Answer:
Explanation:
Hello!
The objective of this exercise is to test if the Y: "number of car deaths in one month" is affected by the variable X: "seat belt law"
The linear regression was estimated:
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
Then the estimated model is:
Yi= 125.870 - 25609Xi
a. Did the seat belt law make a difference?
Yes.
If the hypothesis is that the seat belt law reduces the number of car deaths:
H₀: β ≥ 0
H₁: β < 0
With α: 0.05
The p-value for the test is: 3.29e-06
The p-value is less than the significance level, the seat belt law modifies the average number of car deaths.
b. Is there a need to add more variables to the model?
Yes. According to the given model, the independent variable isn't good enough to explain the variability of the dependent variable, i.e. most of the variability of the dependent variable is given by the errors.
The investigator needs to add new variables or change the model to determine one that is a better predictor of the dependent variable.
c. How would you justify your answer with numbers?
To see if the independent variable is a good predictor of the dependent variable you have to look at the coefficient of determination. This coefficient gives you an idea of how much of the variability of the dependent variable is explained by the independent variable under the estimated model.
The value of R²= 0.11 or 11% means that only 11% of the variability of the number of car deaths is due to the seat belt law.
It looks like the variable "seat belt law" isn't a good regressor.
d. What possible independent/predictor variables could you add to this model?
X: "increasing of traffic controls"
X: "decreasing the speed limits"
X: "opening road safety courses in the communities"
I hope it helps!