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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: Tue, 18 Dec 2007 06:53:55 -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/18/t1197985045pre6q86ar4onim1.htm/, Retrieved Tue, 18 Dec 2007 14:37:38 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,43 1,44 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,57 1,58 1,58 1,58 1,58 1,59 1,6 1,6 1,61 1,61 1,61 1,62 1,63 1,63 1,64 1,64 1,64 1,64 1,64 1,65 1,65 1,65 1,65

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.52166666666667 -0.0349999999999995M1[t] -0.0183333333333335M2[t] -0.0166666666666668M3[t] -0.0150000000000000M4[t] -0.0150000000000001M5[t] -0.0150000000000001M6[t] -0.0116666666666668M7[t] -0.00333333333333336M8[t] -0.0016666666666667M9[t] -4.32435393574798e-17M10[t] -2.40370335797946e-17M11[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)	1.52166666666667	0.03413	44.5844	0	0
M1	-0.0349999999999995	0.048267	-0.7251	0.471191	0.235595
M2	-0.0183333333333335	0.048267	-0.3798	0.705413	0.352706
M3	-0.0166666666666668	0.048267	-0.3453	0.731076	0.365538
M4	-0.0150000000000000	0.048267	-0.3108	0.757052	0.378526
M5	-0.0150000000000001	0.048267	-0.3108	0.757052	0.378526
M6	-0.0150000000000001	0.048267	-0.3108	0.757052	0.378526
M7	-0.0116666666666668	0.048267	-0.2417	0.809829	0.404915
M8	-0.00333333333333336	0.048267	-0.0691	0.945171	0.472586
M9	-0.0016666666666667	0.048267	-0.0345	0.972569	0.486285
M10	-4.32435393574798e-17	0.048267	0	1	0.5
M11	-2.40370335797946e-17	0.048267	0	1	0.5

Multiple Linear Regression - Regression Statistics
Multiple R	0.130939826267598
R-squared	0.0171452381029887
Adjusted R-squared	-0.16304480157813
F-TEST (value)	0.0951508647943614
F-TEST (DF numerator)	11
F-TEST (DF denominator)	60
p-value	0.99991298879269
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0836012360355196
Sum Squared Residuals	0.41935

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.43	1.48666666666666	-0.0566666666666635
2	1.43	1.50333333333333	-0.0733333333333333
3	1.43	1.505	-0.0749999999999998
4	1.43	1.50666666666667	-0.0766666666666667
5	1.43	1.50666666666667	-0.0766666666666667
6	1.43	1.50666666666667	-0.0766666666666667
7	1.43	1.51	-0.08
8	1.43	1.51833333333333	-0.0883333333333333
9	1.43	1.52	-0.09
10	1.43	1.52166666666667	-0.0916666666666668
11	1.43	1.52166666666667	-0.0916666666666667
12	1.43	1.52166666666667	-0.0916666666666668
13	1.43	1.48666666666667	-0.0566666666666673
14	1.43	1.50333333333333	-0.0733333333333334
15	1.43	1.505	-0.075
16	1.43	1.50666666666667	-0.0766666666666667
17	1.43	1.50666666666667	-0.0766666666666667
18	1.43	1.50666666666667	-0.0766666666666667
19	1.44	1.51	-0.07
20	1.48	1.51833333333333	-0.0383333333333334
21	1.48	1.52	-0.04
22	1.48	1.52166666666667	-0.0416666666666667
23	1.48	1.52166666666667	-0.0416666666666667
24	1.48	1.52166666666667	-0.0416666666666667
25	1.48	1.48666666666667	-0.00666666666666728
26	1.48	1.50333333333333	-0.0233333333333333
27	1.48	1.505	-0.025
28	1.48	1.50666666666667	-0.0266666666666667
29	1.48	1.50666666666667	-0.0266666666666667
30	1.48	1.50666666666667	-0.0266666666666667
31	1.48	1.51	-0.03
32	1.48	1.51833333333333	-0.0383333333333334
33	1.48	1.52	-0.04
34	1.48	1.52166666666667	-0.0416666666666667
35	1.48	1.52166666666667	-0.0416666666666667
36	1.48	1.52166666666667	-0.0416666666666667
37	1.48	1.48666666666667	-0.00666666666666728
38	1.48	1.50333333333333	-0.0233333333333333
39	1.48	1.505	-0.025
40	1.48	1.50666666666667	-0.0266666666666667
41	1.48	1.50666666666667	-0.0266666666666667
42	1.48	1.50666666666667	-0.0266666666666667
43	1.48	1.51	-0.03
44	1.48	1.51833333333333	-0.0383333333333334
45	1.48	1.52	-0.04
46	1.48	1.52166666666667	-0.0416666666666667
47	1.48	1.52166666666667	-0.0416666666666667
48	1.48	1.52166666666667	-0.0416666666666667
49	1.48	1.48666666666667	-0.00666666666666728
50	1.57	1.50333333333333	0.0666666666666667
51	1.58	1.505	0.0750000000000001
52	1.58	1.50666666666667	0.0733333333333334
53	1.58	1.50666666666667	0.0733333333333335
54	1.58	1.50666666666667	0.0733333333333334
55	1.59	1.51	0.0800000000000001
56	1.6	1.51833333333333	0.0816666666666668
57	1.6	1.52	0.0800000000000001
58	1.61	1.52166666666667	0.0883333333333334
59	1.61	1.52166666666667	0.0883333333333334
60	1.61	1.52166666666667	0.0883333333333334
61	1.62	1.48666666666667	0.133333333333333
62	1.63	1.50333333333333	0.126666666666667
63	1.63	1.505	0.125
64	1.64	1.50666666666667	0.133333333333333
65	1.64	1.50666666666667	0.133333333333333
66	1.64	1.50666666666667	0.133333333333333
67	1.64	1.51	0.13
68	1.64	1.51833333333333	0.121666666666667
69	1.65	1.52	0.13
70	1.65	1.52166666666667	0.128333333333333
71	1.65	1.52166666666667	0.128333333333333
72	1.65	1.52166666666667	0.128333333333333

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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