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

Title produced by software: Multiple Regression

Date of computation: Mon, 06 Dec 2010 16:38:41 +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/06/t1291653412plzqkd2zgjq7mdm.htm/, Retrieved Mon, 06 Dec 2010 17:37:03 +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/06/t1291653412plzqkd2zgjq7mdm.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 «

3484.74 13830.14 9349.44 7977 -5.6 6 1 3.17 3411.13 14153.22 9327.78 8241 -6.2 3 1 3.17 3288.18 15418.03 9753.63 8444 -7.1 2 1.2 3.36 3280.37 16666.97 10443.5 8490 -1.4 2 1.2 3.11 3173.95 16505.21 10853.87 8388 -0.1 2 0.8 3.11 3165.26 17135.96 10704.02 8099 -0.9 -8 0.7 3.57 3092.71 18033.25 11052.23 7984 0 0 0.7 4.04 3053.05 17671 10935.47 7786 0.1 -2 0.9 4.21 3181.96 17544.22 10714.03 8086 2.6 3 1.2 4.36 2999.93 17677.9 10394.48 9315 6 5 1.3 4.75 3249.57 18470.97 10817.9 9113 6.4 8 1.5 4.43 3210.52 18409.96 11251.2 9023 8.6 8 1.9 4.7 3030.29 18941.6 11281.26 9026 6.4 9 1.8 4.81 2803.47 19685.53 10539.68 9787 7.7 11 1.9 5.01 2767.63 19834.71 10483.39 9536 9.2 13 2.2 5 2882.6 19598.93 10947.43 9490 8.6 12 2.1 4.81 2863.36 17039.97 10580.27 9736 7.4 13 2.2 5.11 2897.06 16969.28 10582.92 9694 8.6 15 2.7 5.1 3012.61 16973.38 10654.41 9647 6.2 13 2.8 5.11 3142.95 16329.89 11014.51 9753 6 16 2.9 5.21 3032.93 16153.34 10967.87 10070 6.6 10 3.4 5.21 3045.78 15311.7 10433.56 10137 5.1 14 3 5.21 3 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	9 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

BEL_20[t] = -1453.14454612382 + 0.0993347391427635Nikkei[t] + 0.361604121076399DJ_Indust[t] + 0.0162644412155995Goudprijs[t] -11.6779957473965Conjunct_Seizoenzuiver[t] + 14.3554763933654Cons_vertrouw[t] + 35.0865681640742Alg_consumptie_index_BE[t] -268.749364521601Gem_rente_kasbon_5j[t] + 1.10899673297789t + 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)	-1453.14454612382	338.602291	-4.2916	3.6e-05	1.8e-05
Nikkei	0.0993347391427635	0.017443	5.6949	0	0
DJ_Indust	0.361604121076399	0.038764	9.3283	0	0
Goudprijs	0.0162644412155995	0.019416	0.8377	0.403827	0.201913
Conjunct_Seizoenzuiver	-11.6779957473965	7.124337	-1.6392	0.103733	0.051867
Cons_vertrouw	14.3554763933654	6.636792	2.163	0.032474	0.016237
Alg_consumptie_index_BE	35.0865681640742	23.017286	1.5244	0.129987	0.064993
Gem_rente_kasbon_5j	-268.749364521601	56.100374	-4.7905	5e-06	2e-06
t	1.10899673297789	2.560983	0.433	0.665747	0.332874

Multiple Linear Regression - Regression Statistics
Multiple R	0.941733009782613
R-squared	0.88686106171422
Adjusted R-squared	0.87950243158181
F-TEST (value)	120.519858418804
F-TEST (DF numerator)	8
F-TEST (DF denominator)	123
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	261.372491501888
Sum Squared Residuals	8402816.25561026

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3484.74	2766.99599832661	717.744001673388
2	3411.13	2760.59989806861	650.530101931395
3	3288.18	2996.74891689690	291.431083103104
4	3280.37	3372.75180740797	-92.381807407968
5	3173.95	3475.3089051621	-301.358905162098
6	3165.26	3218.84075572269	-53.5807557226873
7	3092.71	3411.14699445041	-318.436994450408
8	3053.05	3262.28189469402	-209.231894694022
9	3181.96	3188.39890736132	-6.43890736132138
10	2999.93	2994.92754528548	5.00245471452145
11	3249.57	3356.05328457189	-106.483284571890
12	3210.52	3422.10184302329	-211.581843023293
13	3030.29	3493.91575380119	-463.625753801187
14	2803.47	3276.43004090908	-472.96004090908
