Home » date » 2007 » Dec » 19 » attachments

Multiple Regression

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

Title produced by software: Multiple Regression

Date of computation: Wed, 19 Dec 2007 07:16:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq.htm/, Retrieved Wed, 19 Dec 2007 15:03:34 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.8833 18.33 0 0.87 22.6 0 0.8758 24.9 0 0.8858 24.8 0 0.917 23.8 0 0.9554 25.1 0 0.9922 26 0 0.9778 27.4 0 0.9808 27.3 0 0.9811 24.3 0 1.0014 28.4 0 1.0183 24.4 0 1.0622 30.3 0 1.0773 31.5 0 1.0807 29.8 0 1.0848 25.3 0 1.1582 25.6 1 1.1663 26.7 1 1.1372 27.4 1 1.1139 28.6 1 1.1222 26.3 1 1.1692 28.5 1 1.1702 28.4 1 1.2286 29.4 1 1.2613 30.3 1 1.2646 29.6 1 1.2262 32.1 1 1.1985 32.4 1 1.2007 36.3 1 1.2138 34.6 1 1.2266 36.3 1 1.2176 40.3 1 1.2218 40.4 1 1.249 45.4 1 1.2991 39 1 1.3408 35.7 1 1.3119 40.2 1 1.3014 41.7 1 1.3201 49.1 1 1.2938 49.6 1 1.2694 47 1 1.2165 52 1 1.2037 53.1 1 1.2292 57.8 1 1.2256 57.9 1 1.2015 54.6 1 1.1786 51.3 1 1.1856 52.7 1 1.2103 58.5 1 1.1938 56.6 1 1.202 57.9 1 1.2271 64.4 1 1.277 65.1 1 1.265 64.6 1 1.2684 68.9 1 1.2811 68.8 1 1.2727 59.3 1 1.2611 55 1 1.2881 55.4 1 1.3213 58 1 1.2999 50.8 1 1.3074 54.6 1 1.3242 58.6 1 1.3516 63.6 1 1.3511 64.5 1 1.3419 66.9 1 1.3716 71.9 1 1.3622 68.7 1 1.3896 74.2 1 1.4227 75.8 1

Text written by user:

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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Dollarkoers[t] = + 0.921040858135407 + 0.00340081831326493Olieprijs[t] + 0.202137970751832Inval_in_IraK_mei2003[t] -0.0137909931864788M1[t] -0.0208217741230416M2[t] -0.027360595681306M3[t] -0.0296249791833293M4[t] -0.0425949410234984M5[t] -0.0493193108869674M6[t] -0.0502845127022556M7[t] -0.0578022704532755M8[t] -0.0491380915295684M9[t] -0.0361345127022555M10[t] -0.0330043764241018M11[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	0.921040858135407	0.033043	27.874	0	0
Olieprijs	0.00340081831326493	0.000574	5.9241	0	0
Inval_in_IraK_mei2003	0.202137970751832	0.021897	9.2313	0	0
M1	-0.0137909931864788	0.03684	-0.3744	0.709556	0.354778
M2	-0.0208217741230416	0.036861	-0.5649	0.574415	0.287207
M3	-0.027360595681306	0.036949	-0.7405	0.462091	0.231046
M4	-0.0296249791833293	0.037014	-0.8004	0.426879	0.213439
M5	-0.0425949410234984	0.036803	-1.1574	0.252027	0.126014
M6	-0.0493193108869674	0.036843	-1.3386	0.186098	0.093049
M7	-0.0502845127022556	0.036952	-1.3608	0.179022	0.089511
M8	-0.0578022704532755	0.037036	-1.5607	0.124231	0.062115
M9	-0.0491380915295684	0.036969	-1.3292	0.189185	0.094593
M10	-0.0361345127022555	0.036952	-0.9779	0.332335	0.166168
M11	-0.0330043764241018	0.038395	-0.8596	0.393678	0.196839

Multiple Linear Regression - Regression Statistics
Multiple R	0.91626217604825
R-squared	0.839536375256675
Adjusted R-squared	0.80228589094126
F-TEST (value)	22.5375962403061
F-TEST (DF numerator)	13
F-TEST (DF denominator)	56
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0607069438626921
Sum Squared Residuals	0.206378649856291

