In Medical Engineering & Physics (May 2013), researchers used fractal geometry to characterize human cortical bone. A measure of the variation in the volume of cortical bone tissue-called fractal dimension-was determined for each in a sample of 10 human ribs. The researchers used fractal dimension scores to predict the bone tissue's stiffness index, called Young's Modulus (measured in gigapascals).
Young's Modulus (GPa) __________________________ Fractal Dimension
18.3............................................................2.48
11.6............................................................2.48
32.2............................................................2.39
30.9............................................................2.44
12.5............................................................2.50
9.1............................................................2.58
11.8............................................................2.59
11.0............................................................2.59
19.7............................................................2.51
12.0............................................................2.49
The experimental data are shown in the first column. Consider the linear model
E(y) =β0+ β1x,
where
y = Young's Modulus and x = fractal dimension score. Find an interval estimate of the increase (or decrease) in Young's Modulus for every 1-point increase in a bone tissue's fractal dimension score. Use a confidence coefficient of .90.