Question: "Body Composition Measurement in 9-11-yr.-old Children by Dual-Energy X-Ray Absorptiometry, Skinfold-Thickness Measurements, and Bioimpedance Analysis" Gutin et al. American Journal of Clinical Nutrition Note: this paper is on the D2L site under Gutin Article.

In this study Gutin et al. compared three measurements of body composition, including dual-energy X-ray absorptiometry (DXA). Subjects were apparently healthy children (21 boys and 22 girls) between the ages of 9 and 11 years. Among the data collected were the following measurements of body-composition compartments by DXA. The investigators are interested in the correlation between all possible pairs of these variables.

The variables are contained in the file Gutin DMX.JMP are:

 Percent fat (PERFAT)

 Fat Mass (FATMASS)

 Fat-Free Mass (FATFREE)

 Bone Mineral Content (BMC)

 Fat-Free Soft Tissue (FATFREESOFT)

1. Construct a scatter plot matrix, then find appropriate pair-wise correlations for these data and test whether the population correlation significantly differs from 0. (8 pts.)
   Complete the table, correlation and p-value, below using an appropriate correlation measure for these data. Use the same measure for all pairs.

   correlation (p-value)	PERFAT	FATMASS	FATFREE	BMC	FATFREESOFT
   PERFAT
   FATMASS
   FATFREE
   BMC
   FATFREESOFT

2. Which pair of variables exhibits the strongest degree of correlation?
   The weakest? (2 pts.)
3. Fit the model E(FATMASS|PERFAT) = \[{{\beta }_{o}}+{{\beta }_{1}}PERFAT\] and check the model assumptions. Which assumptions, if any, are violated? Explain. (4 pts.)

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