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WS8 Q3 trend

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

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 09:57:19 -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/18/t119540472010rd2vwg8swheib.htm/, Retrieved Sun, 18 Nov 2007 17:52:00 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1178 0 2141 0 2238 0 2685 0 4341 0 5376 0 4478 0 6404 0 4617 0 3024 0 1897 0 2075 0 1351 0 2211 0 2453 0 3042 0 4765 0 4992 1 4601 1 6266 1 4812 1 3159 1 1916 1 2237 1 1595 1 2453 1 2226 1 3597 1 4706 1 4974 1 5756 1 5493 1 5004 1 3225 1 2006 1 2291 1 1588 1 2105 1 2191 1 3591 1 4668 1 4885 1 5822 1 5599 1 5340 1 3082 1 2010 1 2301 1 1514 1 1979 1 2480 1 3499 1 4676 1 5585 1 5610 1 5796 1 6199 1 3030 1 1930 1 2552 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	5 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

Huwelijken[t] = + 3192.41014977826 + 511.912993560917Dummy[t] + 0.0328591749644455t + 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)	3192.41014977826	413.135581	7.7273	0	0
Dummy	511.912993560917	713.985512	0.717	0.476315	0.238157
t	0.0328591749644455	18.577896	0.0018	0.998595	0.499297

Multiple Linear Regression - Regression Statistics
Multiple R	0.150497327732756
R-squared	0.0226494456547004
Adjusted R-squared	-0.0116435562521524
F-TEST (value)	0.660468445317833
F-TEST (DF numerator)	2
F-TEST (DF denominator)	57
p-value	0.520517533744738
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1557.66549467415
Sum Squared Residuals	138300342.218012

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1178	3192.44300895323	-2014.44300895323
2	2141	3192.47586812819	-1051.47586812819
3	2238	3192.50872730315	-954.508727303154
4	2685	3192.54158647812	-507.541586478118
5	4341	3192.57444565308	1148.42555434692
6	5376	3192.60730482805	2183.39269517195
7	4478	3192.64016400301	1285.35983599699
8	6404	3192.67302317798	3211.32697682202
9	4617	3192.70588235294	1424.29411764706
10	3024	3192.73874152791	-168.738741527905
11	1897	3192.77160070287	-1295.77160070287
12	2075	3192.80445987783	-1117.80445987783
13	1351	3192.8373190528	-1841.8373190528
14	2211	3192.87017822776	-981.870178227763
15	2453	3192.90303740273	-739.903037402727
16	3042	3192.93589657769	-150.935896577692
17	4765	3192.96875575266	1572.03124424734
18	4992	3704.91460848854	1287.08539151146
19	4601	3704.9474676635	896.052532336498
20	6266	3704.98032683847	2561.01967316153
21	4812	3705.01318601343	1106.98681398657
22	3159	3705.04604518840	-546.046045188395
23	1916	3705.07890436336	-1789.07890436336
24	2237	3705.11176353832	-1468.11176353832
25	1595	3705.14462271329	-2110.14462271329
26	2453	3705.17748188825	-1252.17748188825
27	2226	3705.21034106322	-1479.21034106322
28	3597	3705.24320023818	-108.243200238182
29	4706	3705.27605941315	1000.72394058685
30	4974	3705.30891858811	1268.69108141189
31	5756	3705.34177776308	2050.65822223692
32	5493	3705.37463693804	1787.62536306196
33	5004	3705.40749611300	1298.59250388700
34	3225	3705.44035528797	-480.440355287968
35	2006	3705.47321446293	-1699.47321446293
36	2291	3705.5060736379	-1414.50607363790
37	1588	3705.53893281286	-2117.53893281286
38	2105	3705.57179198783	-1600.57179198783
39	2191	3705.60465116279	-1514.60465116279
40	3591	3705.63751033775	-114.637510337755
41	4668	3705.67036951272	962.32963048728
42	4885	3705.70322868768	1179.29677131232
43	5822	3705.73608786265	2116.26391213735
44	5599	3705.76894703761	1893.23105296239
45	5340	3705.80180621258	1634.19819378742
46	3082	3705.83466538754	-623.834665387542
47	2010	3705.86752456251	-1695.86752456251
48	2301	3705.90038373747	-1404.90038373747
49	1514	3705.93324291244	-2191.93324291244
50	1979	3705.9661020874	-1726.9661020874
51	2480	3705.99896126236	-1225.99896126236
52	3499	3706.03182043733	-207.031820437328
53	4676	3706.06467961229	969.935320387707
54	5585	3706.09753878726	1878.90246121274
55	5610	3706.13039796222	1903.86960203778
56	5796	3706.16325713719	2089.83674286281
57	6199	3706.19611631215	2492.80388368785
58	3030	3706.22897548712	-676.228975487115
59	1930	3706.26183466208	-1776.26183466208
60	2552	3706.29469383704	-1154.29469383704

Charts produced by software:

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Parameters:

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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