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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, 21 Nov 2007 06:56:14 -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/Nov/21/t1195652918jhygpn9emb95gue.htm/, Retrieved Wed, 21 Nov 2007 14:48:48 +0100

User-defined keywords:

s0650531

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 1,6 1 1,6 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.40222222222222 + 0.0783333333333335x[t] + 0.00250000000000066M1[t] + 0.0169444444444444M2[t] + 0.0163888888888888M3[t] + 0.0158333333333333M4[t] + 0.0136111111111111M5[t] + 0.0113888888888889M6[t] -0.000555555555555579M7[t] + 0.00555555555555554M8[t] + 0.00499999999999998M9[t] + 0.00444444444444443M10[t] + 0.00222222222222222M11[t] + 0.00222222222222222t + 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)	1.40222222222222	0.010685	131.2371	0	0
x	0.0783333333333335	0.009044	8.6611	0	0
M1	0.00250000000000066	0.012604	0.1983	0.843466	0.421733
M2	0.0169444444444444	0.012591	1.3457	0.183634	0.091817
M3	0.0163888888888888	0.012582	1.3026	0.197861	0.09893
M4	0.0158333333333333	0.012575	1.2591	0.213023	0.106512
M5	0.0136111111111111	0.012571	1.0828	0.283387	0.141693
M6	0.0113888888888889	0.012569	0.9061	0.368631	0.184316
M7	-0.000555555555555579	0.012564	-0.0442	0.964883	0.482441
M8	0.00555555555555554	0.012551	0.4426	0.659685	0.329843
M9	0.00499999999999998	0.012542	0.3987	0.691599	0.3458
M10	0.00444444444444443	0.012535	0.3546	0.724195	0.362098
M11	0.00222222222222222	0.01253	0.1773	0.859854	0.429927
t	0.00222222222222222	0.000188	11.8504	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.96746207394789
R-squared	0.935982864527553
Adjusted R-squared	0.921634196232005
F-TEST (value)	65.2313403061898
F-TEST (DF numerator)	13
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0217009013355194
Sum Squared Residuals	0.0273138888888891

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.43	1.40694444444444	0.0230555555555585
2	1.43	1.42361111111111	0.00638888888888877
3	1.43	1.42527777777778	0.00472222222222195
4	1.43	1.42694444444444	0.00305555555555539
5	1.43	1.42694444444444	0.00305555555555547
6	1.43	1.42694444444444	0.0030555555555554
7	1.43	1.41722222222222	0.0127777777777777
8	1.43	1.42555555555556	0.0044444444444443
9	1.43	1.42722222222222	0.00277777777777762
10	1.43	1.42888888888889	0.00111111111111095
11	1.43	1.42888888888889	0.00111111111111097
12	1.43	1.42888888888889	0.00111111111111097
13	1.43	1.43361111111111	-0.00361111111111185
14	1.43	1.45027777777778	-0.0202777777777779
15	1.43	1.45194444444444	-0.0219444444444445
16	1.43	1.45361111111111	-0.0236111111111112
17	1.43	1.45361111111111	-0.0236111111111112
18	1.43	1.45361111111111	-0.0236111111111112
19	1.44	1.44388888888889	-0.00388888888888897
20	1.48	1.45222222222222	0.0277777777777777
21	1.48	1.45388888888889	0.0261111111111111
22	1.48	1.45555555555556	0.0244444444444444
23	1.48	1.45555555555556	0.0244444444444444
24	1.48	1.45555555555556	0.0244444444444444
25	1.48	1.46027777777778	0.0197222222222216
26	1.48	1.47694444444444	0.00305555555555555
27	1.48	1.47861111111111	0.00138888888888892
28	1.48	1.48027777777778	-0.000277777777777775
29	1.48	1.48027777777778	-0.000277777777777789
30	1.48	1.48027777777778	-0.000277777777777771
31	1.48	1.47055555555556	0.00944444444444446
32	1.48	1.47888888888889	0.00111111111111112
33	1.48	1.48055555555556	-0.000555555555555545
34	1.48	1.48222222222222	-0.00222222222222221
35	1.48	1.48222222222222	-0.00222222222222222
36	1.48	1.48222222222222	-0.00222222222222221
37	1.48	1.48694444444445	-0.00694444444444504
38	1.48	1.50361111111111	-0.0236111111111111
39	1.48	1.50527777777778	-0.0252777777777777
40	1.48	1.50694444444444	-0.0269444444444444
41	1.48	1.50694444444444	-0.0269444444444444
42	1.48	1.50694444444444	-0.0269444444444444
43	1.48	1.49722222222222	-0.0172222222222221
44	1.48	1.50555555555556	-0.0255555555555555
45	1.48	1.50722222222222	-0.0272222222222221
46	1.48	1.50888888888889	-0.0288888888888888
47	1.48	1.50888888888889	-0.0288888888888888
48	1.48	1.50888888888889	-0.0288888888888888
49	1.48	1.51361111111111	-0.0336111111111116
50	1.57	1.53027777777778	0.0397222222222224
51	1.58	1.53194444444444	0.0480555555555558
52	1.58	1.53361111111111	0.0463888888888891
53	1.58	1.53361111111111	0.0463888888888891
54	1.58	1.53361111111111	0.0463888888888891
55	1.59	1.60222222222222	-0.0122222222222221
56	1.6	1.61055555555556	-0.0105555555555554
57	1.6	1.61222222222222	-0.0122222222222221
58	1.61	1.61388888888889	-0.00388888888888877
59	1.61	1.61388888888889	-0.00388888888888877
60	1.61	1.61388888888889	-0.00388888888888876
61	1.62	1.61861111111111	0.00138888888888843
62	1.63	1.63527777777778	-0.00527777777777783
63	1.63	1.63694444444444	-0.00694444444444445
64	1.64	1.63861111111111	0.00138888888888886
65	1.64	1.63861111111111	0.00138888888888886
66	1.64	1.63861111111111	0.00138888888888887
67	1.64	1.62888888888889	0.0111111111111111
68	1.64	1.63722222222222	0.00277777777777776
69	1.65	1.63888888888889	0.0111111111111111
70	1.65	1.64055555555556	0.00944444444444444
71	1.65	1.64055555555556	0.00944444444444445
72	1.65	1.64055555555556	0.00944444444444444

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly 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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FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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