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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: Mon, 19 Nov 2007 10:17:30 -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/19/t1195492762cvaclr5nal2rjic.htm/, Retrieved Mon, 19 Nov 2007 18:19:31 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

103,6500 0 103,8700 0 103,9400 0 105,3200 0 105,5400 0 106,0800 0 106,2100 0 105,5300 0 105,5600 0 105,1400 0 105,9700 0 105,4500 0 106,2200 0 106,3100 0 107,3800 0 109,3100 0 110,8200 0 111,2200 0 110,6600 0 110,7600 0 110,6900 0 111,0800 0 110,9700 0 110,2400 0 112,5100 1 111,5200 1 112,1300 1 112,2300 1 112,9200 1 111,8900 1 111,9900 1 111,5100 1 112,3300 1 112,0400 1 112,0900 1 111,4100 1 112,6100 1 113,1400 1 113,6500 1 114,2600 1 114,4000 1 114,9300 1 114,8600 1 114,9500 1 116,1700 1 114,6000 1 114,6200 1 113,8200 1 115,0200 1 115,1800 1 115,5900 1 116,6000 1 117,0700 1 116,9600 1 116,6600 1 116,0700 1 116,0400 1 115,8100 1 116,2200 1 115,8500 1 116,4300 1 117,3900 1 119,1700 1 119,2400 1 120,0300 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] = + 107.413333333333 + 7.26739837398373x[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)	107.413333333333	0.495847	216.626	0	0
x	7.26739837398373	0.624327	11.6404	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.826206154961996
R-squared	0.682616610497086
Adjusted R-squared	0.677578778917675
F-TEST (value)	135.498100668314
F-TEST (DF numerator)	1
F-TEST (DF denominator)	63
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.42914385395515
Sum Squared Residuals	371.74661138211

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	103.65	107.413333333333	-3.76333333333286
2	103.87	107.413333333333	-3.54333333333337
3	103.94	107.413333333333	-3.47333333333335
4	105.32	107.413333333333	-2.09333333333336
5	105.54	107.413333333333	-1.87333333333335
6	106.08	107.413333333333	-1.33333333333335
7	106.21	107.413333333333	-1.20333333333336
8	105.53	107.413333333333	-1.88333333333335
9	105.56	107.413333333333	-1.85333333333335
10	105.14	107.413333333333	-2.27333333333335
11	105.97	107.413333333333	-1.44333333333335
12	105.45	107.413333333333	-1.96333333333335
13	106.22	107.413333333333	-1.19333333333335
14	106.31	107.413333333333	-1.10333333333335
15	107.38	107.413333333333	-0.0333333333333569
16	109.31	107.413333333333	1.89666666666665
17	110.82	107.413333333333	3.40666666666664
18	111.22	107.413333333333	3.80666666666665
19	110.66	107.413333333333	3.24666666666664
20	110.76	107.413333333333	3.34666666666665
21	110.69	107.413333333333	3.27666666666665
22	111.08	107.413333333333	3.66666666666665
23	110.97	107.413333333333	3.55666666666665
24	110.24	107.413333333333	2.82666666666664
25	112.51	114.680731707317	-2.17073170731707
26	111.52	114.680731707317	-3.16073170731708
27	112.13	114.680731707317	-2.55073170731708
28	112.23	114.680731707317	-2.45073170731707
29	112.92	114.680731707317	-1.76073170731707
30	111.89	114.680731707317	-2.79073170731707
31	111.99	114.680731707317	-2.69073170731708
32	111.51	114.680731707317	-3.17073170731707
33	112.33	114.680731707317	-2.35073170731707
34	112.04	114.680731707317	-2.64073170731707
35	112.09	114.680731707317	-2.59073170731707
36	111.41	114.680731707317	-3.27073170731708
37	112.61	114.680731707317	-2.07073170731707
38	113.14	114.680731707317	-1.54073170731707
39	113.65	114.680731707317	-1.03073170731707
40	114.26	114.680731707317	-0.420731707317068
41	114.4	114.680731707317	-0.280731707317067
42	114.93	114.680731707317	0.249268292682934
43	114.86	114.680731707317	0.179268292682926
44	114.95	114.680731707317	0.269268292682930
45	116.17	114.680731707317	1.48926829268293
46	114.6	114.680731707317	-0.0807317073170788
47	114.62	114.680731707317	-0.0607317073170686
48	113.82	114.680731707317	-0.86073170731708
49	115.02	114.680731707317	0.339268292682923
50	115.18	114.680731707317	0.499268292682934
51	115.59	114.680731707317	0.90926829268293
52	116.6	114.680731707317	1.91926829268292
53	117.07	114.680731707317	2.38926829268292
54	116.96	114.680731707317	2.27926829268292
55	116.66	114.680731707317	1.97926829268292
56	116.07	114.680731707317	1.38926829268292
57	116.04	114.680731707317	1.35926829268293
58	115.81	114.680731707317	1.12926829268293
59	116.22	114.680731707317	1.53926829268293
60	115.85	114.680731707317	1.16926829268292
61	116.43	114.680731707317	1.74926829268293
62	117.39	114.680731707317	2.70926829268293
63	119.17	114.680731707317	4.48926829268293
64	119.24	114.680731707317	4.55926829268292
65	120.03	114.680731707317	5.34926829268293

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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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