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Multiple Linear 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: Tue, 16 Dec 2008 12:08:13 -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/16/t1229454752lm5dt7n1mq0ymyc.htm/, Retrieved Tue, 16 Dec 2008 20:12:42 +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/16/t1229454752lm5dt7n1mq0ymyc.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 «
205597 0 205471 0 211064 0 212856 0 217036 0 219302 0 219759 0 221388 0 220834 0 221788 0 222358 0 222972 0 224164 0 224915 0 226294 0 224690 0 227021 0 229284 0 229189 0 230032 0 229389 0 231053 0 232560 0 232681 0 231555 0 231428 0 232141 0 234939 0 235424 0 235471 0 236355 0 238693 0 236958 0 237060 0 239282 0 238252 0 241552 0 236230 0 238909 0 240723 0 242120 0 242100 0 243276 0 244677 0 243494 0 244902 0 245247 0 245578 0 243052 0 238121 0 241863 0 241203 0 243634 0 242351 0 245180 0 246126 0 244424 0 245166 0 247258 0 245094 0 246020 0 243082 0 245555 0 243685 0 247277 0 245029 0 246169 0 246778 0 244577 0 246048 0 245775 0 245328 0 245477 0 241903 0 243219 0 248088 0 248521 0 247389 0 249057 0 248916 0 249193 0 250768 1 253106 1 249829 1 249447 1 246755 1 250785 1 250140 1 255755 1 254671 1 253919 1 253741 1 252729 1 253810 1 256653 1 255231 1 258405 1 251061 1 254811 1 254895 1 258325 1 257608 1 258759 1 258621 1 257852 1 260560 1 262358 1 260812 1 261165 1 257164 1 260720 1 259581 1 264743 1 261845 1 262262 1 261631 1 258953 1 259966 1 262850 1 262204 1 263418 1 262752 1 266433 1 267722 1 266003 1 262971 1 265521 1 264676 1 270223 1 269508 1 268457 1 265814 1 266680 1 263018 1 269285 1 269829 1 270911 1 266844 1 271244 1 269907 1 271296 1 270157 1 271322 1 267179 1 264101 1 265518 1 269419 1 268714 1 272482 1 268351 1 268175 1 270674 1 272764 1 272599 1 270333 1 270846 1 270491 1 269160 1 274027 1 273784 1 276663 1 274525 1 271344 1 271115 1 270798 1 273911 1 273985 1 271917 1 273338 1 270601 1 273547 1 275363 1 281229 1 277793 1 279913 1 282500 1 280041 1 282166 1 290304 1 283519 1 287816 1 285226 1 287595 1 289741 1 289148 1 288301 1 290155 1 289648 1 288225 1 289351 1 294735 1 305333 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
Brutoschuld[t] = + 236649.641975309 + 31611.1147814480Dummy[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)236649.6419753091242.043307190.532500
Dummy31611.11478144801633.52529519.351500


Multiple Linear Regression - Regression Statistics
Multiple R0.814497791870972
R-squared0.663406652962689
Adjusted R-squared0.661635109030913
F-TEST (value)374.479368568561
F-TEST (DF numerator)1
F-TEST (DF denominator)190
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation11178.3897618880
Sum Squared Residuals23741715557.0496


