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Multiple regression

*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: Sun, 14 Dec 2008 05:27:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/14/t1229257852l1teu1cdolng3nc.htm/, Retrieved Sun, 14 Dec 2008 13:30:53 +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/2008/Dec/14/t1229257852l1teu1cdolng3nc.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

11857.9 0 14616 0 15643.4 0 14077.2 0 14887.5 0 14159.9 0 14643 0 17192.5 0 15386.1 0 14287.1 0 17526.6 0 14497 0 14398.3 0 16629.6 0 16670.7 0 16614.8 0 16869.2 0 15663.9 0 16359.9 0 18447.7 0 16889 0 16505 0 18320.9 0 15052.1 0 15699.8 0 18135.3 0 16768.7 0 18883 0 19021 0 18101.9 0 17776.1 0 21489.9 0 17065.3 0 18690 0 18953.1 0 16398.9 0 16895.7 0 18553 0 19270 0 19422.1 0 17579.4 0 18637.3 0 18076.7 0 20438.6 0 18075.2 0 19563 0 19899.2 0 19227.5 0 17789.6 0 19220.8 0 21968.9 0 21131.5 1 19484.6 1 22404.1 1 21099 1 22486.5 1 23707.5 1 21897.5 1 23326.4 1 23765.4 1 20444 1

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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 13508.8463576159 + 1429.12251655629x[t] -1005.00520235467M1[t] + 1037.89259749816M2[t] + 1560.36178807947M3[t] + 1124.98647534952M4[t] + 556.67566593083M5[t] + 670.82485651214M6[t] + 357.414047093449M7[t] + 2666.58323767476M8[t] + 769.23242825607M9[t] + 622.201618837379M10[t] + 1927.99080941869M11[t] + 110.930809418690t + 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)	13508.8463576159	501.812786	26.9201	0	0
x	1429.12251655629	430.052974	3.3231	0.00173	0.000865
M1	-1005.00520235467	568.024442	-1.7693	0.083332	0.041666
M2	1037.89259749816	596.683852	1.7394	0.088504	0.044252
M3	1560.36178807947	596.22589	2.6171	0.011892	0.005946
M4	1124.98647534952	596.349493	1.8865	0.06542	0.03271
M5	556.67566593083	595.330905	0.9351	0.354532	0.177266
M6	670.82485651214	594.446717	1.1285	0.264842	0.132421
M7	357.414047093449	593.697529	0.602	0.550058	0.275029
M8	2666.58323767476	593.083854	4.4961	4.5e-05	2.3e-05
M9	769.23242825607	592.606111	1.2981	0.200604	0.100302
M10	622.201618837379	592.264631	1.0505	0.298839	0.149419
M11	1927.99080941869	592.059648	3.2564	0.002097	0.001049
t	110.930809418690	8.99567	12.3316	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.94955982952713
R-squared	0.901663869851592
Adjusted R-squared	0.87446451470416
F-TEST (value)	33.1501928984785
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	936.020438435378
Sum Squared Residuals	41178310.2749316

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	11857.9	12614.7719646799	-756.871964679902
2	14616	14768.6005739514	-152.600573951435
3	15643.4	15402.0005739514	241.399426048564
4	14077.2	15077.5560706402	-1000.35607064018
5	14887.5	14620.1760706402	267.323929359823
6	14159.9	14845.2560706402	-685.356070640178
7	14643	14642.7760706402	0.223929359823694
8	17192.5	17062.8760706402	129.623929359822
9	15386.1	15276.4560706402	109.643929359823
10	14287.1	15240.3560706402	-953.256070640177
11	17526.6	16657.0760706402	869.523929359821
12	14497	14840.0160706402	-343.016070640179
13	14398.3	13945.9416777042	452.358322295803
14	16629.6	16099.7702869757	529.82971302428
15	16670.7	16733.1702869757	-62.4702869757174
16	16614.8	16408.7257836645	206.07421633554
17	16869.2	15951.3457836645	917.854216335541
18	15663.9	16176.4257836645	-512.525783664459
19	16359.9	15973.9457836645	385.954216335540
20	18447.7	18394.0457836645	53.6542163355412
21	16889	16607.6257836645	281.374216335540
22	16505	16571.5257836645	-66.5257836644594
23	18320.9	17988.2457836645	332.654216335541
24	15052.1	16171.1857836645	-1119.08578366446
25	15699.8	15277.1113907285	422.68860927152
26	18135.3	17430.94	704.36
27	16768.7	18064.34	-1295.64
28	18883	17739.8954966887	1143.10450331126
29	19021	17282.5154966887	1738.48450331126
30	18101.9	17507.5954966887	594.30450331126
31	17776.1	17305.1154966887	470.984503311257
32	21489.9	19725.2154966887	1764.68450331126
33	17065.3	17938.7954966887	-873.495496688743
34	18690	17902.6954966887	787.304503311258
35	18953.1	19319.4154966887	-366.315496688743
36	16398.9	17502.3554966887	-1103.45549668874
37	16895.7	16608.2811037528	287.418896247240
38	18553	18762.1097130243	-209.109713024281
39	19270	19395.5097130243	-125.509713024282
40	19422.1	19071.0652097130	351.034790286975
41	17579.4	18613.6852097130	-1034.28520971302
42	18637.3	18838.7652097130	-201.465209713025
43	18076.7	18636.2852097130	-559.585209713023
44	20438.6	21056.3852097130	-617.785209713025
45	18075.2	19269.9652097130	-1194.76520971302
46	19563	19233.8652097130	329.134790286976
47	19899.2	20650.5852097130	-751.385209713023
48	19227.5	18833.5252097130	393.974790286975
49	17789.6	17939.4508167770	-149.850816777044
50	19220.8	20093.2794260486	-872.479426048565
51	21968.9	20726.6794260486	1242.22057395144
52	21131.5	21831.3574392936	-699.857439293598
53	19484.6	21373.9774392936	-1889.3774392936
54	22404.1	21599.0574392936	805.042560706401
55	21099	21396.5774392936	-297.577439293598
56	22486.5	23816.6774392936	-1330.17743929360
57	23707.5	22030.2574392936	1677.24256070640
58	21897.5	21994.1574392936	-96.657439293598
59	23326.4	23410.8774392936	-84.477439293597
60	23765.4	21593.8174392936	2171.58256070640
61	20444	20699.7430463576	-255.743046357617

Charts produced by software:

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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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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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