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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 03:29:37 -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/t1195467995fydjg3owuu0zbfu.htm/, Retrieved Mon, 19 Nov 2007 11:26:47 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

15859,4 0 15258,9 0 15498,6 0 15106,5 0 15023,6 1 12083,0 1 15761,3 0 16942,6 0 15070,3 0 13659,6 0 14768,9 0 14725,1 0 15998,1 0 15370,6 0 14956,9 0 15469,7 0 15101,8 1 11703,7 1 16283,6 0 16726,5 0 14968,9 0 14861,0 0 14583,3 0 15305,8 0 17903,9 0 16379,4 0 15420,3 0 17870,5 0 15912,8 1 13866,5 1 17823,2 0 17872,0 0 17422,0 0 16704,5 0 15991,2 0 16583,6 0 19123,5 0 17838,7 0 17209,4 0 18586,5 0 16258,1 1 15141,6 1 19202,1 0 17746,5 0 19090,1 0 18040,3 0 17515,5 0 17751,8 0 21072,4 0 17170,0 0 19439,5 0 19795,4 0 17574,9 1 16165,4 1 19464,6 0 19932,1 0 19961,2 0 17343,4 0 18924,2 0 18574,1 0 21350,6 0

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

x[t] = + 17103.4921568628 -2220.35215686275`y `[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)	17103.4921568628	258.576503	66.1448	0	0
`y `	-2220.35215686275	638.63685	-3.4767	0.000959	0.00048

Multiple Linear Regression - Regression Statistics
Multiple R	0.412355058380166
R-squared	0.17003669417171
Adjusted R-squared	0.155969519496654
F-TEST (value)	12.0874801159058
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	0.00095919990084825
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1846.60558607492
Sum Squared Residuals	201187179.240863

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	15859.4	17103.4921568627	-1244.09215686271
2	15258.9	17103.4921568627	-1844.59215686275
3	15498.6	17103.4921568627	-1604.89215686275
4	15106.5	17103.4921568627	-1996.99215686275
5	15023.6	14883.14	140.46
6	12083	14883.14	-2800.14
7	15761.3	17103.4921568627	-1342.19215686275
8	16942.6	17103.4921568627	-160.892156862747
9	15070.3	17103.4921568627	-2033.19215686275
10	13659.6	17103.4921568627	-3443.89215686275
11	14768.9	17103.4921568627	-2334.59215686275
12	14725.1	17103.4921568627	-2378.39215686275
13	15998.1	17103.4921568627	-1105.39215686275
14	15370.6	17103.4921568627	-1732.89215686275
15	14956.9	17103.4921568627	-2146.59215686275
16	15469.7	17103.4921568627	-1633.79215686274
17	15101.8	14883.14	218.659999999999
18	11703.7	14883.14	-3179.44
19	16283.6	17103.4921568627	-819.892156862745
20	16726.5	17103.4921568627	-376.992156862746
21	14968.9	17103.4921568627	-2134.59215686275
22	14861	17103.4921568627	-2242.49215686275
23	14583.3	17103.4921568627	-2520.19215686275
24	15305.8	17103.4921568627	-1797.69215686275
25	17903.9	17103.4921568627	800.407843137256
26	16379.4	17103.4921568627	-724.092156862746
27	15420.3	17103.4921568627	-1683.19215686275
28	17870.5	17103.4921568627	767.007843137254
29	15912.8	14883.14	1029.66
30	13866.5	14883.14	-1016.64
31	17823.2	17103.4921568627	719.707843137255
32	17872	17103.4921568627	768.507843137254
33	17422	17103.4921568627	318.507843137254
34	16704.5	17103.4921568627	-398.992156862746
35	15991.2	17103.4921568627	-1112.29215686274
36	16583.6	17103.4921568627	-519.892156862747
37	19123.5	17103.4921568627	2020.00784313725
38	17838.7	17103.4921568627	735.207843137255
39	17209.4	17103.4921568627	105.907843137256
40	18586.5	17103.4921568627	1483.00784313725
41	16258.1	14883.14	1374.96
42	15141.6	14883.14	258.46
43	19202.1	17103.4921568627	2098.60784313725
44	17746.5	17103.4921568627	643.007843137254
45	19090.1	17103.4921568627	1986.60784313725
46	18040.3	17103.4921568627	936.807843137254
47	17515.5	17103.4921568627	412.007843137254
48	17751.8	17103.4921568627	648.307843137254
49	21072.4	17103.4921568627	3968.90784313726
50	17170	17103.4921568627	66.5078431372545
51	19439.5	17103.4921568627	2336.00784313725
52	19795.4	17103.4921568627	2691.90784313726
53	17574.9	14883.14	2691.76
54	16165.4	14883.14	1282.26
55	19464.6	17103.4921568627	2361.10784313725
56	19932.1	17103.4921568627	2828.60784313725
57	19961.2	17103.4921568627	2857.70784313726
58	17343.4	17103.4921568627	239.907843137256
59	18924.2	17103.4921568627	1820.70784313726
60	18574.1	17103.4921568627	1470.60784313725
61	21350.6	17103.4921568627	4247.10784313725

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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