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*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Thu, 02 Dec 2010 14:22:08 +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/02/t12912997451rixv8zjjxwg9jw.htm/, Retrieved Thu, 02 Dec 2010 15:22:36 +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/02/t12912997451rixv8zjjxwg9jw.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 «
84738 428 -26007 -1212617 -2402 -17 40949 263 129352 1367203 2427 29 25830 104 245546 1220017 8870 39 12679 122 48020 984885 7135 62 43556 190 32648 -572920 -3129 -18 6532 62 151352 1151176 9235 146 7123 102 288170 790090 5414 83 17821 277 122844 454195 681 14 13326 103 165548 702380 4925 38 16189 290 116384 264449 218 4 7146 83 134028 450033 2381 35 15824 56 63838 541063 5329 22 11326 64 31080 -37216 -1839 -21 8568 34 32168 783310 15765 68 14416 139 49857 467359 741 19 2220 12 301670 821730 28260 280 18562 211 102313 377934 1148 10 10327 74 88577 651939 4966 44 4069 131 79804 225986 179 6 7710 187 128294 348695 182 19 13718 56 96448 373683 2847 13 4525 89 93811 501709 1335 67 6869 88 117520 413743 2036 31 4628 39 69159 379825 2900 39 4901 58 121920 469107 3204 55 2284 41 76403 211928 361 5 2384 77 61348 423262 2302 94 3748 6 50350 509665 34407 83 5371 47 87720 455881 3877 48 1285 51 99489 367772 1568 131 1528 32 60326 232942 867 22 2675 54 59017 361517 2045 60 13253 251 90829 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R Server'Herman Ole Andreas Wold' @ www.wessa.org


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 112200.404639828 -9.55889135755833Costs[t] + 367.777760278712Orders[t] + 3.34229417014197Dividends[t] + 0.326106031720589`Profit/Trades`[t] -0.0604840098092537`Profit/Cost`[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)112200.40463982827238.0029774.11935.5e-052.8e-05
Costs-9.558891357558332.445302-3.90910.0001266.3e-05
Orders367.777760278712375.1884480.98020.3281190.16406
Dividends3.342294170141970.32657710.234300
`Profit/Trades`0.3261060317205890.5181420.62940.5298040.264902
`Profit/Cost`-0.06048400980925370.607411-0.09960.9207780.460389


Multiple Linear Regression - Regression Statistics
Multiple R0.64654374737574
R-squared0.418018817270664
Adjusted R-squared0.403824154277266
F-TEST (value)29.449013158331
F-TEST (DF numerator)5
F-TEST (DF denominator)205
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation154023.847431686
Sum Squared Residuals4863285843420.16


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1-1212617-628097.372760566-584519.627239434
21367203250621.0541913791116581.94580862
31220017727120.293869742492896.706130258
4984885198692.090449285786192.909550715
5-572920-126168.969871309-446751.030128691
61151176581429.613206373569746.386793627
77900901046535.1819411-256445.181941102
8454195454527.857822369-332.85782236926
9702380577613.616810228124766.383189772
10264449453167.476809822-188718.476809822
11450033523153.465658821-73120.4656588211
12541063196637.92600178344425.07399822
13-37216130754.241761845-167970.241761845
14783310155456.13488028627853.86511972
15467359192397.791322095274961.208677905
168217301112861.7021898-291131.702189799
17377934354703.27899369223230.7210063084
18651939338368.459816706313570.540183294
19225986388270.616332064-162284.616332064
20348695536130.283810954-187435.283810954
21373683324952.31327448548730.6867255151
22501709415653.89943056186055.1005694395
23413743472353.31056065-58610.3105606503
24379825314398.25921637465426.7407836261
25469107495217.410521403-26110.4105214026
26211928360925.508289351-148997.508289351
27423262323518.96852283999743.0314771614
28509665258080.167920617251584.832079383
29455881372592.60834884683288.3916511544
30367772451698.810565288-83926.8105652876
31232942311271.948363669-78329.9483636686
32361517304405.80214695957111.1978530409
33360962381460.584705164-20498.5847051645
34235561379486.972590163-143925.972590163
35450296564522.337436091-114226.337436091
36378519208909.704112466169609.295887534
37326638469844.326983828-143206.326983828
38328233378996.283777479-50763.2837774785
39386225504890.835996638-118665.835996638
