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Q3

*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: Mon, 24 Nov 2008 11:56:50 -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/Nov/24/t1227553564bpe9c0aoy25skhk.htm/, Retrieved Mon, 24 Nov 2008 19:06:13 +0000

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/Nov/24/t1227553564bpe9c0aoy25skhk.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},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

91,2 0 99,2 0 108,2 0 101,5 0 106,9 0 104,4 0 77,9 0 60 0 99,5 0 95 0 105,6 0 102,5 0 93,3 0 97,3 0 127 0 111,7 0 96,4 0 133 0 72,2 0 95,8 0 124,1 0 127,6 0 110,7 0 104,6 0 112,7 0 115,3 0 139,4 0 119 0 97,4 0 154 0 81,5 0 88,8 0 127,7 0 105,1 0 114,9 0 106,4 0 104,5 1 121,6 1 141,4 1 99 1 126,7 1 134,1 1 81,3 1 88,6 1 132,7 1 132,9 1 134,4 1 103,7 1 119,7 1 115 1 132,9 1 108,5 1 113,9 1 142 1 97,7 1 92,2 1 128,8 1 134,9 1 128,2 1 114,8 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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 86.6072222222222 -6.55555555555556x[t] + 4.72902777777782M1[t] + 9.5063888888889M2[t] + 28.9837500000000M3[t] + 6.52111111111113M4[t] + 6.21847222222221M5[t] + 30.8358333333334M6[t] -21.1668055555555M7[t] -18.8294444444445M8[t] + 18.0279166666667M9[t] + 13.9452777777778M10[t] + 12.9826388888889M11[t] + 0.622638888888888t + 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)	86.6072222222222	5.52091	15.6871	0	0
x	-6.55555555555556	4.957923	-1.3222	0.192626	0.096313
M1	4.72902777777782	6.154285	0.7684	0.446169	0.223085
M2	9.5063888888889	6.119237	1.5535	0.127152	0.063576
M3	28.9837500000000	6.087352	4.7613	1.9e-05	1e-05
M4	6.52111111111113	6.058682	1.0763	0.287395	0.143697
M5	6.21847222222221	6.033272	1.0307	0.308072	0.154036
M6	30.8358333333334	6.011162	5.1298	6e-06	3e-06
M7	-21.1668055555555	5.992391	-3.5323	0.00095	0.000475
M8	-18.8294444444445	5.976988	-3.1503	0.002866	0.001433
M9	18.0279166666667	5.964981	3.0223	0.00409	0.002045
M10	13.9452777777778	5.95639	2.3412	0.023609	0.011804
M11	12.9826388888889	5.951229	2.1815	0.034294	0.017147
t	0.622638888888888	0.143123	4.3504	7.5e-05	3.7e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.899877752596622
R-squared	0.809779969618348
Adjusted R-squared	0.756022134945272
F-TEST (value)	15.0634781803055
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	1.92490468009510e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.40699772936048
Sum Squared Residuals	4070.61388888889

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	91.2	91.9588888888887	-0.758888888888741
2	99.2	97.3588888888889	1.84111111111113
3	108.2	117.458888888889	-9.25888888888888
4	101.5	95.6188888888889	5.88111111111111
5	106.9	95.9388888888889	10.9611111111111
6	104.4	121.178888888889	-16.7788888888889
7	77.9	69.7988888888889	8.10111111111114
8	60	72.758888888889	-12.7588888888890
9	99.5	110.238888888889	-10.7388888888889
10	95	106.778888888889	-11.7788888888889
11	105.6	106.438888888889	-0.838888888888912
12	102.5	94.0788888888889	8.42111111111111
13	93.3	99.4305555555556	-6.1305555555556
14	97.3	104.830555555556	-7.53055555555555
15	127	124.930555555556	2.06944444444444
16	111.7	103.090555555556	8.60944444444445
17	96.4	103.410555555556	-7.01055555555554
18	133	128.650555555556	4.34944444444446
19	72.2	77.2705555555556	-5.07055555555556
20	95.8	80.2305555555555	15.5694444444445
21	124.1	117.710555555556	6.38944444444444
22	127.6	114.250555555556	13.3494444444444
23	110.7	113.910555555556	-3.21055555555555
24	104.6	101.550555555556	3.04944444444443
25	112.7	106.902222222222	5.79777777777773
26	115.3	112.302222222222	2.99777777777776
27	139.4	132.402222222222	6.99777777777778
28	119	110.562222222222	8.43777777777778
29	97.4	110.882222222222	-13.4822222222222
30	154	136.122222222222	17.8777777777778
31	81.5	84.7422222222222	-3.24222222222223
32	88.8	87.7022222222222	1.09777777777779
33	127.7	125.182222222222	2.51777777777779
34	105.1	121.722222222222	-16.6222222222222
35	114.9	121.382222222222	-6.48222222222221
36	106.4	109.022222222222	-2.62222222222222
37	104.5	107.818333333333	-3.31833333333338
38	121.6	113.218333333333	8.38166666666665
39	141.4	133.318333333333	8.08166666666666
40	99	111.478333333333	-12.4783333333333
41	126.7	111.798333333333	14.9016666666667
42	134.1	137.038333333333	-2.93833333333332
43	81.3	85.6583333333333	-4.35833333333335
44	88.6	88.6183333333333	-0.0183333333333177
45	132.7	126.098333333333	6.60166666666667
46	132.9	122.638333333333	10.2616666666667
47	134.4	122.298333333333	12.1016666666667
48	103.7	109.938333333333	-6.23833333333333
49	119.7	115.29	4.40999999999997
50	115	120.69	-5.69
51	132.9	140.79	-7.89
52	108.5	118.95	-10.45
53	113.9	119.27	-5.36999999999999
54	142	144.51	-2.50999999999998
55	97.7	93.13	4.56999999999999
56	92.2	96.09	-3.88999999999997
57	128.8	133.57	-4.76999999999998
58	134.9	130.11	4.79
59	128.2	129.77	-1.57000000000001
60	114.8	117.41	-2.61000000000000

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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