Toughness and Fibrousness of Asparagus Are Major Determinants of Quality

question 84

Essay

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 Horticultural 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. $$\begin{array} { l l l l l l l l l l } \hline x & 46 & 48 & 55 & 57 & 60 & 72 & 81 & 85 & 94 \\\hline y & 2.18 & 2.10 & 2.13 & 2.28 & 2.34 & 2.53 & 2.28 & 2.62 & 2.63 \\\hline & & & & & & & & & \\\hline x & 109 & 121 & 132 & 137 & 148 & 149 & 184 & 185 & 187 \\\hline y & 2.50 & 2.66 & 2.79 & 2.80 & 3.01 & 2.98 & 3.34 & 3.49 & 3.26 \\\hline\end{array}$$ $n = 18 \quad \sum x _ { i } = 1950 \quad \sum x _ { i} ^ { 2 } = 251,970$ $\sum y _ {i } = 47.92 \sum y _ { i} ^ {2 } = 130.6074 \quad \sum x _ { i } y _ { i } = 5530.92$
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.

---

Definitions:

Minority Relations

The dynamics and interactions between dominant groups and those classified as minorities within a society, often including themes of power, discrimination, and social justice.

American Concept

Ideas, beliefs, or values that are strongly associated with or originating from the United States.

Scapegoat Theory

A sociological concept suggesting that dominant groups project their failures or problems onto a less powerful group, blaming them unjustly.

Discrimination

Unjust or prejudicial treatment of different categories of people or things, especially on the grounds of race, age, sex, or disability.