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Stat Opdr3 Q3-1

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

Title produced by software: Multiple Regression

Date of computation: Wed, 21 Nov 2007 07:00:13 -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/21/t119565339395blqgy1q9q2lpq.htm/, Retrieved Wed, 21 Nov 2007 14:56:43 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

3804 0 3491 0 4151 0 4254 1 4717 1 4866 1 4001 1 3758 1 4780 1 5016 1 4296 0 4467 0 3891 0 3872 0 3867 0 3973 1 4640 1 4538 1 3836 1 3770 1 4374 1 4497 1 3945 0 3862 0 3608 0 3301 0 3882 0 3605 0 4305 1 4216 1 3971 1 3988 1 4317 1 4484 1 4247 0 3520 0 3686 0 3403 0 3990 0 4053 0 4548 1 4559 1 3922 1 4209 1 4517 1 4386 1 3221 0 3127 0 3777 0 3322 0 3899 0 4033 1 4463 1 4819 1 4246 1 4255 1 4760 1 4581 0 4309 0 4016 0 3601 0 3257 0 3823 0 3940 1 4534 1 4575 1 3953 1 4206 1 4649 1 4353 1 3835 0 3944 0

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

Ong[t] = + 3807.66666666667 + 531.51282051282d[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)	3807.66666666667	59.546108	63.9448	0	0
d	531.51282051282	80.907229	6.5694	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.617568879079049
R-squared	0.381391320406953
Adjusted R-squared	0.372554053555624
F-TEST (value)	43.1571578433876
F-TEST (DF numerator)	1
F-TEST (DF denominator)	70
p-value	7.54077034148537e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	342.066348554176
Sum Squared Residuals	8190657.07692308

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3804	3807.66666666665	-3.66666666664862
2	3491	3807.66666666667	-316.666666666666
3	4151	3807.66666666667	343.333333333333
4	4254	4339.17948717949	-85.1794871794872
5	4717	4339.17948717949	377.820512820513
6	4866	4339.17948717949	526.820512820513
7	4001	4339.17948717949	-338.179487179487
8	3758	4339.17948717949	-581.179487179487
9	4780	4339.17948717949	440.820512820513
10	5016	4339.17948717949	676.820512820513
11	4296	3807.66666666667	488.333333333333
12	4467	3807.66666666667	659.333333333333
13	3891	3807.66666666667	83.3333333333328
14	3872	3807.66666666667	64.3333333333328
15	3867	3807.66666666667	59.3333333333328
16	3973	4339.17948717949	-366.179487179487
17	4640	4339.17948717949	300.820512820513
18	4538	4339.17948717949	198.820512820513
19	3836	4339.17948717949	-503.179487179487
20	3770	4339.17948717949	-569.179487179487
21	4374	4339.17948717949	34.8205128205128
22	4497	4339.17948717949	157.820512820513
23	3945	3807.66666666667	137.333333333333
24	3862	3807.66666666667	54.3333333333328
25	3608	3807.66666666667	-199.666666666667
26	3301	3807.66666666667	-506.666666666667
27	3882	3807.66666666667	74.3333333333328
28	3605	3807.66666666667	-202.666666666667
29	4305	4339.17948717949	-34.1794871794872
30	4216	4339.17948717949	-123.179487179487
31	3971	4339.17948717949	-368.179487179487
32	3988	4339.17948717949	-351.179487179487
33	4317	4339.17948717949	-22.1794871794872
34	4484	4339.17948717949	144.820512820513
35	4247	3807.66666666667	439.333333333333
36	3520	3807.66666666667	-287.666666666667
37	3686	3807.66666666667	-121.666666666667
38	3403	3807.66666666667	-404.666666666667
39	3990	3807.66666666667	182.333333333333
40	4053	3807.66666666667	245.333333333333
41	4548	4339.17948717949	208.820512820513
42	4559	4339.17948717949	219.820512820513
43	3922	4339.17948717949	-417.179487179487
44	4209	4339.17948717949	-130.179487179487
45	4517	4339.17948717949	177.820512820513
46	4386	4339.17948717949	46.8205128205128
47	3221	3807.66666666667	-586.666666666667
48	3127	3807.66666666667	-680.666666666667
49	3777	3807.66666666667	-30.6666666666672
50	3322	3807.66666666667	-485.666666666667
51	3899	3807.66666666667	91.3333333333328
52	4033	4339.17948717949	-306.179487179487
53	4463	4339.17948717949	123.820512820513
54	4819	4339.17948717949	479.820512820513
55	4246	4339.17948717949	-93.1794871794872
56	4255	4339.17948717949	-84.1794871794872
57	4760	4339.17948717949	420.820512820513
58	4581	3807.66666666667	773.333333333333
59	4309	3807.66666666667	501.333333333333
60	4016	3807.66666666667	208.333333333333
61	3601	3807.66666666667	-206.666666666667
62	3257	3807.66666666667	-550.666666666667
63	3823	3807.66666666667	15.3333333333328
64	3940	4339.17948717949	-399.179487179487
65	4534	4339.17948717949	194.820512820513
66	4575	4339.17948717949	235.820512820513
67	3953	4339.17948717949	-386.179487179487
68	4206	4339.17948717949	-133.179487179487
69	4649	4339.17948717949	309.820512820513
70	4353	4339.17948717949	13.8205128205128
71	3835	3807.66666666667	27.3333333333328
72	3944	3807.66666666667	136.333333333333

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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