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Multiple Regression

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Sat, 20 Dec 2008 12:32:56 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz.htm/, Retrieved Sat, 20 Dec 2008 20:34:05 +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/2008/Dec/20/t12298016356vmefdl2z2xf8zz.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

67,8 0 66,9 0 71,5 0 75,9 0 71,9 0 70,7 0 73,5 0 76,1 0 82,5 0 87,1 0 83,2 0 86,1 0 85,9 0 77,4 0 74,4 0 69,9 0 73,8 0 69,2 0 69,7 0 71 0 71,2 0 75,8 0 73 0 66,4 0 58,6 0 55,5 0 52,6 0 54,9 0 54,6 0 51,2 0 50,9 0 49,6 0 53,4 0 52 0 47,5 0 42,1 0 44,5 0 43,2 0 51,4 0 59,4 0 60,3 0 61,4 0 68,8 0 73,6 0 81,8 0 79,6 0 85,8 0 88,1 0 89,1 0 95 0 96,2 0 84,2 0 96,9 0 103,1 0 99,3 0 103,5 0 112,4 0 111,1 0 113,7 0 92 0 93 0 98,4 0 92,6 0 94,6 0 99,5 0 97,6 0 91,3 0 93,6 0 93,1 1 78,4 1 70,2 1 69,3 1 71,1 1 73,5 1 85,9 1 91,5 1 91,8 1 88,3 1 91,3 1 94 1 99,3 1 96,7 0 88 0 96,7 0 106,8 0 114,3 0 105,7 0 90,1 0 91,6 0 97,7 0 100,8 0 104,6 0 95,9 0 102,7 0 104 0 107,9 0 113,8 0 113,8 0 123,1 0 125,1 0 137,6 0 134 0 140,3 0 152,1 0 150,6 0 167,3 0 153,2 0 142 0 154,4 0 158,5 0 180,9 0 181,3 0 172,4 0 192 0 199,3 0 215,4 0 214,3 0 201,5 0 190,5 0 196 0 215,7 0 209,4 0 214,1 0 237,8 0 239 0 237,8 0 251,5 0 248,8 0 215,4 0 201,2 0 203,1 0 214,2 0 188,9 0 203 0 213,3 0 228,5 0 228,2 0 240,9 0 258,8 0 248,5 0 269,2 0 289,6 0 323,4 0 317,2 0 322,8 0 340,9 0 368,2 0 388,5 0 441,2 0 474,3 0 483,9 0 417,9 0 365,9 0 263 0 199,4 0

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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

X[t] = -1.88729219193178 -53.7578573116923Y[t] + 5.70329025021818M1[t] + 6.87678879336456M2[t] + 11.3349027211265M3[t] + 13.6160935719653M4[t] + 17.843438268958M5[t] + 20.7092445044122M6[t] + 23.7135122783279M7[t] + 19.6485492830129M8[t] + 18.7188060809049M9[t] + 5.26477713853663M10[t] -1.90018585677839M11[t] + 1.70342453377658t + 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)	-1.88729219193178	16.298825	-0.1158	0.907981	0.453991
Y	-53.7578573116923	14.707588	-3.6551	0.000362	0.000181
M1	5.70329025021818	20.259603	0.2815	0.778732	0.389366
M2	6.87678879336456	20.257752	0.3395	0.734765	0.367382
M3	11.3349027211265	20.25631	0.5596	0.576658	0.288329
M4	13.6160935719653	20.255278	0.6722	0.502541	0.25127
M5	17.843438268958	20.254654	0.881	0.379841	0.189921
M6	20.7092445044122	20.25444	1.0225	0.308317	0.154158
M7	23.7135122783279	20.254636	1.1708	0.243666	0.121833
M8	19.6485492830129	20.255241	0.97	0.333684	0.166842
M9	18.7188060809049	20.282901	0.9229	0.357643	0.178822
M10	5.26477713853663	20.257678	0.2599	0.795327	0.397664
M11	-1.90018585677839	20.25951	-0.0938	0.925407	0.462704
t	1.70342453377658	0.091058	18.707	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.851451682561177
R-squared	0.72496996773626
Adjusted R-squared	0.699612588875064
F-TEST (value)	28.5900988309826
F-TEST (DF numerator)	13
F-TEST (DF denominator)	141
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	50.5950278318227
Sum Squared Residuals	360939.814623711

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	67.8	5.51942259206231	62.2805774079377
2	66.9	8.3963456689862	58.5036543310138
3	71.5	14.5578841305244	56.9421158694756
4	75.9	18.5424995151398	57.3575004848602
5	71.9	24.4732687459089	47.4267312540911
6	70.7	29.0424995151397	41.6575004848603
7	73.5	33.7501918228321	39.7498081771679
8	76.1	31.3886533612936	44.7113466387063
9	82.5	32.1623346929623	50.3376653070377
10	87.1	20.4117302843705	66.6882697156295
11	83.2	14.9501918228321	68.249808177168
12	86.1	18.5538022133871	67.5461977866129
13	85.9	25.9605169973818	59.9394830026182
14	77.4	28.8374400743047	48.5625599256953
