54. Infestation of crops by insects has long been of great concern to farmers and agricultural scientists. The article Cotton Square Damage by the Plant Bug, Lygus hesperus, and Abscission Rates (J. Econ.

Entomology, 1988: 1328—1337) reports data on x 

age of a cotton plant (days) and y  % damaged squares. Consider the accompanying n  12 observations

(read from a scatter plot in the article).

x 9 12 12 15 18 18 y 11 12 23 30 29 52 x 21 21 27 30 30 33 y 41 65 60 72 84 93

a. Why is the relationship between x and y not deterministic?

b. Does a scatter plot suggest that the simple linear regression model will describe the relationship between the two variables?

c. The summary statistics are xi  246, 

5742, yi  572, and xiyi 

14,022. Determine the equation of the least squares line.

d. Predict the percentage of damaged squares when the age is 20 days by giving an interval of plausible values.