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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: Thu, 22 Nov 2007 08:34:59 -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/t119574527009rr3z8sb7pea1l.htm/, Retrieved Thu, 22 Nov 2007 16:27:50 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.44 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 1.48 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 1.60 1 1.60 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

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	7 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.47166666666667 + 0.156111111111111x[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)	1.47166666666667	0.005083	289.5306	0	0
x	0.156111111111111	0.010166	15.3564	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.878126429243398
R-squared	0.771106025735761
Adjusted R-squared	0.7678361118177
F-TEST (value)	235.818448148359
F-TEST (DF numerator)	1
F-TEST (DF denominator)	70
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0373518236523831
Sum Squared Residuals	0.097661111111111

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.43	1.47166666666666	-0.0416666666666631
2	1.43	1.47166666666667	-0.0416666666666669
3	1.43	1.47166666666667	-0.0416666666666668
4	1.43	1.47166666666667	-0.0416666666666668
5	1.43	1.47166666666667	-0.0416666666666668
6	1.43	1.47166666666667	-0.0416666666666668
7	1.43	1.47166666666667	-0.0416666666666668
8	1.43	1.47166666666667	-0.0416666666666668
9	1.43	1.47166666666667	-0.0416666666666668
10	1.43	1.47166666666667	-0.0416666666666668
11	1.43	1.47166666666667	-0.0416666666666668
12	1.43	1.47166666666667	-0.0416666666666668
13	1.43	1.47166666666667	-0.0416666666666668
14	1.43	1.47166666666667	-0.0416666666666668
15	1.43	1.47166666666667	-0.0416666666666668
16	1.43	1.47166666666667	-0.0416666666666668
17	1.43	1.47166666666667	-0.0416666666666668
18	1.43	1.47166666666667	-0.0416666666666668
19	1.44	1.47166666666667	-0.0316666666666668
20	1.48	1.47166666666667	0.00833333333333328
21	1.48	1.47166666666667	0.00833333333333328
22	1.48	1.47166666666667	0.00833333333333328
23	1.48	1.47166666666667	0.00833333333333328
24	1.48	1.47166666666667	0.00833333333333328
25	1.48	1.47166666666667	0.00833333333333328
26	1.48	1.47166666666667	0.00833333333333328
27	1.48	1.47166666666667	0.00833333333333328
28	1.48	1.47166666666667	0.00833333333333328
29	1.48	1.47166666666667	0.00833333333333328
30	1.48	1.47166666666667	0.00833333333333328
31	1.48	1.47166666666667	0.00833333333333328
32	1.48	1.47166666666667	0.00833333333333328
33	1.48	1.47166666666667	0.00833333333333328
34	1.48	1.47166666666667	0.00833333333333328
35	1.48	1.47166666666667	0.00833333333333328
36	1.48	1.47166666666667	0.00833333333333328
37	1.48	1.47166666666667	0.00833333333333328
38	1.48	1.47166666666667	0.00833333333333328
39	1.48	1.47166666666667	0.00833333333333328
40	1.48	1.47166666666667	0.00833333333333328
41	1.48	1.47166666666667	0.00833333333333328
42	1.48	1.47166666666667	0.00833333333333328
43	1.48	1.47166666666667	0.00833333333333328
44	1.48	1.47166666666667	0.00833333333333328
45	1.48	1.47166666666667	0.00833333333333328
46	1.48	1.47166666666667	0.00833333333333328
47	1.48	1.47166666666667	0.00833333333333328
48	1.48	1.47166666666667	0.00833333333333328
49	1.48	1.47166666666667	0.00833333333333328
50	1.57	1.47166666666667	0.0983333333333333
51	1.58	1.47166666666667	0.108333333333333
52	1.58	1.47166666666667	0.108333333333333
53	1.58	1.47166666666667	0.108333333333333
54	1.58	1.47166666666667	0.108333333333333
55	1.59	1.62777777777778	-0.0377777777777777
56	1.6	1.62777777777778	-0.0277777777777777
57	1.6	1.62777777777778	-0.0277777777777777
58	1.61	1.62777777777778	-0.0177777777777777
59	1.61	1.62777777777778	-0.0177777777777777
60	1.61	1.62777777777778	-0.0177777777777777
61	1.62	1.62777777777778	-0.00777777777777766
62	1.63	1.62777777777778	0.00222222222222215
63	1.63	1.62777777777778	0.00222222222222215
64	1.64	1.62777777777778	0.0122222222222222
65	1.64	1.62777777777778	0.0122222222222222
66	1.64	1.62777777777778	0.0122222222222222
67	1.64	1.62777777777778	0.0122222222222222
68	1.64	1.62777777777778	0.0122222222222222
69	1.65	1.62777777777778	0.0222222222222222
70	1.65	1.62777777777778	0.0222222222222222
71	1.65	1.62777777777778	0.0222222222222222
72	1.65	1.62777777777778	0.0222222222222222

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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