Studying the art of walking. American Scientist (July-August 1998) reported on a study of the relationship between self-avoiding and unrooted walks. A self-avoiding walk is one where you never retrace or cross your own path; an unrooted walk is a path in which the starting and ending points are impossible to distinguish. The possible number of walks of each type of various lengths are reproduced in the table. Consider the straight-line model y = β₀ + β₁x + ε, where x is walk length (number of steps).

a) Use the method of least squares to fit the model to the data if y is the possible number of unrooted walks.

(b) Interpret β^{^}₀ and β^{^}₁ in the estimated model, part a.

(c) Repeat parts a and b if y is the possible number of self-avoiding walks.

(d) Find a 99% confidence interval for the number of unrooted walks possible when walk length is four steps.

(e) Would you recommend using simple linear regression to predict the number of walks possible when walk length is 15 steps? Explain.