Arctic Ice These data give the extent of area covered by ice in arctic regions near the North Pole from September 1979 to 2015. The reduction in the amount of arctic ice is related to global climate and rising sea levels.

(a) Use a linear equation to estimate the annual average reduction in the extent of arctic ice using the supplied variable Year as the time index.

(b) Estimate a quadratic equation for the reduction in arctic ice using Year and its square as explanatory variables. How does the estimate of the rate of reduction in arctic ice from this model compare to the linear equation in (b).

(c) Replace Year and Year2 in the equation estimated in (b) by Year-100 and (Year-100)2. Compare the estimated regression models? Explain the differences between the estimated models.

(d) Contrast the linear and quadratic models. Which appears a better summary of the trend in the extent of arctic ice?

(e) Compare prediction intervals of the extent of arctic ice in 2020 offered by the two models. Which do you expect to be more accurate?