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	0.8833	0.969586864631072	-0.0862868646310719
2	0.87	0.977077577892152	-0.107077577892152
3	0.8758	0.978360638454397	-0.102560638454397
4	0.8858	0.975756173121047	-0.0899561731210474
5	0.917	0.959385392967613	-0.0423853929676134
6	0.9554	0.957082086911389	-0.00168208691138883
7	0.9922	0.959177621578039	0.0330223784219609
8	0.9778	0.95642100946559	0.0213789905344099
9	0.9808	0.96474510655797	0.0160548934420293
10	0.9811	0.967546230445489	0.0135537695545112
11	1.0014	0.98461972180803	0.0167802781919713
12	1.0183	1.00402082497907	0.0142791750209292
13	1.0622	1.01029465984086	0.051905340159145
14	1.0773	1.00734486088021	0.0699551391197897
15	1.0807	0.995024648189396	0.0856753518106045
16	1.0848	0.97745658227768	0.10734341772232
17	1.1582	1.16764483668332	-0.00944483668332232
18	1.1663	1.16466136696444	0.00163863303555519
19	1.1372	1.16607673796844	-0.0288767379684419
20	1.1139	1.16263996219334	-0.04873996219334
21	1.1222	1.16348225899654	-0.0412822589965376
22	1.1692	1.18396763811303	-0.0147676381130334
23	1.1702	1.18675769255986	-0.0165576925598607
24	1.2286	1.22316288729723	0.00543711270277254
25	1.2613	1.21243263059269	0.0488673694073131
26	1.2646	1.20302127683684	0.0615787231631612
27	1.2262	1.20498450106174	0.0212154989382632
28	1.1985	1.20374036305369	-0.00524036305369301
29	1.2007	1.20403359263526	-0.00333359263525694
30	1.2138	1.19152783163924	0.0222721683607622
31	1.2266	1.1963440209565	0.0302559790435001
32	1.2176	1.20242953645854	0.0151704635414604
33	1.2218	1.21143379721357	0.0103662027864267
34	1.249	1.24144146760721	0.00755853239278926
35	1.2991	1.22280636668047	0.0762936333195309
36	1.3408	1.24458804267080	0.0962119573292035
37	1.3119	1.24610073189401	0.0657992681059902
38	1.3014	1.24417117842734	0.0572288215726554
39	1.3201	1.26279841238724	0.0573015876127594
40	1.2938	1.26223443804185	0.0315655619581502
41	1.2694	1.24042234858719	0.0289776514128082
42	1.2165	1.25070207029005	-0.0342020702900477
43	1.2037	1.25347776861935	-0.0497777686193508
44	1.2292	1.26194385694068	-0.032743856940676
45	1.2256	1.27094811769571	-0.0453481176957097
46	1.2015	1.27272899608925	-0.0712289960892482
47	1.1786	1.26463643193363	-0.0860364319336276
48	1.1856	1.3024019539963	-0.116801953996300
49	1.2103	1.30833570702676	-0.0980357070267583
50	1.1938	1.29484337129499	-0.101043371294992
51	1.202	1.29272561354397	-0.0907256135439722
52	1.2271	1.31256654907817	-0.0854665490781708
53	1.277	1.30197716005729	-0.0249771600572873
54	1.265	1.29355238103719	-0.0285523810371859
55	1.2684	1.30721069796894	-0.0388106979689368
56	1.2811	1.29935285838659	-0.0182528583865905
57	1.2727	1.27570926333428	-0.00300926333428065
58	1.2611	1.27408932341455	-0.0129893234145541
59	1.2881	1.27857978701801	0.00952021298198607
60	1.3213	1.32042629105660	0.000873708943395337
61	1.2999	1.28214940601462	0.0177505939853819
62	1.3074	1.28804173466846	0.0193582653315377
63	1.3242	1.29510618636326	0.0290938136367424
64	1.3516	1.30984589442756	0.041754105572441
65	1.3511	1.29993666906933	0.0511633309306717
66	1.3419	1.30137426315770	0.0405257368423049
67	1.3716	1.31741315290873	0.0541868470912684
68	1.3622	1.29901277655526	0.0631872234447362
69	1.3896	1.32638145620193	0.0632185437980718
70	1.4227	1.34482634433046	0.0778736556695352

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/1uv3a1198073787.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/1uv3a1198073787.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/2x2mq1198073787.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/2x2mq1198073787.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/3dfh11198073787.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/3dfh11198073787.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/4o4fi1198073787.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/4o4fi1198073787.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/57nr61198073787.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/57nr61198073787.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/6whaq1198073787.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/6whaq1198073787.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/7i1411198073787.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/7i1411198073787.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/8ch8n1198073787.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/8ch8n1198073787.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/94rsv1198073787.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/19/t1198073003x5msm8hvb9nryjq/94rsv1198073787.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice)

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))

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')

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()

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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

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

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

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

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

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

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

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

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

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

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

FreeStatistics.org is powered by