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The Seatbelt Law - Q3

*The author of this computation has been verified*
R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Sun, 23 Nov 2008 05:07:59 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227442175u5eddhk5j4pey8a.htm/, Retrieved Sun, 23 Nov 2008 12:09:35 +0000
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227442175u5eddhk5j4pey8a.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
106,60 106,80 107,00 107,10 107,30 107,40 107,60 107,70 107,90 108,20 108,30 108,50 108,92 109,23 109,41 109,65 109,91 110,01 110,20 110,49 110,57 110,72 110,94 111,09 111,28 111,41 111,62 111,76 111,89 112,04 112,12 112,30 112,47 112,59 112,78 112,73 112,99 113,10 113,33 113,38 113,68 113,65 113,81 113,88 114,02 114,25 114,28 114,38 114,73 114,97 115,05 115,29 115,37 115,54 115,76 115,92 116,02 116,21 116,26 116,51
 
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 computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 106.69025 + 0.0805902777777558M1[t] + 0.113263888888887M2[t] + 0.127937499999999M3[t] + 0.116611111111112M4[t] + 0.145284722222223M5[t] + 0.0779583333333382M6[t] + 0.0826319444444455M7[t] + 0.0773055555555525M8[t] + 0.0499791666666631M9[t] + 0.0826527777777762M10[t] + 0.0353263888888877M11[t] + 0.165326388888889t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)106.690250.146726727.141400
M10.08059027777775580.17850.45150.6537160.326858
M20.1132638888888870.1782330.63550.5281970.264098
M30.1279374999999990.1779920.71880.4758320.237916
M40.1166111111111120.1777750.65590.5150560.257528
M50.1452847222222230.1775840.81810.4174180.208709
M60.07795833333333820.1774180.43940.6623820.331191
M70.08263194444444550.1772770.46610.6432850.321643
M80.07730555555555250.1771620.43640.6645780.332289
M90.04997916666666310.1770730.28230.778990.389495
M100.08265277777777620.1770090.46690.6426990.32135
M110.03532638888888770.1769710.19960.8426410.42132
t0.1653263888888890.00212877.673800


Multiple Linear Regression - Regression Statistics
Multiple R0.996265997226037
R-squared0.992545937228791
Adjusted R-squared0.99064277226593
F-TEST (value)521.52385977948
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.279794725919707
Sum Squared Residuals3.67939916666675


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1106.6106.936166666667-0.336166666666753
2106.8107.134166666667-0.334166666666665
3107107.314166666667-0.314166666666663
4107.1107.468166666667-0.36816666666667
5107.3107.662166666667-0.362166666666666
6107.4107.760166666667-0.360166666666663
7107.6107.930166666667-0.33016666666667
8107.7108.090166666667-0.390166666666657
9107.9108.228166666667-0.328166666666654
10108.2108.426166666667-0.226166666666658
11108.3108.544166666667-0.244166666666665
12108.5108.674166666667-0.174166666666663
13108.92108.920083333333-8.33333333072222e-05
14109.23109.1180833333330.111916666666674
15109.41109.2980833333330.111916666666667
16109.65109.4520833333330.197916666666674
17109.91109.6460833333330.263916666666664
18110.01109.7440833333330.265916666666668
19110.2109.9140833333330.285916666666669
20110.49110.0740833333330.415916666666665
21110.57110.2120833333330.357916666666663
22110.72110.4100833333330.309916666666667
23110.94110.5280833333330.411916666666666
24111.09110.6580833333330.43191666666667
25111.28110.9040.376000000000023
26111.41111.1020.307999999999999
27111.62111.2820.338000000000005
28111.76111.4360.324000000000004
29111.89111.630.26
30112.04111.7280.312000000000000
31112.12111.8980.222000000000002
32112.3112.0580.241999999999998
33112.47112.1960.274
34112.59112.3940.196000000000004
35112.78112.5120.268000000000001
36112.73112.6420.0880000000000035
37112.99112.8879166666670.102083333333349
38113.1113.0859166666670.0140833333333279
39113.33113.2659166666670.0640833333333307
40113.38113.419916666667-0.0399166666666738
41113.68113.6139166666670.0660833333333379
42113.65113.711916666667-0.0619166666666684
43113.81113.881916666667-0.0719166666666679
44113.88114.041916666667-0.161916666666670
45114.02114.179916666667-0.159916666666670
46114.25114.377916666667-0.127916666666667
47114.28114.495916666667-0.215916666666667
48114.38114.625916666667-0.245916666666674
49114.73114.871833333333-0.141833333333312
50114.97115.069833333333-0.0998333333333364
51115.05115.249833333333-0.19983333333334
52115.29115.403833333333-0.113833333333334
53115.37115.597833333333-0.227833333333335
54115.54115.695833333333-0.155833333333337
55115.76115.865833333333-0.105833333333334
56115.92116.025833333333-0.105833333333336
57116.02116.163833333333-0.143833333333339
58116.21116.361833333333-0.151833333333345
59116.26116.479833333333-0.219833333333336
60116.51116.609833333333-0.0998333333333365
 
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')
 





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