15	74.4	34.9989785358433	39.4010214641567
16	69.9	38.9835939204587	30.9164060795413
17	73.8	44.9143631512279	28.8856368487721
18	69.2	49.4835939204587	19.7164060795413
19	69.7	54.191286228151	15.508713771849
20	71	51.8297477666125	19.1702522333875
21	71.2	52.6034290982812	18.5965709017188
22	75.8	40.8528246896895	34.9471753103105
23	73	35.391286228151	37.608713771849
24	66.4	38.994896618706	27.4051033812940
25	58.6	46.4016114027008	12.1983885972992
26	55.5	49.2785344796237	6.2214655203763
27	52.6	55.4400729411622	-2.84007294116220
28	54.9	59.4246883257776	-4.52468832577762
29	54.6	65.3554575565469	-10.7554575565469
30	51.2	69.9246883257776	-18.7246883257776
31	50.9	74.6323806334699	-23.7323806334699
32	49.6	72.2708421719315	-22.6708421719315
33	53.4	73.0445235036001	-19.6445235036001
34	52	61.2939190950084	-9.29391909500836
35	47.5	55.8323806334699	-8.33238063346994
36	42.1	59.4359910240249	-17.3359910240249
37	44.5	66.8427058080197	-22.3427058080197
38	43.2	69.7196288849426	-26.5196288849426
39	51.4	75.8811673464811	-24.4811673464811
40	59.4	79.8657827310965	-20.4657827310965
41	60.3	85.7965519618658	-25.4965519618658
42	61.4	90.3657827310965	-28.9657827310966
43	68.8	95.0734750387888	-26.2734750387888
44	73.6	92.7119365772504	-19.1119365772504
45	81.8	93.485617908919	-11.6856179089190
46	79.6	81.7350135003273	-2.13501350032728
47	85.8	76.2734750387888	9.52652496121116
48	88.1	79.8770854293438	8.22291457065617
49	89.1	87.2838002133386	1.81619978666143
50	95	90.1607232902615	4.83927670973848
51	96.2	96.3222617518	-0.122261751800030
52	84.2	100.306877136415	-16.1068771364155
53	96.9	106.237646367185	-9.33764636718466
54	103.1	110.806877136415	-7.70687713641547
55	99.3	115.514569444108	-16.2145694441077
56	103.5	113.153030982569	-9.65303098256926
57	112.4	113.926712314238	-1.52671231423793
58	111.1	102.176107905646	8.9238920943538
59	113.7	96.7145694441078	16.9854305558923
60	92	100.318179834663	-8.31817983466273
61	93	107.724894618657	-14.7248946186575
62	98.4	110.601817695580	-12.2018176955804
63	92.6	116.763356157119	-24.1633561571190
64	94.6	120.747971541734	-26.1479715417344
65	99.5	126.678740772504	-27.1787407725036
66	97.6	131.247971541734	-33.6479715417344
67	91.3	135.955663849427	-44.6556638494266
68	93.6	133.594125387888	-39.9941253878882
69	93.1	80.6099494078644	12.4900505921356
70	78.4	68.8593449992727	9.54065500072732
71	70.2	63.3978065377342	6.80219346226577
72	69.3	67.0014169282892	2.29858307171078
73	71.1	74.408131712284	-3.30813171228398
74	73.5	77.285054789207	-3.78505478920692
75	85.9	83.4465932507454	2.45340674925459
76	91.5	87.4312086353609	4.06879136463912
77	91.8	93.36197786613	-1.56197786613007
78	88.3	97.9312086353609	-9.63120863536086
79	91.3	102.638900943053	-11.3389009430531
80	94	100.277362481515	-6.27736248151467
81	99.3	101.051043813183	-1.75104381318334
82	96.7	143.058296716284	-46.358296716284
83	88	137.596758254746	-49.5967582547456
84	96.7	141.200368645301	-44.5003686453006
85	106.8	148.607083429295	-41.8070834292953
86	114.3	151.484006506218	-37.1840065062183
87	105.7	157.645544967757	-51.9455449677568
88	90.1	161.630160352372	-71.5301603523722
89	91.6	167.560929583141	-75.9609295831414
90	97.7	172.130160352372	-74.4301603523722
91	100.8	176.837852660064	-76.0378526600645
92	104.6	174.476314198526	-69.876314198526
93	95.9	175.249995530195	-79.3499955301946
94	102.7	163.499391121603	-60.7993911216029
95	104	158.037852660065	-54.0378526600645
96	107.9	161.641463050619	-53.7414630506195
97	113.8	169.048177834614	-55.2481778346142
98	113.8	171.925100911537	-58.1251009115372
99	123.1	178.086639373076	-54.9866393730757
100	125.1	182.071254757691	-56.9712547576911
101	137.6	188.002023988460	-50.4020239884603
102	134	192.571254757691	-58.5712547576911
