Linear model in R software Apply the linear model to the Seatbelt data. Take the

Question

Linear model in R software Apply the linear model to the Seatbelt data. Take the rear seat passenger deaths or serious injuries as respons and as explanatory variables: Km Driven (kms). Petrol Price, and Seat belt Law (law). Front-seat Passengers killed or seriously injured (front). Find the data from the library (faraway) under its name data(Seatbelts). Fit the model to the data, give the interpretation of the coefficients, and comment on model fit as well as on model diagnostics. Given the four explanatory variables there are 2^1 = 16 models possible (keeping the intercept in the model). Write a function to fit all possible models to the data and select the model with the smallest AIC.

Explanation / Answer

:particular, several states moved from secondary enforcement to primary

enforcement.the number of states with mandatory rear seat belt laws and the type of

enforcement, as it evolved during our observation period. The fact that the move towards having

mandatory rear seat belt laws was quite gradual helps us identify the deaths of the law Using our unique data, to quantify the effect of usage rate on fatalities, test the compensating behavior hypothesis,

and measure the deaths of different elements of mandatory rear seat belt laws on rear seat belt usage rate.

We estimate a simple linear equation of traffic fatalities on usage rate. The basic equation is:

ln( F ) = ln(Uit)bF+ X Fgit+ aFi+ tFt+ eFij where Fit is the number of traffic fatalities at state i in year t, Uit is the rear seat belt usage rate, Xit is a

vector of control variables, and ai

F and tt

F are state and year fixed deaths.

The year fixed deaths control for any time specific “macro deaths” which shift the level of

traffic fatalities for all states. In our context, examples of such macro deaths might be

technological changes that introduced safer cars, or national campaigns that affected the behavior

of drivers. The time deaths also capture the increased penetration of air bags over time.17 The

state fixed deaths should capture any unobserved state characteristics, which are fixed over time,

such as population characteristics, general weather conditions, traffic conditions, and others. Our

control variables thus capture characteristics that are changed over time and across states and that

might affect traffic fatalities.

using ordinary least squares regression to estimate

equation (1) is likely to be incorrect. In particular, it is likely to introduce an upward bias to the

coefficient of usage rate because of the endogeneity of the decision to wear rear seat belt. To address

this endogeneity we control for state fixed deaths. These deaths take into account, for example,

that in states with more dangerous traffic conditions (say, due to weather or road conditions)

people are more likely to use rear seat belts, but are also more likely to be involved in a traffic

accident. Of course, adding state fixed deaths cannot eliminate completely problems of

endogeneity. The probable positive correlation between usage rate and the error term is likely to

be lower once fixed deaths are controlled for, but it might still remain. Conditions in any given

state change over time. For example, states that experienced an increase in traffic fatalities might

invest in promoting rear seat belt use. Such investments might lead to an increase in usage rate, which

again might generate a positive correlation between the usage rate and the error term and thereby

introduce an upward bias to our estimated coefficient.

Therefore, it is worthwhile instrumenting for the usage rate. In our case, variables that are

We also estimate how usage rates are affected by the level of the fine, the passage of time since

the adoption of the law, the initial level of rear seat belt usage rate, and whether the insurance coverage

is reduced for violation of the rear seat belt law. We use a simple linear regression to estimate the

deaths of the various features of the law of the law on the level of rear seat belt usage rate. Box-Cox

regression supports this functional form, as discussed in detail in Section V. Our standard

specification is:

(2) Uit= Lit bU+ Xit gU+aUi+ t Ut+ vit

where Uit is rear seat belt usage rate at state i at year t, Lit stands for different elements of the law, Xit

is a set of controls, and ai

U and tt

U are state and year fixed deaths. An alternative specification

would use rear seat belt as a dynamic decision by adding to equation (2) the lagged usage rate, Uit-1,

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