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Q3: Eigen tijdreeksen regression

*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 08:23:20 -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/t1227453932kton2wxzzxhsl52.htm/, Retrieved Sun, 23 Nov 2008 15:25:41 +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/t1227453932kton2wxzzxhsl52.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 «

13698,3 0 12477,6 0 13139,7 0 14532,2 0 15167 0 16071,1 0 14827,5 0 15082 0 14772,7 0 16083 0 14272,5 0 15223,3 0 14897,3 0 13062,6 0 12603,8 0 13629,8 0 14421,1 0 13978,3 0 12927,9 0 13429,9 0 13470,1 0 14785,8 0 14292 0 14308,8 0 14013 0 13240,9 0 12153,4 0 14289,7 0 15669,2 0 14169,5 0 14569,8 0 14469,1 0 14264,9 0 15320,9 0 14433,5 0 13691,5 0 14194,1 0 13519,2 0 11857,9 0 14616 0 15643,4 0 14077,2 0 14887,5 0 14159,9 0 14643 0 17192,5 1 15386,1 1 14287,1 1 17526,6 1 14497 1 14398,3 1 16629,6 1 16670,7 1 16614,8 1 16869,2 1 15663,9 1 16359,9 1 18447,7 1 16889 1 16505 1 18320,9 1 15052,1 1 15699,8 1 18135,3 1 16768,7 1 18883 1 19021 1 18101,9 1 17776,1 1 21489,9 1 17065,3 1 18690 1 18953,1 1 16398,9 1 16895,7 1 18553 1 19270 1 19422,1 1 17579,4 1 18637,3 1 18076,7 1 20438,6 1 18075,2 1 19563 1 19899,2 1 19227,5 1 17789,6 1 19220,8 1 22058,6 1 21230,8 1 19504,4 1 23913,1 1 23165,7 1 23574,3 1 25002 1 22603,9 1 23408,6 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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 14200.8422222222 + 4287.67508547008x[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)	14200.8422222222	294.386144	48.2388	0	0
x	4287.67508547008	402.069898	10.664	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.738137465151604
R-squared	0.544846917460435
Adjusted R-squared	0.540055832381072
F-TEST (value)	113.720985629581
F-TEST (DF numerator)	1
F-TEST (DF denominator)	95
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1974.80228778318
Sum Squared Residuals	370485187.204201

