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Paper Mult Regression

*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 29 Dec 2010 15:48:33 +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/29/t1293637639mfxh77weasuausm.htm/, Retrieved Wed, 29 Dec 2010 16:47:33 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm.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 «
347553 3,25 110,2 113,2 125,01 353245 2,50 110,1 113,2 120,96 347966 2,50 109,9 113,3 117,07 364343 2,50 109,7 113,7 112,45 341713 2,50 109,5 113,7 110,23 361162 2,50 109,3 113,6 107,34 354400 2,50 109,3 113,5 107,73 345183 2,50 109,1 113,4 103,71 341807 1,75 108,8 113,4 105,28 348712 1,75 108,4 113 106,92 349011 1,75 108,2 112,9 107,8 416259 1,75 108,1 112,6 109,7 360289 1,75 108 112,8 111,51 367557 1,75 108 112,8 106,21 364611 1,75 107,7 113 105,14 378688 1,75 107,5 112,8 103,53 351763 1,75 107,4 112,5 103,99 377765 1,75 107,4 112,4 102,72 373212 1,75 107,4 112 98,5 365819 1,75 107,4 111,9 99,85 364686 1,75 107,4 111,8 98,81 363333 1,75 107 111,6 98,42 362536 1,75 106,9 111,5 97,96 428803 1,75 107 111,4 100,13 375361 1,75 107,2 111,5 99,75 377205 1,75 107,2 111,7 98,24 381266 1,75 107 111,6 90,79 390516 1,00 106,9 111,3 83,67 366117 1,00 106,7 111,1 85,1 393928 1,00 106,6 111,1 84,53 387784 1,00 106,6 111 87,22 385656 1,00 106,3 110,4 94,55 385320 0,50 106,3 110,6 100,49 389 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 time36 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
Banknotes[t] = + 3269476.67732246 -4350.02273157751Loan_Rate[t] + 3544.82921163377PriceIndex_Goods[t] -30586.2510429885PriceIndex_Services[t] + 1600.90213739556Exchange_Rate[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)3269476.67732246107556.07814430.397900
Loan_Rate-4350.022731577516187.202295-0.70310.4827920.241396
PriceIndex_Goods3544.82921163377965.9898573.66960.0003080.000154
PriceIndex_Services-30586.2510429885606.787865-50.406800
Exchange_Rate1600.90213739556204.0751797.844700


Multiple Linear Regression - Regression Statistics
Multiple R0.979531391596487
R-squared0.95948174712295
Adjusted R-squared0.958709970877674
F-TEST (value)1243.21233387848
F-TEST (DF numerator)4
F-TEST (DF denominator)210
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation31166.8968761256
Sum Squared Residuals203988846786.280


