Home » date » 2007 » Nov » 15 » attachments

-25 tov economische situatie zonder seisoen en zonder trend

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 06:03:12 -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/15/t119513146634mautcf0aa136f.htm/, Retrieved Thu, 15 Nov 2007 13:57:57 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

140 -1 132 -2 117 -2 114 -1 113 1 110 1 107 1 103 1 98 1 98 1 137 0 148 -1 147 -1 139 -1 130 -1 128 -1 127 -2 123 -2 118 -2 114 -1 108 -1 111 -1 151 -1 159 -1 158 -1 148 -1 138 0 137 0 136 1 133 1 126 1 120 1 114 -1 116 1 153 -1 162 1 161 0 149 -1 139 -1 135 -1 130 -1 127 -1 122 1 117 -1 112 -2 113 -2 149 -2 157 -1 157 -2 147 -1 137 -1 132 -1 125 -1 123 -1 117 -1 114 -1 111 -1 112 -1 144 0 150 -1 149 -1 134 1 123 1 116 -1 117 -1 111 0 105 -1 102 1 95 1 93 1 124 0 130 -1 124 -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

<25[t] = + 125.003416856492 -4.89104024297646eco[t] + 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)	125.003416856492	2.260613	55.2962	0	0
eco	-4.89104024297646	2.00284	-2.4421	0.017096	0.008548

Multiple Linear Regression - Regression Statistics
Multiple R	0.278363511054769
R-squared	0.0774862442867386
Adjusted R-squared	0.0644930927978195
F-TEST (value)	5.9636220167848
F-TEST (DF numerator)	1
F-TEST (DF denominator)	71
p-value	0.0170964072114111
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	17.0140472492815
Sum Squared Residuals	20552.9240698557

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	140	129.894457099469	10.1055429005312
2	132	134.785497342445	-2.78549734244495
3	117	134.785497342445	-17.7854973424449
4	114	129.894457099468	-15.8944570994685
5	113	120.112376613516	-7.11237661351557
6	110	120.112376613516	-10.1123766135156
7	107	120.112376613516	-13.1123766135156
8	103	120.112376613516	-17.1123766135156
9	98	120.112376613516	-22.1123766135156
10	98	120.112376613516	-22.1123766135156
11	137	125.003416856492	11.9965831435080
12	148	129.894457099468	18.1055429005315
13	147	129.894457099468	17.1055429005315
14	139	129.894457099468	9.10554290053152
15	130	129.894457099468	0.105542900531517
16	128	129.894457099468	-1.89445709946848
17	127	134.785497342445	-7.78549734244494
18	123	134.785497342445	-11.7854973424449
19	118	134.785497342445	-16.7854973424449
20	114	129.894457099468	-15.8944570994685
21	108	129.894457099468	-21.8944570994685
22	111	129.894457099468	-18.8944570994685
23	151	129.894457099468	21.1055429005315
24	159	129.894457099468	29.1055429005315
25	158	129.894457099468	28.1055429005315
26	148	129.894457099468	18.1055429005315
27	138	125.003416856492	12.9965831435080
28	137	125.003416856492	11.9965831435080
29	136	120.112376613516	15.8876233864844
30	133	120.112376613516	12.8876233864844
31	126	120.112376613516	5.88762338648443
32	120	120.112376613516	-0.112376613515566
33	114	129.894457099468	-15.8944570994685
34	116	120.112376613516	-4.11237661351557
35	153	129.894457099468	23.1055429005315
36	162	120.112376613516	41.8876233864844
37	161	125.003416856492	35.9965831435080
38	149	129.894457099468	19.1055429005315
39	139	129.894457099468	9.10554290053152
40	135	129.894457099468	5.10554290053152
41	130	129.894457099468	0.105542900531517
42	127	129.894457099468	-2.89445709946848
43	122	120.112376613516	1.88762338648443
44	117	129.894457099468	-12.8944570994685
45	112	134.785497342445	-22.7854973424449
46	113	134.785497342445	-21.7854973424449
47	149	134.785497342445	14.2145026575551
48	157	129.894457099468	27.1055429005315
49	157	134.785497342445	22.2145026575551
50	147	129.894457099468	17.1055429005315
51	137	129.894457099468	7.10554290053152
52	132	129.894457099468	2.10554290053152
53	125	129.894457099468	-4.89445709946848
54	123	129.894457099468	-6.89445709946848
55	117	129.894457099468	-12.8944570994685
56	114	129.894457099468	-15.8944570994685
57	111	129.894457099468	-18.8944570994685
58	112	129.894457099468	-17.8944570994685
59	144	125.003416856492	18.9965831435080
60	150	129.894457099468	20.1055429005315
61	149	129.894457099468	19.1055429005315
62	134	120.112376613516	13.8876233864844
63	123	120.112376613516	2.88762338648443
64	116	129.894457099468	-13.8944570994685
65	117	129.894457099468	-12.8944570994685
66	111	125.003416856492	-14.0034168564920
67	105	129.894457099468	-24.8944570994685
68	102	120.112376613516	-18.1123766135156
69	95	120.112376613516	-25.1123766135156
70	93	120.112376613516	-27.1123766135156
71	124	125.003416856492	-1.00341685649202
72	130	129.894457099468	0.105542900531517
73	124	129.894457099468	-5.89445709946848

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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