40370225497951.77368616-127726.77368616
41269236356402.990092557-87166.9900925565
42365732351716.22157524114015.7784247585
43345811315316.86401892830494.1359810725
44418876581640.177393836-162764.177393836
45297476244133.14605142253342.8539485779
46416776460828.329632345-44052.3296323445
47458343416822.18288341941520.8171165811
48388386463651.589961738-75265.5899617382
49358934465816.739157878-106882.739157878
50407560463469.950462262-55909.9504622624
51392558426874.376825143-34316.3768251429
52428370328965.84100222999404.158997771
53358649236529.145091326122119.854908674
54467427501414.411466967-33987.4114669667
55436230533141.509986334-96911.5099863336
56286849413685.516710042-126836.516710042
57376685463538.905484008-86853.9054840077
58407198493591.46467723-86393.4646772296
59377772340943.17597623736828.8240237635
60271483355920.670926348-84437.670926348
61324881416264.685904128-91383.6859041276
62420968340804.339483980163.6605161003
63191521367105.5621718-175584.5621718
64354624300377.46170781754246.538292183
65363713397390.406606438-33677.4066064379
66456657397122.82160643259534.1783935684
67338381317322.75982865521058.2401713446
68418530414370.8061891814159.1938108186
69351483335701.42075434115781.5792456587
70372928450290.026262225-77362.0262622253
71325314323925.4843233011388.51567669918
72322046311665.27003395910380.7299660405
73325599321991.1515413633607.84845863697
74377028293366.77942792683661.2205720742
75323850335936.35982185-12086.35982185
76331514317616.64086984713897.3591301529
77325632321560.2261515964071.77384840442
78322265311047.265316311217.7346837001
79325906299072.85806320426833.1419367957
80325985330336.3670085-4351.36700849955
81346145328199.0251572917945.9748427103
82325898305220.97450287720677.0254971226
83325356324009.1847636671346.81523633301
84325930356537.964059056-30607.964059056
85318020309664.7520508158355.24794918465
86326389314798.88922244411590.1107775563
87302925309376.637681193-6451.6376811932
88325540329690.211918127-4150.21191812665
89326736338103.157070733-11367.1570707325
90340580320058.0307073420521.9692926601
91331828315045.52242402816782.4775759715
92323299328896.27844157-5597.27844156951
93387722267497.329465757120224.670534243
94324598328671.911268304-4073.91126830426
95328726325210.8530724773515.14692752339
96325043322275.6655097622767.33449023758
97387732351134.66271615636597.3372838438
98332202296963.60956886135238.3904311386
99328451328667.595737449-216.595737448872
100307062338572.027140949-31510.0271409494
101331345321691.8237467969653.17625320357
102331824326520.8975759655303.10242403505
103325685336768.995279782-11083.9952797823
104322741307566.69207057715174.3079294227
105310902320286.738209617-9384.7382096171
106324295324005.552315521289.447684478713
107326156322214.1735390243941.82646097562
108326960315135.95119994111824.0488000591
109333411300237.85370419533173.1462958049
110297761320742.524780904-22981.5247809043
111325536333476.252406657-7940.2524066575
112325762335721.19504183-9959.1950418305
113327957324441.3199295413515.68007045879
114318521338897.389871741-20376.3898717409
115319775329684.368400487-9909.36840048719
116325486352689.660569558-27203.6605695577
117325838322299.5468212993538.45317870066
118331767331726.92392446440.0760755357987
119324523319239.8012960725283.19870392838
120339995344972.321764079-4977.32176407862
121319582326535.069662153-6953.06966215315
122307245294904.94402780212340.0559721984
123317967344889.872968248-26922.8729682478
124331488364815.754422632-33327.7544226321
125335452398787.136287294-63335.1362872935
126334184299590.22110162434593.7788983758
127313213278763.47582511234449.5241748881
128348678362257.917697507-13579.9176975073
129328727312430.90695382716296.0930461728
130387978378771.4681717459206.53182825536
131336704361162.390681515-24458.3906815152
132322076324456.444920821-2380.44492082082
133334272324082.0066073710189.9933926302
134338197333289.6055391224907.39446087785
135322145342571.316027479-20426.3160274788
136323351309506.12160199813844.8783980018
137327748352179.904256144-24431.9042561445
138328157330580.969495052-2423.96949505209
139311594296724.63131673514869.3686832654
