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Paper - Multiple Regression - Olie met Trend & Monthly dummies

*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: Sun, 21 Dec 2008 08:09:11 -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/21/t1229874525uvwjpi3ibzqq9hk.htm/, Retrieved Sun, 21 Dec 2008 16:48:46 +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/21/t1229874525uvwjpi3ibzqq9hk.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 «

20.7246301 0 21.44580352 0 22.09413114 0 21.53321848 0 23.3470789 0 23.5656163 0 26.42117166 0 25.21193138 0 26.43574082 0 29.33500366 0 29.40056488 0 33.05013946 0 28.38072368 0 26.0059506 0 29.31314992 0 30.36212944 0 35.74543406 0 36.15337054 0 34.20838768 0 37.90895432 0 38.70297354 0 42.11944156 0 42.16314904 0 39.79566054 0 37.36261082 0 38.3533137 0 42.60022384 0 41.24529196 0 42.15586446 0 46.94183352 0 47.42990038 0 47.0583868 0 50.18347162 0 50.12519498 0 43.22669772 0 40.04333626 0 40.37114236 0 42.2141411 0 36.99838182 0 39.74466848 0 42.68035422 0 46.2935059 0 46.97097184 0 48.72655562 0 52.36884562 1 50.05234918 1 54.03701444 1 57.78128856 1 64.71620872 1 63.4122689 1 64.3592643 1 66.02743312 1 72.13919574 1 76.60464328 1 86.97060062 1 93.48301514 1 95.58825876 1 81.88596378 1 70.5511573 1 50.38015528 1 36.24807008 0

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

Olie[t] = + 17.6500718165444 + 16.2406478298225Dumivariabele[t] + 0.333236249115063M1[t] + 2.89758274094412M2[t] + 3.12699001784616M3[t] + 3.27918074674819M4[t] + 6.15289056365023M5[t] + 8.29377163255228M6[t] + 10.2248567974543M7[t] + 11.7450916503563M8[t] + 10.1177241412939M9[t] + 7.60812933819593M10[t] + 4.22292801909796M11[t] + 0.557327363097962t + 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)	17.6500718165444	4.197969	4.2044	0.000116	5.8e-05
Dumivariabele	16.2406478298225	3.432567	4.7313	2.1e-05	1e-05
M1	0.333236249115063	4.820103	0.0691	0.945176	0.472588
M2	2.89758274094412	5.033216	0.5757	0.56757	0.283785
M3	3.12699001784616	5.028022	0.6219	0.537005	0.268502
M4	3.27918074674819	5.024257	0.6527	0.517149	0.258574
M5	6.15289056365023	5.021925	1.2252	0.226603	0.113301
M6	8.29377163255228	5.021029	1.6518	0.10524	0.05262
M7	10.2248567974543	5.021568	2.0362	0.047389	0.023694
M8	11.7450916503563	5.023542	2.338	0.023694	0.011847
M9	10.1177241412939	5.005302	2.0214	0.048954	0.024477
M10	7.60812933819593	5.0017	1.5211	0.134932	0.067466
M11	4.22292801909796	4.999538	0.8447	0.402578	0.201289
t	0.557327363097962	0.084906	6.5641	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.920083557992498
R-squared	0.846553753688134
Adjusted R-squared	0.804111174921023
F-TEST (value)	19.9458604608662
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	7.54951656745106e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	7.90382360321959
Sum Squared Residuals	2936.11009488812

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	20.7246301	18.5406354287574	2.18399467124262
2	21.44580352	21.6623092836844	-0.216505763684425
3	22.09413114	22.4490439236844	-0.354912783684422
4	21.53321848	23.1585620156844	-1.62534353568442
5	23.3470789	26.5895991956844	-3.24252029568442
6	23.5656163	29.2878076276844	-5.72219132768441
7	26.42117166	31.7762201556844	-5.35504849568441
8	25.21193138	33.8537823716844	-8.64185099168443
9	26.43574082	32.7837422257199	-6.34800140571993
10	29.33500366	30.8314747857199	-1.49647112571992
11	29.40056488	28.0036008297199	1.39696405028008
12	33.05013946	24.3380001737199	8.71213928628008
13	28.38072368	25.2285637859329	3.15215989406706
14	26.0059506	28.3502376408600	-2.34428704085995
15	29.31314992	29.1369722808600	0.17617763914004
16	30.36212944	29.8464903728600	0.51563906714004
17	35.74543406	33.2775275528600	2.46790650714004
18	36.15337054	35.9757359848600	0.177634555140037
19	34.20838768	38.4641485128600	-4.25576083285996
20	37.90895432	40.54171072886	-2.63275640885996
21	38.70297354	39.4716705828955	-0.768697042895461
22	42.11944156	37.5194031428955	4.60003841710453
23	42.16314904	34.6915291868955	7.47161985310454
24	39.79566054	31.0259285308955	8.76973200910454
25	37.36261082	31.9164921431085	5.44611867689152
26	38.3533137	35.0381659980355	3.3151477019645
27	42.60022384	35.8249006380355	6.7753232019645
28	41.24529196	36.5344187300355	4.7108732299645
29	42.15586446	39.9654559100355	2.19040854996450
30	46.94183352	42.6636643420355	4.2781691779645
31	47.42990038	45.1520768700355	2.2778235099645
32	47.0583868	47.2296390860355	-0.171252286035499
33	50.18347162	46.159598940071	4.023872679929
34	50.12519498	44.207331500071	5.917863479929
35	43.22669772	41.379457544071	1.84724017592899
36	40.04333626	37.713856888071	2.32947937192899
37	40.37114236	38.604420500284	1.76672185971597
38	42.2141411	41.7260943552110	0.488046744788953
39	36.99838182	42.5128289952110	-5.51444717521105
40	39.74466848	43.2223470872110	-3.47767860721104
41	42.68035422	46.653384267211	-3.97303004721105
42	46.2935059	49.351592699211	-3.05808679921105
43	46.97097184	51.840005227211	-4.86903338721105
44	48.72655562	53.917567443211	-5.19101182321105
45	52.36884562	69.088175127069	-16.7193295070690
46	50.05234918	67.135907687069	-17.0835585070690
47	54.03701444	64.308033731069	-10.2710192910690
48	57.78128856	60.642433075069	-2.86114451506903
49	64.71620872	61.532996687282	3.18321203271794
50	63.4122689	64.6546705422091	-1.24240164220907
51	64.3592643	65.4414051822091	-1.08214088220907
52	66.02743312	66.1509232742091	-0.123490154209080
53	72.13919574	69.5819604542091	2.55723528579093
54	76.60464328	72.2801688862091	4.32447439379093
55	86.97060062	74.7685814142091	12.2020192057909
56	93.48301514	76.846143630209	16.6368715097909
57	95.58825876	75.7761034842446	19.8121552757554
58	81.88596378	73.8238360442446	8.06212773575542
59	70.5511573	70.9959620882446	-0.444804788244578
60	50.38015528	67.3303614322446	-16.9502061522446
61	36.24807008	51.9802772146351	-15.7322071346351

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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

library(lattice)

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

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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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