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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: Wed, 24 Dec 2008 05:53:19 -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/24/t1230123297al3wov3aqbdmgtk.htm/, Retrieved Wed, 24 Dec 2008 13:54:57 +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/24/t1230123297al3wov3aqbdmgtk.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 «

1778.8 0 1264.9 0 1749.1 0 1795.6 0 1759 0 1645.1 0 1589.9 0 1712.6 0 1782.5 0 1606.6 0 1882.1 0 1846.9 0 1873.2 0 1368.3 0 1843.5 0 2074.5 0 1848.5 0 1909.3 0 1932.9 0 2119.1 0 2202 0 2260.8 0 2097.1 0 2026.2 0 2475.2 0 1732.3 0 2385.2 0 2362.2 0 2119 0 2260.3 0 2006.5 0 2073.2 0 2207.8 0 2018.9 0 2082.8 0 2314.3 0 2252.7 0 1633.1 0 2161.1 0 1987.9 0 1870.3 0 1984.6 0 1735.9 0 1910 0 2410.1 0 1994.6 0 2152.3 0 2554 0 2754.5 0 1812.3 0 2549.9 0 2558.4 0 2279.2 0 2591.8 0 2442.4 0 2607.7 0 3106.7 0 2447.5 0 3129.5 0 2606.6 0 2964.4 0 2211.6 0 3246.1 0 3141.8 0 3125.9 0 2890.5 0 2554.3 0 2771.1 0 2950 0 2512.1 0 2800 0 2877.2 0 3048.7 0 2082.7 0 2454.8 0 2807.8 0 2627.6 0 2515.9 0 2690.3 0 2770.8 0 2907.7 0 2906.3 0 3104.6 0 2862.1 0 3189.1 0 2071.8 0 2907.7 0 3194.5 0 2722.9 0 2854.8 0 2803 0 2744.9 0 2574.2 0 2740.9 0 2635.9 0 2612.7 0 3094.2 0 2029 0 2931.1 0 2952.2 0 2601.9 0 2874 0 2570.9 0 2849.8 0 3171.5 0 2843.6 0 2831.5 0 3284.4 0 3230.1 0 2412.2 0 3052.7 0 3048.9 0 2819.9 0 2962.7 0 2796.6 0 2857.2 0 3213.1 0 3116.2 0 3340.1 0 3602 0 3626.4 0 2741.6 1 3756.2 1 3140 1 3421.6 1 3243.7 1 3085.2 1 3152.8 1 3543.6 1 2959.3 1 3594.1 1 3207.9 1 3366.7 1 2658.4 1 3340.4 1 3368.4 1 3422.1 1 3268 1 3234.4 1 3365.1 1 3923.6 1 3147.3 1 3447.7 1 3719.8 1 4090.4 1 3386.7 1 3436.8 1 3744.9 1 3325.8 1 3322.1 1 3338.6 1 3464.2 1 3404.1 1 3942 1 3859.9 1 3895.4 1 4472.2 1 3025.5 1 4285.9 1

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

x[t] = + 1860.37374978546 + 31.8182439467815y[t] + 198.457381864272M1[t] -657.709842997264M2[t] + 20.9885209945413M3[t] + 1.38451663698662M4[t] -182.438547942637M5[t] -165.300074060722M6[t] -295.930830948037M7[t] -183.523126296891M8[t] + 35.0999629696392M9[t] -200.061563148446M10[t] -22.7384738819152M11[t] + 12.0230645796233t + 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)	1860.37374978546	74.918721	24.8319	0	0
y	31.8182439467815	63.352087	0.5022	0.616257	0.308129
M1	198.457381864272	88.133782	2.2518	0.025839	0.01292
M2	-657.709842997264	88.273178	-7.4508	0	0
M3	20.9885209945413	88.242258	0.2379	0.812332	0.406166
M4	1.38451663698662	89.844462	0.0154	0.987726	0.493863
M5	-182.438547942637	89.81554	-2.0313	0.044056	0.022028
M6	-165.300074060722	89.790467	-1.841	0.067672	0.033836
M7	-295.930830948037	89.769246	-3.2966	0.001231	0.000615
M8	-183.523126296891	89.75188	-2.0448	0.042685	0.021342
M9	35.0999629696392	89.73837	0.3911	0.69627	0.348135
M10	-200.061563148446	89.728719	-2.2296	0.027309	0.013655
M11	-22.7384738819152	89.722928	-0.2534	0.800295	0.400147
t	12.0230645796233	0.588561	20.4279	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.939939513213987
R-squared	0.883486288500946
Adjusted R-squared	0.873040231607927
F-TEST (value)	84.5760555919816
F-TEST (DF numerator)	13
F-TEST (DF denominator)	145
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	228.7445591583
Sum Squared Residuals	7586990.63495614

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1778.8	2070.85419622936	-292.054196229358
2	1264.9	1226.71003594744	38.1899640525580
3	1749.1	1917.43146451887	-168.331464518871
4	1795.6	1909.85052474094	-114.250524740939
5	1759	1738.05052474094	20.9494752590602
6	1645.1	1767.21206320248	-122.112063202478
7	1589.9	1648.60437089479	-58.7043708947854
8	1712.6	1773.03514012555	-60.435140125555
9	1782.5	2003.68129397171	-221.181293971709
10	1606.6	1780.54283243325	-173.942832433247
11	1882.1	1969.8889862794	-87.7889862794011
12	1846.9	2004.65052474094	-157.750524740939
