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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 07:13:05 -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/22/t11957403833n4roox4yd8u5oa.htm/, Retrieved Thu, 22 Nov 2007 15:06:33 +0100

User-defined keywords:

bridome

Dataseries X:

» Textbox « » Textfile « » CSV «

511 0 492 0 492 0 493 0 481 0 462 0 457 0 442 0 439 0 488 0 521 0 501 0 485 0 464 0 460 0 467 0 460 0 448 0 443 0 436 0 431 0 484 0 510 0 513 0 503 0 471 0 471 0 476 0 475 0 470 0 461 0 455 0 456 0 517 0 525 0 523 0 519 0 509 0 512 0 519 0 517 0 510 0 509 0 501 1 507 1 569 1 580 1 578 1 565 1 547 1 555 1 562 1 561 1 555 1 544 1 537 1 543 1 594 1 611 1 613 1 611 1 594 1 595 1 591 1 589 1 584 1 573 1 567 1 569 1 621 1 629 1 628 1 612 1 595 1 597 1 593 1 590 1 580 1 574 1 573 1 573 1 620 1 626 1 620 1 588 1 566 1 557 1 561 1 549 1 532 1 526 1 511 1 499 1 555 1 565 1 542 1 527 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] = + 505.348670836591 + 80.5628616106333x[t] -11.5396586236353M1[t] -23.2538014363072M2[t] -23.2963855225437M3[t] -20.5889696087800M4[t] -25.7565536950163M5[t] -36.0491377812527M6[t] -42.9667218674891M7[t] -61.3296636550546M8[t] -62.1222477412909M9[t] -8.41483182752728M10[t] + 6.29258408623636M11[t] + 0.167584086236352t + 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)	505.348670836591	9.898297	51.0541	0	0
x	80.5628616106333	9.693855	8.3107	0	0
M1	-11.5396586236353	11.666412	-0.9891	0.325472	0.162736
M2	-23.2538014363072	12.030823	-1.9329	0.056665	0.028332
M3	-23.2963855225437	12.022411	-1.9377	0.056055	0.028027
M4	-20.5889696087800	12.016448	-1.7134	0.090372	0.045186
M5	-25.7565536950163	12.012939	-2.1441	0.034953	0.017476
M6	-36.0491377812527	12.011884	-3.0011	0.003552	0.001776
M7	-42.9667218674891	12.013286	-3.5766	0.000584	0.000292
M8	-61.3296636550546	12.015659	-5.1041	2e-06	1e-06
M9	-62.1222477412909	12.007063	-5.1738	2e-06	1e-06
M10	-8.41483182752728	12.00092	-0.7012	0.485151	0.242575
M11	6.29258408623636	11.997232	0.5245	0.601327	0.300663
t	0.167584086236352	0.171755	0.9757	0.332042	0.166021

Multiple Linear Regression - Regression Statistics
Multiple R	0.91089873882423
R-squared	0.829736512391574
Adjusted R-squared	0.803068737223989
F-TEST (value)	31.1138258507644
F-TEST (DF numerator)	13
F-TEST (DF denominator)	83
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	23.9920047624659
Sum Squared Residuals	47776.1522793415

