Tietokoneharjoitus 4

Seatbelts is a balanced panel from 50 U.S. States, plus the District of Columbia, for the years 1983-1997. These data were provided by Professor Liran Einav of Stanford University and were used in his paper with Alma Cohen ``The Effects of Mandatory Seat Belt Laws on Driving Behavior and Traffic Fatalities,'' The Review of Economics and Statistics, 2003, Vol. 85, No. 4, pp 828-843.

Artikkeli loytyy osoitteesta http://www.stanford.edu/~leinav/pubs/RESTAT2003.pdf

state = State (csv-tiedostossa, mutta ei txt-tiedostossa)
year = Year
fips = State ID Code
vmt = Millions of traffic miles per year. (Note: Number of fatalities =fatalityrate $\times$ vmt)
fatalityrate = Number of fatalities per million of traffic miles
sb_usage = Seat belt usage rate
speed65 = Binary variable for 65 mile per hour speed limit
speed70 = Binary variable for 70 or higher mile per hour speed limit
drinkage21 = Binary variable for age 21 drinking age
ba08 = Binary variable for blood alcohol limit â‰¤ .08\%
income = Per capita income
age = Mean age
primary = Binary variable for primary enforcement of seat belt laws
secondary = Binary variable for secondary enforcement of seat belt laws

Datan lukeminen R:aan

file<-"http://cc.oulu.fi/~jklemela/econometrics/SeatBelts.csv"
data<-read.table(file,skip=1,sep=",")

Datan lukeminen SAS:iin

FILENAME myurl URL 'http://cc.oulu.fi/~jklemela/econometrics/SeatBelts.txt';

DATA SeatBelts;
   INFILE myurl firstobs=2;
   INPUT year fips vmt fatalityrate sb_usage speed65 speed70
   drinkage21 ba08 income age primary secondary;
RUN;

Tehtävä 5

Valitse FatalityRate y-muuttujaksi ja sb_usage, speed65, speed70, drinkage21, ba08, log(income) ja age x-muuttujiksi. Suorita OLS-regressio ja testaa hypoteesia beta3=beta4

file<-"http://cc.oulu.fi/~jklemela/econometrics/SeatBelts.csv"
data<-read.table(file,skip=1,sep=",")

y<-data[,5]
sp.usage<-data[,6]
speed65<-data[,7]
speed70<-data[,8]
drinkage21<-data[,9]
ba08<-data[,10]
log.income<-log(data[,11])
age<-data[,12]

reg.model<-lm(y ~ sp.usage+speed65+speed70+drinkage21+ba08+log.income+age)

library(car)
Q<-1
K<-8
r<-0
R<-matrix(c(0,0,1,-1,0,0,0,0),Q,K)

linearHypothesis(reg.model,R,r)

Linear hypothesis test

Hypothesis:
speed65 - speed70 = 0

Model 1: restricted model
Model 2: y ~ sp.usage + speed65 + speed70 + drinkage21 + ba08 + log.income + 
    age

  Res.Df      RSS Df  Sum of Sq      F   Pr(>F)   
1    549 0.010446                                 
2    548 0.010318  1 0.00012848 6.8237 0.009242 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Waldin testi

F<-6.8237
W<-Q*F
pvalue<-1-pchisq(W, df=Q)
pvalue
# [1] 0.008995601


# Tarkistetaan tulos

ota<-!is.na(sp.usage)
K<-8
y<-data[ota,5]
n<-length(y)
x<-matrix(0,n,K)
x[,1]<-1
x[,2]<-sp.usage[ota]
x[,3]<-speed65[ota]
x[,4]<-speed70[ota]
x[,5]<-drinkage21[ota]
x[,6]<-ba08[ota]
x[,7]<-log.income[ota]
x[,8]<-age[ota]

A<-t(x)%*%x
invA<-solve(A,diag(1,K))
b<-invA%*%t(x)%*%y

Q<-1
r<-0
R<-matrix(c(0,0,1,-1,0,0,0,0),Q,K)

B<-R%*%invA%*%t(R)
invB<-solve(B,diag(1,Q))

e<-y-x%*%b
s2<-sum(e^2)/(n-K)

QF<-t(R%*%b-r)%*%invB%*%(R%*%b-r)/s2
QF
1-pchisq(QF,df=Q)

# Waldin testisuureen arvo QF
# [1,] 6.823729

# p-arvo 1-pchisq(QF,df=Q)
# [1,] 0.008995454

Kokeillaan SAS:ia

FILENAME myurl URL 'http://cc.oulu.fi/~jklemela/econometrics/SeatBelts.txt';
DATA SeatBelts;
   INFILE myurl firstobs=2;
   INPUT number $ year fips vmt fatalityrate sb_usage speed65 speed70 drinkage21 ba08 income age primary secondary;
   logincome=log(income);
RUN;

PROC reg data=SeatBelts;
  model fatalityrate =  sb_usage speed65 speed70 drinkage21 ba08 logincome age;
  hogone: test speed65-speed70=0;
RUN;

PROC reg data=SeatBelts;
  model fatalityrate =  sb_usage speed65 speed70 drinkage21 ba08 logincome age;
  restrict speed65-speed70=0;
RUN;

Saadaan tulokset


The SAS System            10:26 Thursday, February 6, 2014   3

                                              The REG Procedure
                                                Model: MODEL1

                           Test hogone Results for Dependent Variable fatalityrate

                                                          Mean
                          Source             DF         Square    F Value    Pr > F

                          Numerator           1     0.00012848       6.82    0.0092
                          Denominator       548     0.00001883



The SAS System            10:26 Thursday, February 6, 2014   5

                                              The REG Procedure
                                                Model: MODEL1
                                      Dependent Variable: fatalityrate

                                             Parameter Estimates

                                           Parameter       Standard
                   Variable        DF       Estimate          Error    t Value    Pr > |t|

                   Intercept        1        0.19727        0.01046      18.86     <.0001
                   sb_usage         1        0.00356        0.00155       2.29     0.0222
                   speed65          1        0.00101     0.00038486       2.64     0.0086
                   speed70          1        0.00101     0.00038486       2.64     0.0086
                   drinkage21       1     0.00062278        0.00109       0.57     0.5696
                   ba08             1       -0.00130     0.00056977      -2.29     0.0225
                   logincome        1       -0.01780        0.00118     -15.06     <.0001
                   age              1    -0.00015054     0.00013966      -1.08     0.2816
                   RESTRICT        -1       -0.05638        0.02170      -2.60     0.0092*

                               * Probability computed using beta distribution.