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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 12:37:02 +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/t12925029829uv3u1bbah9r94y.htm/, Retrieved Thu, 16 Dec 2010 13:36:25 +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/t12925029829uv3u1bbah9r94y.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	5 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk
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] = + 338.502189030203 + 6.15102312474545`inflatie `[t] + 0.751624934630228t + 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)	338.502189030203	13.288454	25.4734	0	0
`inflatie `	6.15102312474545	3.134231	1.9625	0.054051	0.027026
t	0.751624934630228	0.260247	2.8881	0.005282	0.002641

Multiple Linear Regression - Regression Statistics
Multiple R	0.366656095248077
R-squared	0.134436692182567
Adjusted R-squared	0.107387838813272
F-TEST (value)	4.97014384850695
F-TEST (DF numerator)	2
F-TEST (DF denominator)	64
p-value	0.00985287138616242
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	39.8202844818466
Sum Squared Residuals	101481.923597772

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	300	353.155126226758	-53.1551262267581
2	302	355.813568330059	-53.8135683300592
3	400	359.640704827062	40.3592951729378
4	392	358.485512593021	33.5144874069787
5	373	357.699381746465	15.3006182535348
6	379	360.665375006004	18.3346249939962
7	303	363.077776184315	-60.0777761843153
8	324	363.644870425203	-39.6448704252031
9	353	364.704046516071	-11.7040465160706
10	392	361.211465494627	30.7885345053735
11	327	362.578192741731	-35.5781927417313
12	376	365.29814507628	10.70185492372
13	329	364.450503998476	-35.4505039984764
14	359	363.66437315192	-4.66437315192032
15	413	360.171792130476	52.8282078695238
16	338	362.584193308788	-24.5841933087877
17	422	364.750553562109	57.2494464378906
18	390	363.533851096821	26.466148903179
19	370	362.62469978777	7.37530021222999
20	367	363.560855416143	3.4391445838574
21	406	361.790560869627	44.2094391303728
22	418	362.48067557301	55.51932442699
23	346	364.954586982569	-18.9545869825689
24	350	366.628865385911	-16.628865385911
25	330	367.503510783036	-37.5035107830361
26	318	368.931748261388	-50.9317482613883
27	382	369.990924352256	12.0090756477442
28	337	370.496508361896	-33.4965083618962
29	372	368.172621734154	3.82737826584625
30	422	368.985756900031	53.0142430999686
31	428	370.229463684641	57.7705363153587
32	426	369.443332838085	56.5566671619148
33	396	372.593856791366	23.4061432086339
34	458	377.835728607061	80.1642713929395
35	315	382.893069729013	-67.8930697290126
36	337	384.567348132355	-47.5673481323546
37	386	387.594851623141	-1.59485162314065
38	352	389.453660720225	-37.4536607202251
39	383	394.818552998414	-11.8185529984144
40	439	394.093932383106	44.9060676168943
41	397	401.365641829966	-4.3656418299661
42	453	405.746370408196	47.2536295918039
43	363	407.174607886548	-44.1746078865484
44	365	404.727700796311	-39.727700796311
45	474	405.909897349673	68.0901026503266
46	373	402.109765171992	-29.109765171992
47	403	393.142773569524	9.8572264304756
48	384	390.757376710534	-6.75737671053444
49	364	389.602184476494	-25.6021844764936
50	361	387.954910392473	-26.9549103924731
51	419	380.648695033687	38.3513049663132
52	352	381.277299505822	-29.2772995058221
53	363	376.062432009449	-13.0624320094492
54	410	372.323810063015	37.6761899369847
55	361	369.507841585293	-8.50784158529316
56	383	375.795387332194	7.20461266780571
57	342	374.025092785679	-32.0250927856789
58	369	377.237126970207	-8.2371269702073
59	361	382.109937398417	-21.109937398417
60	317	385.19895112045	-68.1989511204505
61	386	388.164944379989	-2.16494437998906
62	318	389.408651164599	-71.408651164599
63	407	396.065258298985	10.9347417010152
64	393	397.678026471079	-4.67802647107938
65	404	401.32063227434	2.67936772566004
66	498	403.240951602672	94.7590483973282
67	438	404.669189081024	33.3308109189759

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/1yl481292503015.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/1yl481292503015.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/2qv4b1292503015.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/2qv4b1292503015.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/3qv4b1292503015.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/3qv4b1292503015.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/4qv4b1292503015.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/4qv4b1292503015.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/5j43w1292503015.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/5j43w1292503015.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/6j43w1292503015.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/6j43w1292503015.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/7cv2h1292503015.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/7cv2h1292503015.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/8cv2h1292503015.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/8cv2h1292503015.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/9aq9q1292503015.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925029829uv3u1bbah9r94y/9aq9q1292503015.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

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

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