Problem

Walking study. Refer to the American Scientist(July-Aug. 1998) study of the relationship b...

Walking study. Refer to the American Scientist(July-Aug. 1998) study of the relationship between self-avoiding and unrooted walks, presented in Exercise 2.143 (p. 92). Recall that in a self-avoiding walk you never retrace or cross your own path, while 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 next table. Consider the straight-line model y = β0 + β1x + ε where xis walk length (number of steps).

WALK

Walk Length (number of steps)	Unrooted Walks	Self-Avoiding Walks
1	1	4
2	2	12
3	4	36
4	9	100
5	22	284
6	56	780
7	147	2,172
8	388	5,916

Source: Hayes, B. “How to avoid yourself,” American Scientist, Vol. 86, No. 4, July-Aug. 1988, p. 317 (Figure 5).

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 and in the estimated model of 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 that are possible when the walk length is four steps.
e. Would you recommend using simple linear regression to predict the number of walks that are possible when walk length is 15 steps? Explain.