15	2767.63	3292.32814656694	-524.698146566943
16	2882.6	3477.27165405098	-594.671654050984
17	2863.36	3046.67442890199	-183.314428901991
18	2897.06	3075.96473293187	-178.904732931872
19	3012.61	3102.70505215217	-90.0950521521658
20	3142.95	3193.86656105645	-50.9165610564549
21	3032.93	3090.13224952553	-57.2022495255266
22	3045.78	2876.42244796443	169.357552035571
23	3110.52	2952.79039961938	157.72960038062
24	3013.24	3038.34774116808	-25.1077411680752
25	2987.1	2995.86151343951	-8.7615134395138
26	2995.55	2938.39896690172	57.151033098277
27	2833.18	2664.17003993411	169.009960065889
28	2848.96	2827.43437942738	21.5256205726154
29	2794.83	2985.64305393771	-190.81305393771
30	2845.26	3003.57214507104	-158.312145071043
31	2915.02	2807.97066733130	107.049332668695
32	2892.63	2658.22484954271	234.405150457292
33	2604.42	2101.61162828999	502.808371710012
34	2641.65	2160.4405028459	481.2094971541
35	2659.81	2350.4261249428	309.383875057199
36	2638.53	2443.52235378826	195.007646211741
37	2720.25	2500.40131322504	219.848686774959
38	2745.88	2435.14903390667	310.730966093326
39	2735.7	2698.82878310695	36.8712168930473
40	2811.7	2505.23423181217	306.465768187828
41	2799.43	2503.86944411747	295.560555882533
42	2555.28	2234.55068270027	320.729317299735
43	2304.98	1918.15498204515	386.825017954852
44	2214.95	1950.02393840442	264.926061595576
45	2065.81	1785.46616340905	280.343836590952
46	1940.49	1703.82579405983	236.664205940171
47	2042	1878.41750714963	163.582492850369
48	1995.37	1812.83170590496	182.538294095044
49	1946.81	1882.6189924228	64.1910075771997
50	1765.9	1707.04805663169	58.8519433683129
51	1635.25	1672.5761125114	-37.3261125114003
52	1833.42	1812.55667564440	20.8633243556049
53	1910.43	2069.30894539421	-158.878945394211
54	1959.67	2428.55343196377	-468.883431963775
55	1969.6	2385.9292455825	-416.329245582502
56	2061.41	2349.62035802939	-288.210358029395
57	2093.48	2557.12926686677	-463.649266866769
58	2120.88	2416.32504033649	-295.445040336487
59	2174.56	2503.06966170582	-328.509661705824
60	2196.72	2627.1482968952	-430.428296895199
61	2350.44	2841.6957946944	-491.255794694401
62	2440.25	2850.45174241149	-410.201742411485
63	2408.64	2825.65221943099	-417.01221943099
64	2472.81	2951.19003843712	-478.380038437125
65	2407.6	2685.62274814555	-278.022748145552
66	2454.62	2910.07999334351	-455.459993343510
67	2448.05	2684.10744605480	-236.057446054796
68	2497.84	2686.83283914415	-188.992839144146
69	2645.64	2746.62255540934	-100.982555409336
70	2756.76	2631.44916975138	125.310830248617
71	2849.27	2789.8357292938	59.4342707062021
72	2921.44	2930.43082828954	-8.9908282895366
73	2981.85	2922.57357495929	59.2764250407144
74	3080.58	3126.51298782886	-45.9329878288583
75	3106.22	3181.83309590241	-75.6130959024082
76	3119.31	2982.38727777720	136.922722222796
77	3061.26	2911.52610162273	149.733898377267
78	3097.31	3032.38636654856	64.9236334514366
79	3161.69	3125.20451998752	36.485480012479
80	3257.16	3165.57095299068	91.5890470093196
81	3277.01	3153.41500478357	123.594995216432
82	3295.32	3167.71154467449	127.608455325514
83	3363.99	3347.11429505407	16.8757049459335
84	3494.17	3558.78494180609	-64.6149418060879
85	3667.03	3653.55758175301	13.4724182469878
86	3813.06	3694.60315973038	118.456840269625
87	3917.96	3668.40051437262	249.559485627384
88	3895.51	3743.08366498578	152.426335014223
89	3801.06	3641.92529581188	159.134704188118
90	3570.12	3393.84336546784	176.276634532159
