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Q3

*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: Sun, 23 Nov 2008 10:55:15 -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/Nov/23/t122746318374xr9gbduno5y1d.htm/, Retrieved Sun, 23 Nov 2008 17:59:43 +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/Nov/23/t122746318374xr9gbduno5y1d.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)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,1608 0 1,1208 0 1,0883 0 1,0704 0 1,0628 0 1,0378 0 1,0353 0 1,0604 0 1,0501 0 1,0706 0 1,0338 0 1,011 0 1,0137 0 0,9834 0 0,9643 0 0,947 0 0,906 0 0,9492 0 0,9397 0 0,9041 0 0,8721 0 0,8552 0 0,8564 0 0,8973 0 0,9383 0 0,9217 0 0,9095 0 0,892 0 0,8742 0 0,8532 0 0,8607 0 0,9005 0 0,9111 0 0,9059 0 0,8883 0 0,8924 0 0,8833 0 0,87 0 0,8758 0 0,8858 0 0,917 0 0,9554 0 0,9922 0 0,9778 0 0,9808 0 0,9811 0 1,0014 0 1,0183 0 1,0622 0 1,0773 0 1,0807 0 1,0848 0 1,1582 0 1,1663 0 1,1372 0 1,1139 0 1,1222 0 1,1692 0 1,1702 0 1,2286 0 1,2613 0 1,2646 0 1,2262 0 1,1985 0 1,2007 0 1,2138 0 1,2266 0 1,2176 0 1,2218 0 1,249 0 1,2991 0 1,3408 0 1,3119 0 1,3014 0 1,3201 0 1,2938 0 1,2694 0 1,2165 0 1,2037 0 1,2292 0 1,2256 0 1,2015 0 1,1786 0 1,1856 0 1,2103 0 1,1938 0 1,202 0 1,2271 0 1,277 0 1,265 0 1,2684 0 1,2811 0 1,2727 0 1,2611 0 1,2881 0 1,3213 0 1,2999 0 1,3074 0 1,3242 0 1,3516 0 1,3511 0 1,3419 1 1,3716 1 1,3622 1 1,3896 1 1,4227 1 1,4684 1 1,457 1 1,4718 1 1,4748 1 1,5527 1 1,5751 1 1,5557 1 1,5553 1 1,577 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	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.10007326732673 + 0.369626732673267x[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)	1.10007326732673	0.014813	74.2664	0	0
x	0.369626732673267	0.042454	8.7066	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.633639719869416
R-squared	0.401499294596192
Adjusted R-squared	0.396202828176689
F-TEST (value)	75.8051241706706
F-TEST (DF numerator)	1
F-TEST (DF denominator)	113
p-value	2.96429547574917e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.148864065741936
Sum Squared Residuals	2.50413763782178

