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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: Sun, 21 Dec 2008 06:12:19 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/21/t1229865185gopw6b26thomkl2.htm/, Retrieved Sun, 21 Dec 2008 14:13:13 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/21/t1229865185gopw6b26thomkl2.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

519164 0 517009 0 509933 0 509127 0 500857 0 506971 0 569323 0 579714 0 577992 0 565464 0 547344 0 554788 0 562325 0 560854 0 555332 0 543599 0 536662 0 542722 0 593530 0 610763 0 612613 0 611324 0 594167 0 595454 0 590865 0 589379 0 584428 0 573100 0 567456 0 569028 0 620735 0 628884 0 628232 0 612117 0 595404 0 597141 0 593408 0 590072 0 579799 0 574205 0 572775 0 572942 0 619567 0 625809 0 619916 0 587625 0 565742 0 557274 0 560576 1 548854 1 531673 1 525919 1 511038 1 498662 1 555362 1 564591 1 541657 1 527070 1 509846 1 514258 1 516922 1 507561 1 492622 1 490243 1 469357 1 477580 1 528379 1 533590 1 517945 1 506174 1 501866 1

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

WerklozenTotaal[t] = + 574852.791666667 -56081.2699275362Kredietcrisis[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)	574852.791666667	4543.819213	126.5131	0	0
Kredietcrisis	-56081.2699275362	7983.370777	-7.0248	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.645732177560642
R-squared	0.416970045137209
Adjusted R-squared	0.408520335646444
F-TEST (value)	49.3472640204881
F-TEST (DF numerator)	1
F-TEST (DF denominator)	69
p-value	1.19962595412915e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	31480.5029515408
Sum Squared Residuals	68380522559.6558

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	519164	574852.791666667	-55688.7916666668
2	517009	574852.791666667	-57843.7916666667
3	509933	574852.791666667	-64919.7916666667
4	509127	574852.791666667	-65725.7916666667
5	500857	574852.791666667	-73995.7916666667
6	506971	574852.791666667	-67881.7916666667
7	569323	574852.791666667	-5529.79166666666
8	579714	574852.791666667	4861.20833333333
9	577992	574852.791666667	3139.20833333333
10	565464	574852.791666667	-9388.79166666666
11	547344	574852.791666667	-27508.7916666667
12	554788	574852.791666667	-20064.7916666667
13	562325	574852.791666667	-12527.7916666667
14	560854	574852.791666667	-13998.7916666667
15	555332	574852.791666667	-19520.7916666667
16	543599	574852.791666667	-31253.7916666667
17	536662	574852.791666667	-38190.7916666667
18	542722	574852.791666667	-32130.7916666667
19	593530	574852.791666667	18677.2083333333
20	610763	574852.791666667	35910.2083333333
21	612613	574852.791666667	37760.2083333333
22	611324	574852.791666667	36471.2083333333
23	594167	574852.791666667	19314.2083333333
24	595454	574852.791666667	20601.2083333333
25	590865	574852.791666667	16012.2083333333
26	589379	574852.791666667	14526.2083333333
27	584428	574852.791666667	9575.20833333334
28	573100	574852.791666667	-1752.79166666667
29	567456	574852.791666667	-7396.79166666666
30	569028	574852.791666667	-5824.79166666666
31	620735	574852.791666667	45882.2083333333
32	628884	574852.791666667	54031.2083333333
33	628232	574852.791666667	53379.2083333333
34	612117	574852.791666667	37264.2083333333
35	595404	574852.791666667	20551.2083333333
36	597141	574852.791666667	22288.2083333333
37	593408	574852.791666667	18555.2083333333
38	590072	574852.791666667	15219.2083333333
39	579799	574852.791666667	4946.20833333333
40	574205	574852.791666667	-647.791666666665
41	572775	574852.791666667	-2077.79166666666
42	572942	574852.791666667	-1910.79166666666
43	619567	574852.791666667	44714.2083333333
44	625809	574852.791666667	50956.2083333333
45	619916	574852.791666667	45063.2083333333
46	587625	574852.791666667	12772.2083333333
47	565742	574852.791666667	-9110.79166666666
48	557274	574852.791666667	-17578.7916666667
49	560576	518771.52173913	41804.4782608696
50	548854	518771.52173913	30082.4782608696
51	531673	518771.52173913	12901.4782608696
52	525919	518771.52173913	7147.47826086957
53	511038	518771.52173913	-7733.52173913043
54	498662	518771.52173913	-20109.5217391304
55	555362	518771.52173913	36590.4782608696
56	564591	518771.52173913	45819.4782608696
57	541657	518771.52173913	22885.4782608696
58	527070	518771.52173913	8298.47826086956
59	509846	518771.52173913	-8925.52173913044
60	514258	518771.52173913	-4513.52173913043
61	516922	518771.52173913	-1849.52173913043
62	507561	518771.52173913	-11210.5217391304
63	492622	518771.52173913	-26149.5217391304
64	490243	518771.52173913	-28528.5217391304
65	469357	518771.52173913	-49414.5217391304
66	477580	518771.52173913	-41191.5217391304
67	528379	518771.52173913	9607.47826086956
68	533590	518771.52173913	14818.4782608696
69	517945	518771.52173913	-826.521739130435
70	506174	518771.52173913	-12597.5217391304
71	501866	518771.52173913	-16905.5217391304

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)

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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