Refer to Exercise 14.9 and the annual prices of natural gas from 1997 to 2015. A simple linear regression model, E(Yt) = β0 + β1t, where t is the number of years since 1997, is proposed to forecast the annual price of natural gas.

a. Give the least squares estimates of the β's and interpret their values.

b. Evaluate the model's fit.

c. Find and interpret 95% prediction intervals for the years 2016 and 2017.

d. Describe the problems associated with using a simple linear regression model to predict time series data.