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Paper - Multiple Regression - Olie

*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 07:42:00 -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/t1229870663drqjcx8muxilpi6.htm/, Retrieved Sun, 21 Dec 2008 15:44:23 +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/t1229870663drqjcx8muxilpi6.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 0 50.05234918 0 54.03701444 0 57.78128856 0 64.71620872 0 63.4122689 0 64.3592643 0 66.02743312 0 72.13919574 0 76.60464328 0 86.97060062 0 93.48301514 0 95.58825876 0 81.88596378 1 70.5511573 1 50.38015528 1 36.24807008 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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

Olie[t] = + 13.6376764703529 -10.6174574645Dumivariabele[t] -2.05569877512957M1[t] + 1.03489111847419M2[t] + 0.913405451736769M3[t] + 0.714703236999349M4[t] + 3.23752011026193M5[t] + 5.02750823552451M6[t] + 6.6077004567871M7[t] + 7.77704236604968M8[t] + 9.04691147931226M9[t] + 8.30991522547484M10[t] + 4.57382096273742M11[t] + 0.908220306737418t + 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)	13.6376764703529	4.819144	2.8299	0.006828	0.003414
Dumivariabele	-10.6174574645	5.673239	-1.8715	0.067507	0.033754
M1	-2.05569877512957	5.620344	-0.3658	0.716185	0.358093
M2	1.03489111847419	5.955699	0.1738	0.862797	0.431398
M3	0.913405451736769	5.952662	0.1534	0.878704	0.439352
M4	0.714703236999349	5.950575	0.1201	0.904911	0.452455
M5	3.23752011026193	5.949441	0.5442	0.588895	0.294448
M6	5.02750823552451	5.949259	0.8451	0.402356	0.201178
M7	6.6077004567871	5.95003	1.1105	0.272419	0.13621
M8	7.77704236604968	5.951754	1.3067	0.197679	0.098839
M9	9.04691147931226	5.954428	1.5194	0.135371	0.067686
M10	8.30991522547484	5.86123	1.4178	0.162852	0.081426
M11	4.57382096273742	5.85978	0.7805	0.438984	0.219492
t	0.908220306737418	0.075287	12.0634	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.88835779664841
R-squared	0.789179574866017
Adjusted R-squared	0.73086754238215
F-TEST (value)	13.5337346556107
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	9.11781761203656e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.26436051795151
Sum Squared Residuals	4033.93366290920

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	20.7246301	12.4901980019608	8.23443209803924
2	21.44580352	16.4890082023020	4.95679531769804
3	22.09413114	17.2757428423020	4.81838829769803
4	21.53321848	17.9852609343020	3.54795754569804
5	23.3470789	21.4162981143020	1.93078078569803
6	23.5656163	24.1145065463020	-0.548890246301968
7	26.42117166	26.6029190743020	-0.18174741430197
8	25.21193138	28.6804812903020	-3.46854991030197
9	26.43574082	30.8585707103020	-4.42282989030196
10	29.33500366	31.0297947632020	-1.69479110320196
11	29.40056488	28.2019208072020	1.19864407279804
12	33.05013946	24.5363201512020	8.51381930879804
13	28.38072368	23.3888416828098	4.9918819971902
14	26.0059506	27.387651883151	-1.38170128315098
15	29.31314992	28.174386523151	1.13876339684902
16	30.36212944	28.883904615151	1.47822482484902
17	35.74543406	32.314941795151	3.43049226484902
18	36.15337054	35.013150227151	1.14022031284902
19	34.20838768	37.501562755151	-3.29317507515098
20	37.90895432	39.579124971151	-1.67017065115098
21	38.70297354	41.757214391151	-3.05424085115098
22	42.11944156	41.928438444051	0.191003115949017
23	42.16314904	39.100564488051	3.06258455194902
24	39.79566054	35.434963832051	4.36069670794903
25	37.36261082	34.2874853636588	3.07512545634118
26	38.3533137	38.286295564	0.0670181359999994
27	42.60022384	39.073030204	3.527193636
28	41.24529196	39.782548296	1.46274366400000
29	42.15586446	43.213585476	-1.057721016
30	46.94183352	45.911793908	1.03003961200000
31	47.42990038	48.400206436	-0.970306055999997
32	47.0583868	50.477768652	-3.419381852
33	50.18347162	52.655858072	-2.47238645200000
34	50.12519498	52.8270821249	-2.7018871449
35	43.22669772	49.9992081689	-6.7725104489
36	40.04333626	46.3336075129	-6.2902712529
37	40.37114236	45.1861290445078	-4.81498668450784
38	42.2141411	49.184939244849	-6.97079814484902
39	36.99838182	49.971673884849	-12.9732920648490
40	39.74466848	50.681191976849	-10.9365234968490
41	42.68035422	54.112229156849	-11.4318749368490
42	46.2935059	56.810437588849	-10.5169316888490
43	46.97097184	59.298850116849	-12.3278782768490
44	48.72655562	61.376412332849	-12.6498567128490
45	52.36884562	63.554501752849	-11.1856561328490
46	50.05234918	63.725725805749	-13.6733766257490
47	54.03701444	60.897851849749	-6.86083740974902
48	57.78128856	57.232251193749	0.549037366250974
49	64.71620872	56.0847727253569	8.63143599464312
50	63.4122689	60.083582925698	3.32868597430196
51	64.3592643	60.870317565698	3.48894673430196
52	66.02743312	61.579835657698	4.44759746230196
53	72.13919574	65.010872837698	7.12832290230197
54	76.60464328	67.709081269698	8.89556201030197
55	86.97060062	70.197493797698	16.7731068223020
56	93.48301514	72.275056013698	21.2079591263020
57	95.58825876	74.453145433698	21.1351133263020
58	81.88596378	64.006912022098	17.8790517579020
59	70.5511573	61.179038066098	9.37211923390196
60	50.38015528	57.513437410098	-7.13328213009803
61	36.24807008	56.3659589417059	-20.1178888617059

Charts produced by software:

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Parameters (Session):

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