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Multiple Linear Regression Software : Uitvoer

*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, 14 Dec 2008 05:55:02 -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/14/t1229259418t2avnl1uaycaczf.htm/, Retrieved Sun, 14 Dec 2008 13:56:58 +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/14/t1229259418t2avnl1uaycaczf.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 «

11703.7 0 16283.6 0 16726.5 0 14968.9 0 14861 0 14583.3 0 15305.8 0 17903.9 0 16379.4 0 15420.3 0 17870.5 0 15912.8 0 13866.5 0 17823.2 0 17872 0 17420.4 0 16704.4 0 15991.2 0 16583.6 0 19123.5 0 17838.7 0 17209.4 0 18586.5 0 16258.1 0 15141.6 0 19202.1 0 17746.5 0 19090.1 0 18040.3 0 17515.5 0 17751.8 0 21072.4 0 17170 0 19439.5 0 19795.4 0 17574.9 0 16165.4 0 19464.6 0 19932.1 0 19961.2 0 17343.4 0 18924.2 0 18574.1 0 21350.6 0 18594.6 0 19823.1 0 20844.4 0 19640.2 0 17735.4 0 19813.6 0 22160 0 20664.3 1 17877.4 1 21211.2 1 21423.1 1 21688.7 1 23243.2 1 21490.2 1 22925.8 1 23184.8 1 18562.2 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

Uitvoer[t] = + 14807.2256953642 + 657.574337748344x[t] -2466.52148914643M1[t] + 1127.94693340692M2[t] + 1398.62972682119M3[t] + 701.357652685798M4[t] -853.639553899926M5[t] -273.176760485651M6[t] -89.8939670713778M7[t] + 2110.9288263429M8[t] + 428.971619757174M9[t] + 360.974413171449M10[t] + 1589.67720658572M11[t] + 99.3172065857248t + 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)	14807.2256953642	441.892482	33.5087	0	0
x	657.574337748344	378.701343	1.7364	0.089046	0.044523
M1	-2466.52148914643	500.197957	-4.9311	1.1e-05	5e-06
M2	1127.94693340692	525.435214	2.1467	0.03701	0.018505
M3	1398.62972682119	525.031936	2.6639	0.010548	0.005274
M4	701.357652685798	525.140779	1.3356	0.188125	0.094062
M5	-853.639553899926	524.243819	-1.6283	0.110142	0.055071
M6	-273.176760485651	523.46521	-0.5219	0.604217	0.302109
M7	-89.8939670713778	522.805481	-0.1719	0.864219	0.432109
M8	2110.9288263429	522.265083	4.0419	0.000195	9.8e-05
M9	428.971619757174	521.844387	0.822	0.415211	0.207605
M10	360.974413171449	521.543681	0.6921	0.492263	0.246132
M11	1589.67720658572	521.363175	3.0491	0.003763	0.001882
t	99.3172065857248	7.921518	12.5376	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.952331801523674
R-squared	0.906935860193326
Adjusted R-squared	0.881194715140416
F-TEST (value)	35.2329260539561
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	824.25240352269
Sum Squared Residuals	31931425.1615077

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	11703.7	12440.0214128035	-736.321412803533
2	16283.6	16133.8070419426	149.792958057397
3	16726.5	16503.8070419426	222.692958057395
4	14968.9	15905.8521743929	-936.952174392936
5	14861	14450.1721743929	410.827825607064
6	14583.3	15129.9521743929	-546.652174392937
7	15305.8	15412.5521743929	-106.752174392936
8	17903.9	17712.6921743929	191.207825607065
9	16379.4	16130.0521743929	249.347825607064
10	15420.3	16161.3721743929	-741.072174392937
11	17870.5	17489.3921743929	381.107825607063
12	15912.8	15999.0321743929	-86.2321743929377
13	13866.5	13631.8278918322	234.67210816777
14	17823.2	17325.6135209713	497.586479028699
15	17872	17695.6135209713	176.386479028698
16	17420.4	17097.6586534216	322.741346578368
17	16704.4	15641.9786534216	1062.42134657837
18	15991.2	16321.7586534216	-330.558653421633
19	16583.6	16604.3586534216	-20.7586534216341
20	19123.5	18904.4986534216	219.001346578366
21	17838.7	17321.8586534216	516.841346578367
22	17209.4	17353.1786534216	-143.778653421632
23	18586.5	18681.1986534216	-94.6986534216342
24	16258.1	17190.8386534216	-932.738653421634
25	15141.6	14823.6343708609	317.965629139073
26	19202.1	18517.42	684.679999999999
27	17746.5	18887.42	-1140.92
28	19090.1	18289.4651324503	800.634867549668
29	18040.3	16833.7851324503	1206.51486754967
30	17515.5	17513.5651324503	1.93486754966868
31	17751.8	17796.1651324503	-44.3651324503307
32	21072.4	20096.3051324503	976.09486754967
33	17170	18513.6651324503	-1343.66513245033
34	19439.5	18544.9851324503	894.51486754967
35	19795.4	19873.0051324503	-77.6051324503299
36	17574.9	18382.6451324503	-807.74513245033
37	16165.4	16015.4408498896	149.959150110374
38	19464.6	19709.2264790287	-244.626479028698
39	19932.1	20079.2264790287	-147.126479028698
40	19961.2	19481.2716114790	479.928388520972
41	17343.4	18025.5916114790	-682.191611479028
42	18924.2	18705.3716114790	218.828388520972
43	18574.1	18987.9716114790	-413.871611479028
44	21350.6	21288.1116114790	62.4883885209697
45	18594.6	19705.4716114790	-1110.87161147903
46	19823.1	19736.7916114790	86.3083885209699
47	20844.4	21064.8116114790	-220.411611479027
48	19640.2	19574.4516114790	65.7483885209716
49	17735.4	17207.2473289183	528.152671081679
50	19813.6	20901.0329580574	-1087.43295805740
51	22160	21271.0329580574	888.967041942605
52	20664.3	21330.6524282561	-666.352428256071
53	17877.4	19874.9724282561	-1997.57242825607
54	21211.2	20554.7524282561	656.44757174393
55	21423.1	20837.3524282561	585.747571743929
56	21688.7	23137.4924282561	-1448.79242825607
57	23243.2	21554.8524282561	1688.34757174393
58	21490.2	21586.1724282561	-95.97242825607
59	22925.8	22914.1924282561	11.6075717439278
60	23184.8	21423.8324282561	1760.96757174393
61	18562.2	19056.6281456954	-494.428145695363

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 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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