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	13698.3	14200.8422222221	-502.54222222208
2	12477.6	14200.8422222222	-1723.24222222221
3	13139.7	14200.8422222222	-1061.14222222222
4	14532.2	14200.8422222222	331.357777777775
5	15167	14200.8422222222	966.157777777775
6	16071.1	14200.8422222222	1870.25777777777
7	14827.5	14200.8422222222	626.657777777775
8	15082	14200.8422222222	881.157777777775
9	14772.7	14200.8422222222	571.857777777775
10	16083	14200.8422222222	1882.15777777777
11	14272.5	14200.8422222222	71.6577777777745
12	15223.3	14200.8422222222	1022.45777777777
13	14897.3	14200.8422222222	696.457777777774
14	13062.6	14200.8422222222	-1138.24222222223
15	12603.8	14200.8422222222	-1597.04222222223
16	13629.8	14200.8422222222	-571.042222222226
17	14421.1	14200.8422222222	220.257777777775
18	13978.3	14200.8422222222	-222.542222222226
19	12927.9	14200.8422222222	-1272.94222222223
20	13429.9	14200.8422222222	-770.942222222226
21	13470.1	14200.8422222222	-730.742222222225
22	14785.8	14200.8422222222	584.957777777774
23	14292	14200.8422222222	91.1577777777745
24	14308.8	14200.8422222222	107.957777777774
25	14013	14200.8422222222	-187.842222222226
26	13240.9	14200.8422222222	-959.942222222226
27	12153.4	14200.8422222222	-2047.44222222223
28	14289.7	14200.8422222222	88.8577777777752
29	15669.2	14200.8422222222	1468.35777777778
30	14169.5	14200.8422222222	-31.3422222222255
31	14569.8	14200.8422222222	368.957777777774
32	14469.1	14200.8422222222	268.257777777775
33	14264.9	14200.8422222222	64.0577777777741
34	15320.9	14200.8422222222	1120.05777777777
35	14433.5	14200.8422222222	232.657777777774
36	13691.5	14200.8422222222	-509.342222222225
37	14194.1	14200.8422222222	-6.74222222222514
38	13519.2	14200.8422222222	-681.642222222225
39	11857.9	14200.8422222222	-2342.94222222223
40	14616	14200.8422222222	415.157777777775
41	15643.4	14200.8422222222	1442.55777777777
42	14077.2	14200.8422222222	-123.642222222225
43	14887.5	14200.8422222222	686.657777777775
44	14159.9	14200.8422222222	-40.9422222222259
45	14643	14200.8422222222	442.157777777775
46	17192.5	18488.5173076923	-1296.01730769231
47	15386.1	18488.5173076923	-3102.41730769231
48	14287.1	18488.5173076923	-4201.41730769231
49	17526.6	18488.5173076923	-961.91730769231
50	14497	18488.5173076923	-3991.51730769231
51	14398.3	18488.5173076923	-4090.21730769231
52	16629.6	18488.5173076923	-1858.91730769231
53	16670.7	18488.5173076923	-1817.81730769231
54	16614.8	18488.5173076923	-1873.71730769231
55	16869.2	18488.5173076923	-1619.31730769231
56	15663.9	18488.5173076923	-2824.61730769231
57	16359.9	18488.5173076923	-2128.61730769231
58	18447.7	18488.5173076923	-40.8173076923069
59	16889	18488.5173076923	-1599.51730769231
60	16505	18488.5173076923	-1983.51730769231
61	18320.9	18488.5173076923	-167.617307692306
62	15052.1	18488.5173076923	-3436.41730769231
63	15699.8	18488.5173076923	-2788.71730769231
64	18135.3	18488.5173076923	-353.217307692308
65	16768.7	18488.5173076923	-1719.81730769231
66	18883	18488.5173076923	394.482692307692
67	19021	18488.5173076923	532.482692307692
68	18101.9	18488.5173076923	-386.617307692306
69	17776.1	18488.5173076923	-712.417307692309
70	21489.9	18488.5173076923	3001.38269230769
71	17065.3	18488.5173076923	-1423.21730769231
72	18690	18488.5173076923	201.482692307692
73	18953.1	18488.5173076923	464.582692307691
74	16398.9	18488.5173076923	-2089.61730769231
75	16895.7	18488.5173076923	-1592.81730769231
76	18553	18488.5173076923	64.4826923076923
77	19270	18488.5173076923	781.482692307692
78	19422.1	18488.5173076923	933.582692307691
79	17579.4	18488.5173076923	-909.117307692306
80	18637.3	18488.5173076923	148.782692307692
81	18076.7	18488.5173076923	-411.817307692307
82	20438.6	18488.5173076923	1950.08269230769
83	18075.2	18488.5173076923	-413.317307692307
84	19563	18488.5173076923	1074.48269230769
85	19899.2	18488.5173076923	1410.68269230769
86	19227.5	18488.5173076923	738.982692307692
87	17789.6	18488.5173076923	-698.917307692309
88	19220.8	18488.5173076923	732.282692307692
89	22058.6	18488.5173076923	3570.08269230769
90	21230.8	18488.5173076923	2742.28269230769
91	19504.4	18488.5173076923	1015.88269230769
92	23913.1	18488.5173076923	5424.58269230769
93	23165.7	18488.5173076923	4677.18269230769
94	23574.3	18488.5173076923	5085.78269230769
95	25002	18488.5173076923	6513.48269230769
96	22603.9	18488.5173076923	4115.38269230769
97	23408.6	18488.5173076923	4920.08269230769

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/1umsm1227453795.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/2h03g1227453795.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/3t61a1227453795.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/3t61a1227453795.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/4hmze1227453795.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/4hmze1227453795.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/5xy9d1227453796.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/5xy9d1227453796.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/6wi591227453796.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/6wi591227453796.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/73si51227453796.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/73si51227453796.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/8zdp31227453796.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/8zdp31227453796.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/9cz9n1227453796.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227453932kton2wxzzxhsl52/9cz9n1227453796.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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