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*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Mon, 01 Dec 2008 03:00:48 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/01/t1228125865k41o78hsliq2wmm.htm/, Retrieved Mon, 01 Dec 2008 10:04:25 +0000

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/01/t1228125865k41o78hsliq2wmm.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

10511 0 10812 0 10738 0 10171 0 9721 0 9897 0 9828 0 9924 0 10371 0 10846 0 10413 0 10709 0 10662 0 10570 0 10297 0 10635 0 10872 0 10296 0 10383 0 10431 0 10574 0 10653 0 10805 0 10872 0 10625 0 10407 0 10463 0 10556 0 10646 0 10702 0 11353 1 11346 1 11451 1 11964 1 12574 1 13031 1 13812 1 14544 1 14931 1 14886 1 16005 1 17064 1 15168 1 16050 1 15839 1 15137 1 14954 1 15648 1 15305 1 15579 1 16348 1 15928 1 16171 1 15937 1 15713 1 15594 1 15683 1 16438 1 17032 1 17696 1 17745 1

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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 9200.6 + 1938.20833333333x[t] + 160.909027777779M1[t] + 75.4180555555555M2[t] + 158.760416666667M3[t] -51.0972222222222M4[t] + 107.045138888889M5[t] + 113.587500000000M6[t] -653.911805555556M7[t] -563.569444444444M8[t] -538.627083333333M9[t] -404.284722222222M10[t] -345.942361111111M11[t] + 89.6576388888889t + 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)	9200.6	567.14704	16.2226	0	0
x	1938.20833333333	547.52974	3.5399	0.000914	0.000457
M1	160.909027777779	636.499234	0.2528	0.801523	0.400761
M2	75.4180555555555	668.403854	0.1128	0.910643	0.455322
M3	158.760416666667	667.189857	0.238	0.812951	0.406476
M4	-51.0972222222222	666.333965	-0.0767	0.9392	0.4696
M5	107.045138888889	665.837558	0.1608	0.872965	0.436483
M6	113.587500000000	665.701441	0.1706	0.865248	0.432624
M7	-653.911805555556	667.952989	-0.979	0.332603	0.166301
M8	-563.569444444444	666.333965	-0.8458	0.401963	0.200982
M9	-538.627083333333	665.071999	-0.8099	0.422092	0.211046
M10	-404.284722222222	664.169126	-0.6087	0.545649	0.272825
M11	-345.942361111111	663.626813	-0.5213	0.604612	0.302306
t	89.6576388888889	15.492805	5.7871	1e-06	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.936086001609279
R-squared	0.876257002408847
Adjusted R-squared	0.842030215841081
F-TEST (value)	25.6014978407027
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	1.11022302462516e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1049.00014358490
Sum Squared Residuals	51718861.1583334

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	10511	9451.16666666666	1059.83333333334
2	10812	9455.33333333333	1356.66666666667
3	10738	9628.33333333333	1109.66666666667
4	10171	9508.13333333333	662.866666666666
5	9721	9755.93333333333	-34.9333333333336
6	9897	9852.13333333333	44.8666666666663
7	9828	9174.29166666667	653.708333333333
8	9924	9354.29166666667	569.708333333333
9	10371	9468.89166666667	902.108333333333
10	10846	9692.89166666667	1153.10833333333
11	10413	9840.89166666667	572.108333333333
12	10709	10276.4916666667	432.508333333333
13	10662	10527.0583333333	134.941666666665
14	10570	10531.225	38.7750000000003
15	10297	10704.225	-407.225000000000
16	10635	10584.025	50.9750000000001
17	10872	10831.825	40.1750000000001
18	10296	10928.025	-632.025
19	10383	10250.1833333333	132.816666666667
20	10431	10430.1833333333	0.816666666666263
21	10574	10544.7833333333	29.2166666666665
22	10653	10768.7833333333	-115.783333333333
23	10805	10916.7833333333	-111.783333333333
24	10872	11352.3833333333	-480.383333333333
25	10625	11602.95	-977.95
26	10407	11607.1166666667	-1200.11666666667
27	10463	11780.1166666667	-1317.11666666667
28	10556	11659.9166666667	-1103.91666666667
29	10646	11907.7166666667	-1261.71666666667
30	10702	12003.9166666667	-1301.91666666667
31	11353	13264.2833333333	-1911.28333333333
32	11346	13444.2833333333	-2098.28333333333
33	11451	13558.8833333333	-2107.88333333333
34	11964	13782.8833333333	-1818.88333333333
35	12574	13930.8833333333	-1356.88333333333
36	13031	14366.4833333333	-1335.48333333333
37	13812	14617.05	-805.050000000001
38	14544	14621.2166666667	-77.2166666666668
39	14931	14794.2166666667	136.783333333333
40	14886	14674.0166666667	211.983333333333
41	16005	14921.8166666667	1083.18333333333
42	17064	15018.0166666667	2045.98333333333
43	15168	14340.175	827.825
44	16050	14520.175	1529.825
45	15839	14634.775	1204.225
46	15137	14858.775	278.225
47	14954	15006.775	-52.7749999999996
48	15648	15442.375	205.625000000000
49	15305	15692.9416666667	-387.941666666668
50	15579	15697.1083333333	-118.108333333333
51	16348	15870.1083333333	477.891666666667
52	15928	15749.9083333333	178.091666666667
53	16171	15997.7083333333	173.291666666667
54	15937	16093.9083333333	-156.908333333333
55	15713	15416.0666666667	296.933333333334
56	15594	15596.0666666667	-2.06666666666615
57	15683	15710.6666666667	-27.6666666666661
58	16438	15934.6666666667	503.333333333333
59	17032	16082.6666666667	949.333333333333
60	17696	16518.2666666667	1177.73333333333
61	17745	16768.8333333333	976.166666666667

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

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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