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	511	493.976596299191	17.0234037008088
2	492	482.430037572756	9.56996242724384
3	492	482.555037572756	9.4449624272435
4	493	485.430037572757	7.56996242724347
5	481	480.430037572756	0.569962427243631
6	462	470.305037572757	-8.30503757275661
7	457	463.555037572757	-6.55503757275662
8	442	445.359679871427	-3.35967987142745
9	439	444.734679871427	-5.73467987142732
10	488	498.609679871427	-10.6096798714273
11	521	513.484679871427	7.51532012857262
12	501	507.359679871427	-6.35967987142736
13	485	495.987605334028	-10.9876053340285
14	464	484.441046607593	-20.4410466075928
15	460	484.566046607593	-24.5660466075928
16	467	487.441046607593	-20.4410466075928
17	460	482.441046607593	-22.4410466075928
18	448	472.316046607593	-24.3160466075928
19	443	465.566046607593	-22.5660466075928
20	436	447.370688906264	-11.3706889062636
21	431	446.745688906264	-15.7456889062636
22	484	500.620688906264	-16.6206889062636
23	510	515.495688906264	-5.4956889062636
24	513	509.370688906264	3.62931109373641
25	503	497.998614368865	5.00138563113531
26	471	486.452055642429	-15.4520556424290
27	471	486.577055642429	-15.577055642429
28	476	489.452055642429	-13.4520556424290
29	475	484.452055642429	-9.452055642429
30	470	474.327055642429	-4.32705564242898
31	461	467.577055642429	-6.57705564242899
32	455	449.3816979411	5.6183020589002
33	456	448.7566979411	7.24330205890018
34	517	502.6316979411	14.3683020589002
35	525	517.5066979411	7.49330205890017
36	523	511.3816979411	11.6183020589002
37	519	500.009623403701	18.9903765962991
38	509	488.463064677265	20.5369353227347
39	512	488.588064677265	23.4119353227348
40	519	491.463064677265	27.5369353227348
41	517	486.463064677265	30.5369353227348
42	510	476.338064677265	33.6619353227348
43	509	469.588064677265	39.4119353227348
44	501	531.955568586569	-30.9555685865694
45	507	531.330568586569	-24.3305685865694
46	569	585.205568586569	-16.2055685865694
47	580	600.080568586569	-20.0805685865694
48	578	593.955568586569	-15.9555685865694
49	565	582.58349404917	-17.5834940491705
50	547	571.036935322735	-24.0369353227348
51	555	571.161935322735	-16.1619353227348
52	562	574.036935322735	-12.0369353227348
53	561	569.036935322735	-8.03693532273481
54	555	558.911935322735	-3.91193532273477
55	544	552.161935322735	-8.16193532273478
56	537	533.966577621406	3.0334223785944
57	543	533.341577621406	9.65842237859439
58	594	587.216577621406	6.78342237859437
59	611	602.091577621406	8.90842237859439
60	613	595.966577621406	17.0334223785944
61	611	584.594503084007	26.4054969159933
62	594	573.047944357571	20.9520556424289
63	595	573.172944357571	21.8270556424290
64	591	576.047944357571	14.952055642429
65	589	571.047944357571	17.9520556424290
66	584	560.922944357571	23.077055642429
67	573	554.172944357571	18.827055642429
68	567	535.977586656242	31.0224133437582
69	569	535.352586656242	33.6474133437582
70	621	589.227586656242	31.7724133437581
71	629	604.102586656242	24.8974133437582
72	628	597.977586656242	30.0224133437582
73	612	586.605512118843	25.3944878811571
74	595	575.058953392407	19.9410466075927
75	597	575.183953392407	21.8160466075928
76	593	578.058953392407	14.9410466075928
77	590	573.058953392407	16.9410466075927
78	580	562.933953392407	17.0660466075928
79	574	556.183953392407	17.8160466075928
80	573	537.988595691078	35.0114043089220
81	573	537.363595691078	35.6364043089219
82	620	591.238595691078	28.7614043089219
83	626	606.113595691078	19.8864043089219
84	620	599.988595691078	20.0114043089219
85	588	588.616521153679	-0.616521153679177
86	566	577.069962427243	-11.0699624272435
87	557	577.194962427243	-20.1949624272435
88	561	580.069962427243	-19.0699624272435
89	549	575.069962427243	-26.0699624272435
90	532	564.944962427243	-32.9449624272434
91	526	558.194962427243	-32.1949624272435
92	511	539.999604725914	-28.9996047259143
93	499	539.374604725914	-40.3746047259143
94	555	593.249604725914	-38.2496047259143
95	565	608.124604725914	-43.1246047259143
96	542	601.999604725914	-59.9996047259143
97	527	590.627530188515	-63.6275301885154

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t11957403833n4roox4yd8u5oa/1baud1195740780.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t11957403833n4roox4yd8u5oa/6gzuf1195740780.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t11957403833n4roox4yd8u5oa/7twtj1195740780.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t11957403833n4roox4yd8u5oa/86e0q1195740780.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t11957403833n4roox4yd8u5oa/9q5q11195740780.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t11957403833n4roox4yd8u5oa/9q5q11195740780.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.

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