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1347553383744.440696359-36191.440696359
2353245380168.82116746-26923.8211674598
3347966370173.720906367-22207.7209063667
4364343349834.08677207814508.9132279221
5341713345571.118184732-3858.11818473168
6361162343294.17026963117867.8297303691
7354400346977.1472075147422.85279248615
8345183342891.1798771562291.82012284439
9341807347603.66451806-5796.66451805963
10348712361045.712755930-12333.7127559305
11349011364804.165898810-15793.1658988104
12416259376667.27235159639591.7276484045
13360289373093.17209052-12804.1720905203
14367557364608.3907623242948.60923767615
15364611355714.7265032238896.2734967773
16378688358545.55842828720142.4415717131
17351763368103.365803222-16340.3658032220
18377765369128.8451930288636.15480697173
19373212374607.538590415-1395.53859041459
20365819379827.381580197-14008.3815801973
21364686381221.068461605-16535.068461605
22363333385296.035151965-21963.035151965
23362536387263.762351898-24727.7623518983
24428803394150.82801550934652.1719844913
25375361391192.825941327-15831.8259413265
26377205382658.213505261-5453.21350526144
27381266373081.1518436378184.84815636311
28390516373766.63806579716749.3619342033
29366117381464.212488543-15347.2124885434
30393928380197.21534906413730.7846509355
31387784387562.267202957221.732797042761
32385656416585.181732369-30929.1817323695
33385320422152.301585690-36832.3015856905
34389053420636.031321857-31583.0313218569
35390595425727.802140648-35132.8021406480
36462440434791.61430392727648.3856960733
37402532446233.015277243-43701.0152772427
38409070451819.683329564-42749.6833295636
39421329451302.825743724-29973.8257437242
40428841453171.312342604-24330.3123426043
41404864460117.364782648-55253.3647826482
42432633462816.036042038-30183.0360420377
43416886470378.667076164-53492.6670761642
44414893482449.410399621-67556.4103996207
45417914485296.731753248-67382.7317532484
46417518479590.245176628-62072.2451766276
47423137479784.637884051-56647.6378840514
48506710492150.87735223814559.1226477622
49436264504298.959716944-68034.9597169441
50443712509583.319199412-65871.3191994122
51452849496756.484991381-43907.4849913807
52453009456444.105775893-3435.10577589297
53437876451768.991127508-13892.9911275083
54460041443037.22112589317003.7788741065
55450426447987.1952032552438.80479674478
56447873460840.576530289-12967.5765302888
57444955458915.405470731-13960.405470731
58452043454596.654444582-2553.65444458201
59480877457923.34441755522953.6555824447
60546696470764.38360321475931.616396786
61483668482257.9001353351410.09986466513
62489627481788.5892064287838.41079357214
63490007469383.95874987420623.0412501259
64496590479208.44856442117381.5514355794
65480846496419.47017798-15573.4701779796
66497677496160.6197703761516.38022962366
67492795502534.014320957-9739.01432095743
68488495520721.586238328-32226.5862383277
69486769510701.742901978-23932.7429019783
70494455490002.9981521474452.00184785327
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80514103521108.350304224-7005.35030422437
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82522150505800.53939791316349.4606020871
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97575265571006.9289850824258.07101491794
98572364569962.476129182401.52387082060
99586744565586.59500078421157.4049992157
100600389590271.96675972810117.0332402719
101578540604873.037482143-26333.0374821432
102610778610633.520318641144.479681359156
103596577611270.69470079-14693.6947007895
104590558636233.210339647-45675.2103396470
105597294635025.000390005-37731.0003900052
106602384627049.819544975-24665.8195449748
107614190631048.408008465-16858.4080084646
108690042647954.35619404542087.6438059547
109639497673727.439384545-34230.4393845445
110649304665928.339909808-16624.3399098083
111678762653038.37163815425723.6283618459
112691885667414.4140394624470.5859605398
113667973675359.398750309-7386.39875030882
114682032673452.9427777458579.05722225513
115672651670362.7212453822288.27875461814
116671865692923.462063462-21058.4620634624
