To measure the strength of stitching in knitted jerseys, re- searchers applied pressure perpendicular to the fabric

Question:

To measure the strength of stitching in knitted jerseys, re- searchers applied pressure perpendicular to the fabric until it burst. The bursting strength is the pressure applied just before the fabric bursts. Figure 122 shows a scatterplot that compares the lengths of stitches with the bursting strengths for 26-count yarn and 30-count yarn.

Let f(L) and g(L) be the bursting strengths (in kPa) of knitted jerseys with yarn counts 26 and 30, respectively, in which the stitch length is L (in mm).
a. Describe the four characteristics of the association between stitch length and bursting strength for 26-count yarn.
b. Describe the four characteristics of the association between stitch length and bursting strength for 30-count yarn. c. Reasonable models are f (L) = -7.23 L + 26.80 and g (L) = -5.13L + 20.27. Find f(2.75) and g(2.75). What do they mean in this situation?
d. The thinner the yarn, the larger the yarn count. Which type of yarn does this study suggest has greater bursting strength, thinner or thicker yarn? Explain by referring to the scatterplot and the results you found in part (c).
e. For the yarn-count-26 association, r is -0.94. For the yarn-count-30 association, r is also -0.94. But when all the data are combined, r is only -0.83. How is this possible?