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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: Thu, 27 Nov 2008 08:57:54 -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/27/t122780164296oa0qzh5y8ajga.htm/, Retrieved Thu, 27 Nov 2008 16:00:54 +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/27/t122780164296oa0qzh5y8ajga.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)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

119.5 0 125 0 145 0 105.3 0 116.9 0 120.1 0 88.9 0 78.4 0 114.6 0 113.3 0 117 0 99.6 0 99.4 0 101.9 0 115.2 0 108.5 0 113.8 0 121 0 92.2 0 90.2 0 101.5 0 126.6 0 93.9 0 89.8 0 93.4 0 101.5 0 110.4 0 105.9 0 108.4 0 113.9 0 86.1 0 69.4 0 101.2 0 100.5 0 98 0 106.6 0 90.1 0 96.9 0 125.9 0 112 0 100 0 123.9 0 79.8 0 83.4 0 113.6 0 112.9 0 104 0 109.9 0 99 0 106.3 0 128.9 0 111.1 0 102.9 0 130 0 87 0 87.5 0 117.6 0 103.4 0 110.8 0 112.6 0 102.5 0 112.4 0 135.6 0 105.1 0 127.7 0 137 0 91 0 90.5 0 122.4 1 123.3 1 124.3 1 120 1 118.1 1 119 1 142.7 1 123.6 1 129.6 1 151.6 1 110.4 1 99.2 1 130.5 1 136.2 1 129.7 1 128 1 121.6 1

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 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

y[t] = + 104.117760617761 + 18.8378378378379x[t] -3.37722007722016M1[t] + 2.1911196911197M2[t] + 22.2911196911197M3[t] + 3.40540540540541M4[t] + 7.376833976834M5[t] + 21.4054054054054M6[t] -16.0374517374517M7[t] -21.2945945945946M8[t] + 4.98571428571428M9[t] + 7.1M10[t] + 1.60000000000000M11[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)	104.117760617761	3.172699	32.8168	0	0
x	18.8378378378379	2.260805	8.3324	0	0
M1	-3.37722007722016	4.254171	-0.7939	0.429885	0.214943
M2	2.1911196911197	4.404754	0.4974	0.620392	0.310196
M3	22.2911196911197	4.404754	5.0607	3e-06	2e-06
M4	3.40540540540541	4.404754	0.7731	0.441982	0.220991
M5	7.376833976834	4.404754	1.6747	0.098323	0.049162
M6	21.4054054054054	4.404754	4.8596	7e-06	3e-06
M7	-16.0374517374517	4.404754	-3.6409	0.000508	0.000254
M8	-21.2945945945946	4.404754	-4.8345	7e-06	4e-06
M9	4.98571428571428	4.392897	1.1349	0.260161	0.13008
M10	7.1	4.392897	1.6162	0.110415	0.055207
M11	1.60000000000000	4.392897	0.3642	0.716758	0.358379

Multiple Linear Regression - Regression Statistics
Multiple R	0.882344007477198
R-squared	0.778530947530921
Adjusted R-squared	0.741619438786075
F-TEST (value)	21.0918213317308
F-TEST (DF numerator)	12
F-TEST (DF denominator)	72
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	8.21835773764464
Sum Squared Residuals	4862.98108108106