117671463691541.215301556-20078.2153015559
118675917692798.172615416-16881.1726154162
119680952689358.517470952-8406.51747095204
120754718689898.25529579464819.7447042062
121694413711630.615497112-17217.6154971118
122699390707214.890456026-7824.89045602595
123710573684683.88322975725889.116770243
124714217707338.3937251456878.60627485511
125702996714459.162971239-11463.1629712392
126712370712292.47416200977.5258379907291
127708445714044.31084458-5599.31084457947
128707083729561.562665309-22478.5626653091
129700632717617.028676591-16985.0286765915
130706309698751.1265305797557.87346942078
131709523692380.01643093517142.9835690655
132769096696770.57678208172325.4232179186
133715100713558.01221511541.98778490058
134713872708261.7909984475610.2090015535
135714032687815.62343079126216.3765692091
136732269705037.58689184227231.4131081575
137711137722378.063105456-11241.0631054563
138715284718830.913713247-3546.91371324721
139716888714309.9788753532578.0211246472
140716426731187.997512869-14761.9975128686
141714726725235.406419883-10509.4064198832
142718016711255.9226729276760.07732707315
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149734516741460.223789057-6944.22378905728
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151740976747856.059099137-6880.05909913742
152735764761921.05887671-26157.0588767098
153734711750585.348107393-15874.3481073925
154737916748137.83067343-10221.8306734301
155739132753885.06934668-14753.0693466801
156792705761079.49288920531625.5071107947
157747488771620.223513571-24132.2235135710
158746616770472.623283709-23856.6232837090
159749781757309.599626824-7528.59962682395
160760911764170.118171433-3259.11817143277
161739543766153.35612073-26610.356120731
162745626758753.58015847-13127.5801584700
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164744769768917.387723549-24148.3877235489
165741388765318.122772535-23930.1227725349
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167745566760676.90686797-15110.9068679704
168798367769772.73707399728594.2629260029
169752440777727.83826779-25287.8382677903
170756627772938.587929578-16311.5879295776
171758941755983.7106580022957.28934199806
172771287764714.0803657346572.91963426587
173749858765760.618085977-15902.6180859771
174758370763023.55583822-4653.55583822038
175755407757384.273955085-1977.27395508541
176752063762176.863884328-10113.8638843280
177756298749908.9629953216389.03700467872
178755892746023.8201105139868.1798894872
179758486730304.82395754128181.1760424592
180812777724001.41682339188775.5831766086
181762561738983.01931396223577.9806860376
182763579734192.21556364729386.7844363529
183764615719649.63334565744965.3666543435
184773312722502.888165450809.1118345994
185755697720576.77935433135120.2206456692
186762909710188.34783938352720.652160617
187760337715493.2316506444843.7683493603
188759270725919.19305976833350.8069402321
189754929734680.65572550820248.3442744922
190766116745219.37135941820896.6286405823
191765945744729.03782971321215.9621702866
192814783753548.151311261234.8486888004
193768494770952.640547442-2458.64054744215
194769222766408.8612001842813.13879981583
195768977762062.2394184766914.76058152351
196783341779741.6290113833599.37098861726
197764061786235.761972957-22174.7619729568
198767394772935.528341335-5541.52834133473
199763910777591.37083821-13681.3708382104
200761677790015.695060957-28338.6950609566
201759173788065.780926144-28892.7809261440
202762486783308.834991962-20822.8349919623
203762690784606.467745126-21916.4677451258
204809542785537.27543575224004.7245642483
205769041803762.336319616-34721.3363196161
206770889796590.775151274-25701.7751512737
207773527782390.831985081-8863.83198508101
208789890800621.844199881-10731.8441998815
209768325802118.438562342-33793.4385623415
210772712795974.659099562-23262.6590995616
211772944800027.647572792-27083.6475727923
212769637808660.118180848-39023.1181808479
213768546809973.759955385-41427.7599553854
214775013812427.228720284-37414.2287202838
215776635810699.63684096-34064.6368409597