91	3701.61	3382.55303153513	319.056968464874
92	3862.27	3529.39833496757	332.871665032427
93	3970.1	3655.44302808518	314.656971914825
94	4138.52	3905.42625764075	233.093742359249
95	4199.75	3974.79763465317	224.952365346829
96	4290.89	3964.48676149641	326.403238503586
97	4443.91	4145.46477375467	298.445226245325
98	4502.64	4213.92831940261	288.711680597393
99	4356.98	4000.21858938473	356.761410615274
100	4591.27	4240.71722728879	350.552772711214
101	4696.96	4467.93176180266	229.028238197345
102	4621.4	4407.46739411615	213.932605883853
103	4562.84	4415.41773882690	147.422261173104
104	4202.52	4127.75376291685	74.7662370831509
105	4296.49	4267.38233528758	29.1076647124179
106	4435.23	4530.31687238	-95.0868723799948
107	4105.18	4106.26083258733	-1.08083258732591
108	4116.68	4283.6965492157	-167.016549215705
109	3844.49	3758.67275656259	85.8172434374094
110	3720.98	3802.86261229744	-81.882612297439
111	3674.4	3741.10135503184	-66.7013550318403
112	3857.62	3962.33544481343	-104.715444813430
113	3801.06	3989.28702924991	-188.227029249910
114	3504.37	3596.07062259521	-91.7006225952081
115	3032.6	3125.33911141335	-92.7391114133531
116	3047.03	3176.78805032003	-129.758050320029
117	2962.34	3137.48724704799	-175.147247047995
118	2197.82	2088.75824631426	109.061753685742
119	2014.45	1889.62177411535	124.82822588465
120	1862.83	1928.41603708707	-65.5860370870748
121	1905.41	1945.94402890318	-40.534028903176
122	1810.99	1711.01245408028	99.9775459197183
123	1670.07	1591.55824004996	78.5117599500431
124	1864.44	1940.30180012867	-75.861800128671
125	2052.02	2114.29123165485	-62.2712316548458
126	2029.6	2160.53269950454	-130.932699504540
127	2070.83	2147.97412065966	-77.1441206596634
128	2293.41	2544.51899788509	-251.108997885092
129	2443.27	2615.2261978545	-171.956197854502
130	2513.17	2628.69965800967	-115.529658009673
131	2466.92	2797.07993264529	-330.159932645292
132	2502.66	2866.84394707277	-364.183947072775

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
12	0.0476575070204963	0.0953150140409926	0.952342492979504
13	0.0202109127514776	0.0404218255029552	0.979789087248522
14	0.0339508026815418	0.0679016053630836	0.966049197318458
15	0.0318080318474295	0.063616063694859	0.96819196815257
16	0.0208554908500961	0.0417109817001922	0.979144509149904
17	0.0134067541007297	0.0268135082014595	0.98659324589927
18	0.0079009532827308	0.0158019065654616	0.99209904671727
19	0.00818063351419734	0.0163612670283947	0.991819366485803
20	0.00719295204310093	0.0143859040862019	0.992807047956899
21	0.00473845692748019	0.00947691385496038	0.99526154307252
22	0.00405827491768405	0.0081165498353681	0.995941725082316
23	0.00244928873912834	0.00489857747825669	0.997550711260872
24	0.00127419485341924	0.00254838970683847	0.99872580514658
25	0.000617315235008265	0.00123463047001653	0.999382684764992
26	0.00028105034362414	0.00056210068724828	0.999718949656376
27	0.000120276164678915	0.000240552329357831	0.999879723835321
28	6.26728633115159e-05	0.000125345726623032	0.999937327136688
29	5.27441511857481e-05	0.000105488302371496	0.999947255848814
30	3.58548924674708e-05	7.17097849349417e-05	0.999964145107533
31	2.78812692165773e-05	5.57625384331546e-05	0.999972118730783
32	1.45281700170890e-05	2.90563400341779e-05	0.999985471829983
33	8.30034695056207e-06	1.66006939011241e-05	0.99999169965305
34	6.76560623678206e-06	1.35312124735641e-05	0.999993234393763
35	4.27770718206606e-06	8.55541436413212e-06	0.999995722292818
