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8

*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 06:38:48 -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/t122986678380d8juwwx5tf1c3.htm/, Retrieved Sun, 21 Dec 2008 14:39:43 +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/t122986678380d8juwwx5tf1c3.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 «

99984 0 99981 0 99972 0 99989 0 99996 0 99991 0 99988 0 99990 0 99998 0 99987 0 100000 0 100000 0 100004 0 100007 0 100005 0 100002 0 99998 0 100006 0 99997 0 100001 0 100000 0 99993 0 99994 0 99996 0 99996 0 99998 0 100002 0 99995 0 99985 0 99984 0 99982 0 99987 0 99977 0 99990 0 99990 0 99994 0 99997 0 99996 0 99993 0 99993 0 99993 0 99997 0 100000 0 99995 0 99997 0 100003 0 100002 0 99993 0 99999 1 100000 1 99997 1 100004 1 100002 1 100003 1 100000 1 99990 1 99990 1 99991 1 99978 1 99984 1 99982 1 99986 1 99988 1 99983 1 99977 1 99972 1 99969 1 99979 1 99981 1 99978 1 99978 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

Economie[t] = + 99995.6651574803 -5.51082677166121Kredietcrisis[t] + 0.839916885364573M1[t] + 1.87222222222450M2[t] + 0.071194225723746M3[t] + 1.60349956255633M4[t] -0.86419510061109M5[t] -0.498556430445174M6[t] -3.29958442694593M7[t] -2.26727909011334M8[t] -2.06830708661410M9[t] -2.20266841644818M10[t] -2.1703630796156M11[t] -0.0323053368325819t + 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)	99995.6651574803	4.999508	20001.1002	0	0
Kredietcrisis	-5.51082677166121	4.140074	-1.3311	0.188458	0.094229
M1	0.839916885364573	5.700611	0.1473	0.883385	0.441693
M2	1.87222222222450	5.685826	0.3293	0.743152	0.371576
M3	0.071194225723746	5.672605	0.0126	0.99003	0.495015
M4	1.60349956255633	5.66096	0.2833	0.778007	0.389004
M5	-0.86419510061109	5.6509	-0.1529	0.878993	0.439497
M6	-0.498556430445174	5.642434	-0.0884	0.929902	0.464951
M7	-3.29958442694593	5.635568	-0.5855	0.560527	0.280264
M8	-2.26727909011334	5.630309	-0.4027	0.688681	0.344341
M9	-2.06830708661410	5.626661	-0.3676	0.71454	0.35727
M10	-2.20266841644818	5.624627	-0.3916	0.696806	0.348403
M11	-2.1703630796156	5.624209	-0.3859	0.70101	0.350505
t	-0.0323053368325819	0.095348	-0.3388	0.735995	0.367997

Multiple Linear Regression - Regression Statistics
Multiple R	0.395519290525086
R-squared	0.156435509177467
Adjusted R-squared	-0.035956392238198
F-TEST (value)	0.813108597744383
F-TEST (DF numerator)	13
F-TEST (DF denominator)	57
p-value	0.644252316785673
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.2734731333788
Sum Squared Residuals	4901.84632546341

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	99984	99996.472769029	-12.4727690290012
2	99981	99997.4727690289	-16.4727690288645
3	99972	99995.6394356955	-23.6394356955312
4	99989	99997.1394356955	-8.1394356955312
5	99996	99994.6394356955	1.36056430446881
6	99991	99994.9727690289	-3.97276902886453
7	99988	99992.1394356955	-4.1394356955312
8	99990	99993.1394356955	-3.13943569553120
9	99998	99993.3061023622	4.69389763780214
10	99987	99993.1394356955	-6.1394356955312
11	1e+05	99993.1394356955	6.8605643044688
12	1e+05	99995.2774934383	4.72250656168579
13	100004	99996.0851049869	7.9148950131538
14	100007	99997.0851049869	9.91489501312646
15	100005	99995.2517716535	9.74822834645979
16	100002	99996.7517716535	5.24822834645979
17	99998	99994.2517716535	3.74822834645979
18	100006	99994.5851049869	11.4148950131265
19	99997	99991.7517716535	5.24822834645979
20	100001	99992.7517716535	8.24822834645979
21	1e+05	99992.9184383202	7.08156167979312
22	99993	99992.7517716535	0.248228346459788
23	99994	99992.7517716535	1.24822834645979
24	99996	99994.8898293963	1.11017060367677
25	99996	99995.6974409449	0.30255905514478
26	99998	99996.6974409449	1.30255905511744
27	100002	99994.8641076115	7.13589238845078
28	99995	99996.3641076115	-1.36410761154923
29	99985	99993.8641076115	-8.86410761154923
30	99984	99994.1974409449	-10.1974409448826
31	99982	99991.3641076115	-9.36410761154923
32	99987	99992.3641076115	-5.36410761154923
33	99977	99992.5307742782	-15.5307742782159
34	99990	99992.3641076115	-2.36410761154923
35	99990	99992.3641076115	-2.36410761154923
36	99994	99994.5021653543	-0.502165354332246
37	99997	99995.3097769029	1.69022309713576
38	99996	99996.3097769029	-0.309776902891579
39	99993	99994.4764435696	-1.47644356955825
40	99993	99995.9764435696	-2.97644356955825
41	99993	99993.4764435696	-0.476443569558245
42	99997	99993.8097769029	3.19022309710842
43	1e+05	99990.9764435696	9.02355643044175
44	99995	99991.9764435696	3.02355643044175
45	99997	99992.1431102362	4.85688976377509
46	100003	99991.9764435696	11.0235564304418
47	100002	99991.9764435696	10.0235564304418
48	99993	99994.1145013123	-1.11450131234126
49	99999	99989.4112860892	9.58871391078796
50	1e+05	99990.4112860892	9.58871391076062
51	99997	99988.577952756	8.42204724409395
52	100004	99990.077952756	13.9220472440940
53	100002	99987.577952756	14.4220472440939
54	100003	99987.9112860892	15.0887139107606
55	1e+05	99985.077952756	14.9220472440940
56	99990	99986.077952756	3.92204724409395
57	99990	99986.2446194226	3.75538057742729
58	99991	99986.077952756	4.92204724409395
59	99978	99986.077952756	-8.07795275590605
60	99984	99988.2160104987	-4.21601049868907
61	99982	99989.0236220472	-7.02362204722106
62	99986	99990.0236220472	-4.0236220472484
63	99988	99988.190288714	-0.190288713915067
64	99983	99989.690288714	-6.69028871391507
65	99977	99987.190288714	-10.1902887139151
66	99972	99987.5236220472	-15.5236220472484
67	99969	99984.690288714	-15.6902887139151
68	99979	99985.690288714	-6.69028871391507
69	99981	99985.8569553806	-4.85695538058173
70	99978	99985.690288714	-7.69028871391507
71	99978	99985.690288714	-7.69028871391507

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 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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