13	1873.2	2215.13097118483	-341.930971184835
14	1368.3	1370.98681090292	-2.68681090292151
15	1843.5	2061.70823947435	-218.208239474351
16	2074.5	2054.12729969642	20.3727003035804
17	1848.5	1882.32729969642	-33.8272996964194
18	1909.3	1911.48883815796	-2.18883815795797
19	1932.9	1792.88114585027	140.018854149734
20	2119.1	1917.31191508103	201.788084918965
21	2202	2147.95806892719	54.0419310728112
22	2260.8	1924.81960738873	335.980392611273
23	2097.1	2114.16576123488	-17.0657612348812
24	2026.2	2148.92729969642	-122.727299696420
25	2475.2	2359.40774614031	115.792253859685
26	1732.3	1515.26358585840	217.036414141597
27	2385.2	2205.98501442983	179.214985570169
28	2362.2	2198.4040746519	163.795925348100
29	2119	2026.6040746519	92.3959253481005
30	2260.3	2055.76561311344	204.534386886562
31	2006.5	1937.15792080575	69.3420791942541
32	2073.2	2061.58869003651	11.6113099634849
33	2207.8	2292.23484388267	-84.4348438826686
34	2018.9	2069.09638234421	-50.1963823442072
35	2082.8	2258.44253619036	-175.642536190361
36	2314.3	2293.2040746519	21.0959253481005
37	2252.7	2503.68452109580	-250.984521095795
38	1633.1	1659.54036081388	-26.4403608138824
39	2161.1	2350.26178938531	-189.161789385311
40	1987.9	2342.68084960738	-354.78084960738
41	1870.3	2170.88084960738	-300.580849607380
42	1984.6	2200.04238806892	-215.442388068918
43	1735.9	2081.43469576123	-345.534695761226
44	1910	2205.86546499199	-295.865464991995
45	2410.1	2436.51161883815	-26.4116188381489
46	1994.6	2213.37315729969	-218.773157299687
47	2152.3	2402.71931114584	-250.419311145841
48	2554	2437.48084960738	116.519150392620
49	2754.5	2647.96129605127	106.538703948725
50	1812.3	1803.81713576936	8.48286423063748
51	2549.9	2494.53856434079	55.3614356592092
52	2558.4	2486.95762456286	71.4423754371405
53	2279.2	2315.15762456286	-35.9576245628599
54	2591.8	2344.3191630244	247.480836975602
55	2442.4	2225.71147071671	216.688529283294
56	2607.7	2350.14223994747	257.557760052525
57	3106.7	2580.78839379363	525.911606206371
58	2447.5	2357.64993225517	89.8500677448326
59	3129.5	2546.99608610132	582.503913898679
60	2606.6	2581.75762456286	24.8423754371402
61	2964.4	2792.23807100676	172.161928993245
62	2211.6	1948.09391072484	263.506089275157
63	3246.1	2638.81533929627	607.284660703729
64	3141.8	2631.23439951834	510.56560048166
65	3125.9	2459.43439951834	666.46560048166
66	2890.5	2488.59593797988	401.904062020122
67	2554.3	2369.98824567219	184.311754327814
68	2771.1	2494.41901490296	276.680985097045
69	2950	2725.06516874911	224.934831250891
70	2512.1	2501.92670721065	10.1732927893524
71	2800	2691.2728610568	108.727138943199
72	2877.2	2726.03439951834	151.16560048166
73	3048.7	2936.51484596224	112.185154037765
74	2082.7	2092.37068568032	-9.67068568032276
75	2454.8	2783.09211425175	-328.292114251751
76	2807.8	2775.51117447382	32.2888255261804
77	2627.6	2603.71117447382	23.8888255261802
78	2515.9	2632.87271293536	-116.972712935358
79	2690.3	2514.26502062767	176.034979372334
80	2770.8	2638.69578985844	132.104210141565
81	2907.7	2869.34194370459	38.3580562954109
82	2906.3	2646.20348216613	260.096517833873
83	3104.6	2835.54963601228	269.050363987718
84	2862.1	2870.31117447382	-8.21117447382002
85	3189.1	3080.79162091772	108.308379082285
86	2071.8	2236.64746063580	-164.847460635802
87	2907.7	2927.36888920723	-19.6688892072313
88	3194.5	2919.7879494293	274.7120505707
89	2722.9	2747.9879494293	-25.0879494292996
90	2854.8	2777.14948789084	77.6505121091618
91	2803	2658.54179558315	144.458204416854
92	2744.9	2782.97256481392	-38.072564813915
93	2574.2	3013.61871866007	-439.418718660069
94	2740.9	2790.48025712161	-49.5802571216073
95	2635.9	2979.82641096776	-343.926410967761
96	2612.7	3014.5879494293	-401.8879494293
97	3094.2	3225.06839587320	-130.868395873195
98	2029	2380.92423559128	-351.924235591283
99	2931.1	3071.64566416271	-140.545664162711
100	2952.2	3064.06472438478	-111.86472438478
101	2601.9	2892.26472438478	-290.364724384780