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
80.05156531019859550.1031306203971910.948434689801404
90.01430630356704800.02861260713409600.985693696432952
100.006427730577697410.01285546115539480.993572269422303
110.001827803893288400.003655607786576810.998172196106712
120.1228777807842690.2457555615685380.877122219215731
130.08314116481371370.1662823296274270.916858835186286
140.04717164108099010.09434328216198020.95282835891901
150.02530774118596410.05061548237192820.974692258814036
160.01351391981973970.02702783963947940.98648608018026
170.01546583511149280.03093167022298550.984534164888507
180.008185373481250620.01637074696250120.99181462651875
190.004229521379075930.008459042758151870.995770478620924
200.002339824055651240.004679648111302480.99766017594435
210.001212078871019680.002424157742039360.99878792112898
220.0006822382528688210.001364476505737640.999317761747131
230.0003787841835226550.000757568367045310.999621215816477
240.004996340081120290.009992680162240590.99500365991888
250.00300876607344140.00601753214688280.996991233926559
260.001741302779193410.003482605558386810.998258697220807
270.001053827221863210.002107654443726420.998946172778137
280.0006430318815257790.001286063763051560.999356968118474
290.0004975271996811740.0009950543993623480.999502472800319
300.0003059800859437710.0006119601718875410.999694019914056
310.0001609665543289860.0003219331086579720.999839033445671
320.0001133106391655630.0002266212783311250.999886689360834
336.65948053279565e-050.0001331896106559130.999933405194672
343.62639540203357e-057.25279080406714e-050.99996373604598
351.95918547172399e-053.91837094344798e-050.999980408145283
360.0005264762275743450.001052952455148690.999473523772426
370.0003941798785696720.0007883597571393430.99960582012143
380.0002661711651647900.0005323423303295810.999733828834835
390.0001665966401061610.0003331932802123220.999833403359894
400.000107637023372510.000215274046745020.999892362976627
410.0001107433830554090.0002214867661108190.999889256616945
427.46011495704917e-050.0001492022991409830.99992539885043
436.23710618729556e-050.0001247421237459110.999937628938127
447.42989728444284e-050.0001485979456888570.999925701027156
458.45650772493036e-050.0001691301544986070.99991543492275
469.13930519160155e-050.0001827861038320310.999908606948084
479.11657308452284e-050.0001823314616904570.999908834269155
480.004323350305932130.008646700611864260.995676649694068
490.005315056673360980.01063011334672200.994684943326639
500.006270069601908540.01254013920381710.993729930398092
510.006769719954079620.01353943990815920.99323028004592
520.0095774071219470.0191548142438940.990422592878053
530.008841714698701150.01768342939740230.991158285301299
540.01388547257006090.02777094514012190.98611452742994
550.01420209955904990.02840419911809970.98579790044095
560.01320349705631930.02640699411263870.98679650294368
570.01184682219778430.02369364439556860.988153177802216
580.01099787445248190.02199574890496370.989002125547518
590.0151662374411460.0303324748822920.984833762558854
600.1502281981578070.3004563963156140.849771801842193
610.1349647307823880.2699294615647760.865035269217612
620.1278584012734530.2557168025469060.872141598726547
630.1080339980846390.2160679961692780.891966001915361
640.08951915687361660.1790383137472330.910480843126383
650.08384889825479820.1676977965095960.916151101745202
660.07022043366221860.1404408673244370.929779566337781
670.06183909073909180.1236781814781840.938160909260908
680.06693791789260450.1338758357852090.933062082107395
690.06754566669450960.1350913333890190.93245433330549
700.06662355508530630.1332471101706130.933376444914694
710.06518277263384470.1303655452676890.934817227366155
720.2225652833172530.4451305666345070.777434716682747
730.2297639681179350.4595279362358690.770236031882065
740.2255067644285980.4510135288571960.774493235571402
750.2061213052893330.4122426105786650.793878694710668
760.1899364473553600.3798728947107190.81006355264464
770.1899525040296210.3799050080592420.810047495970379
780.1785548426136810.3571096852273630.821445157386319
790.1772699270930290.3545398541860580.82273007290697
800.2013404901960240.4026809803920480.798659509803976
810.2323990814546830.4647981629093660.767600918545317
820.2621324063475630.5242648126951260.737867593652437
830.2970000357857050.594000071571410.702999964214295
840.9835469871664710.03290602566705690.0164530128335285
850.9867390556720170.02652188865596630.0132609443279832
860.9879348791609990.02413024167800290.0120651208390014
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1960.999716133395220.000567733209558410.000283866604779205
1970.9993514302941760.001297139411648180.000648569705824088
1980.9984551766491520.003089646701696820.00154482335084841
1990.9966128244963970.006774351007205040.00338717550360252
2000.9939963498839470.01200730023210620.00600365011605308
2010.9919697680605830.01606046387883490.00803023193941745
2020.9883375179563540.02332496408729230.0116624820436462
2030.989842666482120.02031466703576080.0101573335178804
2040.9992564081628130.001487183674373530.000743591837186763
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2060.9896838681613850.02063226367723000.0103161318386150
2070.9617376238793330.07652475224133450.0382623761206672


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1400.7NOK
5% type I error level1700.85NOK
10% type I error level1730.865NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/10qnte1293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/10qnte1293637675.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/1j4wk1293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/1j4wk1293637675.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/2cvvn1293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/2cvvn1293637675.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/3cvvn1293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/3cvvn1293637675.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/4cvvn1293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/4cvvn1293637675.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/55nd81293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/55nd81293637675.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/65nd81293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/65nd81293637675.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/7xwct1293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/7xwct1293637675.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/8qnte1293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/8qnte1293637675.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/9qnte1293637675.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637639mfxh77weasuausm/9qnte1293637675.ps (open in new window)


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




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