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Case III Question III

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 11:20:32 -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/t1195755209pbepm5rztppg6nr.htm/, Retrieved Thu, 22 Nov 2007 19:13:29 +0100

User-defined keywords:

Eigen gegevens zonder seasonal dummies zonder linear trend

Dataseries X:

» Textbox « » Textfile « » CSV «

77,80 0 81,30 0 87,70 0 78,40 0 76,20 0 85,30 0 69,30 0 66,80 0 77,10 0 79,40 0 68,60 0 70,60 0 75,60 0 71,50 0 92,20 0 76,40 0 75,00 0 86,40 0 66,90 0 76,00 0 80,40 0 106,20 0 83,90 0 99,50 0 100,10 0 97,00 0 112,70 0 89,10 0 99,10 0 89,20 0 71,70 0 80,00 0 90,50 0 100,80 0 102,70 0 87,70 0 109,10 0 113,50 0 122,50 0 89,30 1 107,80 1 94,00 1 83,00 1 92,40 1 94,10 1 97,80 1 101,70 1 73,40 1 98,90 1 95,90 1 108,00 1 98,50 1 97,60 1 97,30 1 86,50 1 96,80 1 106,70 1 112,60 1 96,10 1 86,80 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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 86.5179487179487 + 9.44395604395605x[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)	86.5179487179487	2.045439	42.298	0	0
x	9.44395604395605	3.457424	2.7315	0.008339	0.00417

Multiple Linear Regression - Regression Statistics
Multiple R	0.337605647932651
R-squared	0.113977573516025
Adjusted R-squared	0.0987013247835427
F-TEST (value)	7.46109699521133
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0.00833929729316496
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	12.7737655181309
Sum Squared Residuals	9463.80695970696

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	77.8	86.5179487179489	-8.71794871794886
2	81.3	86.5179487179487	-5.21794871794872
3	87.7	86.5179487179487	1.18205128205129
4	78.4	86.5179487179487	-8.11794871794871
5	76.2	86.5179487179487	-10.3179487179487
6	85.3	86.5179487179487	-1.21794871794872
7	69.3	86.5179487179487	-17.2179487179487
8	66.8	86.5179487179487	-19.7179487179487
9	77.1	86.5179487179487	-9.41794871794872
10	79.4	86.5179487179487	-7.11794871794871
11	68.6	86.5179487179487	-17.9179487179487
12	70.6	86.5179487179487	-15.9179487179487
13	75.6	86.5179487179487	-10.9179487179487
14	71.5	86.5179487179487	-15.0179487179487
15	92.2	86.5179487179487	5.68205128205129
16	76.4	86.5179487179487	-10.1179487179487
17	75	86.5179487179487	-11.5179487179487
18	86.4	86.5179487179487	-0.117948717948708
19	66.9	86.5179487179487	-19.6179487179487
20	76	86.5179487179487	-10.5179487179487
21	80.4	86.5179487179487	-6.11794871794871
22	106.2	86.5179487179487	19.6820512820513
23	83.9	86.5179487179487	-2.61794871794871
24	99.5	86.5179487179487	12.9820512820513
25	100.1	86.5179487179487	13.5820512820513
26	97	86.5179487179487	10.4820512820513
27	112.7	86.5179487179487	26.1820512820513
28	89.1	86.5179487179487	2.58205128205128
29	99.1	86.5179487179487	12.5820512820513
30	89.2	86.5179487179487	2.68205128205129
31	71.7	86.5179487179487	-14.8179487179487
32	80	86.5179487179487	-6.51794871794871
33	90.5	86.5179487179487	3.98205128205129
34	100.8	86.5179487179487	14.2820512820513
35	102.7	86.5179487179487	16.1820512820513
36	87.7	86.5179487179487	1.18205128205129
37	109.1	86.5179487179487	22.5820512820513
38	113.5	86.5179487179487	26.9820512820513
39	122.5	86.5179487179487	35.9820512820513
40	89.3	95.9619047619048	-6.66190476190476
41	107.8	95.9619047619048	11.8380952380952
42	94	95.9619047619048	-1.96190476190476
43	83	95.9619047619048	-12.9619047619048
44	92.4	95.9619047619048	-3.56190476190476
45	94.1	95.9619047619048	-1.86190476190477
46	97.8	95.9619047619048	1.83809523809524
47	101.7	95.9619047619048	5.73809523809524
48	73.4	95.9619047619048	-22.5619047619048
49	98.9	95.9619047619048	2.93809523809524
50	95.9	95.9619047619048	-0.0619047619047556
51	108	95.9619047619048	12.0380952380952
52	98.5	95.9619047619048	2.53809523809524
53	97.6	95.9619047619048	1.63809523809523
54	97.3	95.9619047619048	1.33809523809524
55	86.5	95.9619047619048	-9.46190476190476
56	96.8	95.9619047619048	0.838095238095236
57	106.7	95.9619047619048	10.7380952380952
58	112.6	95.9619047619048	16.6380952380952
59	96.1	95.9619047619048	0.138095238095233
60	86.8	95.9619047619048	-9.16190476190476

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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