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multiple regression import: zonder seizoen en zonder trend

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 03:49:04 -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/t11974556791wlnar0olc14m2o.htm/, Retrieved Wed, 12 Dec 2007 11:34:49 +0100

User-defined keywords:

Dataseries X:

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733,6 0 844,9 0 864,3 0 833,5 0 814,9 0 820,4 0 710,8 0 773,1 0 801,2 0 832,9 0 808,3 0 817,2 0 745,5 0 932,6 0 1057,0 0 879,9 0 1089,5 0 903,0 0 846,1 0 959,1 0 952,0 0 1092,5 0 1188,9 0 996,7 0 1034,3 0 898,2 0 1111,6 0 900,5 0 1049,2 0 1010,9 0 875,9 0 849,9 0 713,4 1 918,6 1 912,5 1 767,0 1 902,2 1 891,9 1 874,0 1 930,9 1 944,2 1 935,9 1 937,1 1 885,1 1 892,4 1 987,3 1 946,3 1 799,6 1 875,4 1 846,2 1 880,6 1 885,7 1 868,9 1 882,5 1 789,6 1 773,3 1 804,3 1 817,8 1 836,7 1 721,8 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

import[t] = + 907.1375 -42.0946428571429dummy[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)	907.1375	17.763611	51.0672	0	0
dummy	-42.0946428571429	26.003263	-1.6188	0.110911	0.055456

Multiple Linear Regression - Regression Statistics
Multiple R	0.207916482235032
R-squared	0.0432292635849902
Adjusted R-squared	0.0267332164054211
F-TEST (value)	2.62058316846541
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0.110911337858779
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	100.486156498212
Sum Squared Residuals	585653.123571429

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	733.6	907.1375	-173.5375
2	844.9	907.1375	-62.2375
3	864.3	907.1375	-42.8375
4	833.5	907.1375	-73.6375
5	814.9	907.1375	-92.2375
6	820.4	907.1375	-86.7375
7	710.8	907.1375	-196.3375
8	773.1	907.1375	-134.0375
9	801.2	907.1375	-105.9375
10	832.9	907.1375	-74.2375
11	808.3	907.1375	-98.8375
12	817.2	907.1375	-89.9375
13	745.5	907.1375	-161.6375
14	932.6	907.1375	25.4625000000000
15	1057	907.1375	149.8625
16	879.9	907.1375	-27.2375
17	1089.5	907.1375	182.3625
18	903	907.1375	-4.1375
19	846.1	907.1375	-61.0375
20	959.1	907.1375	51.9625
21	952	907.1375	44.8625
22	1092.5	907.1375	185.3625
23	1188.9	907.1375	281.7625
24	996.7	907.1375	89.5625
25	1034.3	907.1375	127.1625
26	898.2	907.1375	-8.93749999999995
27	1111.6	907.1375	204.4625
28	900.5	907.1375	-6.6375
29	1049.2	907.1375	142.0625
30	1010.9	907.1375	103.7625
31	875.9	907.1375	-31.2375
32	849.9	907.1375	-57.2375
33	713.4	865.042857142857	-151.642857142857
34	918.6	865.042857142857	53.5571428571429
35	912.5	865.042857142857	47.4571428571429
36	767	865.042857142857	-98.0428571428571
37	902.2	865.042857142857	37.1571428571429
38	891.9	865.042857142857	26.8571428571428
39	874	865.042857142857	8.95714285714287
40	930.9	865.042857142857	65.8571428571428
41	944.2	865.042857142857	79.157142857143
42	935.9	865.042857142857	70.8571428571428
43	937.1	865.042857142857	72.0571428571429
44	885.1	865.042857142857	20.0571428571429
45	892.4	865.042857142857	27.3571428571428
46	987.3	865.042857142857	122.257142857143
47	946.3	865.042857142857	81.2571428571428
48	799.6	865.042857142857	-65.4428571428571
49	875.4	865.042857142857	10.3571428571428
50	846.2	865.042857142857	-18.8428571428571
51	880.6	865.042857142857	15.5571428571429
52	885.7	865.042857142857	20.6571428571429
53	868.9	865.042857142857	3.85714285714285
54	882.5	865.042857142857	17.4571428571429
55	789.6	865.042857142857	-75.4428571428571
56	773.3	865.042857142857	-91.7428571428572
57	804.3	865.042857142857	-60.7428571428572
58	817.8	865.042857142857	-47.2428571428572
59	836.7	865.042857142857	-28.3428571428571
60	721.8	865.042857142857	-143.242857142857

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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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