140335962326867.1199966729094.8800033281
141372426388656.291555648-16230.2915556476
142319844316912.8916584922931.10834150761
143311464324440.893669147-12976.8936691469
144353417321349.9912767232067.00872328
145325590319988.443345475601.55665453
146326126299398.41151377426727.5884862258
147369376412539.128736447-43163.1287364473
148325871325960.876125347-89.8761253470948
149342165336204.9433116645960.05668833626
150324967352907.699878477-27940.6998784771
151314832322660.370564107-7828.37056410722
152325557318251.4110395117305.58896048895
153322649334967.326617758-12318.3266177584
154324598322606.0539393251991.94606067482
155325567328250.546497647-2683.54649764672
156324005322210.6431937541794.35680624635
157325748356570.125203698-30822.1252036984
158323385317367.113959536017.88604046979
159315409326654.892758486-11245.8927584855
160312275315801.241381886-3526.2413818858
161320576308958.46153849911617.5384615012
162325246322452.9240267452793.07597325455
163332961313050.65904657719910.340953423
164323010338719.209800727-15709.209800727
165345253377003.432781828-31750.4327818281
166325559315514.44780239210044.5521976085
167319951316623.3603157633327.63968423696
168318519311248.3773282397270.62267176097
169343222373923.200494577-30701.2004945769
170317234366477.886749162-49243.8867491624
171314025304345.029374329679.97062568026
172320249314520.5076792695728.4923207311
173349365359983.501123561-10618.501123561
174289197250873.67433338138323.3256666187
175329245327963.6278371011281.37216289872
176240869326027.105631516-85158.1056315161
177327182318309.9357025318872.06429746909
178322876306510.4430061216365.5569938797
179323117327762.716390114-4645.71639011354
180306351307622.910119474-1271.91011947364
181335137326065.0021326059071.9978673952
182308271312786.114121214-4515.1141212143
183301731317639.205549197-15908.2055491966
184382409342669.37815389939739.6218461009
185298731307613.807914121-8882.80791412086
186243650251609.734832198-7959.73483219766
187319771327516.673764519-7745.67376451944
188347262348105.465749713-843.465749713367
189343945327604.97142232616340.0285776738
190311874310946.178686521927.82131347854
191316708329350.482110074-12642.4821100743
192333463344568.464310812-11105.4643108119
193344282340529.3954141363752.60458586425
194319635307660.8002928211974.1997071797
195301186309232.083649938-8046.0836499378
196300381351160.88984963-50779.8898496296
197318765354840.623544312-36075.6235443124
198312448371660.458444228-59212.4584442278
199299715360169.710993394-60454.7109933941
200373399208204.887256343165194.112743657
201325586341763.193417503-16177.193417503
202291221336481.346221694-45260.3462216941
203261173346047.865857355-84874.865857355
204255027355425.022903842-100398.022903842
205-58143240539.430936442-298682.430936442
206227033282688.837938903-55655.8379389034
20721267251056.773918372-229789.773918372
208238675387137.930777243-148462.930777243
209197687301260.586507083-103573.586507083
210418341257807.57029265160533.42970735
211-29770655110.3911066286-352816.391106629


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
913.87188403680054e-271.93594201840027e-27
1011.80489241755293e-279.02446208776465e-28
1111.31035641297382e-266.5517820648691e-27
1212.72818951018991e-271.36409475509495e-27
1314.92127343672458e-282.46063671836229e-28
1418.68346569531875e-404.34173284765938e-40
1511.02588889700918e-415.12944448504592e-42
1612.22365854584213e-541.11182927292106e-54
1719.16030053275391e-544.58015026637696e-54
1814.51609908966401e-582.25804954483201e-58
1911.55068083097424e-597.7534041548712e-60
2015.19568829365494e-602.59784414682747e-60
2112.00952637770705e-601.00476318885353e-60
2212.96837520183669e-601.48418760091835e-60
2311.23049593384702e-596.15247966923511e-60
2413.28501705561148e-591.64250852780574e-59
2511.07071785490377e-585.35358927451887e-59
2612.23990568142306e-591.11995284071153e-59
2715.5672627755991e-592.78363138779955e-59
2814.71483596378643e-642.35741798189321e-64
2912.41231882512028e-641.20615941256014e-64
3019.38699769453655e-644.69349884726827e-64
3111.30101875424217e-636.50509377121085e-64
