In the manufacture of cloth, the weft packages should not disintegrate unduly during weaving. A direct mea sure of the tendency to disintegrate exists, but it is laborious and uneconomical to carry out. In addition, there are indirect measures based on laboratory tests. Managers of the Brockway Textile Company want to determine the extent to which one of these indirect measures is correlated with the direct mea sure. If the correlation is high enough, they believe that they may be able to use the indirect mea sure instead of the direct measure. An experiment was carried out in which both the direct and indirect measures of the tendency to disintegrate were calculated for 18 lots of packages. The results follow:

a. What is the coefficient of determination between the two measures?
b. What linear regression line would you use to predict the value of the direct mea sure on the basis of knowledge of the indirect mea sure?
c. On the basis of your findings, write a brief report indicating the factors to be weighed in deciding whether to substitute the indirect mea sure for the direct measure.

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221499431 66 0822771 -11170500 33225831 0123456789 Measure Lot Direct Indirect 10 10.7 12 13 14 15 16 17 18 35 63 10 51 24 15 80 90 3.5 5.0 4.5 9.5 8.5 2.6 2.9