102	2874	2921.42626284632	-47.4262628463183
103	2570.9	2802.81857053863	-231.918570538626
104	2849.8	2927.24933976940	-77.4493397693951
105	3171.5	3157.89549361555	13.6045063844511
106	2843.6	2934.75703207709	-91.1570320770877
107	2831.5	3124.10318592324	-292.603185923241
108	3284.4	3158.86472438478	125.535275615221
109	3230.1	3369.34517082868	-139.245170828675
110	2412.2	2525.20101054676	-113.001010546763
111	3052.7	3215.92243911819	-163.222439118191
112	3048.9	3208.34149934026	-159.44149934026
113	2819.9	3036.54149934026	-216.64149934026
114	2962.7	3065.7030378018	-103.003037801798
115	2796.6	2947.09534549411	-150.495345494106
116	2857.2	3071.52611472488	-214.326114724875
117	3213.1	3302.17226857103	-89.0722685710288
118	3116.2	3079.03380703257	37.1661929674326
119	3340.1	3268.37996087872	71.7200391212786
120	3602	3303.14149934026	298.85850065974
121	3626.4	3513.62194578416	112.778054215845
122	2741.6	2701.29602944902	40.303970550976
123	3756.2	3392.01745802045	364.182541979548
124	3140	3384.43651824252	-244.436518242521
125	3421.6	3212.63651824252	208.963481757479
126	3243.7	3241.79805670406	1.90194329594045
127	3085.2	3123.19036439637	-37.9903643963674
128	3152.8	3247.62113362714	-94.821133627136
129	3543.6	3478.26728747329	65.3327125267097
130	2959.3	3255.12882593483	-295.828825934829
131	3594.1	3444.47497978098	149.625020219018
132	3207.9	3479.23651824252	-271.336518242521
133	3366.7	3689.71696468642	-323.016964686417
134	2658.4	2845.57280440450	-187.172804404504
135	3340.4	3536.29423297593	-195.894232975932
136	3368.4	3528.713293198	-160.313293198001
137	3422.1	3356.913293198	65.1867068019989
138	3268	3386.07483165954	-118.074831659539
139	3234.4	3267.46713935185	-33.0671393518472
140	3365.1	3391.89790858262	-26.7979085826166
141	3923.6	3622.54406242877	301.055937571230
142	3147.3	3399.40560089031	-252.105600890309
143	3447.7	3588.75175473646	-141.051754736463
144	3719.8	3623.513293198	96.286706801999
145	4090.4	3833.9937396419	256.406260358104
146	3386.7	2989.84957935998	396.850420640016
147	3436.8	3680.57100793141	-243.771007931412
148	3744.9	3672.99006815348	71.909931846519
149	3325.8	3501.19006815348	-175.390068153481
150	3322.1	3530.35160661502	-208.251606615020
151	3338.6	3411.74391430733	-73.1439143073275
152	3464.2	3536.17468353810	-71.9746835380966
153	3404.1	3766.82083738425	-362.720837384251
154	3942	3543.68237584579	398.317624154211
155	3859.9	3733.02852969194	126.871470308058
156	3895.4	3767.79006815348	127.609931846519
157	4472.2	3978.27051459738	493.929485402623
158	3025.5	3134.12635431546	-108.626354315464
159	4285.9	3824.84778288689	461.052217113107

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.0308743423764285	0.0617486847528571	0.969125657623572
18	0.0161746386238728	0.0323492772477457	0.983825361376127
19	0.0150256707909269	0.0300513415818537	0.984974329209073
20	0.0170713990096017	0.0341427980192034	0.982928600990398
21	0.0150316963518565	0.030063392703713	0.984968303648143
22	0.0583002690512841	0.116600538102568	0.941699730948716
23	0.0318648691973671	0.0637297383947341	0.968135130802633
24	0.017936153671244	0.035872307342488	0.982063846328756
25	0.0195220260257392	0.0390440520514784	0.98047797397426
26	0.0103263762545408	0.0206527525090816	0.98967362374546
27	0.00698311513234517	0.0139662302646903	0.993016884867655
28	0.0035300123065083	0.0070600246130166	0.996469987693492
29	0.0022990441434188	0.0045980882868376	0.997700955856581
30	0.00114662546081689	0.00229325092163377	0.998853374539183
31	0.00103106239209432	0.00206212478418864	0.998968937607906
32	0.00146353537518671	0.00292707075037342	0.998536464624813
33	0.00121841187189720	0.00243682374379440	0.998781588128103
34	0.00201778514824267	0.00403557029648535	0.997982214851757
35	0.00266056329796591	0.00532112659593182	0.997339436702034
36	0.00146372509450028	0.00292745018900055	0.9985362749055
