[Please use R to answer these question - data is named "petrol" in library fpp2]

Use the mts petrol to answer the following questions.

a. Using the backwards stepwise method, starting with a model that contains Chemicals, Coal, Vehicles, trend, season, trading days, and an intervention spike for the oil crisis that lasted from October 1973 Through December 1974, determine the Time Series regression model that best predicts Petrol sales.

b. Now use a forward stepwise method. Did you end with the same model?

c. Forecast for 12 periods the model(s) you arrived at from part (a) and (b) using ets forecasts of the predictor variables and plot them.

d. Add to that plot two scenario forecasts, one where vehicle sales double to 40, and another where they shrink to 10. Keep your forecasts of the other variables the same. Plot the resulting forecasts of Petrol.

brief #comment would be appreciated.