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1205597236649.641975307-31052.6419753074
2205471236649.641975308-31178.6419753082
3211064236649.641975309-25585.6419753087
4212856236649.641975309-23793.6419753087
5217036236649.641975309-19613.6419753087
6219302236649.641975309-17347.6419753087
7219759236649.641975309-16890.6419753087
8221388236649.641975309-15261.6419753087
9220834236649.641975309-15815.6419753087
10221788236649.641975309-14861.6419753087
11222358236649.641975309-14291.6419753087
12222972236649.641975309-13677.6419753087
13224164236649.641975309-12485.6419753087
14224915236649.641975309-11734.6419753087
15226294236649.641975309-10355.6419753087
16224690236649.641975309-11959.6419753087
17227021236649.641975309-9628.64197530865
18229284236649.641975309-7365.64197530865
19229189236649.641975309-7460.64197530865
20230032236649.641975309-6617.64197530865
21229389236649.641975309-7260.64197530865
22231053236649.641975309-5596.64197530865
23232560236649.641975309-4089.64197530865
24232681236649.641975309-3968.64197530865
25231555236649.641975309-5094.64197530865
26231428236649.641975309-5221.64197530865
27232141236649.641975309-4508.64197530865
28234939236649.641975309-1710.64197530865
29235424236649.641975309-1225.64197530865
30235471236649.641975309-1178.64197530865
31236355236649.641975309-294.641975308653
32238693236649.6419753092043.35802469135
33236958236649.641975309308.358024691347
34237060236649.641975309410.358024691347
35239282236649.6419753092632.35802469135
36238252236649.6419753091602.35802469135
37241552236649.6419753094902.35802469135
38236230236649.641975309-419.641975308653
39238909236649.6419753092259.35802469135
40240723236649.6419753094073.35802469135
41242120236649.6419753095470.35802469135
42242100236649.6419753095450.35802469135
43243276236649.6419753096626.35802469135
44244677236649.6419753098027.35802469135
45243494236649.6419753096844.35802469135
46244902236649.6419753098252.35802469135
47245247236649.6419753098597.35802469135
48245578236649.6419753098928.35802469135
49243052236649.6419753096402.35802469135
50238121236649.6419753091471.35802469135
51241863236649.6419753095213.35802469135
52241203236649.6419753094553.35802469135
53243634236649.6419753096984.35802469135
54242351236649.6419753095701.35802469135
55245180236649.6419753098530.35802469135
56246126236649.6419753099476.35802469135
57244424236649.6419753097774.35802469135
58245166236649.6419753098516.35802469135
59247258236649.64197530910608.3580246913
60245094236649.6419753098444.35802469135
61246020236649.6419753099370.35802469135
62243082236649.6419753096432.35802469135
63245555236649.6419753098905.35802469135
64243685236649.6419753097035.35802469135
65247277236649.64197530910627.3580246913
66245029236649.6419753098379.35802469135
67246169236649.6419753099519.35802469135
68246778236649.64197530910128.3580246913
69244577236649.6419753097927.35802469135
70246048236649.6419753099398.35802469135
71245775236649.6419753099125.35802469135
72245328236649.6419753098678.35802469135
73245477236649.6419753098827.35802469135
74241903236649.6419753095253.35802469135
75243219236649.6419753096569.35802469135
76248088236649.64197530911438.3580246913
77248521236649.64197530911871.3580246913
78247389236649.64197530910739.3580246913
79249057236649.64197530912407.3580246913
80248916236649.64197530912266.3580246913
81249193236649.64197530912543.3580246913
82250768268260.756756757-17492.7567567568
83253106268260.756756757-15154.7567567568
84249829268260.756756757-18431.7567567568
85249447268260.756756757-18813.7567567568
86246755268260.756756757-21505.7567567568
87250785268260.756756757-17475.7567567568
88250140268260.756756757-18120.7567567568
89255755268260.756756757-12505.7567567568
90254671268260.756756757-13589.7567567568
91253919268260.756756757-14341.7567567568
92253741268260.756756757-14519.7567567568
93252729268260.756756757-15531.7567567568
94253810268260.756756757-14450.7567567568
95256653268260.756756757-11607.7567567568
96255231268260.756756757-13029.7567567568
97258405268260.756756757-9855.75675675676
