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Lineaire trend olieprijs

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

Title produced by software: Multiple Regression

Date of computation: Mon, 19 Nov 2007 03:43:39 -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/19/t11954687207lod88w6mt5f831.htm/, Retrieved Mon, 19 Nov 2007 11:38:51 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

96.8 0 87.0 0 96.3 0 107.1 0 115.2 0 106.1 1 89.5 1 91.3 1 97.6 1 100.7 1 104.6 1 94.7 1 101.8 1 102.5 1 105.3 1 110.3 1 109.8 1 117.3 1 118.8 1 131.3 1 125.9 1 133.1 1 147.0 1 145.8 1 164.4 1 149.8 1 137.7 1 151.7 1 156.8 1 180.0 1 180.4 1 170.4 1 191.6 1 199.5 1 218.2 1 217.5 1 205.0 1 194.0 1 199.3 1 219.3 1 211.1 1 215.2 1 240.2 1 242.2 1 240.7 1 255.4 1 253.0 1 218.2 1 203.7 1 205.6 1 215.6 1 188.5 1 202.9 1 214.0 1 230.3 1 230.0 1 241.0 1 259.6 1 247.8 1 270.3 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

ruwe_olie[t] = + 90.9079452054795 -20.6678206724782inval_IRAK[t] + 3.19068493150685t + 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)	90.9079452054795	8.19519	11.0928	0	0
inval_IRAK	-20.6678206724782	9.733917	-2.1233	0.038084	0.019042
t	3.19068493150685	0.155347	20.5391	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.947353960131115
R-squared	0.897479525776105
Adjusted R-squared	0.893882316154214
F-TEST (value)	249.493251745586
F-TEST (DF numerator)	2
F-TEST (DF denominator)	57
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	18.295347689748
Sum Squared Residuals	19079.0255840598

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	96.8	94.0986301369862	2.70136986301378
2	87	97.289315068493	-10.2893150684930
3	96.3	100.480000000000	-4.18000000000023
4	107.1	103.670684931507	3.42931506849318
5	115.2	106.861369863014	8.33863013698634
6	106.1	89.3842341220424	16.7157658779576
7	89.5	92.5749190535492	-3.07491905354919
8	91.3	95.765603985056	-4.46560398505605
9	97.6	98.9562889165629	-1.35628891656289
10	100.7	102.146973848070	-1.44697384806974
11	104.6	105.337658779577	-0.737658779576585
12	94.7	108.528343711083	-13.8283437110834
13	101.8	111.719028642590	-9.9190286425903
14	102.5	114.909713574097	-12.4097135740971
15	105.3	118.100398505604	-12.800398505604
16	110.3	121.291083437111	-10.9910834371108
17	109.8	124.481768368618	-14.6817683686177
18	117.3	127.672453300125	-10.3724533001245
19	118.8	130.863138231631	-12.0631382316314
20	131.3	134.053823163138	-2.75382316313822
21	125.9	137.244508094645	-11.3445080946451
22	133.1	140.435193026152	-7.33519302615194
23	147	143.625877957659	3.37412204234121
24	145.8	146.816562889166	-1.01656288916562
25	164.4	150.007247820672	14.3927521793275
26	149.8	153.197932752179	-3.39793275217932
27	137.7	156.388617683686	-18.6886176836862
28	151.7	159.579302615193	-7.87930261519304
29	156.8	162.7699875467	-5.96998754669987
30	180	165.960672478207	14.0393275217933
31	180.4	169.151357409714	11.2486425902864
32	170.4	172.342042341220	-1.94204234122042
33	191.6	175.532727272727	16.0672727272727
34	199.5	178.723412204234	20.7765877957659
35	218.2	181.914097135741	36.285902864259
36	217.5	185.104782067248	32.3952179327522
37	205	188.295466998755	16.7045330012453
38	194	191.486151930262	2.51384806973848
39	199.3	194.676836861768	4.62316313823164
40	219.3	197.867521793275	21.4324782067248
41	211.1	201.058206724782	10.0417932752179
42	215.2	204.248891656289	10.9511083437111
43	240.2	207.439576587796	32.7604234122042
44	242.2	210.630261519303	31.5697384806974
45	240.7	213.820946450809	26.8790535491905
46	255.4	217.011631382316	38.3883686176837
47	253	220.202316313823	32.7976836861768
48	218.2	223.39300124533	-5.19300124533002
49	203.7	226.583686176837	-22.8836861768369
50	205.6	229.774371108344	-24.1743711083437
51	215.6	232.965056039851	-17.3650560398506
52	188.5	236.155740971357	-47.6557409713574
53	202.9	239.346425902864	-36.4464259028643
54	214	242.537110834371	-28.5371108343711
55	230.3	245.727795765878	-15.4277957658779
56	230	248.918480697385	-18.9184806973848
57	241	252.109165628892	-11.1091656288917
58	259.6	255.299850560399	4.30014943960151
59	247.8	258.490535491905	-10.6905354919053
60	270.3	261.681220423412	8.6187795765878

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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