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

Title produced by software: Multiple Regression

Date of computation: Fri, 14 Dec 2007 04:53:28 -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/14/t1197632441h6934bwt4myvhjx.htm/, Retrieved Fri, 14 Dec 2007 12:40:41 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

36845 0 35338 0 35022 0 34777 0 26887 0 23970 0 22780 0 17351 0 21382 0 24561 0 17409 0 11514 0 31514 0 27071 0 29462 1 26105 1 22397 1 23843 1 21705 1 18089 1 20764 1 25316 1 17704 1 15548 1 28029 1 29383 1 36438 1 32034 1 22679 1 24319 1 18004 1 17537 1 20366 1 22782 1 19169 1 13807 1 29743 1 25591 1 29096 1 26482 1 22405 1 27044 1 17970 1 18730 1 19684 1 19785 1 18479 1 10698 1 31956 1 29506 1 34506 1 27165 1 26736 1 23691 1 18157 1 17328 1 18205 1 20995 1 17382 1 9367 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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

auto[t] = + 14352.9629370629 -1191.91958041958irak[t] + 18821.6910839161M1[t] + 16615.7751748252M2[t] + 20414.8431818182M3[t] + 16856.3272727273M4[t] + 11798.2113636364M5[t] + 12184.4954545455M6[t] + 7367.97954545454M7[t] + 5485.46363636364M8[t] + 7792.34772727273M9[t] + 10433.6318181818M10[t] + 5808.11590909091M11[t] -33.6840909090909t + 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)	14352.9629370629	1242.168143	11.5548	0	0
irak	-1191.91958041958	1075.749168	-1.108	0.273626	0.136813
M1	18821.6910839161	1498.363088	12.5615	0	0
M2	16615.7751748252	1496.269889	11.1048	0	0
M3	20414.8431818182	1504.286905	13.5711	0	0
M4	16856.3272727273	1500.346244	11.235	0	0
M5	11798.2113636364	1496.860575	7.882	0	0
M6	12184.4954545455	1493.833082	8.1565	0	0
M7	7367.97954545454	1491.266558	4.9408	1.1e-05	5e-06
M8	5485.46363636364	1489.163383	3.6836	0.000604	0.000302
M9	7792.34772727273	1487.525525	5.2385	4e-06	2e-06
M10	10433.6318181818	1486.354522	7.0196	0	0
M11	5808.11590909091	1485.651477	3.9095	0.000302	0.000151
t	-33.6840909090909	26.390998	-1.2763	0.208239	0.10412

Multiple Linear Regression - Regression Statistics
Multiple R	0.94830974746031
R-squared	0.899291377128238
Adjusted R-squared	0.870830244577523
F-TEST (value)	31.5971746916879
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2348.65058371101
Sum Squared Residuals	253743339.960839

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	36845	33140.9699300700	3704.03006993005
2	35338	30901.3699300699	4436.63006993007
3	35022	34666.7538461538	355.246153846153
4	34777	31074.5538461538	3702.44615384615
5	26887	25982.7538461538	904.246153846162
6	23970	26335.3538461538	-2365.35384615385
7	22780	21485.1538461538	1294.84615384616
8	17351	19568.9538461538	-2217.95384615385
9	21382	21842.1538461538	-460.153846153844
10	24561	24449.7538461538	111.246153846153
11	17409	19790.5538461538	-2381.55384615385
12	11514	13948.7538461538	-2434.75384615384
13	31514	32736.7608391608	-1222.76083916084
14	27071	30497.1608391608	-3426.16083916084
15	29462	33070.6251748252	-3608.62517482517
16	26105	29478.4251748252	-3373.42517482517
17	22397	24386.6251748252	-1989.62517482518
18	23843	24739.2251748252	-896.225174825174
19	21705	19889.0251748252	1815.97482517483
20	18089	17972.8251748252	116.174825174826
21	20764	20246.0251748252	517.974825174825
22	25316	22853.6251748252	2462.37482517483
23	17704	18194.4251748252	-490.425174825174
24	15548	12352.6251748252	3195.37482517482
25	28029	31140.6321678322	-3111.63216783216
26	29383	28901.0321678322	481.967832167833
27	36438	32666.4160839161	3771.58391608392
28	32034	29074.2160839161	2959.78391608392
29	22679	23982.4160839161	-1303.41608391609
30	24319	24335.0160839161	-16.0160839160838
31	18004	19484.8160839161	-1480.81608391608
32	17537	17568.6160839161	-31.6160839160839
33	20366	19841.8160839161	524.183916083916
34	22782	22449.4160839161	332.583916083916
35	19169	17790.2160839161	1378.78391608392
36	13807	11948.4160839161	1858.58391608392
37	29743	30736.4230769231	-993.423076923071
38	25591	28496.8230769231	-2905.82307692308
39	29096	32262.206993007	-3166.20699300699
40	26482	28670.006993007	-2188.00699300699
41	22405	23578.206993007	-1173.20699300700
42	27044	23930.806993007	3113.19300699301
43	17970	19080.606993007	-1110.60699300699
44	18730	17164.406993007	1565.59300699301
45	19684	19437.606993007	246.393006993007
46	19785	22045.206993007	-2260.20699300699
47	18479	17386.006993007	1092.99300699301
48	10698	11544.206993007	-846.206993006994
49	31956	30332.213986014	1623.78601398602
50	29506	28092.613986014	1413.38601398601
51	34506	31857.9979020979	2648.0020979021
52	27165	28265.7979020979	-1100.79790209790
53	26736	23173.9979020979	3562.00209790210
54	23691	23526.5979020979	164.402097902097
55	18157	18676.3979020979	-519.397902097904
56	17328	16760.1979020979	567.802097902097
57	18205	19033.3979020979	-828.397902097903
58	20995	21640.9979020979	-645.997902097904
59	17382	16981.7979020979	400.202097902097
60	9367	11139.9979020979	-1772.99790209790

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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