3217.15483378703779e-633.57741689351889e-63
3312.21370516520976e-621.10685258260488e-62
3411.24365839607946e-626.21829198039732e-63
3515.0847801209458e-622.5423900604729e-62
3611.00262516129606e-625.01312580648031e-63
3711.05718643077449e-625.28593215387247e-63
3815.76070857197284e-622.88035428598642e-62
3911.67058838722775e-618.35294193613875e-62
4015.31712400849589e-612.65856200424794e-61
4111.59722238418518e-607.9861119209259e-61
4218.60314484255331e-604.30157242127666e-60
4314.73771902130104e-592.36885951065052e-59
4411.02490569506642e-585.12452847533209e-59
4515.08132945900714e-582.54066472950357e-58
4612.51435924106698e-571.25717962053349e-57
4711.29877773809361e-566.49388869046806e-57
4816.58402658316374e-563.29201329158187e-56
4911.34784355773223e-556.73921778866116e-56
5016.78997409924704e-553.39498704962352e-55
5113.52857245926358e-541.76428622963179e-54
5216.88303560684969e-543.44151780342484e-54
5318.34504616193585e-544.17252308096793e-54
5412.34744903544973e-531.17372451772486e-53
5515.22557586969015e-532.61278793484507e-53
5613.84914191225206e-531.92457095612603e-53
5711.02749527914009e-525.13747639570043e-53
5812.96147281088386e-521.48073640544193e-52
5911.15931704158358e-515.79658520791792e-52
6011.72559486023556e-518.6279743011778e-52
6114.5305930569e-512.26529652845e-51
6216.63571484551566e-513.31785742275783e-51
6316.55483125401344e-523.27741562700672e-52
6411.93124568450415e-519.65622842252077e-52
6516.32922189508212e-513.16461094754106e-51
6611.27886246918524e-506.39431234592621e-51
6715.36323859258519e-502.68161929629259e-50
6811.40868356845609e-497.04341784228043e-50
6916.01835833925139e-493.0091791696257e-49
7012.26340432309209e-491.13170216154605e-49
7112.47533770098338e-491.23766885049169e-49
7211.17460316900582e-485.87301584502909e-49
7319.28408443734125e-494.64204221867063e-49
7411.22106007703696e-486.10530038518478e-49
7514.550840792091e-482.2754203960455e-48
7611.92437968290355e-479.62189841451775e-48
7719.07403868025372e-474.53701934012686e-47
7814.03615990967349e-462.01807995483674e-46
7911.49855940521158e-457.49279702605792e-46
8016.83355685483329e-453.41677842741664e-45
8112.93850548110219e-441.46925274055109e-44
8211.19212176219238e-435.96060881096189e-44
8311.75772316167222e-438.78861580836112e-44
8414.01569577749098e-432.00784788874549e-43
8511.69793474651162e-428.48967373255812e-43
8617.52951756944098e-423.76475878472049e-42
8713.2603089237348e-411.6301544618674e-41
8811.40870923213407e-407.04354616067035e-41
8915.51569180971058e-402.75784590485529e-40
9012.01594307420397e-391.00797153710198e-39
9117.64970286768989e-393.82485143384495e-39
9213.11977990679273e-381.55988995339636e-38
9311.15295545550466e-385.76477727752328e-39
9414.79906382424969e-382.39953191212485e-38
9511.95656984041119e-379.78284920205596e-38
9617.89832459241512e-373.94916229620756e-37
9712.47542555907562e-361.23771277953781e-36
9817.06742007705009e-363.53371003852505e-36
9912.76924812702804e-351.38462406351402e-35
10019.94196082414099e-354.97098041207049e-35
10113.65011908087206e-341.82505954043603e-34
10211.3800472244675e-336.90023612233751e-34
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13311.74682358011831e-188.73411790059154e-19
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13918.54700981967497e-164.27350490983748e-16
1400.9999999999999992.31214527292907e-151.15607263646454e-15
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1420.9999999999999921.61151690587969e-148.05758452939846e-15
1430.9999999999999794.25569384261315e-142.12784692130658e-14
1440.999999999999959.85064925558446e-144.92532462779223e-14
1450.9999999999998732.5469537978763e-131.27347689893815e-13
1460.9999999999997025.95575139012674e-132.97787569506337e-13
1470.999999999999491.01822067849405e-125.09110339247026e-13
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1500.9999999999921381.57239956744707e-117.86199783723534e-12
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1520.9999999999533739.32538391149662e-114.66269195574831e-11
1530.9999999998879972.24006221517678e-101.12003110758839e-10
1540.9999999997391955.21610352070068e-102.60805176035034e-10
