Solved: Toughness and fibrousness of asparagus are major

Chapter 12, Problem 59E

(choose chapter or problem)

Toughness and fibrousness of asparagus are major determinants of quality. This was the focus of a study reported in “Post-Harvest Glyphosphate Application Reduces Toughening, Fiber Content, and Lignification of Stored Asparagus Spears” (J. of the Amer. Soc. of Hort. Science, 1988: 569–572). The article reported the accompanying data (read from a graph) on x = shear force (kg) and y = percent fiber dry weight.

                                             

\(n=18, \Sigma x_i=1950, \Sigma x_i^2=251,970\),

\(\Sigma y_i=47.92, \Sigma y_i^2=130.6074, \Sigma x_i y_i=5530.92\)

a. Calculate the value of the sample correlation coefficient. Based on this value, how would you describe the nature of the relationship between the two variables?

b. If a first specimen has a larger value of shear force than does a second specimen, what tends to be true of percent dry fiber weight for the two specimens?

c. If shear force is expressed in pounds, what happens to the value of r ? Why?

d. If the simple linear regression model were fit to this data, what proportion of observed variation in percent fiber dry weight could be explained by the model relationship?

e. Carry out a test at significance level .01 to decide whether there is a positive linear association between the two variables.