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seatbelt law Question 3:

*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: Mon, 24 Nov 2008 10:59:58 -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/24/t1227549657bm5u6fl0plmrn50.htm/, Retrieved Mon, 24 Nov 2008 18:01:10 +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/24/t1227549657bm5u6fl0plmrn50.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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User-defined keywords:

Question 3: Apply this type of analysis (see Q1 & Q2) to the time series that you selected in previous workshops. Use the following components to explain your endogenous time series: a constant term, a linear trend, seasonal dummies, and a meaningful dummy variable (about an intervention).

Dataseries X:

» Textbox « » Textfile « » CSV «

112.1 0 104.2 0 102.4 0 100.3 0 102.6 0 101.5 0 103.4 0 99.4 0 97.9 0 98 0 90.2 0 87.1 0 91.8 0 94.8 0 91.8 0 89.3 0 91.7 0 86.2 0 82.8 0 82.3 0 79.8 0 79.4 0 85.3 0 87.5 0 88.3 0 88.6 0 94.9 0 94.7 0 92.6 0 91.8 0 96.4 0 96.4 0 107.1 0 111.9 0 107.8 0 109.2 0 115.3 0 119.2 0 107.8 0 106.8 0 104.2 0 94.8 0 97.5 0 98.3 0 100.6 0 94.9 1 93.6 1 98 1 104.3 1 103.9 1 105.3 1 102.6 1 103.3 1 107.9 1 107.8 1 109.8 1 110.6 1 110.8 1 119.3 1 128.1 1 127.6 1 137.9 1 151.4 1 143.6 1 143.4 1 141.9 1 135.2 1 133.1 1 129.6 1 134.1 1 136.8 1 143.5 1 162.5 1 163.1 1 157.2 1 158.8 1 155.4 1 148.5 1 154.2 1 153.3 1 149.4 1 147.9 1 156 1 163 1 159.1 1 159.5 1 157.3 1 156.4 1 156.6 1 162.4 1 166.8 1 162.6 1 168.1 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

genotsmiddelen[t] = + 73.6306878306878 -3.15231481481482uitvoersubsidie[t] + 7.93784722222222M1[t] + 8.27953042328043M2[t] + 6.95871362433864M3[t] + 4.07539682539685M4[t] + 2.80458002645505M5[t] + 0.0212632275132471M6[t] + 0.225446428571446M7[t] -1.82037037037036M8[t] -1.76618716931215M9[t] -3.76193783068781M10[t] -2.98096891534390M11[t] + 0.9333167989418t + 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)	73.6306878306878	5.688793	12.9431	0	0
uitvoersubsidie	-3.15231481481482	5.581109	-0.5648	0.573797	0.286899
M1	7.93784722222222	6.846786	1.1594	0.249804	0.124902
M2	8.27953042328043	6.84494	1.2096	0.230046	0.115023
M3	6.95871362433864	6.844676	1.0167	0.312418	0.156209
M4	4.07539682539685	6.845995	0.5953	0.553347	0.276673
M5	2.80458002645505	6.848896	0.4095	0.683286	0.341643
M6	0.0212632275132471	6.853377	0.0031	0.997532	0.498766
M7	0.225446428571446	6.859435	0.0329	0.973864	0.486932
M8	-1.82037037037036	6.867066	-0.2651	0.791633	0.395816
M9	-1.76618716931215	6.876265	-0.2569	0.79796	0.39898
M10	-3.76193783068781	7.069219	-0.5322	0.59611	0.298055
M11	-2.98096891534390	7.06692	-0.4218	0.674302	0.337151
t	0.9333167989418	0.104094	8.9661	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.890002599298968
R-squared	0.79210462675892
Adjusted R-squared	0.757893995719248
F-TEST (value)	23.1537566740694
F-TEST (DF numerator)	13
F-TEST (DF denominator)	79
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	13.2195614704814
Sum Squared Residuals	13805.7876322751