98251061268260.756756757-17199.7567567568
99254811268260.756756757-13449.7567567568
100254895268260.756756757-13365.7567567568
101258325268260.756756757-9935.75675675676
102257608268260.756756757-10652.7567567568
103258759268260.756756757-9501.75675675676
104258621268260.756756757-9639.75675675676
105257852268260.756756757-10408.7567567568
106260560268260.756756757-7700.75675675676
107262358268260.756756757-5902.75675675676
108260812268260.756756757-7448.75675675676
109261165268260.756756757-7095.75675675676
110257164268260.756756757-11096.7567567568
111260720268260.756756757-7540.75675675676
112259581268260.756756757-8679.75675675676
113264743268260.756756757-3517.75675675676
114261845268260.756756757-6415.75675675676
115262262268260.756756757-5998.75675675676
116261631268260.756756757-6629.75675675676
117258953268260.756756757-9307.75675675676
118259966268260.756756757-8294.75675675676
119262850268260.756756757-5410.75675675676
120262204268260.756756757-6056.75675675676
121263418268260.756756757-4842.75675675676
122262752268260.756756757-5508.75675675676
123266433268260.756756757-1827.75675675676
124267722268260.756756757-538.756756756764
125266003268260.756756757-2257.75675675676
126262971268260.756756757-5289.75675675676
127265521268260.756756757-2739.75675675676
128264676268260.756756757-3584.75675675676
129270223268260.7567567571962.24324324324
130269508268260.7567567571247.24324324324
131268457268260.756756757196.243243243236
132265814268260.756756757-2446.75675675676
133266680268260.756756757-1580.75675675676
134263018268260.756756757-5242.75675675676
135269285268260.7567567571024.24324324324
136269829268260.7567567571568.24324324324
137270911268260.7567567572650.24324324324
138266844268260.756756757-1416.75675675676
139271244268260.7567567572983.24324324324
140269907268260.7567567571646.24324324324
141271296268260.7567567573035.24324324324
142270157268260.7567567571896.24324324324
143271322268260.7567567573061.24324324324
144267179268260.756756757-1081.75675675676
145264101268260.756756757-4159.75675675676
146265518268260.756756757-2742.75675675676
147269419268260.7567567571158.24324324324
148268714268260.756756757453.243243243236
149272482268260.7567567574221.24324324324
150268351268260.75675675790.2432432432356
151268175268260.756756757-85.7567567567644
152270674268260.7567567572413.24324324324
153272764268260.7567567574503.24324324324
154272599268260.7567567574338.24324324324
155270333268260.7567567572072.24324324324
156270846268260.7567567572585.24324324324
157270491268260.7567567572230.24324324324
158269160268260.756756757899.243243243236
159274027268260.7567567575766.24324324324
160273784268260.7567567575523.24324324324
161276663268260.7567567578402.24324324324
162274525268260.7567567576264.24324324324
163271344268260.7567567573083.24324324324
164271115268260.7567567572854.24324324324
165270798268260.7567567572537.24324324324
166273911268260.7567567575650.24324324324
167273985268260.7567567575724.24324324324
168271917268260.7567567573656.24324324324
169273338268260.7567567575077.24324324324
170270601268260.7567567572340.24324324324
171273547268260.7567567575286.24324324324
172275363268260.7567567577102.24324324324
173281229268260.75675675712968.2432432432
174277793268260.7567567579532.24324324324
175279913268260.75675675711652.2432432432
176282500268260.75675675714239.2432432432
177280041268260.75675675711780.2432432432
178282166268260.75675675713905.2432432432
179290304268260.75675675722043.2432432432
180283519268260.75675675715258.2432432432
181287816268260.75675675719555.2432432432
182285226268260.75675675716965.2432432432
183287595268260.75675675719334.2432432432
184289741268260.75675675721480.2432432432
185289148268260.75675675720887.2432432432
186288301268260.75675675720040.2432432432
187290155268260.75675675721894.2432432432
188289648268260.75675675721387.2432432432
189288225268260.75675675719964.2432432432
190289351268260.75675675721090.2432432432
191294735268260.75675675726474.2432432432
192305333268260.75675675737072.2432432432