36	1.93118332393193e-06	3.86236664786385e-06	0.999998068816676
37	8.75721984740245e-07	1.75144396948049e-06	0.999999124278015
38	6.43131381251995e-07	1.28626276250399e-06	0.999999356868619
39	3.51726586945225e-07	7.0345317389045e-07	0.999999648273413
40	3.19698350180899e-06	6.39396700361798e-06	0.999996803016498
41	6.99883321185139e-06	1.39976664237028e-05	0.999993001166788
42	3.94928057510057e-06	7.89856115020114e-06	0.999996050719425
43	2.36821782852202e-06	4.73643565704404e-06	0.999997631782171
44	2.43961072146233e-06	4.87922144292466e-06	0.999997560389279
45	2.89631760488448e-06	5.79263520976896e-06	0.999997103682395
46	9.58847870474431e-06	1.91769574094886e-05	0.999990411521295
47	2.39219962583601e-05	4.78439925167203e-05	0.999976078003742
48	4.63647264392903e-05	9.27294528785807e-05	0.99995363527356
49	8.22842318976783e-05	0.000164568463795357	0.999917715768102
50	8.68382479638484e-05	0.000173676495927697	0.999913161752036
51	6.90242134638745e-05	0.000138048426927749	0.999930975786536
52	0.000156303055250604	0.000312606110501209	0.99984369694475
53	0.000233163092222457	0.000466326184444914	0.999766836907778
54	0.000237379600558971	0.000474759201117942	0.99976262039944
55	0.000437623616451563	0.000875247232903126	0.999562376383548
56	0.00101316937627049	0.00202633875254098	0.99898683062373
57	0.00147541285097299	0.00295082570194598	0.998524587149027
58	0.00615352668311002	0.0123070533662200	0.99384647331689
59	0.00750370300617507	0.0150074060123501	0.992496296993825
60	0.00636131087681125	0.0127226217536225	0.993638689123189
61	0.00733715076990603	0.0146743015398121	0.992662849230094
62	0.00888990609276702	0.0177798121855340	0.991110093907233
63	0.0256840460341197	0.0513680920682395	0.97431595396588
64	0.161311508653545	0.322623017307089	0.838688491346455
65	0.378779611405421	0.757559222810841	0.62122038859458
66	0.695784642746379	0.608430714507242	0.304215357253621
67	0.871683037875539	0.256633924248922	0.128316962124461
68	0.95624528367655	0.087509432646901	0.0437547163234505
69	0.988499362937142	0.0230012741257155	0.0115006370628577
70	0.99766205914719	0.00467588170561885	0.00233794085280943
71	0.999291812385651	0.00141637522869722	0.000708187614348611
72	0.999852305083643	0.000295389832713169	0.000147694916356584
73	0.999969374445153	6.12511096947673e-05	3.06255548473837e-05
74	0.999992876767177	1.42464656451399e-05	7.12323282256996e-06
75	0.999998130685534	3.73862893208016e-06	1.86931446604008e-06
76	0.999999297931661	1.40413667753727e-06	7.02068338768634e-07
77	0.999999562179329	8.75641342515923e-07	4.37820671257961e-07
78	0.999999584464032	8.31071935920193e-07	4.15535967960096e-07
79	0.999999472218051	1.05556389811456e-06	5.27781949057281e-07
80	0.999999362668235	1.27466353017977e-06	6.37331765089884e-07
81	0.999999203612848	1.59277430462590e-06	7.9638715231295e-07
82	0.99999898521265	2.02957469974918e-06	1.01478734987459e-06
83	0.99999879448179	2.41103642036709e-06	1.20551821018355e-06
84	0.99999968588276	6.28234480159581e-07	3.14117240079791e-07
85	0.999999927411276	1.45177447640092e-07	7.25887238200459e-08
86	0.999999952817983	9.43640336154442e-08	4.71820168077221e-08
87	0.999999934822133	1.3035573479117e-07	6.5177867395585e-08
88	0.999999975792037	4.84159261112242e-08	2.42079630556121e-08
89	0.999999996907562	6.18487627510569e-09	3.09243813755285e-09
90	0.999999999418483	1.16303350765796e-09	5.81516753828979e-10
91	0.99999999944746	1.10508165918326e-09	5.52540829591632e-10
