Question

Suppose frank has estimated a cross sectional regression model for demand for gasoline by state: PCONi = 389.6 + 60.8 UHMi - 36.5TAXi - 0.061REGi T Stat : 5.92 -2.77 -1.43 N =50 R2 = .919 Where: PCONi = petroleum consumption in the ith state (trillions of BTUs). UHMi = urban highway miles within the ith state. TAXi = the gasoline tax rate in the ith state (cents per gallon). REGi = motor vehicle registration in the ith state (in thousands)

a. What do you expect the signs of the explanatory variables to be? Explain why.

b. According to the estimated equation, motor vehicle registrations variable is insignificant and it has a negative sign. Does this make sense to you? Why or why not. Explain carefully.

c. Suppose the simple correlation coefficient between REG and UHM is 0.98. What do you infer from that? In light of this added information, what, if anything you would do and why? What would you expect to find?

d. What is VIF? (Not related to above)

e. What is heteroschedasticity? (Not related to above)

Answer 1

Answer a)

The urban highway miles are to be positive because as there is an increase in miles on urban highway, petrol consumption would increase. This is because as a vehicle travels more, it requires more petrol consumption.

The gasoline tax rate should be negative because any change in the gasoline tax rate would have an indirect reaction to petroleum consumption. The increase in tax rate is liable to decrease the petrol consumption in vehicles.

The vehicle motor registration in ith state should be positive because as the number of motor registrations increases, so does their petrol consumption in the ith state

Answer b)

The vehicle motor registration suggests that with a 1 unit increase in motor vehicle registration there is 0.061 units decrease in petrol consumption. However, the result is insignificant and this means that this explanatory variable is not statistically significant in this equation. However, it would be better if this variable is omitted from this model.

Answer c)

It can be inferred that urban highway miles and motor vehicle registration in the ith state have a strong and positive correlation suggesting that as urban highway miles increase so does motor vehicle registration as r = 0.98 which is close to 1. In this light of the information, two explanatory variables are correlated suggesting that there is multicollinearity in the equation.

Answer d)
It helps in the detection of multicollinearity. where R² is the coefficient of determination.

It determines the multiple terms variance in a model by the single term variance in the model.

Answer e)

Heteroscedasticity occurs when the error term in the model have unequal variance than the required OLS assumption that error terms are normally distributed and are equal (homoscedastic) in the model