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Multiple Linear Regression

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

Title produced by software: Multiple Regression

Date of computation: Wed, 12 Dec 2007 03:05:24 -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/Dec/12/t1197453112390s9ft915da0mz.htm/, Retrieved Wed, 12 Dec 2007 10:52:03 +0100

User-defined keywords:

Monthly dummy, linear trend

Dataseries X:

» Textbox « » Textfile « » CSV «

523000 519000 509000 512000 519000 517000 510000 509000 501000 507000 569000 580000 578000 565000 547000 555000 562000 561000 555000 544000 537000 543000 594000 611000 613000 611000 594000 595000 591000 589000 584000 573000 567000 569000 621000 629000 628000 612000 595000 597000 593000 590000 580000 574000 573000 573000 620000 626000 620000 588000 566000 557000 561000 549000 532000 526000 511000 499000 555000 565000 542000

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	11 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 578882.352941177 -14961.4379084967M1[t] -16722.8758169936M2[t] -34170.5882352942M3[t] -33818.3006535949M4[t] -32466.0130718955M5[t] -37113.7254901961M6[t] -46761.4379084968M7[t] -54409.1503267974M8[t] -62456.8627450981M9[t] -62704.5751633988M10[t] -9752.28758169938M11[t] + 647.712418300652t + 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)	578882.352941177	16469.671251	35.1484	0	0
M1	-14961.4379084967	19207.511251	-0.7789	0.43984	0.21992
M2	-16722.8758169936	20160.315253	-0.8295	0.410931	0.205465
M3	-34170.5882352942	20134.570309	-1.6971	0.096152	0.048076
M4	-33818.3006535949	20111.507424	-1.6815	0.099154	0.049577
M5	-32466.0130718955	20091.135834	-1.6159	0.112662	0.056331
M6	-37113.7254901961	20073.463733	-1.8489	0.070637	0.035318
M7	-46761.4379084968	20058.498256	-2.3313	0.023986	0.011993
M8	-54409.1503267974	20046.245465	-2.7142	0.009202	0.004601
M9	-62456.8627450981	20036.710336	-3.1171	0.003082	0.001541
M10	-62704.5751633988	20029.89675	-3.1305	0.002968	0.001484
M11	-9752.28758169938	20025.807486	-0.487	0.628485	0.314242
t	647.712418300652	233.665254	2.772	0.007907	0.003953

Multiple Linear Regression - Regression Statistics
Multiple R	0.629253196570935
R-squared	0.39595958539474
Adjusted R-squared	0.244949481743425
F-TEST (value)	2.62207346277318
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.00894497169121755
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	31661.4262949836
Sum Squared Residuals	48117403921.5686

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	523000	564568.62745098	-41568.6274509798
2	519000	563454.901960784	-44454.9019607844
3	509000	546654.901960784	-37654.9019607843
4	512000	547654.901960784	-35654.9019607842
5	519000	549654.901960784	-30654.9019607843
6	517000	545654.901960784	-28654.9019607843
7	510000	536654.901960784	-26654.9019607844
8	509000	529654.901960784	-20654.9019607843
9	501000	522254.901960784	-21254.9019607845
10	507000	522654.901960784	-15654.9019607844
11	569000	576254.901960784	-7254.90196078425
12	580000	586654.901960784	-6654.90196078437
13	578000	572341.176470588	5658.82352941166
14	565000	571227.450980392	-6227.45098039218
15	547000	554427.450980392	-7427.45098039216
16	555000	555427.450980392	-427.450980392176
17	562000	557427.450980392	4572.54901960783
18	561000	553427.450980392	7572.54901960783
19	555000	544427.450980392	10572.5490196078
20	544000	537427.450980392	6572.54901960783
21	537000	530027.450980392	6972.54901960786
22	543000	530427.450980392	12572.5490196078
23	594000	584027.450980392	9972.54901960781
24	611000	594427.450980392	16572.5490196078
25	613000	580113.725490196	32886.2745098038
26	611000	579000	32000
27	594000	562200	31800
28	595000	563200	31800
29	591000	565200	25800
30	589000	561200	27800
31	584000	552200	31800
32	573000	545200	27800
33	567000	537800	29200
34	569000	538200	30800
35	621000	591800	29200.0000000000
36	629000	602200	26799.9999999999
37	628000	587886.274509804	40113.725490196
38	612000	586772.549019608	25227.4509803922
39	595000	569972.549019608	25027.4509803922
40	597000	570972.549019608	26027.4509803922
41	593000	572972.549019608	20027.4509803922
42	590000	568972.549019608	21027.4509803922
43	580000	559972.549019608	20027.4509803922
44	574000	552972.549019608	21027.4509803922
45	573000	545572.549019608	27427.4509803922
46	573000	545972.549019608	27027.4509803922
47	620000	599572.549019608	20427.4509803921
48	626000	609972.549019608	16027.4509803921
49	620000	595658.823529412	24341.1764705881
50	588000	594545.098039216	-6545.09803921566
51	566000	577745.098039216	-11745.0980392157
52	557000	578745.098039216	-21745.0980392157
53	561000	580745.098039216	-19745.0980392157
54	549000	576745.098039216	-27745.0980392157
55	532000	567745.098039216	-35745.0980392157
56	526000	560745.098039216	-34745.0980392157
57	511000	553345.098039216	-42345.0980392156
58	499000	553745.098039216	-54745.0980392156
59	555000	607345.098039216	-52345.0980392157
60	565000	617745.098039216	-52745.0980392157
61	542000	603431.37254902	-61431.3725490197

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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

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