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.

Understand the role and characteristics of responsibility centers, including profit and investment centers.

Learn about controllable and uncontrollable costs and their relevance to managerial decision making and budgeting.

Comprehend direct and indirect fixed costs and their allocation to different responsibility centers.

Understand the preparation process and utility of a flexible budget.

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Definitions:

Interaction Effect

In statistics, a situation where the effect of one independent variable on the dependent variable differs depending on the level of another independent variable.

Profile Plots

Graphical displays of the estimated values across different factors or conditions, often used to assess interactions in multivariate data.

Marginal Means

It refers to the average value of a variable within a dataset, taking into account the levels of another variable.

Profile Plot

A profile plot is a graph that displays the interactions between factors in a multivariate analysis, showing how different profiles respond across conditions.