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Multiple regressiondollar-euroinvoering(seizoenaliteit en trend)

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 29 Nov 2007 02:35:21 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/29/t1196328320941i33za4l0k0zp.htm/, Retrieved Thu, 29 Nov 2007 10:25:29 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.9383 0 0.9217 0 0.9095 0 0.892 0 0.8742 0 0.8532 0 0.8607 0 0.9005 0 0.9111 0 0.9059 0 0.8883 0 0.8924 0 0.8833 1 0.87 1 0.8758 1 0.8858 1 0.917 1 0.9554 1 0.9922 1 0.9778 1 0.9808 1 0.9811 1 1.0014 1 1.0183 1 1.0622 1 1.0773 1 1.0807 1 1.0848 1 1.1582 1 1.1663 1 1.1372 1 1.1139 1 1.1222 1 1.1692 1 1.1702 1 1.2286 1 1.2613 1 1.2646 1 1.2262 1 1.1985 1 1.2007 1 1.2138 1 1.2266 1 1.2176 1 1.2218 1 1.249 1 1.2991 1 1.3408 1 1.3119 1 1.3014 1 1.3201 1 1.2938 1 1.2694 1 1.2165 1 1.2037 1 1.2292 1 1.2256 1 1.2015 1 1.1786 1 1.1856 1 1.2103 1 1.1938 1 1.202 1 1.2271 1 1.277 1 1.265 1 1.2684 1 1.2811 1 1.2727 1 1.2611 1 1.2881 1 1.3213 1

Text written by user:

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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Dollar[t] = + 0.867408333333334 + 0.0476524999999999Euroinvoering[t] + 0.0141260416666673M1[t] + 0.00158125000000005M2[t] -0.0069635416666666M3[t] -0.0184749999999999M4[t] -0.00551979166666656M5[t] -0.0160312500000000M6[t] -0.0190593749999999M7[t] -0.0199708333333333M8[t] -0.0237489583333332M9[t] -0.0242770833333332M10[t] -0.0207552083333332M11[t] + 0.006128125t + 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)	0.867408333333334	0.035897	24.1638	0	0
Euroinvoering	0.0476524999999999	0.030373	1.5689	0.122109	0.061055
M1	0.0141260416666673	0.042357	0.3335	0.739958	0.369979
M2	0.00158125000000005	0.042281	0.0374	0.970296	0.485148
M3	-0.0069635416666666	0.042212	-0.165	0.869546	0.434773
M4	-0.0184749999999999	0.042151	-0.4383	0.662793	0.331397
M5	-0.00551979166666656	0.042097	-0.1311	0.896133	0.448066
M6	-0.0160312500000000	0.04205	-0.3812	0.704413	0.352207
M7	-0.0190593749999999	0.04201	-0.4537	0.651744	0.325872
M8	-0.0199708333333333	0.041977	-0.4758	0.636034	0.318017
M9	-0.0237489583333332	0.041951	-0.5661	0.573506	0.286753
M10	-0.0242770833333332	0.041933	-0.5789	0.564868	0.282434
M11	-0.0207552083333332	0.041922	-0.4951	0.622409	0.311205
t	0.006128125	0.000552	11.0951	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.905386104795673
R-squared	0.819723998757082
Adjusted R-squared	0.779317308823324
F-TEST (value)	20.286838642337
F-TEST (DF numerator)	13
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0726053856334949
Sum Squared Residuals	0.305749437333334

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	0.9383	0.887662499999998	0.0506375000000023
2	0.9217	0.881245833333334	0.0404541666666664
3	0.9095	0.878829166666667	0.0306708333333332
4	0.892	0.873445833333334	0.0185541666666663
5	0.8742	0.892529166666667	-0.0183291666666668
6	0.8532	0.888145833333333	-0.0349458333333334
7	0.8607	0.891245833333333	-0.0305458333333334
8	0.9005	0.8964625	0.00403749999999986
9	0.9111	0.8988125	0.0122874999999999
10	0.9059	0.9044125	0.00148749999999986
11	0.8883	0.9140625	-0.0257625000000002
12	0.8924	0.940945833333333	-0.0485458333333335
13	0.8833	1.0088525	-0.125552500000000
14	0.87	1.00243583333333	-0.132435833333334
15	0.8758	1.00001916666667	-0.124219166666667
16	0.8858	0.994635833333333	-0.108835833333333
17	0.917	1.01371916666667	-0.0967191666666666
18	0.9554	1.00933583333333	-0.0539358333333333
19	0.9922	1.01243583333333	-0.0202358333333333
20	0.9778	1.0176525	-0.0398525
21	0.9808	1.0200025	-0.0392025
22	0.9811	1.0256025	-0.0445025000000001
23	1.0014	1.0352525	-0.0338524999999999
24	1.0183	1.06213583333333	-0.0438358333333334
25	1.0622	1.08239	-0.0201900000000005
26	1.0773	1.07597333333333	0.00132666666666677
27	1.0807	1.07355666666667	0.00714333333333339
28	1.0848	1.06817333333333	0.0166266666666667
29	1.1582	1.08725666666667	0.0709433333333332
30	1.1663	1.08287333333333	0.0834266666666667
31	1.1372	1.08597333333333	0.0512266666666667
32	1.1139	1.09119	0.0227099999999999
33	1.1222	1.09354	0.0286600000000001
34	1.1692	1.09914	0.07006
35	1.1702	1.10879	0.06141
36	1.2286	1.13567333333333	0.0929266666666666
37	1.2613	1.1559275	0.105372500000000
38	1.2646	1.14951083333333	0.115089166666667
39	1.2262	1.14709416666667	0.0791058333333333
40	1.1985	1.14171083333333	0.0567891666666666
41	1.2007	1.16079416666667	0.0399058333333334
42	1.2138	1.15641083333333	0.0573891666666668
43	1.2266	1.15951083333333	0.0670891666666666
44	1.2176	1.1647275	0.0528725000000001
45	1.2218	1.1670775	0.0547225
46	1.249	1.1726775	0.0763225000000001
47	1.2991	1.1823275	0.1167725
48	1.3408	1.20921083333333	0.131589166666667
49	1.3119	1.229465	0.0824349999999996
50	1.3014	1.22304833333333	0.0783516666666668
51	1.3201	1.22063166666667	0.0994683333333335
52	1.2938	1.21524833333333	0.0785516666666668
53	1.2694	1.23433166666667	0.0350683333333335
54	1.2165	1.22994833333333	-0.0134483333333333
55	1.2037	1.23304833333333	-0.0293483333333333
56	1.2292	1.238265	-0.00906499999999984
57	1.2256	1.240615	-0.0150149999999999
58	1.2015	1.246215	-0.044715
59	1.1786	1.255865	-0.0772649999999998
60	1.1856	1.28274833333333	-0.0971483333333333
61	1.2103	1.3030025	-0.0927025000000006
62	1.1938	1.29658583333333	-0.102785833333333
63	1.202	1.29416916666667	-0.0921691666666666
64	1.2271	1.28878583333333	-0.0616858333333332
65	1.277	1.30786916666667	-0.0308691666666667
66	1.265	1.30348583333333	-0.0384858333333333
67	1.2684	1.30658583333333	-0.0381858333333333
68	1.2811	1.3118025	-0.0307025000000001
69	1.2727	1.3141525	-0.0414525
70	1.2611	1.3197525	-0.0586524999999999
71	1.2881	1.3294025	-0.0413024999999999
72	1.3213	1.35628583333333	-0.0349858333333333

Charts produced by software:

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Parameters:

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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