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case multiple regression: 1 Irak

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

Title produced by software: Multiple Regression

Date of computation: Sat, 17 Nov 2007 08:03:16 -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/17/t1195311478caz4snhhruvbqz8.htm/, Retrieved Sat, 17 Nov 2007 15:58:08 +0100

User-defined keywords:

S0650921

Dataseries X:

» Textbox « » Textfile « » CSV «

99,9 0 98,2 0 104,5 0 100,8 0 101,5 0 103,9 0 99,6 0 98,4 0 112,7 0 118,4 0 108,1 0 105,4 0 114,6 0 106,9 0 115,9 1 109,8 1 101,8 1 114,2 2 110,8 2 108,4 2 127,5 2 128,6 2 116,6 2 127,4 2 105 2 108,3 2 125 2 111,6 2 106,5 2 130,3 2 115 2 116,1 2 134 2 126,5 2 125,8 2 136,4 2 114,9 2 110,9 2 125,5 2 116,8 2 116,8 2 125,5 2 104,2 2 115,1 2 132,8 2 123,3 2 124,8 2 122 2 117,4 2 117,9 2 137,4 2 114,6 2 124,7 2 129,6 2 109,4 2 120,9 2 134,9 2 136,3 2 133,2 2 127,2 2

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] = + 104.805040713455 + 8.11457929430014x[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)	104.805040713455	2.251438	46.5503	0	0
x	8.11457929430014	1.318307	6.1553	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.62859047461288
R-squared	0.395125984774045
Adjusted R-squared	0.384697122442563
F-TEST (value)	37.8877361897150
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	7.54743660902335e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	8.64304404088527
Sum Squared Residuals	4332.72819697558

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	99.9	104.805040713455	-4.90504071345533
2	98.2	104.805040713455	-6.60504071345484
3	104.5	104.805040713455	-0.305040713454791
4	100.8	104.805040713455	-4.00504071345479
5	101.5	104.805040713455	-3.30504071345479
6	103.9	104.805040713455	-0.905040713454786
7	99.6	104.805040713455	-5.2050407134548
8	98.4	104.805040713455	-6.40504071345479
9	112.7	104.805040713455	7.89495928654521
10	118.4	104.805040713455	13.5949592865452
11	108.1	104.805040713455	3.2949592865452
12	105.4	104.805040713455	0.594959286545214
13	114.6	104.805040713455	9.7949592865452
14	106.9	104.805040713455	2.09495928654521
15	115.9	112.919620007755	2.98037999224508
16	109.8	112.919620007755	-3.11962000775493
17	101.8	112.919620007755	-11.1196200077549
18	114.2	121.034199302055	-6.83419930205506
19	110.8	121.034199302055	-10.2341993020551
20	108.4	121.034199302055	-12.6341993020551
21	127.5	121.034199302055	6.46580069794494
22	128.6	121.034199302055	7.56580069794493
23	116.6	121.034199302055	-4.43419930205507
24	127.4	121.034199302055	6.36580069794495
25	105	121.034199302055	-16.0341993020551
26	108.3	121.034199302055	-12.7341993020551
27	125	121.034199302055	3.96580069794494
28	111.6	121.034199302055	-9.43419930205507
29	106.5	121.034199302055	-14.5341993020551
30	130.3	121.034199302055	9.26580069794495
31	115	121.034199302055	-6.03419930205506
32	116.1	121.034199302055	-4.93419930205507
33	134	121.034199302055	12.9658006979449
34	126.5	121.034199302055	5.46580069794494
35	125.8	121.034199302055	4.76580069794494
36	136.4	121.034199302055	15.3658006979449
37	114.9	121.034199302055	-6.13419930205505
38	110.9	121.034199302055	-10.1341993020551
39	125.5	121.034199302055	4.46580069794494
40	116.8	121.034199302055	-4.23419930205506
41	116.8	121.034199302055	-4.23419930205506
42	125.5	121.034199302055	4.46580069794494
43	104.2	121.034199302055	-16.8341993020551
44	115.1	121.034199302055	-5.93419930205507
45	132.8	121.034199302055	11.7658006979450
46	123.3	121.034199302055	2.26580069794494
47	124.8	121.034199302055	3.76580069794494
48	122	121.034199302055	0.96580069794494
49	117.4	121.034199302055	-3.63419930205505
50	117.9	121.034199302055	-3.13419930205505
51	137.4	121.034199302055	16.3658006979449
52	114.6	121.034199302055	-6.43419930205507
53	124.7	121.034199302055	3.66580069794494
54	129.6	121.034199302055	8.56580069794493
55	109.4	121.034199302055	-11.6341993020551
56	120.9	121.034199302055	-0.134199302055055
57	134.9	121.034199302055	13.8658006979449
58	136.3	121.034199302055	15.2658006979450
59	133.2	121.034199302055	12.1658006979449
60	127.2	121.034199302055	6.16580069794494

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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