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

Title produced by software: Multiple Regression

Date of computation: Fri, 21 Dec 2007 06:14:57 -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/Dec/21/t1198241814ydk0oanxhagjvx9.htm/, Retrieved Fri, 21 Dec 2007 13:57:04 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

8.1 8.3 8.2 8.1 7.7 7.6 7.7 8.2 8.4 8.4 8.6 8.4 8.5 8.7 8.7 8.6 7.4 7.3 7.4 9 9.2 9.2 8.5 8.3 8.3 8.6 8.6 8.5 8.1 8.1 8 8.6 8.7 8.7 8.6 8.4 8.4 8.7 8.7 8.5 8.3 8.3 8.3 8.1 8.2 8.1 8.1 7.9 7.7 8.1 8 7.7 7.8 7.6 7.4 7.7 7.8 7.5 7.2 7

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

Werkl[t] = + 8.46881355932202 -0.00946929702695185t + 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)	8.46881355932202	0.120319	70.3863	0	0
t	-0.00946929702695185	0.00343	-2.7604	0.007716	0.003858

Multiple Linear Regression - Regression Statistics
Multiple R	0.340760119769236
R-squared	0.116117459225144
Adjusted R-squared	0.100878105073854
F-TEST (value)	7.61957876117147
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0.00771617930509949
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.460180470344337
Sum Squared Residuals	12.2824317866074

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	8.1	8.45934426229513	-0.359344262295127
2	8.3	8.44987496526813	-0.149874965268126
3	8.2	8.44040566824117	-0.240405668241176
4	8.1	8.43093637121422	-0.330936371214223
5	7.7	8.42146707418727	-0.721467074187271
6	7.6	8.41199777716032	-0.81199777716032
7	7.7	8.40252848013337	-0.702528480133367
8	8.2	8.39305918310642	-0.193059183106416
9	8.4	8.38358988607946	0.0164101139205365
10	8.4	8.37412058905251	0.0258794109474883
11	8.6	8.36465129202556	0.235348707974439
12	8.4	8.3551819949986	0.0448180050013921
13	8.5	8.34571269797166	0.154287302028344
14	8.7	8.3362434009447	0.363756599055295
15	8.7	8.32677410391775	0.373225896082247
16	8.6	8.3173048068908	0.282695193109199
17	7.4	8.30783550986385	-0.907835509863849
18	7.3	8.2983662128369	-0.998366212836897
19	7.4	8.28889691580994	-0.888896915809945
20	9	8.279427618783	0.720572381217006
21	9.2	8.26995832175604	0.930041678243958
22	9.2	8.26048902472909	0.93951097527091
23	8.5	8.25101972770214	0.248980272297862
24	8.3	8.24155043067519	0.0584495693248146
25	8.3	8.23208113364823	0.0679188663517664
26	8.6	8.22261183662128	0.377388163378717
27	8.6	8.21314253959433	0.386857460405669
28	8.5	8.20367324256738	0.296326757432621
29	8.1	8.19420394554043	-0.0942039455404272
30	8.1	8.18473464851347	-0.0847346485134754
31	8	8.17526535148652	-0.175265351486523
32	8.6	8.16579605445957	0.434203945540428
33	8.7	8.15632675743262	0.54367324256738
34	8.7	8.14685746040567	0.553142539594332
35	8.6	8.13738816337872	0.462611836621284
36	8.4	8.12791886635176	0.272081133648236
37	8.4	8.11844956932481	0.281550430675188
38	8.7	8.10898027229786	0.591019727702139
39	8.7	8.09951097527091	0.600489024729091
40	8.5	8.09004167824396	0.409958321756043
41	8.3	8.080572381217	0.219427618782996
42	8.3	8.07110308419005	0.228896915809948
43	8.3	8.0616337871631	0.238366212836900
44	8.1	8.05216449013615	0.0478355098638505
45	8.2	8.0426951931092	0.157304806890802
46	8.1	8.03322589608224	0.0667741039177542
47	8.1	8.0237565990553	0.076243400944706
48	7.9	8.01428730202834	-0.114287302028341
49	7.7	8.00481800500139	-0.30481800500139
50	8.1	7.99534870797444	0.104651292025562
51	8	7.98587941094749	0.0141205890525137
52	7.7	7.97641011392053	-0.276410113920534
53	7.8	7.96694081689358	-0.166940816893583
54	7.6	7.95747151986663	-0.357471519866631
55	7.4	7.94800222283968	-0.548002222839678
56	7.7	7.93853292581273	-0.238532925812727
57	7.8	7.92906362878577	-0.129063628785775
58	7.5	7.91959433175882	-0.419594331758823
59	7.2	7.91012503473187	-0.710125034731871
60	7	7.90065573770492	-0.90065573770492

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

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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