103	140.3	197.278947065383	-56.9789470653834
104	152.1	194.917408603845	-42.8174086038449
105	150.6	195.691089935514	-45.0910899355136
106	167.3	183.940485526922	-16.6404855269218
107	153.2	178.478947065383	-25.2789470653834
108	142	182.082557455938	-40.0825574559384
109	154.4	189.489272239933	-35.0892722399332
110	158.5	192.366195316856	-33.8661953168561
111	180.9	198.527733778395	-17.6277337783946
112	181.3	202.51234916301	-21.21234916301
113	172.4	208.443118393779	-36.0431183937792
114	192	213.01234916301	-21.01234916301
115	199.3	217.720041470702	-18.4200414707023
116	215.4	215.358503009164	0.0414969908361726
117	214.3	216.132184340833	-1.83218434083249
118	201.5	204.381579932241	-2.88157993224076
119	190.5	198.920041470702	-8.4200414707023
120	196	202.523651861257	-6.5236518612573
121	215.7	209.930366645252	5.76963335474793
122	209.4	212.807289722175	-3.407289722175
123	214.1	218.968828183714	-4.86882818371352
124	237.8	222.953443568329	14.8465564316711
125	239	228.884212799098	10.1157872009018
126	237.8	233.453443568329	4.34655643167108
127	251.5	238.161135876021	13.3388641239788
128	248.8	235.799597414483	13.0004025855172
129	215.4	236.573278746151	-21.1732787461514
130	201.2	224.822674337560	-23.6226743375597
131	203.1	219.361135876021	-16.2611358760212
132	214.2	222.964746266576	-8.76474626657622
133	188.9	230.371461050571	-41.4714610505710
134	203	233.248384127494	-30.2483841274939
135	213.3	239.409922589032	-26.1099225890324
136	228.5	243.394537973648	-14.8945379736478
137	228.2	249.325307204417	-21.1253072044171
138	240.9	253.894537973648	-12.9945379736479
139	258.8	258.60223028134	0.197769718659861
140	248.5	256.240691819802	-7.74069181980168
141	269.2	257.014373151470	12.1856268485296
142	289.6	245.263768742879	44.3362312571214
143	323.4	239.80223028134	83.5977697186598
144	317.2	243.405840671895	73.7941593281049
145	322.8	250.81255545589	71.9874445441102
146	340.9	253.689478532813	87.2105214671871
147	368.2	259.851016994351	108.348983005649
148	388.5	263.835632378967	124.664367621033
149	441.2	269.766401609736	171.433598390264
150	474.3	274.335632378967	199.964367621033
151	483.9	279.043324686659	204.856675313341
152	417.9	276.681786225121	141.218213774879
153	365.9	277.455467556789	88.4445324432107
154	263	265.704863148198	-2.70486314819752
155	199.4	260.243324686659	-60.8433246866591

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.00515664397215696	0.0103132879443139	0.994843356027843
18	0.000825998771445238	0.00165199754289048	0.999174001228555
19	0.000143198875084766	0.000286397750169531	0.999856801124915
20	2.56538708562389e-05	5.13077417124777e-05	0.999974346129144
21	8.29535243629215e-06	1.65907048725843e-05	0.999991704647564
22	2.31227852275527e-06	4.62455704551054e-06	0.999997687721477
23	5.33166621952148e-07	1.06633324390430e-06	0.999999466833378
24	3.40986280546667e-07	6.81972561093334e-07	0.99999965901372
25	1.28722914374838e-07	2.57445828749676e-07	0.999999871277086
26	3.18839173774167e-08	6.37678347548334e-08	0.999999968116083
27	9.63970461441931e-09	1.92794092288386e-08	0.999999990360295
28	2.07682323226429e-09	4.15364646452858e-09	0.999999997923177
29	4.20486232197879e-10	8.40972464395758e-10	0.999999999579514
30	8.19636093883434e-11	1.63927218776687e-10	0.999999999918036
31	1.74220270624028e-11	3.48440541248057e-11	0.999999999982578
32	4.76654308754459e-12	9.53308617508917e-12	0.999999999995233
33	1.14415891528161e-12	2.28831783056323e-12	0.999999999998856
34	5.46848769906236e-13	1.09369753981247e-12	0.999999999999453
35	2.61314524269991e-13	5.22629048539982e-13	0.999999999999739
36	1.70468069086631e-13	3.40936138173261e-13	0.99999999999983
37	2.96279913379152e-14	5.92559826758303e-14	0.99999999999997
