Home » date » 2007 » Nov » 21 » attachments

Workshop 3 Q3

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

Title produced by software: Multiple Regression

Date of computation: Wed, 21 Nov 2007 15:07:37 -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/21/t1195682436ww0ravwr3wza6q8.htm/, Retrieved Wed, 21 Nov 2007 23:00:45 +0100

User-defined keywords:

Linear trend

Dataseries X:

» Textbox « » Textfile « » CSV «

523 0 519 1 509 1 512 1 519 0 517 0 510 1 509 1 501 0 507 1 569 0 580 0 578 1 565 1 547 0 555 0 562 0 561 0 555 1 544 1 537 1 543 1 594 1 611 0 613 1 611 1 594 1 595 0 591 0 589 0 584 1 573 1 567 0 569 1 621 0 629 0 628 1 612 1 595 1 597 0 593 1 590 0 580 1 574 1 573 1 573 1 620 0 626 0 620 1 588 1 566 1 557 0 561 1 549 1 532 1 526 1 511 1 499 1 555 0 565 1 542 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 578.648557692308 -9.9362980769231x[t] -8.35996928418795M1[t] -8.15687767094017M2[t] -27.6535456730769M3[t] -33.3247329059829M4[t] -30.0468816773504M5[t] -36.7435496794872M6[t] -38.5039196047009M7[t] -46.2133279914530M8[t] -58.2972556089744M9[t] -54.6321447649573M10[t] -9.69059161324788M11[t] + 0.709408386752137t + 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)	578.648557692308	16.534748	34.9959	0	0
x	-9.9362980769231	12.441378	-0.7986	0.428511	0.214256
M1	-8.35996928418795	20.977524	-0.3985	0.692051	0.346026
M2	-8.15687767094017	22.903424	-0.3561	0.723328	0.361664
M3	-27.6535456730769	21.796097	-1.2687	0.210782	0.105391
M4	-33.3247329059829	20.197267	-1.65	0.105619	0.052809
M5	-30.0468816773504	20.393564	-1.4734	0.147323	0.073661
M6	-36.7435496794872	20.154952	-1.8231	0.074659	0.03733
M7	-38.5039196047009	22.634141	-1.7011	0.095524	0.047762
M8	-46.2133279914530	22.588	-2.0459	0.046382	0.023191
M9	-58.2972556089744	20.776147	-2.806	0.007276	0.003638
M10	-54.6321447649573	22.503565	-2.4277	0.019078	0.009539
M11	-9.69059161324788	20.101933	-0.4821	0.631992	0.315996
t	0.709408386752137	0.246946	2.8727	0.006089	0.003045

Multiple Linear Regression - Regression Statistics
Multiple R	0.63564715575808
R-squared	0.404047306623337
Adjusted R-squared	0.239209327604260
F-TEST (value)	2.45117847857487
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	0.0125067927957605
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	31.7815489584879
Sum Squared Residuals	47473.1421474359

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	523	570.997996794872	-47.9979967948715
2	519	561.974198717949	-42.9741987179487
3	509	543.186939102564	-34.1869391025641
4	512	538.22516025641	-26.2251602564102
5	519	552.148717948718	-33.148717948718
6	517	546.161458333333	-29.1614583333334
7	510	535.174198717949	-25.1741987179488
8	509	528.174198717949	-19.1741987179487
9	501	526.735977564103	-25.7359775641026
10	507	521.174198717949	-14.1741987179488
11	569	576.761458333333	-7.76145833333337
12	580	587.161458333333	-7.16145833333332
13	578	569.574599358974	8.42540064102559
14	565	570.487099358974	-5.48709935897435
15	547	561.636137820513	-14.6361378205129
16	555	556.674358974359	-1.67435897435899
17	562	560.661618589744	1.3383814102564
18	561	554.674358974359	6.32564102564101
19	555	543.687099358974	11.3129006410257
20	544	536.687099358974	7.31290064102566
21	537	525.312580128205	11.6874198717949
22	543	529.687099358974	13.3129006410257
23	594	575.338060897436	18.6619391025641
24	611	595.674358974359	15.325641025641
25	613	578.0875	34.9125000000000
26	611	579	32
27	594	560.212740384615	33.7872596153846
28	595	565.187259615385	29.8127403846154
29	591	569.174519230769	21.8254807692308
30	589	563.187259615385	25.8127403846154
31	584	552.2	31.8
32	573	545.2	27.8
33	567	543.761778846154	23.2382211538461
34	569	538.2	30.8
35	621	593.787259615385	27.2127403846154
36	629	604.187259615385	24.8127403846154
37	628	586.600400641026	41.3995993589743
38	612	587.512900641026	24.4870993589744
39	595	568.725641025641	26.274358974359
40	597	573.70016025641	23.2998397435897
41	593	567.751121794872	25.2488782051282
42	590	571.70016025641	18.2998397435897
43	580	560.712900641026	19.2870993589744
44	574	553.712900641026	20.2870993589744
45	573	542.338381410256	30.6616185897436
46	573	546.712900641026	26.2870993589744
47	620	602.30016025641	17.6998397435897
48	626	612.70016025641	13.2998397435897
49	620	595.113301282051	24.8866987179487
50	588	596.025801282051	-8.02580128205129
51	566	577.238541666667	-11.2385416666667
52	557	582.213060897436	-25.2130608974359
53	561	576.264022435897	-15.2640224358974
54	549	570.276762820513	-21.2767628205128
55	532	569.225801282051	-37.2258012820513
56	526	562.225801282051	-36.2258012820513
57	511	550.851282051282	-39.851282051282
58	499	555.225801282051	-56.2258012820513
59	555	610.813060897436	-55.8130608974359
60	565	611.276762820513	-46.2767628205128
61	542	603.626201923077	-61.626201923077

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/14yx11195682851.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/14yx11195682851.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/2ge0c1195682851.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/2ge0c1195682851.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/3epvh1195682851.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/3epvh1195682851.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/478zs1195682851.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/478zs1195682851.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/5naxr1195682851.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/5naxr1195682851.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/6hoh01195682851.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/6hoh01195682851.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/7ldwr1195682852.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/7ldwr1195682852.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/8jsei1195682852.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/8jsei1195682852.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/91p5r1195682852.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195682436ww0ravwr3wza6q8/91p5r1195682852.ps (open in new window)

Parameters:

par1 = 1 ; par2 = Include Monthly 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