1670.36705771811	-35.1170577181129
83	1765.9	1720.25817483313	45.6418251668717
84	1946.81	1891.29763852223	55.5123614777717
85	1995.37	1859.64897370778	135.721026292218
86	2042	1879.97266766233	162.027332337666
87	1940.49	1670.36917534796	270.120824652043
88	2065.81	1756.03466110150	309.775338898505
89	2214.95	1932.83801757163	282.111982428373
90	2304.98	1917.64454304317	387.33545695683
91	2555.28	2264.37000383401	290.90999616599
92	2799.43	2536.57533329	262.854666710002
93	2811.7	2563.27152205295	248.42847794705
94	2735.7	2734.35725724899	1.34274275100743
95	2745.88	2439.41233038517	306.467669614827
96	2720.25	2491.83154128404	228.418458715962
97	2638.53	2493.58463544675	144.945364553250
98	2659.81	2390.83514693340	268.974853066597
99	2641.65	2209.88724011270	431.762759887296
100	2604.42	2112.56021057837	491.859789421631
101	2892.63	2713.33566559789	179.294334402113
102	2915.02	2798.44071145629	116.57928854371
103	2845.26	2989.69016603734	-144.430166037342
104	2794.83	2969.44689232447	-174.616892324469
105	2848.96	2794.01475923299	54.945240767011
106	2833.18	2635.65397809555	197.52602190445
107	2995.55	2925.20133865871	70.3486613412945
108	2987.1	2940.79350014004	46.3064998599592
109	3013.24	2985.71997463777	27.5200253622277
110	3110.52	2975.45863018740	135.061369812605
111	3045.78	2947.7526895259	98.0273104741005
112	3032.93	3185.88454968944	-152.954549689442
113	3142.95	3245.81074999731	-102.860749997309
114	3012.61	3142.74270665803	-130.132706658026
115	2897.06	3131.9064255591	-234.846425559103
116	2863.36	3095.80195009596	-232.441950095957
117	2882.6	3489.99777924289	-607.397779242891
118	2767.63	3327.2355623782	-559.605562378198
119	2803.47	3304.09320449827	-500.623204498266
120	3030.29	3529.97354726504	-499.683547265035
121	3210.52	3518.52154362114	-308.001543621135
122	3249.57	3376.43400347089	-126.864003470894
123	2999.93	3084.13682615803	-84.2068261580265
124	3181.96	3240.37038639344	-58.4103863934407
125	3053.05	3331.50119020751	-278.451190207512
126	3092.71	3477.93225110056	-385.222251100558
127	3165.26	3298.09356676188	-132.833566761878
128	3173.95	3428.73693195226	-254.78693195226
129	3280.37	3316.86255514234	-36.492555142343
130	3288.18	2974.31084614725	313.869153852753
131	3411.13	2710.07675021468	701.053249785323
132	3484.74	2701.25075600359	783.489243996414

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.00837925485437199	0.0167585097087440	0.991620745145628
12	0.00138264756008401	0.00276529512016803	0.998617352439916
13	0.000218769613389439	0.000437539226778878	0.99978123038661
14	0.00190693972842896	0.00381387945685792	0.998093060271571
15	0.000480249440218446	0.000960498880436891	0.999519750559782
16	0.000186660677030363	0.000373321354060725	0.99981333932297
17	6.16783286402733e-05	0.000123356657280547	0.99993832167136
18	1.48463054721708e-05	2.96926109443415e-05	0.999985153694528
19	6.66048854981156e-05	0.000133209770996231	0.999933395114502
20	0.000165056514690149	0.000330113029380299	0.99983494348531
21	0.000133191619123800	0.000266383238247600	0.999866808380876
22	0.000844707109184393	0.00168941421836879	0.999155292890816
23	0.000490015063497834	0.000980030126995667	0.999509984936502
24	0.000600544493099973	0.00120108898619995	0.9993994555069
25	0.000847784449130985	0.00169556889826197	0.999152215550869
26	0.00113846196934114	0.00227692393868228	0.998861538030659
27	0.000739191844236883	0.00147838368847377	0.999260808155763
28	0.000526400182418505	0.00105280036483701	0.999473599817582
29	0.000452184221984258	0.000904368443968516	0.999547815778016
30	0.000454558590662444	0.000909117181324889	0.999545441409338
31	0.000641955283908422	0.00128391056781684	0.999358044716092
32	0.00122003440146802	0.00244006880293605	0.998779965598532
33	0.00169907435102891	0.00339814870205782	0.998300925648971
34	0.00107528327930279	0.00215056655860557	0.998924716720697
35	0.000590313779224334	0.00118062755844867	0.999409686220776
36	0.000379491826948297	0.000758983653896594	0.999620508173052
37	0.000306283422605646	0.000612566845211292	0.999693716577394
38	0.000166623823829667	0.000333247647659334	0.99983337617617
39	0.000115617171703129	0.000231234343406258	0.999884382828297
40	6.93271389727521e-05	0.000138654277945504	0.999930672861027
41	4.09072253222763e-05	8.18144506445526e-05	0.999959092774678
42	2.50165820305362e-05	5.00331640610723e-05	0.99997498341797
43	2.18040145910562e-05	4.36080291821124e-05	0.999978195985409
44	1.56058261470398e-05	3.12116522940796e-05	0.999984394173853
45	1.55500980230747e-05	3.11001960461495e-05	0.999984449901977
46	1.48911661705728e-05	2.97823323411456e-05	0.99998510883383
47	1.43794770167795e-05	2.8758954033559e-05	0.999985620522983
48	2.030310008557e-05	4.060620017114e-05	0.999979696899914
49	2.15719245619662e-05	4.31438491239325e-05	0.999978428075438
50	1.68886148271296e-05	3.37772296542592e-05	0.999983111385173
51	2.27168423572026e-05	4.54336847144051e-05	0.999977283157643
52	2.96680674735825e-05	5.9336134947165e-05	0.999970331932526
53	2.64450160345815e-05	5.2890032069163e-05	0.999973554983965
54	2.01523541843326e-05	4.03047083686653e-05	0.999979847645816
55	1.78481934998145e-05	3.5696386999629e-05	0.9999821518065
56	1.74240651158559e-05	3.48481302317118e-05	0.999982575934884
57	1.6393917125737e-05	3.2787834251474e-05	0.999983606082874
58	1.93068248607007e-05	3.86136497214014e-05	0.99998069317514