38	4.89020606396659e-15	9.78041212793317e-15	0.999999999999995
39	1.28776009229568e-15	2.57552018459136e-15	0.999999999999999
40	7.96449903934942e-16	1.59289980786988e-15	1
41	4.43435265060183e-16	8.86870530120367e-16	1
42	3.70954943104163e-16	7.41909886208326e-16	1
43	6.71386330764474e-16	1.34277266152895e-15	1
44	1.50394428939190e-15	3.00788857878379e-15	0.999999999999998
45	4.64357828057482e-15	9.28715656114964e-15	0.999999999999995
46	4.93871642754447e-15	9.87743285508893e-15	0.999999999999995
47	1.76303259711693e-14	3.52606519423385e-14	0.999999999999982
48	8.00432352177206e-14	1.60086470435441e-13	0.99999999999992
49	4.08016598820398e-13	8.16033197640796e-13	0.999999999999592
50	3.60597226461751e-12	7.21194452923502e-12	0.999999999996394
51	1.37837667957233e-11	2.75675335914466e-11	0.999999999986216
52	1.01769875905269e-11	2.03539751810537e-11	0.999999999989823
53	1.72892661089114e-11	3.45785322178228e-11	0.99999999998271
54	4.65335246168401e-11	9.30670492336802e-11	0.999999999953467
55	5.54535026580856e-11	1.10907005316171e-10	0.999999999944547
56	7.44737902449342e-11	1.48947580489868e-10	0.999999999925526
57	1.47059543006969e-10	2.94119086013938e-10	0.99999999985294
58	2.83595936978976e-10	5.67191873957952e-10	0.999999999716404
59	8.90409182172009e-10	1.78081836434402e-09	0.99999999910959
60	7.32403326508487e-10	1.46480665301697e-09	0.999999999267597
61	6.34338388322644e-10	1.26867677664529e-09	0.999999999365662
62	7.26417439510348e-10	1.45283487902070e-09	0.999999999273583
63	5.73073688549135e-10	1.14614737709827e-09	0.999999999426926
64	4.74385877819824e-10	9.48771755639647e-10	0.999999999525614
65	4.28520465127407e-10	8.57040930254813e-10	0.99999999957148
66	3.42278555435881e-10	6.84557110871763e-10	0.999999999657721
67	2.12733039460029e-10	4.25466078920059e-10	0.999999999787267
68	1.68340446004804e-10	3.36680892009607e-10	0.99999999983166
69	8.2666879144041e-11	1.65333758288082e-10	0.999999999917333
70	4.32906036199201e-11	8.65812072398402e-11	0.99999999995671
71	2.43987372206421e-11	4.87974744412842e-11	0.999999999975601
72	1.01421845411765e-11	2.02843690823529e-11	0.999999999989858
73	4.07372037025925e-12	8.14744074051851e-12	0.999999999995926
74	1.58387647209064e-12	3.16775294418128e-12	0.999999999998416
75	7.15083701009718e-13	1.43016740201944e-12	0.999999999999285
76	3.593732609069e-13	7.187465218138e-13	0.99999999999964
77	1.52788372416782e-13	3.05576744833563e-13	0.999999999999847
78	5.8823977428626e-14	1.17647954857252e-13	0.999999999999941
79	2.42053365784135e-14	4.8410673156827e-14	0.999999999999976
80	9.60887458312592e-15	1.92177491662518e-14	0.99999999999999
81	3.54960488858900e-15	7.09920977717799e-15	0.999999999999996
82	2.24231521008743e-15	4.48463042017486e-15	0.999999999999998
83	1.74334187333548e-15	3.48668374667097e-15	0.999999999999998
84	9.00623614829214e-16	1.80124722965843e-15	1
85	6.42481171657278e-16	1.28496234331456e-15	1
86	6.49993091779764e-16	1.29998618355953e-15	1
87	3.05968576245317e-16	6.11937152490635e-16	1
88	1.21287531889454e-16	2.42575063778909e-16	1
89	4.7233510947672e-17	9.4467021895344e-17	1
90	1.57878189700894e-17	3.15756379401788e-17	1
91	5.31669934479374e-18	1.06333986895875e-17	1
92	1.68456895712037e-18	3.36913791424074e-18	1
93	6.89683957094425e-19	1.37936791418885e-18	1
94	2.66664560410606e-19	5.33329120821212e-19	1
95	1.30184290168503e-19	2.60368580337007e-19	1
96	4.7460866517168e-20	9.4921733034336e-20	1
97	1.95288331193131e-20	3.90576662386262e-20	1
98	7.11953794569904e-21	1.42390758913981e-20	1
99	3.42627876024700e-21	6.85255752049401e-21	1
100	1.81105760258473e-21	3.62211520516946e-21	1
101	1.83880039243151e-21	3.67760078486302e-21	1
102	1.39215517837973e-21	2.78431035675945e-21	1
103	1.58682031947650e-21	3.17364063895301e-21	1
