Home » date » 2010 » Nov » 22 »

meervoudige regressie model 1

*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: Mon, 22 Nov 2010 11:01:02 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423608fg1nk4o2gke94qw.htm/, Retrieved Sat, 25 May 2013 09:55:32 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t12903340716o7nq28pydj9qhz (pk = 98330)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Correlation Matrix « » Notched Boxplots «

16198.9	16896.2	0
16554.2	16698	0
19554.2	19691.6	0
15903.8	15930.7	0
18003.8	17444.6	0
18329.6	17699.4	0
16260.7	15189.8	0
14851.9	15672.7	0
18174.1	17180.8	0
18406.6	17664.9	0
18466.5	17862.9	0
16016.5	16162.3	0
17428.5	17463.6	0
17167.2	16772.1	0
19630	19106.9	0
17183.6	16721.3	0
18344.7	18161.3	0
19301.4	18509.9	0
18147.5	17802.7	0
16192.9	16409.9	0
18374.4	17967.7	0
20515.2	20286.6	0
18957.2	19537.3	0
16471.5	18021.9	0
18746.8	20194.3	0
19009.5	19049.6	0
19211.2	20244.7	0
20547.7	21473.3	0
19325.8	19673.6	0
20605.5	21053.2	0
20056.9	20159.5	0
16141.4	18203.6	0
20359.8	21289.5	0
19711.6	20432.3	1
15638.6	17180.4	1
14384.5	15816.8	1
13855.6	15071.8	1
14308.3	14521.1	1
15290.6	15668.8	1
14423.8	14346.9	1
13779.7	13881	1
15686.3	15465.9	1
14733.8	14238.2	1
12522.5	13557.7	1
16189.4	16127.6	1
16059.1	16793.9	1
16007.1	16014	1
15806.8	16867.9	1
15160	16014.6	0
15692.1	15878.6	0
18908.9	18664.9	0
16969.9	17962.5	0
16997.5	17332.7	0
19858.9	19542.1	0
17681.2	17203.6	0

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	7 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Multiple Linear Regression - Estimated Regression Equation

uitvoer[t] = + 2113.94008826516 + 0.87631681502034invoer[t] -673.894099652128crisis[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)	2113.94008826516	1023.768921	2.0649	0.043939	0.021969
invoer	0.87631681502034	0.056187	15.5964	0	0
crisis	-673.894099652128	245.819041	-2.7414	0.008367	0.004184

Multiple Linear Regression - Regression Statistics
Multiple R	0.943748599824329
R-squared	0.890661419670381
Adjusted R-squared	0.886456089657704
F-TEST (value)	211.793466145425
F-TEST (DF numerator)	2
F-TEST (DF denominator)	52
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	680.349569326576
Sum Squared Residuals	24069527.8971086

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	16198.9	16920.3642582118	-721.464258211822
2	16554.2	16746.6782654748	-192.478265474802
3	19554.2	19370.0202829197	184.179717080307
4	15903.8	16074.2803733097	-170.480373309698
5	18003.8	17400.936399569	602.863600431011
6	18329.6	17624.2219240362	705.378075963825
7	16260.7	15425.0172450611	835.682754938875
8	14851.9	15848.1906350344	-996.29063503445
9	18174.1	17169.7640237666	1004.33597623338
10	18406.6	17593.988993918	812.611006082027
11	18466.5	17767.499723292	699.000276708
12	16016.5	16277.2353476684	-260.735347668407
13	17428.5	17417.5864190544	10.9135809456248
14	17167.2	16811.6133414678	355.586658532191
15	19630	18857.6378411773	772.362158822697
16	17183.6	16767.0964472648	416.503552735221
17	18344.7	18028.9926608941	315.707339105934
18	19301.4	18334.4767026102	966.923297389841
19	18147.5	17714.7454510278	432.754548972226
20	16192.9	16494.2113910674	-301.311391067445
21	18374.4	17859.3377255061	515.062274493871
22	20515.2	19891.4287878568	623.771212143204
23	18957.2	19234.8045983621	-277.604598362055
24	16471.5	17906.8340968802	-1435.33409688023
25	18746.8	19810.5447458304	-1063.74474583042
26	19009.5	18807.4248876766	202.075112323365
27	19211.2	19854.7111133074	-643.511113307445
28	20547.7	20931.3539522414	-383.653952241434
29	19325.8	19354.2465802493	-28.4465802493284
30	20605.5	20563.2132582514	42.2867417486085
31	20056.9	19780.0489206677	276.851079332289
32	16141.4	18066.0608621694	-1924.66086216943
33	20359.8	20770.2869216407	-410.486921640698
34	19711.6	19345.2140481531	366.385951846866
35	15638.6	16495.5193973885	-856.919397388489
36	14384.5	15300.5737884268	-916.073788426751
37	13855.6	14647.7177612366	-792.117761236598
38	14308.3	14165.1300912049	143.169908795102
39	15290.6	15170.8788998037	119.72110019626
40	14423.8	14012.4757020284	411.324297971646
41	13779.7	13604.1996979104	175.500302089624
42	15686.3	14993.0742180361	693.225781963885
43	14733.8	13917.2200642356	816.579935764356
44	12522.5	13320.8864716143	-798.386471614302
45	16189.4	15572.9330545351	616.466945464926
46	16059.1	16156.8229483831	-97.7229483831274
47	16007.1	15473.3834643488	533.716535651237
48	15806.8	16221.6703926946	-414.870392694634
49	15160	16147.8033540899	-987.803354089903
50	15692.1	16028.6242672471	-336.524267247137
51	18908.9	18470.3058089383	438.594191061689
52	16969.9	17854.780878068	-884.880878068023
53	16997.5	17302.8765479682	-305.376547968215
54	19858.9	19239.0109190742	619.889080925849
55	17681.2	17189.7440471491	491.455952850914