37	0.00201082148165198	0.00402164296330395	0.997989178518348
38	0.00234538487953296	0.00469076975906593	0.997654615120467
39	0.00270899180646573	0.00541798361293145	0.997291008193534
40	0.0136952499583442	0.0273904999166883	0.986304750041656
41	0.0277443309191072	0.0554886618382145	0.972255669080893
42	0.0323555663290591	0.0647111326581181	0.96764443367094
43	0.0644810549051568	0.128962109810314	0.935518945094843
44	0.0906682708431166	0.181336541686233	0.909331729156883
45	0.0737340452756738	0.147468090551348	0.926265954724326
46	0.079505252225853	0.159010504451706	0.920494747774147
47	0.0821225287324079	0.164245057464816	0.917877471267592
48	0.080117549658113	0.160235099316226	0.919882450341887
49	0.098062543340385	0.19612508668077	0.901937456659615
50	0.0777352150046527	0.155470430009305	0.922264784995347
51	0.0690529679970562	0.138105935994112	0.930947032002944
52	0.0585962494539301	0.117192498907860	0.94140375054607
53	0.048167729680744	0.096335459361488	0.951832270319256
54	0.0497189905022923	0.0994379810045846	0.950281009497708
55	0.047589995173663	0.095179990347326	0.952410004826337
56	0.0470321790119612	0.0940643580239224	0.952967820988039
57	0.116568139889433	0.233136279778867	0.883431860110567
58	0.0938994825940779	0.187798965188156	0.906100517405922
59	0.243194685483897	0.486389370967794	0.756805314516103
60	0.209882405788841	0.419764811577682	0.790117594211159
61	0.188350441070455	0.376700882140911	0.811649558929545
62	0.163398190700247	0.326796381400494	0.836601809299753
63	0.308271996982315	0.61654399396463	0.691728003017685
64	0.395875165489383	0.791750330978767	0.604124834510617
65	0.629184248313446	0.741631503373108	0.370815751686554
66	0.656931824790163	0.686136350419673	0.343068175209837
67	0.620877370735676	0.758245258528648	0.379122629264324
68	0.607642171074672	0.784715657850655	0.392357828925328
69	0.589418781042769	0.821162437914463	0.410581218957231
70	0.559087824574287	0.881824350851426	0.440912175425713
71	0.521335584921765	0.957328830156469	0.478664415078234
72	0.482134676463818	0.964269352927636	0.517865323536182
73	0.435260258233724	0.870520516467447	0.564739741766276
74	0.439306929189921	0.878613858379842	0.560693070810079
75	0.587981454303044	0.824037091393912	0.412018545696956
76	0.561763234488345	0.87647353102331	0.438236765511655
77	0.539718838589584	0.920562322820833	0.460281161410416
78	0.549488969695135	0.90102206060973	0.450511030304865
79	0.529572620625318	0.940854758749363	0.470427379374682
80	0.511825852173509	0.976348295652982	0.488174147826491
81	0.490833806377128	0.981667612754257	0.509166193622872
82	0.505898073258861	0.988203853482278	0.494101926741139
83	0.54443507040753	0.91112985918494	0.45556492959247
84	0.51109900925949	0.97780198148102	0.48890099074051
85	0.47631857497706	0.95263714995412	0.52368142502294
86	0.491916240400988	0.983832480801976	0.508083759599012
87	0.456410841353243	0.912821682706485	0.543589158646757
88	0.534736345450269	0.930527309099462	0.465263654549731
89	0.523905124330112	0.952189751339776	0.476094875669888
90	0.529723559653436	0.940552880693127	0.470276440346564
91	0.568547632045151	0.862904735909698	0.431452367954849
92	0.571001013551117	0.857997972897767	0.428998986448884
93	0.693882640441267	0.612234719117466	0.306117359558733
94	0.672719995659665	0.654560008680671	0.327280004340335
95	0.713765983169358	0.572468033661285	0.286234016830642
96	0.780604869563831	0.438790260872338	0.219395130436169
97	0.750602900106557	0.498794199786887	0.249397099893443
98	0.784718816079722	0.430562367840556	0.215281183920278
99	0.755213374962853	0.489573250074295	0.244786625037147
100	0.73088072255499	0.538238554890021	0.269119277445010
101	0.735146498573033	0.529707002853934	0.264853501426967
102	0.705643400815676	0.588713198368647	0.294356599184324
103	0.686071601294602	0.627856797410797	0.313928398705398
104	0.650415031948067	0.699169936103865	0.349584968051933