104	3.00649529936343e-21	6.01299059872686e-21	1
105	2.86755057052884e-21	5.73510114105768e-21	1
106	3.78809059825684e-20	7.57618119651367e-20	1
107	1.24700962011247e-19	2.49401924022494e-19	1
108	7.53609340331656e-20	1.50721868066331e-19	1
109	8.3642064484121e-20	1.67284128968242e-19	1
110	9.98653931674975e-20	1.99730786334995e-19	1
111	6.98834307725067e-19	1.39766861545013e-18	1
112	2.94230710126133e-18	5.88461420252267e-18	1
113	3.4338639172186e-18	6.8677278344372e-18	1
114	1.54819070621921e-17	3.09638141243842e-17	1
115	8.1853718744572e-17	1.63707437489144e-16	1
116	9.30787542480266e-16	1.86157508496053e-15	1
117	6.03671415718515e-15	1.20734283143703e-14	0.999999999999994
118	3.50858894697759e-14	7.01717789395517e-14	0.999999999999965
119	1.80157533380548e-13	3.60315066761097e-13	0.99999999999982
120	2.7515792150663e-13	5.5031584301326e-13	0.999999999999725
121	1.62746961632796e-12	3.25493923265592e-12	0.999999999998373
122	3.40474096398613e-12	6.80948192797226e-12	0.999999999996595
123	5.21465728557039e-12	1.04293145711408e-11	0.999999999994785
124	2.51083309008252e-11	5.02166618016505e-11	0.999999999974892
125	5.75376540360562e-11	1.15075308072112e-10	0.999999999942462
126	7.8246045040138e-11	1.56492090080276e-10	0.999999999921754
127	1.40554076408410e-10	2.81108152816821e-10	0.999999999859446
128	2.65563715814464e-10	5.31127431628929e-10	0.999999999734436
129	1.51947421335605e-10	3.03894842671209e-10	0.999999999848053
130	1.95441667429651e-10	3.90883334859301e-10	0.999999999804558
131	1.34227898505410e-09	2.68455797010820e-09	0.99999999865772
132	6.09998207256042e-10	1.21999641451208e-09	0.999999999390002
133	1.88295201730055e-10	3.76590403460110e-10	0.999999999811705
134	5.7932432778674e-11	1.15864865557348e-10	0.999999999942068
135	2.07381299218737e-11	4.14762598437474e-11	0.999999999979262
136	9.3163822887565e-12	1.8632764577513e-11	0.999999999990684
137	2.64079078879104e-11	5.28158157758207e-11	0.999999999973592
138	9.97048737921123e-10	1.99409747584225e-09	0.999999999002951

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	121	0.991803278688525	NOK
5% type I error level	122	1	NOK
10% type I error level	122	1	NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/10qpzv1229801569.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/10qpzv1229801569.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/1h0eu1229801569.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/2qngf1229801569.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/2qngf1229801569.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/3hcti1229801569.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/3hcti1229801569.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/4d9kd1229801569.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/4d9kd1229801569.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/5ukms1229801569.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/5ukms1229801569.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/64yvw1229801569.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/64yvw1229801569.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/7zgkn1229801569.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/7zgkn1229801569.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/8wkz01229801569.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/8wkz01229801569.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/9h8zz1229801569.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12298016356vmefdl2z2xf8zz/9h8zz1229801569.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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FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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