Question: 11.3 Characterizing bone with fractal geometry. _ Experimental data on fractal dimension, x (a measure of the variation in the vol- ume of cortical bone

11.3 Characterizing bone with fractal geometry. _ Experimental data on fractal dimension, x (a measure of the variation in the vol- ume of cortical bone tissue) and Young's Modulus, v (a measure of bone tissue's stiffness) for each in a sample of 10 human ribs are reproduced in the table below. Consider the linear model, E(v) = B, + Bx. & corRTBONE Young's Fractal Modulus (GPa) Dimension 18.3 248 11.6 248 22 2.39 30.9 2.44 125 2.50 9.1 2.58 11.8 2.59 11.0 2.59 19.7 2.51 12.0 249 . Construct and X matrices for the data. . Find X'X and X'Y. ) c. Find the least squares estimates B = (X 'X) - 1xy, (5ee Theorem A.l in Appendix A for information on finding (X" X)". d. Find SSE and s. e. Conduct the test, Hy: B, =0 vs. H: B,

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