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.1762037050136430.3524074100272860.823796294986357
60.1804008574356970.3608017148713950.819599142564303
70.1603816828505490.3207633657010980.839618317149451
80.1527948307719240.3055896615438480.847205169228076
90.1265530072789620.2531060145579230.873446992721038
100.1084884654170990.2169769308341980.891511534582901
110.09330929217043480.1866185843408700.906690707829565
120.0812041317176260.1624082634352520.918795868282374
130.07533272149665490.1506654429933100.924667278503345
140.0714248614145180.1428497228290360.928575138585482
150.07314394032262540.1462878806452510.926856059677375
160.06336231678481730.1267246335696350.936637683215183
170.0639760043892090.1279520087784180.93602399561079
180.07523389335481860.1504677867096370.924766106645181
190.08183124626403280.1636624925280660.918168753735967
200.09043113652678420.1808622730535680.909568863473216
210.0915405439617630.1830810879235260.908459456038237
220.1003558495982740.2007116991965490.899644150401726
230.1167913309111940.2335826618223870.883208669088806
240.1302355262597380.2604710525194750.869764473740262
250.1320000278191230.2640000556382460.867999972180877
260.1307000046723690.2614000093447370.869299995327631
270.1316754030819690.2633508061639370.868324596918032
280.1498002663647290.2996005327294570.850199733635271
290.1683661869715240.3367323739430470.831633813028476
300.1835615732786930.3671231465573850.816438426721307
310.202659910039860.405319820079720.79734008996014
320.2411646840608170.4823293681216340.758835315939183
330.2568911678164600.5137823356329210.74310883218354
340.2695305227308960.5390610454617920.730469477269104
350.2997279963668530.5994559927337060.700272003633147
360.3145727769212650.6291455538425290.685427223078735
370.3602561535586170.7205123071172330.639743846441383
380.3513878330153540.7027756660307070.648612166984646
390.3603047608401010.7206095216802020.639695239159899
400.3822049375441990.7644098750883970.617795062455802
410.4136335829107240.8272671658214490.586366417089276
420.4391995172086370.8783990344172740.560800482791363
430.4717330513770940.9434661027541880.528266948622906
440.513518910974760.972962178050480.48648108902524
450.5360182403805260.9279635192389470.463981759619474
460.5673016702593630.8653966594812740.432698329740637
470.5959699137257600.8080601725484790.404030086274240
480.6220884644435330.7558230711129340.377911535556467
490.6230696773837570.7538606452324870.376930322616244
500.5985589331779010.8028821336441970.401441066822099
510.5890280804608730.8219438390782550.410971919539128
520.5745966150032480.8508067699935040.425403384996752
530.5728478167138960.8543043665722090.427152183286104
540.5614842303146620.8770315393706760.438515769685338
550.5665260620115140.8669478759769720.433473937988486
560.5759717463976330.8480565072047350.424028253602367
570.5708930663601220.8582138672797550.429106933639878
580.5686568686486140.8626862627027710.431343131351386
590.5791793666592990.8416412666814010.420820633340701
600.5722886229008950.855422754198210.427711377099105
610.5694070555778640.8611858888442720.430592944422136
620.5495876505046130.9008246989907750.450412349495387
630.5409215384348510.9181569231302990.459078461565149
640.5216788879188650.956642224162270.478321112081135
650.5208997082081280.9582005835837430.479100291791872
660.5055015618384740.9889968763230530.494498438161526
670.4949061454535990.9898122909071970.505093854546401
680.4864153308864010.9728306617728020.513584669113599
690.4659539992653890.9319079985307780.534046000734611
700.4513812484173990.9027624968347990.548618751582601
710.4346092405580510.8692184811161020.565390759441949
720.4152320818022420.8304641636044840.584767918197758
730.3959902013372780.7919804026745570.604009798662722
740.3675191693877670.7350383387755340.632480830612233
750.3426068381726090.6852136763452180.65739316182739
760.3343392150564080.6686784301128150.665660784943592
770.3270618833479480.6541237666958950.672938116652052
780.3138599619525570.6277199239051140.686140038047443
790.3071469359695800.6142938719391610.69285306403042
800.2987255741144490.5974511482288980.701274425885551
810.2905822162609390.5811644325218770.709417783739061
820.2896585355680990.5793170711361980.710341464431901
830.2817127434814030.5634254869628060.718287256518597
840.2883593688818160.5767187377636320.711640631118184
850.2989377990643210.5978755981286420.701062200935679
860.3293383662720790.6586767325441580.670661633727921
870.3388419543290930.6776839086581860.661158045670907
880.3544462453446830.7088924906893670.645553754655317
890.3497429744936530.6994859489873060.650257025506347
900.3482223795234740.6964447590469480.651777620476526
910.3505708633437660.7011417266875320.649429136656234
920.3552921632141460.7105843264282920.644707836785854
930.3671565254426310.7343130508852620.632843474557369
940.3757946592040730.7515893184081460.624205340795927
950.3743817946893760.7487635893787530.625618205310624
960.3796088481803240.7592176963606470.620391151819676
970.3749673548656190.7499347097312380.625032645134381
980.4118505250993810.8237010501987630.588149474900619
990.4261769285392510.8523538570785020.573823071460749
1000.4428041686180970.8856083372361940.557195831381903
1010.4447040513353090.8894081026706190.55529594866469
1020.4507230437228510.9014460874457010.549276956277149
1030.4532784832853690.9065569665707380.546721516714631
1040.4575570763938190.9151141527876390.542442923606181
1050.4670561196184820.9341122392369630.532943880381518
1060.4666013437453090.9332026874906180.533398656254691
1070.4619329785877630.9238659571755260.538067021412237
1080.4614887923664870.9229775847329740.538511207633513
1090.4605539964190850.921107992838170.539446003580915
1100.482740569712760.965481139425520.51725943028724
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1120.4976669950849870.9953339901699750.502333004915013
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1170.5251224567558440.9497550864883110.474877543244156
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1200.5610837236853530.8778325526292940.438916276314647
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1250.5641086206139290.8717827587721420.435891379386071
1260.5777614587611830.8444770824776340.422238541238817
1270.578892104389370.842215791221260.42110789561063
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Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level60.0327868852459016OK
10% type I error level110.0601092896174863OK
 
Charts produced by software:
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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')
}
 




Copyright

Creative Commons License

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.


Privacy Policy

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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