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Seatbelt law - Q3

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

Title produced by software: Multiple Regression

Date of computation: Sun, 09 Dec 2007 03:38:19 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/09/t119719586057ty8frondy8ucm.htm/, Retrieved Sun, 09 Dec 2007 11:24:30 +0100

User-defined keywords:

s0650550 s0650062

Dataseries X:

» Textbox « » Textfile « » CSV «

8,0 0 8,1 0 8,3 0 8,2 0 8,1 0 7,7 0 7,6 0 7,7 0 8,2 0 8,4 0 8,4 0 8,6 0 8,4 0 8,5 0 8,7 0 8,7 0 8,6 0 7,4 0 7,3 0 7,4 0 9,0 0 9,2 0 9,2 0 8,5 0 8,3 0 8,3 0 8,6 0 8,6 0 8,5 0 8,1 0 8,1 0 8,0 0 8,6 0 8,7 0 8,7 0 8,6 0 8,4 0 8,4 0 8,7 0 8,7 0 8,5 0 8,3 0 8,3 0 8,3 0 8,1 0 8,2 0 8,1 0 8,1 0 7,9 0 7,7 0 8,1 0 8,0 0 7,7 1 7,8 1 7,6 1 7,4 1 7,7 1 7,8 1 7,5 1 7,2 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 8.2903846153846 -0.702884615384614x[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)	8.2903846153846	0.054911	150.9782	0	0
x	-0.702884615384614	0.15038	-4.674	1.8e-05	9e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.523075617402426
R-squared	0.273608101520929
Adjusted R-squared	0.261084103271290
F-TEST (value)	21.8467055062717
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	1.80405013676666e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.39596983313545
Sum Squared Residuals	9.09394230769233

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	8	8.29038461538466	-0.290384615384662
2	8.1	8.29038461538461	-0.190384615384615
3	8.3	8.29038461538461	0.0096153846153864
4	8.2	8.29038461538461	-0.090384615384615
5	8.1	8.29038461538461	-0.190384615384615
6	7.7	8.29038461538461	-0.590384615384614
7	7.6	8.29038461538461	-0.690384615384615
8	7.7	8.29038461538461	-0.590384615384614
9	8.2	8.29038461538461	-0.090384615384615
10	8.4	8.29038461538461	0.109615384615386
11	8.4	8.29038461538461	0.109615384615386
12	8.6	8.29038461538461	0.309615384615385
13	8.4	8.29038461538461	0.109615384615386
14	8.5	8.29038461538461	0.209615384615386
15	8.7	8.29038461538461	0.409615384615385
16	8.7	8.29038461538461	0.409615384615385
17	8.6	8.29038461538461	0.309615384615385
18	7.4	8.29038461538461	-0.890384615384614
19	7.3	8.29038461538461	-0.990384615384615
20	7.4	8.29038461538461	-0.890384615384614
21	9	8.29038461538461	0.709615384615386
22	9.2	8.29038461538461	0.909615384615385
23	9.2	8.29038461538461	0.909615384615385
24	8.5	8.29038461538461	0.209615384615386
25	8.3	8.29038461538461	0.0096153846153864
26	8.3	8.29038461538461	0.0096153846153864
27	8.6	8.29038461538461	0.309615384615385
28	8.6	8.29038461538461	0.309615384615385
29	8.5	8.29038461538461	0.209615384615386
30	8.1	8.29038461538461	-0.190384615384615
31	8.1	8.29038461538461	-0.190384615384615
32	8	8.29038461538461	-0.290384615384614
33	8.6	8.29038461538461	0.309615384615385
34	8.7	8.29038461538461	0.409615384615385
35	8.7	8.29038461538461	0.409615384615385
36	8.6	8.29038461538461	0.309615384615385
37	8.4	8.29038461538461	0.109615384615386
38	8.4	8.29038461538461	0.109615384615386
39	8.7	8.29038461538461	0.409615384615385
40	8.7	8.29038461538461	0.409615384615385
41	8.5	8.29038461538461	0.209615384615386
42	8.3	8.29038461538461	0.0096153846153864
43	8.3	8.29038461538461	0.0096153846153864
44	8.3	8.29038461538461	0.0096153846153864
45	8.1	8.29038461538461	-0.190384615384615
46	8.2	8.29038461538461	-0.090384615384615
47	8.1	8.29038461538461	-0.190384615384615
48	8.1	8.29038461538461	-0.190384615384615
49	7.9	8.29038461538461	-0.390384615384614
50	7.7	8.29038461538461	-0.590384615384614
51	8.1	8.29038461538461	-0.190384615384615
52	8	8.29038461538461	-0.290384615384614
53	7.7	7.5875	0.112500000000000
54	7.8	7.5875	0.2125
55	7.6	7.5875	0.0124999999999996
56	7.4	7.5875	-0.187500000000000
57	7.7	7.5875	0.112500000000000
58	7.8	7.5875	0.2125
59	7.5	7.5875	-0.0875
60	7.2	7.5875	-0.3875

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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