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	112.1	82.501851851852	29.598148148148
2	104.2	83.7768518518518	20.4231481481482
3	102.4	83.3893518518519	19.0106481481481
4	100.3	81.4393518518518	18.8606481481482
5	102.6	81.1018518518518	21.4981481481481
6	101.5	79.2518518518518	22.2481481481482
7	103.4	80.3893518518518	23.0106481481482
8	99.4	79.2768518518518	20.1231481481482
9	97.9	80.2643518518519	17.6356481481482
10	98	79.201917989418	18.7980820105820
11	90.2	80.9162037037037	9.2837962962963
12	87.1	84.8304894179894	2.26951058201060
13	91.8	93.7016534391534	-1.90165343915343
14	94.8	94.9766534391534	-0.176653439153407
15	91.8	94.5891534391534	-2.78915343915344
16	89.3	92.6391534391534	-3.33915343915345
17	91.7	92.3016534391534	-0.601653439153434
18	86.2	90.4516534391534	-4.25165343915343
19	82.8	91.5891534391534	-8.78915343915343
20	82.3	90.4766534391534	-8.17665343915343
21	79.8	91.4641534391534	-11.6641534391534
22	79.4	90.4017195767196	-11.0017195767196
23	85.3	92.1160052910053	-6.8160052910053
24	87.5	96.030291005291	-8.53029100529098
25	88.3	104.901455026455	-16.601455026455
26	88.6	106.176455026455	-17.5764550264550
27	94.9	105.788955026455	-10.8889550264550
28	94.7	103.838955026455	-9.13895502645503
29	92.6	103.501455026455	-10.9014550264550
30	91.8	101.651455026455	-9.85145502645503
31	96.4	102.788955026455	-6.38895502645502
32	96.4	101.676455026455	-5.27645502645502
33	107.1	102.663955026455	4.43604497354497
34	111.9	101.601521164021	10.2984788359788
35	107.8	103.315806878307	4.48419312169312
36	109.2	107.230092592593	1.96990740740743
37	115.3	116.101256613757	-0.801256613756592
38	119.2	117.376256613757	1.82374338624339
39	107.8	116.988756613757	-9.18875661375662
40	106.8	115.038756613757	-8.23875661375663
41	104.2	114.701256613757	-10.5012566137566
42	94.8	112.851256613757	-18.0512566137566
43	97.5	113.988756613757	-16.4887566137566
44	98.3	112.876256613757	-14.5762566137566
45	100.6	113.863756613757	-13.2637566137566
46	94.9	109.649007936508	-14.7490079365079
47	93.6	111.363293650794	-17.7632936507936
48	98	115.277579365079	-17.2775793650793
49	104.3	124.148743386243	-19.8487433862434
50	103.9	125.423743386243	-21.5237433862434
51	105.3	125.036243386243	-19.7362433862434
52	102.6	123.086243386243	-20.4862433862434
53	103.3	122.748743386243	-19.4487433862434
54	107.9	120.898743386243	-12.9987433862434
55	107.8	122.036243386243	-14.2362433862434
56	109.8	120.923743386243	-11.1237433862434
57	110.6	121.911243386243	-11.3112433862434
58	110.8	120.848809523810	-10.0488095238095
59	119.3	122.563095238095	-3.26309523809524
60	128.1	126.477380952381	1.62261904761906
61	127.6	135.348544973545	-7.74854497354495
62	137.9	136.623544973545	1.27645502645504
63	151.4	136.236044973545	15.1639550264550
64	143.6	134.286044973545	9.31395502645501
65	143.4	133.948544973545	9.45145502645503
66	141.9	132.098544973545	9.80145502645503
67	135.2	133.236044973545	1.96395502645501
68	133.1	132.123544973545	0.976455026455022
69	129.6	133.111044973545	-3.51104497354498
70	134.1	132.048611111111	2.05138888888887
71	136.8	133.762896825397	3.03710317460318
72	143.5	137.677182539683	5.82281746031748
73	162.5	146.548346560847	15.9516534391535
74	163.1	147.823346560847	15.2766534391534
75	157.2	147.435846560847	9.76415343915342
76	158.8	145.485846560847	13.3141534391534
77	155.4	145.148346560847	10.2516534391534
78	148.5	143.298346560847	5.20165343915343
79	154.2	144.435846560847	9.76415343915342
80	153.3	143.323346560847	9.97665343915345
81	149.4	144.310846560847	5.08915343915345
82	147.9	143.248412698413	4.65158730158729
83	156	144.962698412698	11.0373015873016
84	163	148.876984126984	14.1230158730159
85	159.1	157.748148148148	1.35185185185187
86	159.5	159.023148148148	0.476851851851852
87	157.3	158.635648148148	-1.33564814814815
88	156.4	156.685648148148	-0.285648148148153
89	156.6	156.348148148148	0.251851851851833
90	162.4	154.498148148148	7.90185185185185
91	166.8	155.635648148148	11.1643518518519
92	162.6	154.523148148148	8.07685185185185
93	168.1	155.510648148148	12.5893518518518

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227549657bm5u6fl0plmrn50/18nlp1227549594.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227549657bm5u6fl0plmrn50/37kef1227549594.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227549657bm5u6fl0plmrn50/43jxk1227549594.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227549657bm5u6fl0plmrn50/5wi471227549594.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227549657bm5u6fl0plmrn50/6vvsa1227549594.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227549657bm5u6fl0plmrn50/7qq0k1227549594.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227549657bm5u6fl0plmrn50/82h6v1227549594.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227549657bm5u6fl0plmrn50/9i6vf1227549594.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227549657bm5u6fl0plmrn50/9i6vf1227549594.ps (open in new window)

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')

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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