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*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: Mon, 01 Dec 2008 02:11:10 -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/01/t12281227704x1drj7dz67bsok.htm/, Retrieved Mon, 01 Dec 2008 09:12:50 +0000

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/01/t12281227704x1drj7dz67bsok.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},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

41.1 0 58 0 63 0 53.8 0 54.7 0 55.5 0 56.1 0 69.6 0 69.4 0 57.2 0 68 0 53.3 0 47.9 0 60.8 0 61.7 0 57.8 0 51.4 0 50.5 0 48.1 0 58.7 0 54 0 56.1 0 60.4 0 51.2 0 50.7 0 56.4 0 53.3 0 52.6 0 47.7 0 49.5 0 48.5 0 55.3 0 49.8 0 57.4 0 64.6 0 53 0 41.5 0 55.9 0 58.4 0 53.5 0 50.6 0 58.5 1 49.1 1 61.1 1 52.3 1 58.4 1 65.5 1 61.7 1 45.1 1 52.1 1 59.3 1 57.9 1 45 1 64.9 1 63.8 1 69.4 1 71.1 1 62.9 1 73.5 1 62.6 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

Tabakproductie[t] = + 57.0989753320683 + 6.21726755218216rookverbod[t] -10.8422327640734M1[t] + 0.627375079063883M2[t] + 3.21698292220114M3[t] -0.713409234661608M4[t] -5.86380139152435M5[t] -1.11764705882353M6[t] -3.68803921568627M7[t] + 6.10156862745098M8[t] + 2.69117647058824M9[t] + 1.86078431372549M10[t] + 9.95039215686274M11[t] -0.0896078431372547t + 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)	57.0989753320683	2.824045	20.2189	0	0
rookverbod	6.21726755218216	2.432053	2.5564	0.013943	0.006972
M1	-10.8422327640734	3.25275	-3.3333	0.001702	0.000851
M2	0.627375079063883	3.246872	0.1932	0.847634	0.423817
M3	3.21698292220114	3.242294	0.9922	0.326294	0.163147
M4	-0.713409234661608	3.239019	-0.2203	0.826647	0.413324
M5	-5.86380139152435	3.237053	-1.8115	0.076601	0.038301
M6	-1.11764705882353	3.247041	-0.3442	0.732261	0.36613
M7	-3.68803921568627	3.239844	-1.1383	0.260873	0.130437
M8	6.10156862745098	3.233943	1.8867	0.065518	0.032759
M9	2.69117647058824	3.229346	0.8334	0.408954	0.204477
M10	1.86078431372549	3.226058	0.5768	0.566888	0.283444
M11	9.95039215686274	3.224084	3.0863	0.003427	0.001714
t	-0.0896078431372547	0.06515	-1.3754	0.175664	0.087832

Multiple Linear Regression - Regression Statistics
Multiple R	0.78401888630232
R-squared	0.61468561407873
Adjusted R-squared	0.505792418057501
F-TEST (value)	5.64484868236301
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	5.22449834428063e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.09668393303671
Sum Squared Residuals	1194.90460721063

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	41.1	46.1671347248577	-5.06713472485774
2	58	57.5471347248577	0.45286527514232
3	63	60.0471347248577	2.95286527514232
4	53.8	56.0271347248577	-2.22713472485768
5	54.7	50.7871347248577	3.91286527514232
6	55.5	55.4436812144213	0.0563187855787496
7	56.1	52.7836812144213	3.31631878557875
8	69.6	62.4836812144212	7.11631878557875
9	69.4	58.9836812144213	10.4163187855788
10	57.2	58.0636812144213	-0.863681214421245
11	68	66.0636812144213	1.93631878557875
12	53.3	56.0236812144213	-2.72368121442125
13	47.9	45.0918406072106	2.80815939278939
14	60.8	56.4718406072106	4.32815939278937
15	61.7	58.9718406072106	2.72815939278938
16	57.8	54.9518406072106	2.84815939278937
17	51.4	49.7118406072106	1.68815939278937
18	50.5	54.3683870967742	-3.86838709677419
19	48.1	51.7083870967742	-3.60838709677419
20	58.7	61.4083870967742	-2.70838709677419
21	54	57.9083870967742	-3.90838709677419
22	56.1	56.9883870967742	-0.888387096774191
23	60.4	64.9883870967742	-4.58838709677419
24	51.2	54.9483870967742	-3.74838709677419
25	50.7	44.0165464895636	6.68345351043645
26	56.4	55.3965464895636	1.00345351043643
27	53.3	57.8965464895636	-4.59654648956357
28	52.6	53.8765464895636	-1.27654648956357
29	47.7	48.6365464895636	-0.936546489563567
30	49.5	53.2930929791271	-3.79309297912714
31	48.5	50.6330929791271	-2.13309297912714
32	55.3	60.3330929791271	-5.03309297912714
33	49.8	56.8330929791271	-7.03309297912714
34	57.4	55.9130929791271	1.48690702087286
35	64.6	63.9130929791271	0.686907020872859
36	53	53.8730929791271	-0.873092979127137
37	41.5	42.9412523719165	-1.4412523719165
38	55.9	54.3212523719165	1.57874762808349
39	58.4	56.8212523719165	1.57874762808349
40	53.5	52.8012523719165	0.69874762808349
41	50.6	47.5612523719165	3.03874762808349
42	58.5	58.4350664136622	0.0649335863377607
43	49.1	55.7750664136622	-6.67506641366224
44	61.1	65.4750664136622	-4.37506641366224
45	52.3	61.9750664136622	-9.67506641366224
46	58.4	61.0550664136622	-2.65506641366224
47	65.5	69.0550664136622	-3.55506641366224
48	61.7	59.0150664136622	2.68493358633776
49	45.1	48.0832258064516	-2.9832258064516
50	52.1	59.4632258064516	-7.36322580645161
51	59.3	61.9632258064516	-2.66322580645162
52	57.9	57.9432258064516	-0.0432258064516136
53	45	52.7032258064516	-7.70322580645162
54	64.9	57.3597722960152	7.54022770398482
55	63.8	54.6997722960152	9.10022770398481
56	69.4	64.3997722960152	5.00022770398482
57	71.1	60.8997722960152	10.2002277039848
58	62.9	59.9797722960152	2.92022770398482
59	73.5	67.9797722960152	5.52022770398482
60	62.6	57.9397722960152	4.66022770398482

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 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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