58. Toughness and brousness 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 Ligni cation of Stored Asparagus Spears (J. Amer.

Soc. Horticult. Sci., 1988: 569—572). The article reported the accompanying data (read from a graph)

on x  shear force (kg) and y  percent ber dry weight.

x 46 48 55 57 60 72 81 85 94 y 2.18 2.10 2.13 2.28 2.34 2.53 2.28 2.62 2.63 x 109 121 132 137 148 149 184 185 187 y 2.50 2.66 2.79 2.80 3.01 2.98 3.34 3.49 3.26

a. Calculate the value of the sample correlation coef cient. Based on this value and a scatter plot, how would you describe the nature of the relationship between the two variables?

b. If a rst specimen has a larger value of shear force than does a second specimen, what tends to be true of percent ber dry 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 t to this data, what proportion of observed variation in percent ber dry weight could be explained by the model relationship?

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