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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, 12 Dec 2007 02:57:31 -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/12/t1197455074zq4eoc23cs7n767.htm/, Retrieved Wed, 12 Dec 2007 11:24:44 +0100

User-defined keywords:

fredje

Dataseries X:

» Textbox « » Textfile « » CSV «

12398.4 0 13882.3 0 15861.5 0 13286.1 0 15634.9 0 14211 0 13646.8 0 12224.6 0 15916.4 0 16535.9 0 15796 0 14418.6 0 15044.5 0 14944.2 0 16754.8 0 14254 0 15454.9 0 15644.8 0 14568.3 0 12520.2 0 14803 0 15873.2 0 14755.3 0 12875.1 0 14291.1 1 14205.3 1 15859.4 1 15258.9 1 15498.6 1 14106.5 1 15023.6 1 12083 1 15761.3 1 16943 1 15070.3 1 13659.6 1 14768.9 1 14725.1 1 15998.1 1 15370.6 1 14956.9 1 15469.7 1 15101.8 1 11703.7 1 16283.6 1 16726.5 1 14968.9 1 14861 1 14583.3 1 15305.8 1 17903.9 1 16379.4 1 15420.3 1 17870.5 1 15912.8 1 13866.5 1 17823.2 1 17872 1 17420.4 1 16704.4 1 15991.2 1 16583.6 1 19123.5 1 17838.7 1 17209.4 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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 14637.7 + 1033.13658536586x[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)	14637.7	298.825271	48.9841	0	0
x	1033.13658536586	376.25482	2.7458	0.007857	0.003929

Multiple Linear Regression - Regression Statistics
Multiple R	0.326933189100534
R-squared	0.106885310135445
Adjusted R-squared	0.0927088864868016
F-TEST (value)	7.53965265038275
F-TEST (DF numerator)	1
F-TEST (DF denominator)	63
p-value	0.0078570299419064
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1463.93887164819
Sum Squared Residuals	135016372.255122

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	12398.4	14637.7000000000	-2239.30000000005
2	13882.3	14637.7	-755.400000000005
3	15861.5	14637.7	1223.80000000000
4	13286.1	14637.7	-1351.60000000000
5	15634.9	14637.7	997.200000000002
6	14211	14637.7	-426.699999999998
7	13646.8	14637.7	-990.899999999998
8	12224.6	14637.7	-2413.1
9	15916.4	14637.7	1278.70000000000
10	16535.9	14637.7	1898.20000000000
11	15796	14637.7	1158.30000000000
12	14418.6	14637.7	-219.099999999998
13	15044.5	14637.7	406.800000000002
14	14944.2	14637.7	306.500000000003
15	16754.8	14637.7	2117.1
16	14254	14637.7	-383.699999999998
17	15454.9	14637.7	817.200000000002
18	15644.8	14637.7	1007.10000000000
19	14568.3	14637.7	-69.3999999999986
20	12520.2	14637.7	-2117.50000000000
21	14803	14637.7	165.300000000002
22	15873.2	14637.7	1235.50000000000
23	14755.3	14637.7	117.600000000001
24	12875.1	14637.7	-1762.60000000000
25	14291.1	15670.8365853659	-1379.73658536585
26	14205.3	15670.8365853659	-1465.53658536585
27	15859.4	15670.8365853659	188.563414634146
28	15258.9	15670.8365853659	-411.936585365854
29	15498.6	15670.8365853659	-172.236585365853
30	14106.5	15670.8365853659	-1564.33658536585
31	15023.6	15670.8365853659	-647.236585365853
32	12083	15670.8365853659	-3587.83658536585
33	15761.3	15670.8365853659	90.4634146341456
34	16943	15670.8365853659	1272.16341463415
35	15070.3	15670.8365853659	-600.536585365854
36	13659.6	15670.8365853659	-2011.23658536585
37	14768.9	15670.8365853659	-901.936585365854
38	14725.1	15670.8365853659	-945.736585365853
39	15998.1	15670.8365853659	327.263414634147
40	15370.6	15670.8365853659	-300.236585365853
41	14956.9	15670.8365853659	-713.936585365854
42	15469.7	15670.8365853659	-201.136585365853
43	15101.8	15670.8365853659	-569.036585365854
44	11703.7	15670.8365853659	-3967.13658536585
45	16283.6	15670.8365853659	612.763414634147
46	16726.5	15670.8365853659	1055.66341463415
47	14968.9	15670.8365853659	-701.936585365854
48	14861	15670.8365853659	-809.836585365854
49	14583.3	15670.8365853659	-1087.53658536585
50	15305.8	15670.8365853659	-365.036585365854
51	17903.9	15670.8365853659	2233.06341463415
52	16379.4	15670.8365853659	708.563414634146
53	15420.3	15670.8365853659	-250.536585365854
54	17870.5	15670.8365853659	2199.66341463415
55	15912.8	15670.8365853659	241.963414634146
56	13866.5	15670.8365853659	-1804.33658536585
57	17823.2	15670.8365853659	2152.36341463415
58	17872	15670.8365853659	2201.16341463415
59	17420.4	15670.8365853659	1749.56341463415
60	16704.4	15670.8365853659	1033.56341463415
61	15991.2	15670.8365853659	320.363414634147
62	16583.6	15670.8365853659	912.763414634145
63	19123.5	15670.8365853659	3452.66341463415
64	17838.7	15670.8365853659	2167.86341463415
65	17209.4	15670.8365853659	1538.56341463415

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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