Home » date » 2007 » Nov » 25 » attachments

Workshop 3 Q3 assessment part 1b

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

Title produced by software: Multiple Regression

Date of computation: Sun, 25 Nov 2007 07:15:47 -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/25/t11959997381xrltqr3t8bphpp.htm/, Retrieved Sun, 25 Nov 2007 15:08:59 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

15761.3 0 16943.0 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 0 11703.7 0 16283.6 0 16726.5 0 14968.9 0 14861.0 1 14583.3 1 15305.8 1 17903.9 1 16379.4 0 15420.3 0 17870.5 1 15912.8 1 13866.5 1 17823.2 1 17872.0 1 17420.4 1 16704.4 1 15991.2 1 16583.6 1 19123.5 1 17838.7 1 17209.4 1 18586.5 1 16258.1 1 15141.6 1 19202.1 1 17746.5 1 19090.1 0 18040.3 0 17515.5 1 17751.8 0 21072.4 0 17170.0 1 19439.5 1 19795.4 1 17574.9 1 16165.4 1 19464.6 1 19932.1 1 19961.2 1 17343.4 1 18924.2 1 18574.1 1 21350.6 1 18840.1 1 20304.8 1 21132.4 1 19753.9 1 18009.9 1 20390.4 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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 14459.5894260997 -381.304728660039x[t] + 97.2643755443243t + 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)	14459.5894260997	344.914597	41.9222	0	0
x	-381.304728660039	459.873859	-0.8292	0.410419	0.205209
t	97.2643755443243	12.409883	7.8377	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.781363387391381
R-squared	0.610528743155733
Adjusted R-squared	0.597098699816276
F-TEST (value)	45.4599235254885
F-TEST (DF numerator)	2
F-TEST (DF denominator)	58
p-value	1.32982513889601e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1312.88925657213
Sum Squared Residuals	99973335.601307

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	15761.3	14556.8538016441	1204.44619835593
2	16943	14654.1181771884	2288.88182281161
3	15070.3	14751.3825527327	318.917447267284
4	13659.6	14848.6469282770	-1189.04692827704
5	14768.9	14945.9113038214	-177.011303821364
6	14725.1	15043.1756793657	-318.075679365688
7	15998.1	15140.44005491	857.659945089988
8	15370.6	15237.7044304543	132.895569545664
9	14956.9	15334.9688059987	-378.068805998662
10	15469.7	15432.233181543	37.4668184570153
11	15101.8	15529.4975570873	-427.697557087310
12	11703.7	15626.7619326316	-3923.06193263163
13	16283.6	15724.0263081760	559.573691824042
14	16726.5	15821.2906837203	905.209316279717
15	14968.9	15918.5550592646	-949.655059264607
16	14861	15634.5147061489	-773.514706148892
17	14583.3	15731.7790816932	-1148.47908169322
18	15305.8	15829.0434572375	-523.243457237541
19	17903.9	15926.3078327819	1977.59216721814
20	16379.4	16404.8769369862	-25.476936986229
21	15420.3	16502.1413125306	-1081.84131253055
22	17870.5	16218.1009594148	1652.39904058516
23	15912.8	16315.3653349592	-402.565334959163
24	13866.5	16412.6297105035	-2546.12971050349
25	17823.2	16509.8940860478	1313.30591395219
26	17872	16607.1584615921	1264.84153840787
27	17420.4	16704.4228371365	715.977162863542
28	16704.4	16801.6872126808	-97.2872126807823
29	15991.2	16898.9515882251	-907.751588225107
30	16583.6	16996.2159637694	-412.615963769434
31	19123.5	17093.4803393138	2030.01966068624
32	17838.7	17190.7447148581	647.95528514192
33	17209.4	17288.0090904024	-78.609090402404
34	18586.5	17385.2734659467	1201.22653405327
35	16258.1	17482.5378414911	-1224.43784149105
36	15141.6	17579.8022170354	-2438.20221703538
37	19202.1	17677.0665925797	1525.03340742030
38	17746.5	17774.3309681240	-27.8309681240271
39	19090.1	18252.9000723284	837.199927671607
40	18040.3	18350.1644478727	-309.864447872716
41	17515.5	18066.124094757	-550.624094757
42	17751.8	18544.6931989614	-792.893198961365
43	21072.4	18641.9575745057	2430.44242549431
44	17170	18357.9172213900	-1187.91722138997
45	19439.5	18455.1815969343	984.318403065702
46	19795.4	18552.4459724786	1242.95402752138
47	17574.9	18649.7103480229	-1074.81034802294
48	16165.4	18746.9747235673	-2581.57472356727
49	19464.6	18844.2390991116	620.360900888404
50	19932.1	18941.5034746559	990.59652534408
51	19961.2	19038.7678502002	922.432149799757
52	17343.4	19136.0322257446	-1792.63222574457
53	18924.2	19233.2966012889	-309.096601288891
54	18574.1	19330.5609768332	-756.460976833218
55	21350.6	19427.8253523775	1922.77464762246
56	18840.1	19525.0897279219	-684.989727921866
57	20304.8	19622.3541034662	682.44589653381
58	21132.4	19719.6184790105	1412.78152098949
59	19753.9	19816.8828545548	-62.9828545548366
60	18009.9	19914.1472300992	-1904.24723009916
61	20390.4	20011.4116056435	378.988394356515

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/1j0951196000138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/1j0951196000138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/2voql1196000138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/2voql1196000138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/3gndd1196000138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/3gndd1196000138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/4ti0m1196000138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/4ti0m1196000138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/5ceno1196000138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/5ceno1196000138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/6zilt1196000138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/6zilt1196000138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/7zkz01196000138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/7zkz01196000138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/8piah1196000138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/8piah1196000138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/9reiy1196000138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t11959997381xrltqr3t8bphpp/9reiy1196000138.ps (open in new window)

Parameters:

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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.

FreeStatistics.org is powered by