105	0.609045890903431	0.781908218193138	0.390954109096569
106	0.56146468729479	0.87707062541042	0.43853531270521
107	0.567643274155075	0.86471345168985	0.432356725844925
108	0.533905467730304	0.932189064539392	0.466094532269696
109	0.500644090127391	0.99871181974522	0.49935590987261
110	0.451838432140106	0.903676864280213	0.548161567859893
111	0.425350769210798	0.850701538421596	0.574649230789202
112	0.381550897955203	0.763101795910406	0.618449102044797
113	0.370185621282264	0.740371242564527	0.629814378717736
114	0.321159442446528	0.642318884893056	0.678840557553472
115	0.283192872821885	0.56638574564377	0.716807127178115
116	0.263034019742799	0.526068039485599	0.7369659802572
117	0.230227509738374	0.460455019476747	0.769772490261626
118	0.187676489122260	0.375352978244519	0.81232351087774
119	0.154511324691519	0.309022649383037	0.845488675308481
120	0.154136472313399	0.308272944626797	0.845863527686601
121	0.123764959849788	0.247529919699577	0.876235040150212
122	0.097106275447027	0.194212550894054	0.902893724552973
123	0.142123895044577	0.284247790089154	0.857876104955423
124	0.127999545970684	0.255999091941369	0.872000454029316
125	0.140718937996170	0.281437875992340	0.85928106200383
126	0.137309655390582	0.274619310781164	0.862690344609418
127	0.113760346412104	0.227520692824207	0.886239653587896
128	0.08981270245631	0.17962540491262	0.91018729754369
129	0.0833768428477677	0.166753685695535	0.916623157152232
130	0.0694366428961155	0.138873285792231	0.930563357103884
131	0.0767782972283243	0.153556594456649	0.923221702771676
132	0.060016355058883	0.120032710117766	0.939983644941117
133	0.0982813856854654	0.196562771370931	0.901718614314535
134	0.0774996797797916	0.154999359559583	0.922500320220208
135	0.0608509330165447	0.121701866033089	0.939149066983455
136	0.0432908484371088	0.0865816968742176	0.956709151562891
137	0.0335049648085557	0.0670099296171114	0.966495035191444
138	0.0207214381307402	0.0414428762614805	0.97927856186926
139	0.0114610232867659	0.0229220465735318	0.988538976713234
140	0.00590372330545338	0.0118074466109068	0.994096276694547
141	0.0447056939928583	0.0894113879857166	0.955294306007142
142	0.0522404704876393	0.104480940975279	0.94775952951236

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	12	0.0952380952380952	NOK
5% type I error level	24	0.190476190476190	NOK
10% type I error level	35	0.277777777777778	NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/10spdt1230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/10spdt1230123185.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/1ok661230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/1ok661230123185.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/2dn0h1230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/2dn0h1230123185.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/3y46n1230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/3y46n1230123185.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/4zprv1230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/4zprv1230123185.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/513rz1230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/513rz1230123185.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/619v31230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/619v31230123185.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/7vjvs1230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/7vjvs1230123185.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/8p0wv1230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/8p0wv1230123185.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/995ez1230123185.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230123297al3wov3aqbdmgtk/995ez1230123185.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

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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