The article “Bone Density and Insertion Torque as Predictors of Anterior Cruciate Ligament Graft Fixation Strength” (The Amer. J. of Sports Med., 2004: 1421–1429)

gave the accompanying data on maximum insertion torque and yield load (N), the latter being one measure of graft strength, for 15 different specimens.

(N # m)

V(gdi Yi

) 5 gdi 2 # V(Yi

)

V(bˆ

0 1 b

a. Is it plausible that yield load is normally distributed?

b. Estimate true average yield load by calculating a confidence interval with a confidence level of 95%, and interpret the interval.

c. Here is output from Minitab for the regression of yield load on torque. Does the simple linear regression model specify a useful relationship between the variables?
Predictor Coef SE Coef T P Constant 152.44 91.17 1.67 0.118 Torque 178.23 45.97 3.88 0.002 Source DF SS MS F P Regression 1 80554 80554 15.03 0.002 Residual Error 13 69684 5360 Total 14 150238

d. The authors of the cited paper state, “Consequently, we cannot but conclude that simple regression analysisbased methods are not clinically sufficient to predict individual fixation strength.” Do you agree? [Hint:
Consider predicting yield load when torque is 2.0.]