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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: Thu, 29 Nov 2007 03:25:21 -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/29/t1196331346abuk4dqi3964xyv.htm/, Retrieved Thu, 29 Nov 2007 11:16:24 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

15859,4 0 15258,9 0 15498,6 0 15106,5 0 15023,6 0 12083,0 0 15761,3 0 16942,6 0 15070,3 0 13659,6 0 14768,9 0 14725,1 0 15998,1 0 15370,6 0 14956,9 0 15469,7 0 15101,8 0 11703,7 0 16283,6 0 16726,5 0 14968,9 0 14861,0 0 14583,3 0 15305,8 0 17903,9 0 16379,4 0 15420,3 0 17870,5 0 15912,8 0 13866,5 0 17823,2 0 17872,0 0 17422,0 0 16704,5 0 15991,2 0 16583,6 0 19123,5 0 17838,7 0 17209,4 0 18586,5 0 16258,1 0 15141,6 1 19202,1 1 17746,5 1 19090,1 1 18040,3 1 17515,5 1 17751,8 1 21072,4 1 17170,0 1 19439,5 1 19795,4 1 17574,9 1 16165,4 1 19464,6 1 19932,1 1 19961,2 1 17343,4 1 18924,2 1 18574,1 1 21350,6 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] = + 15850.0926829268 + 2712.69231707317`x `[t] + 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)	15850.0926829268	243.548152	65.0799	0	0
`x `	2712.69231707317	425.338562	6.3777	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.638810198823146
R-squared	0.408078470120468
Adjusted R-squared	0.398045901817425
F-TEST (value)	40.6753742206466
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	3.0290149388712e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1559.46907693626
Sum Squared Residuals	143484684.313305

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	15859.4	15850.0926829268	9.30731707320342
2	15258.9	15850.0926829268	-591.192682926829
3	15498.6	15850.0926829268	-351.49268292683
4	15106.5	15850.0926829268	-743.59268292683
5	15023.6	15850.0926829268	-826.49268292683
6	12083	15850.0926829268	-3767.09268292683
7	15761.3	15850.0926829268	-88.7926829268307
8	16942.6	15850.0926829268	1092.50731707317
9	15070.3	15850.0926829268	-779.792682926831
10	13659.6	15850.0926829268	-2190.49268292683
11	14768.9	15850.0926829268	-1081.19268292683
12	14725.1	15850.0926829268	-1124.99268292683
13	15998.1	15850.0926829268	148.007317073170
14	15370.6	15850.0926829268	-479.49268292683
15	14956.9	15850.0926829268	-893.19268292683
16	15469.7	15850.0926829268	-380.392682926829
17	15101.8	15850.0926829268	-748.292682926831
18	11703.7	15850.0926829268	-4146.39268292683
19	16283.6	15850.0926829268	433.507317073170
20	16726.5	15850.0926829268	876.40731707317
21	14968.9	15850.0926829268	-881.19268292683
22	14861	15850.0926829268	-989.09268292683
23	14583.3	15850.0926829268	-1266.79268292683
24	15305.8	15850.0926829268	-544.292682926831
25	17903.9	15850.0926829268	2053.80731707317
26	16379.4	15850.0926829268	529.30731707317
27	15420.3	15850.0926829268	-429.792682926831
28	17870.5	15850.0926829268	2020.40731707317
29	15912.8	15850.0926829268	62.7073170731693
30	13866.5	15850.0926829268	-1983.59268292683
31	17823.2	15850.0926829268	1973.10731707317
32	17872	15850.0926829268	2021.90731707317
33	17422	15850.0926829268	1571.90731707317
34	16704.5	15850.0926829268	854.40731707317
35	15991.2	15850.0926829268	141.107317073171
36	16583.6	15850.0926829268	733.507317073169
37	19123.5	15850.0926829268	3273.40731707317
38	17838.7	15850.0926829268	1988.60731707317
39	17209.4	15850.0926829268	1359.30731707317
40	18586.5	15850.0926829268	2736.40731707317
41	16258.1	15850.0926829268	408.007317073170
42	15141.6	18562.785	-3421.185
43	19202.1	18562.785	639.314999999999
44	17746.5	18562.785	-816.285
45	19090.1	18562.785	527.314999999999
46	18040.3	18562.785	-522.485000000001
47	17515.5	18562.785	-1047.285
48	17751.8	18562.785	-810.985
49	21072.4	18562.785	2509.615
50	17170	18562.785	-1392.785
51	19439.5	18562.785	876.715
52	19795.4	18562.785	1232.61500000000
53	17574.9	18562.785	-987.884999999998
54	16165.4	18562.785	-2397.385
55	19464.6	18562.785	901.814999999999
56	19932.1	18562.785	1369.315
57	19961.2	18562.785	1398.415
58	17343.4	18562.785	-1219.38500000000
59	18924.2	18562.785	361.415000000001
60	18574.1	18562.785	11.3149999999987
61	21350.6	18562.785	2787.815

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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