Question

Here are the results of a regression of Car Deaths in the UK by month from Jan 1969 to Dec 1984 on a dummy variable: 0 = no seatbelt law, and 1 = seat belt law (the law was instituted in February 1983)

Coefficients:

	Estimate	Std. Error	t value	Pr(> | t |)
(Intercept)	125.870	1.849	68.082	< 2e-16	***
Seatbelts	-25.609	5.342	-4.794	3.29e-06	***

R-squared = 0.11

Justify your answer with numbers.

#1. How would you justify your answer with numbers?

#2. Is there a need to add more variables to the model?

#3. Did the seat belt law make a difference?

Answer 1

Que.1

Least square regression equation is,

car deaths = 125.87 - 25.609 * Seat belts

Que.2

Since our fitted model explain only 11% (R²) variation in the car deaths, we need to add more variable to the model in order to explain more variation in the car deaths in the UK.

Que.3

For seat belt variable,

test statistic , t = -4.794 and

p-value = 3.29e-06 which is less than 0.05, hence we reject null hypothesis () and conclude that seat belt variable has significant effect on car deaths. It means that seat belt law make a difference.