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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, 22 Dec 2008 15:28:47 -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/22/t12299849792azx7bro2gwa44a.htm/, Retrieved Mon, 22 Dec 2008 23:29:39 +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/22/t12299849792azx7bro2gwa44a.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 «

17,3 0 15,4 0 16,9 0 20,8 0 16,4 0 11,3 0 17,5 0 16,6 0 17,5 0 19,5 0 18,8 0 20,2 0 19,2 0 14,4 0 24,5 0 25,7 0 27,1 0 21 0 18,6 0 20 0 21,8 0 20,4 0 18 1 21,5 1 19,1 1 19,7 1 26 1 26,3 1 24,6 1 22,4 1 32 1 24 1 30 1 24,1 1 26,3 1 29,8 1 21,9 1 22,8 1 29,2 1 27,5 1 27,4 1 31 1 26,1 1 22,2 1 34 1 26,9 1 31,9 1 34,2 1 31,2 1 28,5 1 37,1 1 36 1 34,8 1 32,1 1 37,2 1 36,3 1 39,5 1 37,1 1 35,6 1 36,2 1 35,9 1 32,5 1 39,2 1 39,4 1 42,8 1 34,5 1 43,7 1 46,3 1 40,8 1 48,4 1 43,2 1 48,1 1 42,8 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	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 15.5292371134021 -3.9141443298969x[t] -3.05177712322042M1[t] -5.48349631811487M2[t] + 0.654617574864998M3[t] + 0.659398134511537M4[t] -0.235821305841926M5[t] -4.16437407952872M6[t] -0.826260186548845M7[t] -2.90481296023564M8[t] -0.333365733922435M9[t] -1.99525184094256M10[t] -2.23811389297987M11[t] + 0.461886107020128t + 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)	15.5292371134021	1.391937	11.1566	0	0
x	-3.9141443298969	1.253735	-3.122	0.002781	0.001391
M1	-3.05177712322042	1.63822	-1.8629	0.067462	0.033731
M2	-5.48349631811487	1.705414	-3.2153	0.002115	0.001057
M3	0.654617574864998	1.703921	0.3842	0.702224	0.351112
M4	0.659398134511537	1.702866	0.3872	0.69998	0.34999
M5	-0.235821305841926	1.702249	-0.1385	0.890289	0.445145
M6	-4.16437407952872	1.702071	-2.4467	0.017418	0.008709
M7	-0.826260186548845	1.702332	-0.4854	0.629212	0.314606
M8	-2.90481296023564	1.703032	-1.7057	0.093329	0.046665
M9	-0.333365733922435	1.70417	-0.1956	0.845582	0.422791
M10	-1.99525184094256	1.705745	-1.1697	0.246816	0.123408
M11	-2.23811389297987	1.69761	-1.3184	0.192468	0.096234
t	0.461886107020128	0.027336	16.8964	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.956071854573462
R-squared	0.914073391107539
Adjusted R-squared	0.895140409487166
F-TEST (value)	48.2794210355095
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.93996566100965
Sum Squared Residuals	509.96048718704

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	17.3	12.9393460972018	4.36065390279825
2	15.4	10.9695130093274	4.43048699067256
3	16.9	17.5695130093274	-0.669513009327444
4	20.8	18.0361796759941	2.76382032400589
5	16.4	17.6028463426608	-1.20284634266078
6	11.3	14.1361796759941	-2.83617967599411
7	17.5	17.9361796759941	-0.436179675994112
8	16.6	16.3195130093274	0.280486990672557
9	17.5	19.3528463426608	-1.85284634266078
10	19.5	18.1528463426608	1.34715365733922
11	18.8	18.3718703976436	0.428129602356406
12	20.2	21.0718703976436	-0.871870397643594
13	19.2	18.4819793814433	0.718020618556698
14	14.4	16.5121462935690	-2.11214629356898
15	24.5	23.1121462935690	1.38785370643103
16	25.7	23.5788129602356	2.12118703976436
17	27.1	23.1454796269023	3.95452037309769
18	21	19.6788129602356	1.32118703976436
19	18.6	23.4788129602356	-4.87881296023564
20	20	21.8621462935690	-1.86214629356897
21	21.8	24.8954796269023	-3.09547962690231
22	20.4	23.6954796269023	-3.29547962690231
23	18	20.0003593519882	-2.00035935198822
24	21.5	22.7003593519882	-1.20035935198822
25	19.1	20.1104683357879	-1.01046833578792
26	19.7	18.1406352479136	1.55936475208640
27	26	24.7406352479136	1.2593647520864
28	26.3	25.2073019145803	1.09269808541973
29	24.6	24.7739685812469	-0.173968581246931
30	22.4	21.3073019145803	1.09269808541973
31	32	25.1073019145803	6.89269808541973
32	24	23.4906352479136	0.509364752086404
33	30	26.5239685812469	3.47603141875307
34	24.1	25.3239685812469	-1.22396858124693
35	26.3	25.5429926362298	0.757007363770248
36	29.8	28.2429926362298	1.55700736377025
37	21.9	25.6531016200295	-3.75310162002946
38	22.8	23.6832685321551	-0.883268532155128
39	29.2	30.2832685321551	-1.08326853215513
40	27.5	30.7499351988218	-3.24993519882180
41	27.4	30.3166018654885	-2.91660186548846
42	31	26.8499351988218	4.1500648011782
43	26.1	30.6499351988218	-4.5499351988218
44	22.2	29.0332685321551	-6.83326853215513
45	34	32.0666018654885	1.93339813451154
46	26.9	30.8666018654885	-3.96660186548846
47	31.9	31.0856259204713	0.814374079528716
48	34.2	33.7856259204713	0.414374079528724
49	31.2	31.195734904271	0.00426509572901176
50	28.5	29.2259018163967	-0.72590181639666
51	37.1	35.8259018163967	1.27409818360334
52	36	36.2925684830633	-0.292568483063328
53	34.8	35.85923514973	-1.05923514973000
54	32.1	32.3925684830633	-0.292568483063327
55	37.2	36.1925684830633	1.00743151693667
56	36.3	34.5759018163967	1.72409818360334
57	39.5	37.60923514973	1.89076485027000
58	37.1	36.40923514973	0.690764850270007
59	35.6	36.6282592047128	-1.02825920471281
60	36.2	39.3282592047128	-3.12825920471281
61	35.9	36.7383681885125	-0.838368188512521
62	32.5	34.7685351006382	-2.26853510063819
63	39.2	41.3685351006382	-2.16853510063819
64	39.4	41.8352017673049	-2.43520176730486
65	42.8	41.4018684339715	1.39813156602847
66	34.5	37.9352017673049	-3.43520176730486
67	43.7	41.7352017673049	1.96479823269514
68	46.3	40.1185351006382	6.1814648993618
69	40.8	43.1518684339715	-2.35186843397153
70	48.4	41.9518684339715	6.44813156602847
71	43.2	42.1708924889543	1.02910751104566
72	48.1	44.8708924889543	3.22910751104566
73	42.8	42.2810014727540	0.518998527245946

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299849792azx7bro2gwa44a/33nmu1229984918.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299849792azx7bro2gwa44a/4dyje1229984918.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299849792azx7bro2gwa44a/5b28g1229984918.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299849792azx7bro2gwa44a/986t41229984919.ps (open in new window)

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 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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