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
6	0.512235793360664	0.975528413278672	0.487764206639336
7	0.587549005183318	0.824901989633363	0.412450994816682
8	0.708054266700753	0.583891466598493	0.291945733299247
9	0.755040102646188	0.489919794707624	0.244959897353812
10	0.723650761982486	0.552698476035028	0.276349238017514
11	0.663712673533466	0.672574652933069	0.336287326466534
12	0.580187316471073	0.839625367057853	0.419812683528927
13	0.488532343090435	0.97706468618087	0.511467656909565
14	0.404507739516898	0.809015479033797	0.595492260483102
15	0.349800106672512	0.699600213345023	0.650199893327488
16	0.289247961199047	0.578495922398093	0.710752038800953
17	0.225353447621683	0.450706895243367	0.774646552378317
18	0.239049383386556	0.478098766773113	0.760950616613444
19	0.195000378615763	0.390000757231525	0.804999621384237
20	0.156687017787507	0.313374035575014	0.843312982212493
21	0.133121321551605	0.266242643103211	0.866878678448395
22	0.122875368183478	0.245750736366957	0.877124631816522
23	0.152785478219056	0.305570956438112	0.847214521780944
24	0.48686811235452	0.97373622470904	0.51313188764548
25	0.657412408805518	0.685175182388963	0.342587591194482
26	0.597524969274574	0.804950061450852	0.402475030725426
27	0.588011049380148	0.823977901239703	0.411988950619852
28	0.527374212395278	0.945251575209443	0.472625787604722
29	0.448380437201945	0.896760874403889	0.551619562798055
30	0.371784222772703	0.743568445545406	0.628215777227297
31	0.323504324539428	0.647008649078855	0.676495675460572
32	0.775653398198049	0.448693203603903	0.224346601801951
33	0.731389231547832	0.537221536904336	0.268610768452168
34	0.65732917089006	0.685341658219879	0.342670829109939
35	0.741262459705623	0.517475080588755	0.258737540294378
36	0.813785533175404	0.372428933649192	0.186214466824596
37	0.851029221124117	0.297941557751765	0.148970778875883
38	0.802725120957756	0.394549758084487	0.197274879042244
39	0.741669845897481	0.516660308205038	0.258330154102519
40	0.694055203915248	0.611889592169505	0.305944796084752
41	0.616734818239378	0.766530363521244	0.383265181760622
42	0.599307962892157	0.801384074215685	0.400692037107843
43	0.757251169298324	0.485497661403351	0.242748830701676
44	0.689131377523516	0.621737244952968	0.310868622476484
45	0.678873770592512	0.642252458814976	0.321126229407488
46	0.567058966539006	0.865882066921988	0.432941033460994
47	0.63756199985283	0.72487600029434	0.36243800014717
48	0.490098675387734	0.980197350775468	0.509901324612266
49	0.41707780919956	0.83415561839912	0.58292219080044

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
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))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$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')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$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()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
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')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}