Free Statistics

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Author's title

Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationWed, 14 Nov 2007 11:15:39 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/14/t1195063832mn4m3r32oyfwusd.htm/, Retrieved Thu, 31 Oct 2024 22:54:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5391, Retrieved Thu, 31 Oct 2024 22:54:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSeatbelt Law Q1
Estimated Impact345
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Seatbelt Law ] [2007-11-14 18:15:39] [bd7b8d7754bcf95ad80b21f541dc6b78] [Current]
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Dataseries X:
1687	0
1508	0
1507	0
1385	0
1632	0
1511	0
1559	0
1630	0
1579	0
1653	0
2152	0
2148	0
1752	0
1765	0
1717	0
1558	0
1575	0
1520	0
1805	0
1800	0
1719	0
2008	0
2242	0
2478	0
2030	0
1655	0
1693	0
1623	0
1805	0
1746	0
1795	0
1926	0
1619	0
1992	0
2233	0
2192	0
2080	0
1768	0
1835	0
1569	0
1976	0
1853	0
1965	0
1689	0
1778	0
1976	0
2397	0
2654	0
2097	0
1963	0
1677	0
1941	0
2003	0
1813	0
2012	0
1912	0
2084	0
2080	0
2118	0
2150	0
1608	0
1503	0
1548	0
1382	0
1731	0
1798	0
1779	0
1887	0
2004	0
2077	0
2092	0
2051	0
1577	0
1356	0
1652	0
1382	0
1519	0
1421	0
1442	0
1543	0
1656	0
1561	0
1905	0
2199	0
1473	0
1655	0
1407	0
1395	0
1530	0
1309	0
1526	0
1327	0
1627	0
1748	0
1958	0
2274	0
1648	0
1401	0
1411	0
1403	0
1394	0
1520	0
1528	0
1643	0
1515	0
1685	0
2000	0
2215	0
1956	0
1462	0
1563	0
1459	0
1446	0
1622	0
1657	0
1638	0
1643	0
1683	0
2050	0
2262	0
1813	0
1445	0
1762	0
1461	0
1556	0
1431	0
1427	0
1554	0
1645	0
1653	0
2016	0
2207	0
1665	0
1361	0
1506	0
1360	0
1453	0
1522	0
1460	0
1552	0
1548	0
1827	0
1737	0
1941	0
1474	0
1458	0
1542	0
1404	0
1522	0
1385	0
1641	0
1510	0
1681	0
1938	0
1868	0
1726	0
1456	0
1445	0
1456	0
1365	0
1487	0
1558	0
1488	0
1684	0
1594	0
1850	0
1998	0
2079	0
1494	0
1057	1
1218	1
1168	1
1236	1
1076	1
1174	1
1139	1
1427	1
1487	1
1483	1
1513	1
1357	1
1165	1
1282	1
1110	1
1297	1
1185	1
1222	1
1284	1
1444	1
1575	1
1737	1
1763	1




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5391&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5391&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5391&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Y [t] = + 1717.75147928994 -396.055827116028 X + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y [t] =   +  1717.75147928994   -396.055827116028   X   + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5391&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y [t] =   +  1717.75147928994   -396.055827116028   X   + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5391&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5391&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Estimated Regression Equation
Y [t] = + 1717.75147928994 -396.055827116028 X + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1717.7514792899420.000333562848685.88614154319585.68074202608117e-1542.84037101304058e-154
X-396.05582711602857.7861732311232-6.853816492259359.76295455223808e-114.88147727611904e-11

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 1717.75147928994 & 20.0003335628486 & 85.8861415431958 & 5.68074202608117e-154 & 2.84037101304058e-154 \tabularnewline
X & -396.055827116028 & 57.7861732311232 & -6.85381649225935 & 9.76295455223808e-11 & 4.88147727611904e-11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5391&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]1717.75147928994[/C][C]20.0003335628486[/C][C]85.8861415431958[/C][C]5.68074202608117e-154[/C][C]2.84037101304058e-154[/C][/ROW]
[ROW][C]X[/C][C]-396.055827116028[/C][C]57.7861732311232[/C][C]-6.85381649225935[/C][C]9.76295455223808e-11[/C][C]4.88147727611904e-11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5391&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5391&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1717.7514792899420.000333562848685.88614154319585.68074202608117e-1542.84037101304058e-154
X-396.05582711602857.7861732311232-6.853816492259359.76295455223808e-114.88147727611904e-11







Multiple Linear Regression - Regression Statistics
Multiple R0.445226892939612
R-squared0.198226986196661
Adjusted R-squared0.194007128229275
F-TEST (value)46.9748005095663
F-TEST (DF numerator)1
F-TEST (DF denominator)190
p-value9.762957109416e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation260.004336317031
Sum Squared Residuals12844428.4316954

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.445226892939612 \tabularnewline
R-squared & 0.198226986196661 \tabularnewline
Adjusted R-squared & 0.194007128229275 \tabularnewline
F-TEST (value) & 46.9748005095663 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 190 \tabularnewline
p-value & 9.762957109416e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 260.004336317031 \tabularnewline
Sum Squared Residuals & 12844428.4316954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5391&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.445226892939612[/C][/ROW]
[ROW][C]R-squared[/C][C]0.198226986196661[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.194007128229275[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]46.9748005095663[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]190[/C][/ROW]
[ROW][C]p-value[/C][C]9.762957109416e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]260.004336317031[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]12844428.4316954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5391&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5391&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Regression Statistics
Multiple R0.445226892939612
R-squared0.198226986196661
Adjusted R-squared0.194007128229275
F-TEST (value)46.9748005095663
F-TEST (DF numerator)1
F-TEST (DF denominator)190
p-value9.762957109416e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation260.004336317031
Sum Squared Residuals12844428.4316954



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
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, 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] = ', '')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], ' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') myeq <- paste(myeq, rownames(mysum$coefficients)[i], '')
}
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('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
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,mysum$coefficients[i,2])
a<-table.element(a,mysum$coefficients[i,3])
a<-table.element(a,mysum$coefficients[i,4])
a<-table.element(a,mysum$coefficients[i,4]/2)
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')