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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: Wed, 12 Dec 2007 01:56:14 -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/12/t1197448896bl7d65xc3ii0q9q.htm/, Retrieved Wed, 12 Dec 2007 09:41:47 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.9383 0 0.9217 0 0.9095 0 0.8920 0 0.8742 0 0.8532 0 0.8607 0 0.9005 0 0.9111 0 0.9059 0 0.8883 0 0.8924 0 0.8833 1 0.8700 1 0.8758 1 0.8858 1 0.9170 1 0.9554 1 0.9922 1 0.9778 1 0.9808 1 0.9811 1 1.0014 1 1.0183 1 1.0622 1 1.0773 1 1.0807 1 1.0848 1 1.1582 1 1.1663 1 1.1372 1 1.1139 1 1.1222 1 1.1692 1 1.1702 1 1.2286 1 1.2613 1 1.2646 1 1.2262 1 1.1985 1 1.2007 1 1.2138 1 1.2266 1 1.2176 1 1.2218 1 1.2490 1 1.2991 1 1.3408 1 1.3119 1 1.3014 1 1.3201 1 1.2938 1 1.2694 1 1.2165 1 1.2037 1 1.2292 1 1.2256 1 1.2015 1 1.1786 1 1.1856 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	11 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 0.89565 + 0.245329166666667x[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)	0.89565	0.034605	25.8818	0	0
x	0.245329166666667	0.03869	6.3409	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.639852117567922
R-squared	0.409410732356155
Adjusted R-squared	0.399228158776088
F-TEST (value)	40.2069996486575
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	3.71244064378828e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.119876475875756
Sum Squared Residuals	0.833481429166667

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	0.9383	0.895650000000002	0.0426499999999985
2	0.9217	0.89565	0.0260499999999998
3	0.9095	0.89565	0.0138500000000002
4	0.892	0.89565	-0.00364999999999976
5	0.8742	0.89565	-0.0214499999999998
6	0.8532	0.89565	-0.0424499999999998
7	0.8607	0.89565	-0.0349499999999998
8	0.9005	0.89565	0.00485000000000019
9	0.9111	0.89565	0.0154500000000002
10	0.9059	0.89565	0.0102500000000003
11	0.8883	0.89565	-0.0073499999999998
12	0.8924	0.89565	-0.0032499999999998
13	0.8833	1.14097916666667	-0.257679166666667
14	0.87	1.14097916666667	-0.270979166666667
15	0.8758	1.14097916666667	-0.265179166666667
16	0.8858	1.14097916666667	-0.255179166666667
17	0.917	1.14097916666667	-0.223979166666667
18	0.9554	1.14097916666667	-0.185579166666667
19	0.9922	1.14097916666667	-0.148779166666667
20	0.9778	1.14097916666667	-0.163179166666667
21	0.9808	1.14097916666667	-0.160179166666667
22	0.9811	1.14097916666667	-0.159879166666667
23	1.0014	1.14097916666667	-0.139579166666667
24	1.0183	1.14097916666667	-0.122679166666667
25	1.0622	1.14097916666667	-0.0787791666666666
26	1.0773	1.14097916666667	-0.0636791666666667
27	1.0807	1.14097916666667	-0.0602791666666666
28	1.0848	1.14097916666667	-0.0561791666666667
29	1.1582	1.14097916666667	0.0172208333333333
30	1.1663	1.14097916666667	0.0253208333333333
31	1.1372	1.14097916666667	-0.00377916666666665
32	1.1139	1.14097916666667	-0.0270791666666668
33	1.1222	1.14097916666667	-0.0187791666666666
34	1.1692	1.14097916666667	0.0282208333333334
35	1.1702	1.14097916666667	0.0292208333333333
36	1.2286	1.14097916666667	0.0876208333333333
37	1.2613	1.14097916666667	0.120320833333333
38	1.2646	1.14097916666667	0.123620833333333
39	1.2262	1.14097916666667	0.0852208333333333
40	1.1985	1.14097916666667	0.0575208333333333
41	1.2007	1.14097916666667	0.0597208333333335
42	1.2138	1.14097916666667	0.0728208333333333
43	1.2266	1.14097916666667	0.0856208333333333
44	1.2176	1.14097916666667	0.0766208333333334
45	1.2218	1.14097916666667	0.0808208333333334
46	1.249	1.14097916666667	0.108020833333333
47	1.2991	1.14097916666667	0.158120833333333
48	1.3408	1.14097916666667	0.199820833333333
49	1.3119	1.14097916666667	0.170920833333333
50	1.3014	1.14097916666667	0.160420833333333
51	1.3201	1.14097916666667	0.179120833333333
52	1.2938	1.14097916666667	0.152820833333333
53	1.2694	1.14097916666667	0.128420833333333
54	1.2165	1.14097916666667	0.0755208333333333
55	1.2037	1.14097916666667	0.0627208333333334
56	1.2292	1.14097916666667	0.0882208333333334
57	1.2256	1.14097916666667	0.0846208333333334
58	1.2015	1.14097916666667	0.0605208333333334
59	1.1786	1.14097916666667	0.0376208333333335
60	1.1856	1.14097916666667	0.0446208333333333

Charts produced by software:

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Parameters:

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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