The body armor report introduced in Example 12.1 also reported studies in which two different methods were used to measure the same body armor deformations from bullet impact. The goal of these studies was to assess the extent to which two different measurement instruments agree. Eighty-three back-face deformations (mm) were measured using a digital caliper (x) and a laser arm (y), resulting in a sample correlation coefficient of r = .878.

In Example 12.1

a. Compute a 90% CI for the true correlation coefficient ρ.

b. Test H₀: ρ = .8 versus H_a: ρ > .8 at level .05.
c. In a regression analysis of y on x, what proportion of variation in laser arm measurements could be explained by variation in digital caliper measurements?

d. If you decide to perform a regression analysis with digital caliper measurement as the response variable, what proportion of its variation is explainable by variation in laser arm measurement?

Transcribed Image Text:

i Yi i Yi 1 670 66.4 11 738 78.6 2 675 64.5 12 740 87.9 3 679 63.6 13 762 92.6 4 681 72.9 14 762 83.0 5 694 79.1 15 768 79.0 6 699 76.7 16 780 75.3 7 699 65.5 17 792 83.4 8 708 68.0 18. 786 100.7 9 726 57.8 19 790 106.6 10 732 72.4 20 787 112.8