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Multiple regression (normal)

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 08:35:06 -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/15/t1195140753by17oiioza84jc2.htm/, Retrieved Thu, 15 Nov 2007 16:32:33 +0100

User-defined keywords:

W9Q3G7

Dataseries X:

» Textbox « » Textfile « » CSV «

140 1 132 0 117 0 114 1 113 1 110 1 107 0 103 0 98 0 98 1 137 1 148 0 147 0 139 1 130 0 128 1 127 1 123 1 118 0 114 1 108 0 111 1 151 1 159 1 158 0 148 0 138 0 137 1 136 1 133 1 126 1 120 0 114 0 116 1 153 1 162 1 161 1 149 1 139 0 135 1 130 1 127 1 122 0 117 0 112 0 113 1 149 1 157 1 157 0 147 0 137 0 132 1 125 1 123 0 117 0 114 0 111 1 112 0 144 1 150 1 149 0 134 0 123 0 116 0 117 1 111 0 105 0 102 0 95 0 93 0 124 1 130 1 124 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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 123.194444444444 + 8.72447447447448X[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)	123.194444444444	2.85886	43.0922	0	0
X	8.72447447447448	4.015628	2.1726	0.033148	0.016574

Multiple Linear Regression - Regression Statistics
Multiple R	0.249677596603614
R-squared	0.062338902245757
Adjusted R-squared	0.0491324079111903
F-TEST (value)	4.72032173463253
F-TEST (DF numerator)	1
F-TEST (DF denominator)	71
p-value	0.0331476117092382
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	17.1531607753953
Sum Squared Residuals	20890.3956456456

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	140	131.918918918919	8.0810810810811
2	132	123.194444444444	8.80555555555555
3	117	123.194444444444	-6.19444444444444
4	114	131.918918918919	-17.9189189189189
5	113	131.918918918919	-18.9189189189189
6	110	131.918918918919	-21.9189189189189
7	107	123.194444444444	-16.1944444444444
8	103	123.194444444444	-20.1944444444444
9	98	123.194444444444	-25.1944444444444
10	98	131.918918918919	-33.9189189189189
11	137	131.918918918919	5.08108108108108
12	148	123.194444444444	24.8055555555556
13	147	123.194444444444	23.8055555555556
14	139	131.918918918919	7.08108108108108
15	130	123.194444444444	6.80555555555556
16	128	131.918918918919	-3.91891891891892
17	127	131.918918918919	-4.91891891891892
18	123	131.918918918919	-8.91891891891892
19	118	123.194444444444	-5.19444444444444
20	114	131.918918918919	-17.9189189189189
21	108	123.194444444444	-15.1944444444444
22	111	131.918918918919	-20.9189189189189
23	151	131.918918918919	19.0810810810811
24	159	131.918918918919	27.0810810810811
25	158	123.194444444444	34.8055555555556
26	148	123.194444444444	24.8055555555556
27	138	123.194444444444	14.8055555555556
28	137	131.918918918919	5.08108108108108
29	136	131.918918918919	4.08108108108108
30	133	131.918918918919	1.08108108108108
31	126	131.918918918919	-5.91891891891892
32	120	123.194444444444	-3.19444444444444
33	114	123.194444444444	-9.19444444444444
34	116	131.918918918919	-15.9189189189189
35	153	131.918918918919	21.0810810810811
36	162	131.918918918919	30.0810810810811
37	161	131.918918918919	29.0810810810811
38	149	131.918918918919	17.0810810810811
39	139	123.194444444444	15.8055555555556
40	135	131.918918918919	3.08108108108108
41	130	131.918918918919	-1.91891891891892
42	127	131.918918918919	-4.91891891891892
43	122	123.194444444444	-1.19444444444444
44	117	123.194444444444	-6.19444444444444
45	112	123.194444444444	-11.1944444444444
46	113	131.918918918919	-18.9189189189189
47	149	131.918918918919	17.0810810810811
48	157	131.918918918919	25.0810810810811
49	157	123.194444444444	33.8055555555556
50	147	123.194444444444	23.8055555555556
51	137	123.194444444444	13.8055555555556
52	132	131.918918918919	0.0810810810810795
53	125	131.918918918919	-6.91891891891892
54	123	123.194444444444	-0.194444444444444
55	117	123.194444444444	-6.19444444444444
56	114	123.194444444444	-9.19444444444444
57	111	131.918918918919	-20.9189189189189
58	112	123.194444444444	-11.1944444444444
59	144	131.918918918919	12.0810810810811
60	150	131.918918918919	18.0810810810811
61	149	123.194444444444	25.8055555555556
62	134	123.194444444444	10.8055555555556
63	123	123.194444444444	-0.194444444444444
64	116	123.194444444444	-7.19444444444444
65	117	131.918918918919	-14.9189189189189
66	111	123.194444444444	-12.1944444444444
67	105	123.194444444444	-18.1944444444444
68	102	123.194444444444	-21.1944444444444
69	95	123.194444444444	-28.1944444444444
70	93	123.194444444444	-30.1944444444444
71	124	131.918918918919	-7.91891891891892
72	130	131.918918918919	-1.91891891891892
73	124	123.194444444444	0.805555555555556

Charts produced by software:

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Parameters:

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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