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	119.5	100.740540540541	18.7594594594589
2	125	106.308880308880	18.6911196911197
3	145	126.408880308880	18.5911196911197
4	105.3	107.523166023166	-2.22316602316603
5	116.9	111.494594594595	5.40540540540541
6	120.1	125.523166023166	-5.42316602316601
7	88.9	88.0803088803089	0.819691119691102
8	78.4	82.823166023166	-4.42316602316602
9	114.6	109.103474903475	5.49652509652507
10	113.3	111.217760617761	2.08223938223938
11	117	105.717760617761	11.2822393822394
12	99.6	104.117760617761	-4.51776061776064
13	99.4	100.740540540540	-1.34054054054046
14	101.9	106.308880308880	-4.4088803088803
15	115.2	126.408880308880	-11.2088803088803
16	108.5	107.523166023166	0.97683397683398
17	113.8	111.494594594595	2.30540540540540
18	121	125.523166023166	-4.52316602316602
19	92.2	88.0803088803089	4.11969111969113
20	90.2	82.823166023166	7.37683397683398
21	101.5	109.103474903475	-7.60347490347489
22	126.6	111.217760617761	15.3822393822394
23	93.9	105.717760617761	-11.8177606177606
24	89.8	104.117760617761	-14.3177606177606
25	93.4	100.740540540540	-7.34054054054047
26	101.5	106.308880308880	-4.8088803088803
27	110.4	126.408880308880	-16.0088803088803
28	105.9	107.523166023166	-1.62316602316601
29	108.4	111.494594594595	-3.09459459459459
30	113.9	125.523166023166	-11.6231660231660
31	86.1	88.0803088803089	-1.98030888030888
32	69.4	82.823166023166	-13.4231660231660
33	101.2	109.103474903475	-7.90347490347489
34	100.5	111.217760617761	-10.7177606177606
35	98	105.717760617761	-7.71776061776062
36	106.6	104.117760617761	2.48223938223938
37	90.1	100.740540540540	-10.6405405405405
38	96.9	106.308880308880	-9.4088803088803
39	125.9	126.408880308880	-0.508880308880307
40	112	107.523166023166	4.47683397683398
41	100	111.494594594595	-11.4945945945946
42	123.9	125.523166023166	-1.62316602316602
43	79.8	88.0803088803089	-8.28030888030888
44	83.4	82.823166023166	0.576833976833985
45	113.6	109.103474903475	4.4965250965251
46	112.9	111.217760617761	1.68223938223940
47	104	105.717760617761	-1.71776061776061
48	109.9	104.117760617761	5.78223938223939
49	99	100.740540540540	-1.74054054054047
50	106.3	106.308880308880	-0.00888030888031
51	128.9	126.408880308880	2.49111969111969
52	111.1	107.523166023166	3.57683397683398
53	102.9	111.494594594595	-8.59459459459459
54	130	125.523166023166	4.47683397683398
55	87	88.0803088803089	-1.08030888030887
56	87.5	82.823166023166	4.67683397683398
57	117.6	109.103474903475	8.4965250965251
58	103.4	111.217760617761	-7.81776061776061
59	110.8	105.717760617761	5.08223938223939
60	112.6	104.117760617761	8.48223938223938
61	102.5	100.740540540540	1.75945945945953
62	112.4	106.308880308880	6.0911196911197
63	135.6	126.408880308880	9.19111969111968
64	105.1	107.523166023166	-2.42316602316603
65	127.7	111.494594594595	16.2054054054054
66	137	125.523166023166	11.4768339768340
67	91	88.0803088803089	2.91969111969112
68	90.5	82.823166023166	7.67683397683398
69	122.4	127.941312741313	-5.54131274131273
70	123.3	130.055598455598	-6.75559845559846
71	124.3	124.555598455598	-0.25559845559846
72	120	122.955598455598	-2.95559845559846
73	118.1	119.578378378378	-1.47837837837832
74	119	125.146718146718	-6.14671814671815
75	142.7	145.246718146718	-2.54671814671817
76	123.6	126.361003861004	-2.76100386100387
77	129.6	130.332432432432	-0.732432432432446
78	151.6	144.361003861004	7.23899613899611
79	110.4	106.918146718147	3.48185328185328
80	99.2	101.661003861004	-2.46100386100387
81	130.5	127.941312741313	2.55868725868726
82	136.2	130.055598455598	6.14440154440153
83	129.7	124.555598455598	5.14440154440153
84	128	122.955598455598	5.04440154440154
85	121.6	119.578378378378	2.02162162162168

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/1pwbl1227801470.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/1pwbl1227801470.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/2fnm41227801470.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/2fnm41227801470.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/3opnv1227801470.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/3opnv1227801470.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/4yku81227801470.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/4yku81227801470.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/5shop1227801470.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/5shop1227801470.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/697rb1227801470.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/697rb1227801470.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/75nsf1227801470.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/75nsf1227801470.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/8ckh31227801470.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/8ckh31227801470.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/9dqj51227801470.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t122780164296oa0qzh5y8ajga/9dqj51227801470.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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')

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Software written by Ed van Stee & Patrick Wessa

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