92	0.999999999553546	8.92908118445662e-10	4.46454059222831e-10
93	0.999999999658185	6.836306062013e-10	3.41815303100650e-10
94	0.99999999994169	1.16619021726663e-10	5.83095108633314e-11
95	0.999999999994972	1.00565369558518e-11	5.0282684779259e-12
96	0.999999999994622	1.07570015620056e-11	5.37850078100281e-12
97	0.999999999995685	8.63037439632665e-12	4.31518719816333e-12
98	0.999999999989831	2.03377044008344e-11	1.01688522004172e-11
99	0.99999999996734	6.53210895503978e-11	3.26605447751989e-11
100	0.999999999899761	2.00477861183788e-10	1.00238930591894e-10
101	0.99999999968181	6.36380913404988e-10	3.18190456702494e-10
102	0.999999999131579	1.73684199806065e-09	8.68420999030325e-10
103	0.999999998242456	3.51508765695705e-09	1.75754382847853e-09
104	0.999999993688262	1.26234752767366e-08	6.31173763836831e-09
105	0.999999977066974	4.58660512138252e-08	2.29330256069126e-08
106	0.999999929679193	1.40641614874939e-07	7.03208074374695e-08
107	0.999999775408498	4.491830040018e-07	2.245915020009e-07
108	0.999999589818983	8.20362034704074e-07	4.10181017352037e-07
109	0.99999914874328	1.70251344176004e-06	8.5125672088002e-07
110	0.999998425937336	3.14812532838379e-06	1.57406266419189e-06
111	0.999998005859362	3.98828127691557e-06	1.99414063845779e-06
112	0.999992228294707	1.55434105854535e-05	7.77170529272677e-06
113	0.999978270330297	4.34593394055065e-05	2.17296697027533e-05
114	0.999955438995916	8.9122008167321e-05	4.45610040836605e-05
115	0.999816638732102	0.000366722535795326	0.000183361267897663
116	0.999315423196271	0.00136915360745775	0.000684576803728874
117	0.998050811184074	0.00389837763185158	0.00194918881592579
118	0.992795453747004	0.0144090925059930	0.00720454625299652
119	0.999241542859685	0.0015169142806301	0.00075845714031505
120	0.99471589457329	0.0105682108534191	0.00528410542670957

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	86	0.788990825688073	NOK
5% type I error level	100	0.91743119266055	NOK
10% type I error level	105	0.963302752293578	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/10yllm1291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/10yllm1291653511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/1926s1291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/1926s1291653511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/2ku6d1291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/2ku6d1291653511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/3ku6d1291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/3ku6d1291653511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/4ku6d1291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/4ku6d1291653511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/5d35g1291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/5d35g1291653511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/6d35g1291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/6d35g1291653511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/7nc411291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/7nc411291653511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/8nc411291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/8nc411291653511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/9yllm1291653511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653412plzqkd2zgjq7mdm/9yllm1291653511.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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