59	2.04165371211879e-05	4.08330742423757e-05	0.999979583462879
60	2.5989725810406e-05	5.1979451620812e-05	0.99997401027419
61	3.44632222259375e-05	6.8926444451875e-05	0.999965536777774
62	6.67116041386617e-05	0.000133423208277323	0.999933288395861
63	0.000198505555069282	0.000397011110138564	0.99980149444493
64	0.000496420353369561	0.000992840706739121	0.99950357964663
65	0.00123141968290464	0.00246283936580928	0.998768580317095
66	0.00398944461370823	0.00797888922741647	0.996010555386292
67	0.0111044618014797	0.0222089236029595	0.98889553819852
68	0.0162973365970406	0.0325946731940812	0.98370266340296
69	0.0488459357419172	0.0976918714838345	0.951154064258083
70	0.0727664720378295	0.145532944075659	0.92723352796217
71	0.0699263981489827	0.139852796297965	0.930073601851017
72	0.0897611519767056	0.179522303953411	0.910238848023294
73	0.0841748459451168	0.168349691890234	0.915825154054883
74	0.0699068623048815	0.139813724609763	0.930093137695118
75	0.0748203292731258	0.149640658546252	0.925179670726874
76	0.079069265811445	0.15813853162289	0.920930734188555
77	0.0669184196638453	0.133836839327691	0.933081580336155
78	0.0890444700114291	0.178088940022858	0.91095552998857
79	0.203535543943612	0.407071087887224	0.796464456056388
80	0.353805481275289	0.707610962550578	0.646194518724711
81	0.59183072939086	0.81633854121828	0.40816927060914
82	0.613368543192005	0.77326291361599	0.386631456807995
83	0.581920394220478	0.836159211559044	0.418079605779522
84	0.616516361851051	0.766967276297898	0.383483638148949
85	0.660557557197428	0.678884885605145	0.339442442802572
86	0.779339073712688	0.441321852574624	0.220660926287312
87	0.889977147771173	0.220045704457655	0.110022852228827
88	0.95294762187595	0.0941047562480994	0.0470523781240497
89	0.986482533538153	0.0270349329236945	0.0135174664618473
90	0.99711063564082	0.00577872871835856	0.00288936435917928
91	0.99735866032676	0.00528267934648166	0.00264133967324083
92	0.996535497736787	0.00692900452642529	0.00346450226321264
93	0.997371792573701	0.00525641485259729	0.00262820742629864
94	0.995958968874474	0.00808206225105253	0.00404103112552627
95	0.995827130643053	0.0083457387138942	0.0041728693569471
96	0.994428346548995	0.0111433069020109	0.00557165345100545
97	0.991939038866117	0.0161219222677661	0.00806096113388304
98	0.990479428261503	0.0190411434769937	0.00952057173849685
99	0.988726357225786	0.0225472855484286	0.0112736427742143
100	0.98856709428619	0.0228658114276189	0.0114329057138095
101	0.982060562136557	0.0358788757268865	0.0179394378634432
102	0.97626330589224	0.0474733882155208	0.0237366941077604
103	0.973507467312926	0.0529850653741476	0.0264925326870738
104	0.976484383218675	0.0470312335626507	0.0235156167813254
105	0.981752958530994	0.0364940829380126	0.0182470414690063
106	0.990366574704206	0.0192668505915882	0.0096334252957941
107	0.989976043912867	0.0200479121742667	0.0100239560871333
108	0.994380909506003	0.0112381809879944	0.00561909049399721
109	0.995192708910706	0.0096145821785883	0.00480729108929415
110	0.991169862542113	0.0176602749157745	0.00883013745788727
111	0.984905108468663	0.0301897830626747	0.0150948915313373
112	0.979763810245588	0.040472379508823	0.0202361897544115
113	0.97540967626136	0.0491806474772794	0.0245903237386397
114	0.969343774948014	0.0613124501039729	0.0306562250519864
115	0.967026735496939	0.0659465290061228	0.0329732645030614
116	0.987926527309034	0.0241469453819316	0.0120734726909658
117	0.984370856289316	0.0312582874213681	0.0156291437106840
118	0.99069851247519	0.0186029750496201	0.00930148752481003
119	0.998381575790776	0.00323684841844866	0.00161842420922433
120	0.993037819393562	0.0139243612128756	0.0069621806064378
121	0.973661064968014	0.0526778700639716	0.0263389350319858

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	63	0.567567567567568	NOK
5% type I error level	87	0.783783783783784	NOK
10% type I error level	93	0.837837837837838	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/106rmo1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/106rmo1291238041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/1h87u1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/1h87u1291238041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/2h87u1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/2h87u1291238041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/3h87u1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/3h87u1291238041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/4az7x1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/4az7x1291238041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/5az7x1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/5az7x1291238041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/6az7x1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/6az7x1291238041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/77udo1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/77udo1291238041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/8i3ca1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/8i3ca1291238041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/9i3ca1291238041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291238073mnx5ywq7leejjnv/9i3ca1291238041.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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