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*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: Thu, 16 Dec 2010 12:41:25 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd.htm/, Retrieved Thu, 16 Dec 2010 13:39:39 +0100

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/2010/Dec/16/t129250317986ai207t0tmj7kd.htm/},
    year = {2010},
}
@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 = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

300 2.26 302 2.57 400 3.07 392 2.76 373 2.51 379 2.87 303 3.14 324 3.11 353 3.16 392 2.47 327 2.57 376 2.89 329 2.63 359 2.38 413 1.69 338 1.96 422 2.19 390 1.87 370 1.60 367 1.63 406 1.22 418 1.21 346 1.49 350 1.64 330 1.66 318 1.77 382 1.82 337 1.78 372 1.28 422 1.29 428 1.37 426 1.12 396 1.51 458 2.24 315 2.94 337 3.09 386 3.46 352 3.64 383 4.39 439 4.15 397 5.21 453 5.80 363 5.91 365 5.39 474 5.46 373 4.72 403 3.14 384 2.63 364 2.32 361 1.93 419 0.62 352 0.60 363 -0.37 410 -1.10 361 -1.68 383 -0.78 342 -1.19 369 -0.79 361 -0.12 317 0.26 386 0.62 318 0.70 407 1.66 393 1.80 404 2.27 498 2.46 438 2.57

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	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Multiple Linear Regression - Estimated Regression Equation

bouwvergunningen[t] = + 314.705816342766 + 5.96101603224808`inflatie `[t] -0.418563909059995M1[t] -15.3350853480929M2[t] + 49.3631559583583M3[t] + 23.3517418272819M4[t] + 35.9352203882489M5[t] + 71.9590887888935M6[t] + 23.3604882049137M7[t] + 23.0881467901967M8[t] + 43.9476151187114M9[t] + 51.4070834472261M10[t] -1.10570576335502M11[t] + 0.71011466548467t + 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)	314.705816342766	18.309283	17.1883	0	0
`inflatie `	5.96101603224808	2.61961	2.2755	0.026943	0.013472
M1	-0.418563909059995	20.151655	-0.0208	0.983507	0.491753
M2	-15.3350853480929	20.141369	-0.7614	0.449809	0.224905
M3	49.3631559583583	20.133852	2.4517	0.017545	0.008773
M4	23.3517418272819	20.128185	1.1602	0.251187	0.125593
M5	35.9352203882489	20.125294	1.7856	0.07989	0.039945
M6	71.9590887888935	20.125194	3.5756	0.000756	0.000378
M7	23.3604882049137	20.12558	1.1607	0.250951	0.125475
M8	23.0881467901967	21.036781	1.0975	0.277378	0.138689
M9	43.9476151187114	21.030892	2.0897	0.041463	0.020731
M10	51.4070834472261	21.027652	2.4447	0.017854	0.008927
M11	-1.10570576335502	21.021815	-0.0526	0.95825	0.479125
t	0.71011466548467	0.218233	3.2539	0.001984	0.000992

Multiple Linear Regression - Regression Statistics
Multiple R	0.707630098284765
R-squared	0.500740355998506
Adjusted R-squared	0.378280443318894
F-TEST (value)	4.08901447862843
F-TEST (DF numerator)	13
F-TEST (DF denominator)	53
p-value	0.000122121050988078
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	33.2330516823352
Sum Squared Residuals	58535.0933784005

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	300	328.469263332072	-28.469263332072
2	302	316.110771528520	-14.1107715285204
3	400	384.49963551658	15.5003644834197
4	392	357.350421080992	34.6495789190083
5	373	369.153760299381	3.84623970061865
6	379	408.03370913712	-29.0337091371199
7	303	361.754697547332	-58.7546975473317
8	324	362.013640317132	-38.013640317132
9	353	383.881274112744	-30.8812741127438
10	392	387.937756044492	4.06224395550801
11	327	336.73118310262	-9.73118310262034
12	376	340.454528661779	35.5454713382206
13	329	339.196215249820	-10.1962152498196
14	359	323.499554468209	35.5004455317907
15	413	384.794809377894	28.205190622106
16	338	361.102984241009	-23.1029842410093
17	422	375.767611154878	46.232388845122
18	390	410.594069090688	-20.5940690906878
19	370	361.096108843486	8.90389115651424
20	367	361.712712575221	5.28728742477916
21	406	380.838278995999	25.1617210040015
22	418	388.948251829675	29.0517481703246
23	346	338.814661773608	7.18533822639155
24	350	341.524634607285	8.47536539271465
25	330	341.935405684355	-11.9354056843550
26	318	328.384710674354	-10.384710674354
27	382	394.091117447902	-12.0911174479023
28	337	368.551377341021	-31.5513773410207
29	372	378.864462551348	-6.86446255134831
30	422	415.6580557778	6.34194422220001
31	428	368.246451141885	59.7535488581153
32	426	367.193970384590	58.8060296154096
33	396	391.088349631166	4.91165036883351
34	458	403.609474328707	54.390525671293
35	315	355.979511006184	-40.9795110061842
36	337	358.689483839861	-21.6894838398611
37	386	361.186610528218	24.8133894717825
38	352	348.053186640474	3.94681335952606
39	383	417.932304636596	-34.9323046365959
40	439	391.200361323265	47.7996386767354
41	397	410.812631543899	-13.8126315438993
42	453	451.063614069055	1.93638593094517
43	363	403.830839914107	-40.830839914107
44	365	401.168884828106	-36.1688848281057
45	474	423.155738944362	50.8442610556375
46	373	426.914170074498	-53.9141700744983
47	403	365.69309019845	37.3069098015502
48	384	364.468792450843	19.5312075491570
49	364	362.912428237271	1.08757176272920
50	361	346.381225211146	14.6187747888542
51	419	403.980650180837	15.0193498191633
52	352	378.5601303946	-26.5601303946
53	363	386.071538069771	-23.0715380697711
54	410	418.453979432359	-8.45397943235916
55	361	367.10810421516	-6.10810421516018
56	383	372.910791894951	10.0892081050489
57	342	392.036358315729	-50.0363583157288
58	369	402.590347722627	-33.5903477226274
59	361	354.781553919137	6.21844608086284
60	317	358.862560440231	-41.8625604402311
61	386	361.300076968265	24.6999230317349
62	318	347.570551477297	-29.5705514772967
63	407	418.701482840191	-11.7014828401907
64	393	394.234725619114	-1.23472561911373
65	404	410.329996380722	-6.32999638072201
66	498	448.196572492978	49.8034275070217
67	438	400.963798338031	37.0362016619695

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/1g22x1292503278.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/1g22x1292503278.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/2g22x1292503278.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/2g22x1292503278.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/39t2i1292503278.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/39t2i1292503278.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/49t2i1292503278.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/49t2i1292503278.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/59t2i1292503278.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/59t2i1292503278.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/6kkj31292503278.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/6kkj31292503278.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/7dtio1292503278.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/7dtio1292503278.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/8dtio1292503278.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/8dtio1292503278.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/9dtio1292503278.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t129250317986ai207t0tmj7kd/9dtio1292503278.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

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

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