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.1608	1.10007326732673	0.0607267326732693
2	1.1208	1.10007326732673	0.0207267326732672
3	1.0883	1.10007326732673	-0.0117732673267326
4	1.0704	1.10007326732673	-0.0296732673267327
5	1.0628	1.10007326732673	-0.0372732673267327
6	1.0378	1.10007326732673	-0.0622732673267326
7	1.0353	1.10007326732673	-0.0647732673267326
8	1.0604	1.10007326732673	-0.0396732673267327
9	1.0501	1.10007326732673	-0.0499732673267327
10	1.0706	1.10007326732673	-0.0294732673267327
11	1.0338	1.10007326732673	-0.0662732673267326
12	1.011	1.10007326732673	-0.0890732673267328
13	1.0137	1.10007326732673	-0.0863732673267327
14	0.9834	1.10007326732673	-0.116673267326733
15	0.9643	1.10007326732673	-0.135773267326733
16	0.947	1.10007326732673	-0.153073267326733
17	0.906	1.10007326732673	-0.194073267326733
18	0.9492	1.10007326732673	-0.150873267326733
19	0.9397	1.10007326732673	-0.160373267326733
20	0.9041	1.10007326732673	-0.195973267326733
21	0.8721	1.10007326732673	-0.227973267326733
22	0.8552	1.10007326732673	-0.244873267326733
23	0.8564	1.10007326732673	-0.243673267326733
24	0.8973	1.10007326732673	-0.202773267326733
25	0.9383	1.10007326732673	-0.161773267326733
26	0.9217	1.10007326732673	-0.178373267326733
27	0.9095	1.10007326732673	-0.190573267326733
28	0.892	1.10007326732673	-0.208073267326733
29	0.8742	1.10007326732673	-0.225873267326733
30	0.8532	1.10007326732673	-0.246873267326733
31	0.8607	1.10007326732673	-0.239373267326733
32	0.9005	1.10007326732673	-0.199573267326733
33	0.9111	1.10007326732673	-0.188973267326733
34	0.9059	1.10007326732673	-0.194173267326733
35	0.8883	1.10007326732673	-0.211773267326733
36	0.8924	1.10007326732673	-0.207673267326733
37	0.8833	1.10007326732673	-0.216773267326733
38	0.87	1.10007326732673	-0.230073267326733
39	0.8758	1.10007326732673	-0.224273267326733
40	0.8858	1.10007326732673	-0.214273267326733
41	0.917	1.10007326732673	-0.183073267326733
42	0.9554	1.10007326732673	-0.144673267326733
43	0.9922	1.10007326732673	-0.107873267326733
44	0.9778	1.10007326732673	-0.122273267326733
45	0.9808	1.10007326732673	-0.119273267326733
46	0.9811	1.10007326732673	-0.118973267326733
47	1.0014	1.10007326732673	-0.0986732673267326
48	1.0183	1.10007326732673	-0.0817732673267327
49	1.0622	1.10007326732673	-0.0378732673267327
50	1.0773	1.10007326732673	-0.0227732673267328
51	1.0807	1.10007326732673	-0.0193732673267327
52	1.0848	1.10007326732673	-0.0152732673267327
53	1.1582	1.10007326732673	0.0581267326732672
54	1.1663	1.10007326732673	0.0662267326732672
55	1.1372	1.10007326732673	0.0371267326732673
56	1.1139	1.10007326732673	0.0138267326732672
57	1.1222	1.10007326732673	0.0221267326732674
58	1.1692	1.10007326732673	0.0691267326732673
59	1.1702	1.10007326732673	0.0701267326732672
60	1.2286	1.10007326732673	0.128526732673267
61	1.2613	1.10007326732673	0.161226732673267
62	1.2646	1.10007326732673	0.164526732673267
63	1.2262	1.10007326732673	0.126126732673267
64	1.1985	1.10007326732673	0.0984267326732672
65	1.2007	1.10007326732673	0.100626732673267
66	1.2138	1.10007326732673	0.113726732673267
67	1.2266	1.10007326732673	0.126526732673267
68	1.2176	1.10007326732673	0.117526732673267
69	1.2218	1.10007326732673	0.121726732673267
70	1.249	1.10007326732673	0.148926732673267
71	1.2991	1.10007326732673	0.199026732673267
72	1.3408	1.10007326732673	0.240726732673267
73	1.3119	1.10007326732673	0.211826732673267
74	1.3014	1.10007326732673	0.201326732673267
75	1.3201	1.10007326732673	0.220026732673267
76	1.2938	1.10007326732673	0.193726732673267
77	1.2694	1.10007326732673	0.169326732673267
78	1.2165	1.10007326732673	0.116426732673267
79	1.2037	1.10007326732673	0.103626732673267
80	1.2292	1.10007326732673	0.129126732673267
81	1.2256	1.10007326732673	0.125526732673267
82	1.2015	1.10007326732673	0.101426732673267
83	1.1786	1.10007326732673	0.0785267326732674
84	1.1856	1.10007326732673	0.0855267326732673
85	1.2103	1.10007326732673	0.110226732673267
86	1.1938	1.10007326732673	0.0937267326732673
87	1.202	1.10007326732673	0.101926732673267
88	1.2271	1.10007326732673	0.127026732673267
89	1.277	1.10007326732673	0.176926732673267
90	1.265	1.10007326732673	0.164926732673267
91	1.2684	1.10007326732673	0.168326732673267
92	1.2811	1.10007326732673	0.181026732673267
93	1.2727	1.10007326732673	0.172626732673267
94	1.2611	1.10007326732673	0.161026732673267
95	1.2881	1.10007326732673	0.188026732673267
96	1.3213	1.10007326732673	0.221226732673267
97	1.2999	1.10007326732673	0.199826732673267
98	1.3074	1.10007326732673	0.207326732673267
99	1.3242	1.10007326732673	0.224126732673267
100	1.3516	1.10007326732673	0.251526732673267
101	1.3511	1.10007326732673	0.251026732673267
102	1.3419	1.4697	-0.1278
103	1.3716	1.4697	-0.0981
104	1.3622	1.4697	-0.1075
105	1.3896	1.4697	-0.0801
106	1.4227	1.4697	-0.0469999999999999
107	1.4684	1.4697	-0.00130000000000008
108	1.457	1.4697	-0.0126999999999999
109	1.4718	1.4697	0.00209999999999999
110	1.4748	1.4697	0.0051000000000001
111	1.5527	1.4697	0.083
112	1.5751	1.4697	0.1054
113	1.5557	1.4697	0.086
114	1.5553	1.4697	0.0855999999999999
115	1.577	1.4697	0.1073

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/1zfd51227462902.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/2agdc1227462902.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/32zcy1227462902.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/32zcy1227462902.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/46hjm1227462902.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/5uhe51227462902.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/6p1gi1227462902.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/6p1gi1227462902.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/7k9561227462902.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/7k9561227462902.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/853og1227462902.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/853og1227462902.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/9d7du1227462902.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t122746318374xr9gbduno5y1d/9d7du1227462902.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

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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