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Gemiddelde consumptieprijs brood (2)

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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 11:28:04 -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/22/t11957556570ymwnjbart1ens4.htm/, Retrieved Thu, 22 Nov 2007 19:20:58 +0100

User-defined keywords:

met seizoenaliteit en zonder trend

Dataseries X:

» Textbox « » Textfile « » CSV «

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 1,65 1 1,66 1 1,66 1 1,67 1 1,68 1 1,68 1 1,68 1 1,68 1 1,69 1 1,7 1 1,7 1 1,71 1 1,72 1 1,73 1 1,74 1 1,74 1 1,75 1 1,75 1 1,75 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	10 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.48253061224490 + 0.172448979591837x[t] + 0.00291156462585029M1[t] + 0.0229115646258503M2[t] + 0.0262448979591837M3[t] + 0.029578231292517M4[t] + 0.0329115646258503M5[t] + 0.0329115646258503M6[t] + 0.00583673469387754M7[t] -0.0100000000000000M8[t] -0.00600000000000001M9[t] -0.00200000000000001M10[t] -0.00200000000000001M11[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)	1.48253061224490	0.020464	72.4447	0	0
x	0.172448979591837	0.010746	16.0479	0	0
M1	0.00291156462585029	0.02632	0.1106	0.912325	0.456163
M2	0.0229115646258503	0.02632	0.8705	0.387873	0.193936
M3	0.0262448979591837	0.02632	0.9972	0.323133	0.161567
M4	0.029578231292517	0.02632	1.1238	0.266064	0.133032
M5	0.0329115646258503	0.02632	1.2505	0.216523	0.108262
M6	0.0329115646258503	0.02632	1.2505	0.216523	0.108262
M7	0.00583673469387754	0.026307	0.2219	0.825255	0.412627
M8	-0.0100000000000000	0.027467	-0.3641	0.717225	0.358612
M9	-0.00600000000000001	0.027467	-0.2184	0.827907	0.413953
M10	-0.00200000000000001	0.027467	-0.0728	0.942223	0.471111
M11	-0.00200000000000001	0.027467	-0.0728	0.942223	0.471111

Multiple Linear Regression - Regression Statistics
Multiple R	0.910367038497732
R-squared	0.828768144783132
Adjusted R-squared	0.790716621401605
F-TEST (value)	21.7801567751553
F-TEST (DF numerator)	12
F-TEST (DF denominator)	54
p-value	1.11022302462516e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0434291051670534
Sum Squared Residuals	0.101848707482993

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.48	1.48544217687075	-0.00544217687074854
2	1.48	1.50544217687075	-0.0254421768707483
3	1.48	1.50877551020408	-0.0287755102040816
4	1.48	1.51210884353742	-0.032108843537415
5	1.48	1.51544217687075	-0.0354421768707483
6	1.48	1.51544217687075	-0.0354421768707483
7	1.48	1.48836734693878	-0.00836734693877551
8	1.48	1.47253061224490	0.00746938775510203
9	1.48	1.47653061224490	0.00346938775510202
10	1.48	1.48053061224490	-0.000530612244897973
11	1.48	1.48053061224490	-0.000530612244897982
12	1.48	1.48253061224490	-0.00253061224489799
13	1.48	1.48544217687075	-0.00544217687074828
14	1.48	1.50544217687075	-0.0254421768707483
15	1.48	1.50877551020408	-0.0287755102040816
16	1.48	1.51210884353742	-0.032108843537415
17	1.48	1.51544217687075	-0.0354421768707483
18	1.48	1.51544217687075	-0.0354421768707483
19	1.48	1.48836734693878	-0.00836734693877552
20	1.48	1.47253061224490	0.00746938775510203
21	1.48	1.47653061224490	0.00346938775510203
22	1.48	1.48053061224490	-0.00053061224489798
23	1.48	1.48053061224490	-0.000530612244897978
24	1.48	1.48253061224490	-0.00253061224489799
25	1.48	1.48544217687075	-0.00544217687074827
26	1.57	1.50544217687075	0.0645578231292518
27	1.58	1.50877551020408	0.0712244897959185
28	1.58	1.51210884353742	0.0678911564625851
29	1.58	1.51544217687075	0.0645578231292518
30	1.58	1.51544217687075	0.0645578231292518
31	1.59	1.66081632653061	-0.0708163265306122
32	1.6	1.64497959183673	-0.0449795918367346
33	1.6	1.64897959183673	-0.0489795918367346
34	1.61	1.65297959183673	-0.0429795918367346
35	1.61	1.65297959183673	-0.0429795918367346
36	1.61	1.65497959183673	-0.0449795918367346
37	1.62	1.65789115646258	-0.0378911564625849
38	1.63	1.67789115646258	-0.0478911564625851
39	1.63	1.68122448979592	-0.0512244897959184
40	1.64	1.68455782312925	-0.0445578231292518
41	1.64	1.68789115646258	-0.0478911564625851
42	1.64	1.68789115646258	-0.0478911564625851
43	1.64	1.66081632653061	-0.0208163265306123
44	1.64	1.64497959183673	-0.00497959183673476
45	1.65	1.64897959183673	0.00102040816326525
46	1.65	1.65297959183673	-0.00297959183673476
47	1.65	1.65297959183673	-0.00297959183673476
48	1.65	1.65497959183673	-0.00497959183673477
49	1.65	1.65789115646258	-0.00789115646258507
50	1.66	1.67789115646258	-0.0178911564625851
51	1.66	1.68122448979592	-0.0212244897959184
52	1.67	1.68455782312925	-0.0145578231292517
53	1.68	1.68789115646258	-0.00789115646258507
54	1.68	1.68789115646258	-0.00789115646258507
55	1.68	1.66081632653061	0.0191836734693877
56	1.68	1.64497959183673	0.0350204081632653
57	1.69	1.64897959183673	0.0410204081632653
58	1.7	1.65297959183673	0.0470204081632653
59	1.7	1.65297959183673	0.0470204081632653
60	1.71	1.65497959183673	0.0550204081632653
61	1.72	1.65789115646258	0.062108843537415
62	1.73	1.67789115646258	0.052108843537415
63	1.74	1.68122448979592	0.0587755102040817
64	1.74	1.68455782312925	0.0554421768707483
65	1.75	1.68789115646258	0.062108843537415
66	1.75	1.68789115646258	0.062108843537415
67	1.75	1.66081632653061	0.0891836734693878

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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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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