Spot price of natural gas. Refer to Exercise 14.9 (p. 14-10) and the annual prices of natural gas from 2000 to 2020. A simple linear regression model, E1Yt2 = b0 + b1t, where t is the number of years since 2000, is proposed to forecast the annual price of natural gas.

a. Give the least squares estimates of the b’s and interpret their values.

b. Evaluate the model’s fit.

c. Find and interpret 95% prediction intervals for the years 2021 and 2022.

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