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broodprijs (poging tot nieuw model)

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

Title produced by software: Multiple Regression

Date of computation: Sat, 24 Nov 2007 08:03:11 -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/24/t11959162104p8tagyu6o9bb7k.htm/, Retrieved Sat, 24 Nov 2007 15:57:00 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.44 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.57 0 1.58 0 1.58 0 1.58 0 1.58 0 1.59 1 1.6 1 1.6 1 1.61 1 1.61 1 1.61 1 1.62 1 1.63 1 1.63 1 1.64 1 1.64 1 1.64 1 1.64 1 1.64 1 1.65 1 1.65 1 1.65 1 1.65 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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.41039718423761 + 0.0759037886585307x[t] + 0.00222798117923834t + 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)	1.41039718423761	0.00569	247.8678	0	0
x	0.0759037886585307	0.008601	8.8248	0	0
t	0.00222798117923834	0.000179	12.4323	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.96403014784424
R-squared	0.929354125952587
Adjusted R-squared	0.92730641945846
F-TEST (value)	453.851237283101
F-TEST (DF numerator)	2
F-TEST (DF denominator)	69
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0209007806089203
Sum Squared Residuals	0.0301421414742932

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.43	1.41262516541685	0.017374834583153
2	1.43	1.41485314659609	0.015146853403911
3	1.43	1.41708112777533	0.0129188722246726
4	1.43	1.41930910895457	0.0106908910454343
5	1.43	1.42153709013380	0.00846290986619592
6	1.43	1.42376507131304	0.00623492868695757
7	1.43	1.42599305249228	0.00400694750771923
8	1.43	1.42822103367152	0.00177896632848088
9	1.43	1.43044901485076	-0.000449014850757457
10	1.43	1.43267699603000	-0.00267699602999580
11	1.43	1.43490497720923	-0.00490497720923414
12	1.43	1.43713295838847	-0.00713295838847248
13	1.43	1.43936093956771	-0.00936093956771082
14	1.43	1.44158892074695	-0.0115889207469492
15	1.43	1.44381690192619	-0.0138169019261875
16	1.43	1.44604488310543	-0.0160448831054258
17	1.43	1.44827286428466	-0.0182728642846642
18	1.43	1.45050084546390	-0.0205008454639025
19	1.44	1.45272882664314	-0.0127288266431409
20	1.48	1.45495680782238	0.0250431921776208
21	1.48	1.45718478900162	0.0228152109983825
22	1.48	1.45941277018086	0.0205872298191441
23	1.48	1.46164075136009	0.0183592486399058
24	1.48	1.46386873253933	0.0161312674606675
25	1.48	1.46609671371857	0.0139032862814291
26	1.48	1.46832469489781	0.0116753051021908
27	1.48	1.47055267607705	0.00944732392295244
28	1.48	1.47278065725629	0.0072193427437141
29	1.48	1.47500863843552	0.00499136156447576
30	1.48	1.47723661961476	0.00276338038523742
31	1.48	1.479464600794	0.000535399205999073
32	1.48	1.48169258197324	-0.00169258197323927
33	1.48	1.48392056315248	-0.00392056315247761
34	1.48	1.48614854433172	-0.00614854433171595
35	1.48	1.48837652551095	-0.00837652551095429
36	1.48	1.49060450669019	-0.0106045066901926
37	1.48	1.49283248786943	-0.0128324878694310
38	1.48	1.49506046904867	-0.0150604690486693
39	1.48	1.49728845022791	-0.0172884502279077
40	1.48	1.49951643140715	-0.019516431407146
41	1.48	1.50174441258638	-0.0217444125863843
42	1.48	1.50397239376562	-0.0239723937656227
43	1.48	1.50620037494486	-0.026200374944861
44	1.48	1.5084283561241	-0.0284283561240994
45	1.48	1.51065633730334	-0.0306563373033377
46	1.48	1.51288431848258	-0.0328843184825760
47	1.48	1.51511229966181	-0.0351122996618144
48	1.48	1.51734028084105	-0.0373402808410527
49	1.48	1.51956826202029	-0.0395682620202911
50	1.57	1.52179624319953	0.0482037568004707
51	1.58	1.52402422437877	0.0559757756212323
52	1.58	1.52625220555801	0.053747794441994
53	1.58	1.52848018673724	0.0515198132627557
54	1.58	1.53070816791648	0.0492918320835173
55	1.59	1.60883993775425	-0.0188399377542518
56	1.6	1.61106791893349	-0.0110679189334901
57	1.6	1.61329590011273	-0.0132959001127285
58	1.61	1.61552388129197	-0.00552388129196678
59	1.61	1.61775186247121	-0.00775186247120512
60	1.61	1.61997984365044	-0.00997984365044346
61	1.62	1.62220782482968	-0.00220782482968179
62	1.63	1.62443580600892	0.00556419399107965
63	1.63	1.62666378718816	0.00333621281184131
64	1.64	1.62889176836740	0.0111082316326030
65	1.64	1.63111974954664	0.00888025045336464
66	1.64	1.63334773072587	0.00665226927412629
67	1.64	1.63557571190511	0.00442428809488795
68	1.64	1.63780369308435	0.00219630691564961
69	1.65	1.64003167426359	0.00996832573641128
70	1.65	1.64225965544283	0.00774034455717293
71	1.65	1.64448763662207	0.00551236337793459
72	1.65	1.64671561780130	0.00328438219869625

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal 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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