Tietokoneharjoitus 3

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 ≤ .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 luettele kertoimien pienimmän neliösumman estimaatit. Suorita t-testit ja F-testi.

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)

summary(reg.model)

plot(reg.model)

Saadaan tulos

Call:
lm(formula = y ~ sp.usage + speed65 + speed70 + drinkage21 + 
    ba08 + log.income + age)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0109890 -0.0025729 -0.0002924  0.0027982  0.0132925 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.2008411  0.0104949  19.137  < 2e-16 ***
sp.usage     0.0039306  0.0015512   2.534 0.011557 *  
speed65      0.0001167  0.0005145   0.227 0.820618    
speed70      0.0023957  0.0006527   3.670 0.000266 ***
drinkage21   0.0012843  0.0011180   1.149 0.251131    
ba08        -0.0013994  0.0005679  -2.464 0.014047 *  
log.income  -0.0182520  0.0011886 -15.356  < 2e-16 ***
age         -0.0001334  0.0001391  -0.959 0.337916    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.004339 on 548 degrees of freedom
  (209 observations deleted due to missingness)
Multiple R-squared: 0.4279,	Adjusted R-squared: 0.4206 
F-statistic: 58.56 on 7 and 548 DF,  p-value: < 2.2e-16 

Kokeillaan laskea omalla koodilla

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
b

[1,]  0.2008410835
[2,]  0.0039306452
[3,]  0.0001167195
[4,]  0.0023956645
[5,]  0.0012843398
[6,] -0.0013993839
[7,] -0.0182519776
[8,] -0.0001333946

Vertaillaan p-arvoja:

sp_usage_estimate<-0.0039306
sp_usage_standard_error<-0.0015512
df<-548   #degrees of freedom

t_statistics<-sp_usage_estimate/sp_usage_standard_error
t_statistics
#[1] 2.533909

#Pr(>|t|) 
# t-jakauma
2*(1-pt(t_statistics,df=548))
#[1] 0.01155724

# normaalijakauma
2*(1-pnorm(t_statistics))
#[1] 0.01127979

2*(1-pt(t_statistics,df=54))
#[1] 0.01421385


# F-statistic: 58.56 on 7 and 548 DF,  p-value: < 2.2e-16
F<-58.56
1-pf(F, df1=7, df2=548)
#[1] 0

Q<-7
W<-Q*F
1-pchisq(W, df=7)
#[1] 0

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;
RUN;

Saadaan tulokset

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

Intercept        1        0.20084        0.01049      19.14      <.0001
sb_usage         1        0.00393        0.00155       2.53      0.0116
speed65          1     0.00011672     0.00051450       0.23      0.8206
speed70          1        0.00240     0.00065274       3.67      0.0003
drinkage21       1        0.00128        0.00112       1.15      0.2511
ba08             1       -0.00140     0.00056794      -2.46      0.0140
logincome        1       -0.01825        0.00119     -15.36      <.0001
age              1    -0.00013339     0.00013908      -0.96      0.3379