1550.999999999388531.22294087919833e-096.11470439599165e-10
1560.9999999986097452.78050909048336e-091.39025454524168e-09
1570.9999999969314936.13701400927421e-093.06850700463711e-09
1580.9999999931779241.36441524258841e-086.82207621294204e-09
1590.999999984808693.03826194860295e-081.51913097430148e-08
1600.999999966985976.60280614079187e-083.30140307039594e-08
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1620.9999998585328822.82934235957819e-071.41467117978909e-07
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1660.999998075196063.84960788236004e-061.92480394118002e-06
1670.99999613093667.7381268014503e-063.86906340072515e-06
1680.9999926066921571.47866156854934e-057.39330784274668e-06
1690.9999863102204522.73795590953713e-051.36897795476857e-05
1700.999981837474013.63250519808544e-051.81625259904272e-05
1710.999965555197976.88896040596879e-053.44448020298439e-05
1720.9999374053872530.0001251892254934256.25946127467124e-05
1730.9998834475344450.0002331049311091470.000116552465554573
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1780.9985687806574510.002862438685097140.00143121934254857
1790.9990811892119550.001837621576090620.00091881078804531
1800.9983785326166490.003242934766702810.00162146738335141
1810.9974952874661590.005009425067682770.00250471253384139
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1830.993071396922170.01385720615566010.00692860307783007
1840.9886483350667450.02270332986650970.0113516649332548
1850.9818030756809520.03639384863809680.0181969243190484
1860.978312472321780.04337505535644060.0216875276782203
1870.967224237375980.06555152524803820.0327757626240191
1880.9502308637030160.09953827259396740.0497691362969837
1890.9258378152006210.1483243695987580.0741621847993788
1900.8923368559766870.2153262880466250.107663144023313
1910.8504982305552730.2990035388894540.149501769444727
1920.796441877016770.407116245966460.20355812298323
1930.7360297573639470.5279404852721050.263970242636053
1940.6600139429289380.6799721141421250.339986057071062
1950.6343797322604080.7312405354791840.365620267739592
1960.5549825106120620.8900349787758760.445017489387938
1970.500264774472170.999470451055660.49973522552783
1980.398238263880940.796476527761880.60176173611906
1990.2950316112572980.5900632225145950.704968388742702
2000.4026755642817750.805351128563550.597324435718225
2010.2863563717562680.5727127435125360.713643628243732
2020.3937115072798090.7874230145596190.60628849272019


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1740.896907216494845NOK
5% type I error level1780.917525773195876NOK
10% type I error level1800.927835051546392NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/102v9y1291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/102v9y1291299719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/1ecu41291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/1ecu41291299719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/2ecu41291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/2ecu41291299719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/3o3tp1291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/3o3tp1291299719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/4o3tp1291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/4o3tp1291299719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/5o3tp1291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/5o3tp1291299719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/6huas1291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/6huas1291299719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/7smsv1291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/7smsv1291299719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/8smsv1291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/8smsv1291299719.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/9smsv1291299719.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t12912997451rixv8zjjxwg9jw/9smsv1291299719.ps (open in new window)


 
Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 




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