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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 05:32:03 -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/t1195647962dmuxhlat9b47d2u.htm/, Retrieved Wed, 21 Nov 2007 13:26:12 +0100

User-defined keywords:

textiel

Dataseries X:

» Textbox « » Textfile « » CSV «

101.5 0 99.2 0 107.8 0 92.3 0 99.2 0 101.6 0 87 0 71.4 0 104.7 0 115.1 0 102.5 0 75.3 0 96.7 1 94.6 1 98.6 1 99.5 1 92 1 93.6 1 89.3 1 66.9 1 108.8 1 113.2 1 105.5 1 77.8 1 102.1 1 97 1 95.5 1 99.3 1 86.4 1 92.4 1 85.7 1 61.9 1 104.9 1 107.9 1 95.6 1 79.8 1 94.8 1 93.7 1 108.1 1 96.9 1 88.8 1 106.7 1 86.8 1 69.8 1 110.9 1 105.4 1 99.2 1 84.4 1 87.2 1 91.9 1 97.9 1 94.5 1 85 1 100.3 1 78.7 1 65.8 1 104.8 1 96 1 103.3 1 82.9 1 91.4 1 94.5 1 109.3 1 92.1 1 99.3 1 109.6 1 87.5 1 73.1 1 110.7 1 111.6 1 110.7 1 84 1 101.6 1 102.1 1 113.9 1 99 1 100.4 1 109.5 1 93 1 76.8 1 105.3 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] = + 96.4666666666666 -1.47826086956518x[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)	96.4666666666666	3.509054	27.4908	0	0
x	-1.47826086956518	3.801964	-0.3888	0.698459	0.349229

Multiple Linear Regression - Regression Statistics
Multiple R	0.0437033195659165
R-squared	0.00190998014108062
Adjusted R-squared	-0.0107240707432097
F-TEST (value)	0.151177176550365
F-TEST (DF numerator)	1
F-TEST (DF denominator)	79
p-value	0.698458914502653
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	12.1557182414647
Sum Squared Residuals	11673.1573913043

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	101.5	96.4666666666671	5.0333333333329
2	99.2	96.4666666666666	2.73333333333336
3	107.8	96.4666666666666	11.3333333333334
4	92.3	96.4666666666666	-4.16666666666663
5	99.2	96.4666666666666	2.73333333333337
6	101.6	96.4666666666666	5.13333333333336
7	87	96.4666666666666	-9.46666666666663
8	71.4	96.4666666666666	-25.0666666666666
9	104.7	96.4666666666666	8.23333333333337
10	115.1	96.4666666666666	18.6333333333334
11	102.5	96.4666666666666	6.03333333333337
12	75.3	96.4666666666666	-21.1666666666666
13	96.7	94.9884057971014	1.71159420289855
14	94.6	94.9884057971014	-0.388405797101454
15	98.6	94.9884057971014	3.61159420289855
16	99.5	94.9884057971014	4.51159420289855
17	92	94.9884057971014	-2.98840579710145
18	93.6	94.9884057971014	-1.38840579710145
19	89.3	94.9884057971014	-5.68840579710145
20	66.9	94.9884057971014	-28.0884057971014
21	108.8	94.9884057971014	13.8115942028985
22	113.2	94.9884057971014	18.2115942028986
23	105.5	94.9884057971014	10.5115942028986
24	77.8	94.9884057971014	-17.1884057971015
25	102.1	94.9884057971014	7.11159420289855
26	97	94.9884057971014	2.01159420289855
27	95.5	94.9884057971014	0.511594202898552
28	99.3	94.9884057971014	4.31159420289855
29	86.4	94.9884057971014	-8.58840579710144
30	92.4	94.9884057971014	-2.58840579710144
31	85.7	94.9884057971014	-9.28840579710145
32	61.9	94.9884057971014	-33.0884057971015
33	104.9	94.9884057971014	9.91159420289856
34	107.9	94.9884057971014	12.9115942028986
35	95.6	94.9884057971014	0.611594202898546
36	79.8	94.9884057971014	-15.1884057971015
37	94.8	94.9884057971014	-0.188405797101451
38	93.7	94.9884057971014	-1.28840579710145
39	108.1	94.9884057971014	13.1115942028985
40	96.9	94.9884057971014	1.91159420289856
41	88.8	94.9884057971014	-6.18840579710145
42	106.7	94.9884057971014	11.7115942028986
43	86.8	94.9884057971014	-8.18840579710145
44	69.8	94.9884057971014	-25.1884057971015
45	110.9	94.9884057971014	15.9115942028986
46	105.4	94.9884057971014	10.4115942028986
47	99.2	94.9884057971014	4.21159420289855
48	84.4	94.9884057971014	-10.5884057971014
49	87.2	94.9884057971014	-7.78840579710145
50	91.9	94.9884057971014	-3.08840579710144
51	97.9	94.9884057971014	2.91159420289856
52	94.5	94.9884057971014	-0.488405797101448
53	85	94.9884057971014	-9.98840579710145
54	100.3	94.9884057971014	5.31159420289855
55	78.7	94.9884057971014	-16.2884057971014
56	65.8	94.9884057971014	-29.1884057971015
57	104.8	94.9884057971014	9.81159420289855
58	96	94.9884057971014	1.01159420289855
59	103.3	94.9884057971014	8.31159420289855
60	82.9	94.9884057971014	-12.0884057971014
61	91.4	94.9884057971014	-3.58840579710144
62	94.5	94.9884057971014	-0.488405797101448
63	109.3	94.9884057971014	14.3115942028985
64	92.1	94.9884057971014	-2.88840579710145
65	99.3	94.9884057971014	4.31159420289855
66	109.6	94.9884057971014	14.6115942028985
67	87.5	94.9884057971014	-7.48840579710145
68	73.1	94.9884057971014	-21.8884057971015
69	110.7	94.9884057971014	15.7115942028986
70	111.6	94.9884057971014	16.6115942028985
71	110.7	94.9884057971014	15.7115942028986
72	84	94.9884057971014	-10.9884057971014
73	101.6	94.9884057971014	6.61159420289855
74	102.1	94.9884057971014	7.11159420289855
75	113.9	94.9884057971014	18.9115942028986
76	99	94.9884057971014	4.01159420289855
77	100.4	94.9884057971014	5.41159420289856
78	109.5	94.9884057971014	14.5115942028986
79	93	94.9884057971014	-1.98840579710145
80	76.8	94.9884057971014	-18.1884057971015
81	105.3	94.9884057971014	10.3115942028985

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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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