Chapter 12.5, Problem 59E

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 Ligniflcation 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.

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

$\begin{array}{l}n=18,\sum x_i=1950,\sum x_i^2=251,970,\\ \sum y_i=47.90,\sum y_i^2=130.6074,\sum x_i{y}_i=5530.9\end{array}$

1. 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?
2. 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?
3. c. If shear force is expressed in pounds, what happens to the value of r? Why?
4. 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?
5. e. Carry out a test at significance level .01 to decide whether there is a positive linear association between the two variables.