stat assignment.

Task 8: Estimating Percent Bodyfat

It is sometimes desirable to know a person’s percent body fat as a measure of their health. Unfortunately, this is a difficult quantity to measure. However, the values of many variables that are related to percent body fat (such as weight, abdominal circumference) are much easier to measure. The dataset ‘bodyfat4.txt’ contains health and body-related measurements (including percent bodyfat) for 250 men. Use these data to identify an easily measured variable that might be used to estimate percent body fat, find a regression line for predicting percent body fat based on the variable you identified, and discuss the utility of this line.

1. Use summary techniques to explore the data. What patterns or trends do you see? Are there any outliers? If so, are you justified in removing them? Explain.

1. Identify the variable(s) that will be most useful in predicting percent body fat. Justify your choice based on statistical methods. Is it a clear choice or are there multiple contenders?

1. Find two different lines that might be used to predict percent body fat based on the variable you identified above. You may use any method you choose for one line, the other should be the least squares regression line. Discuss advantages or disadvantages of these methods. How would these lines be interpreted? What is the meaning of the slope? the intercept? Use both lines to predict the percent body fat of a man who is 25 years old, 6 feet tall, weighs 180 lbs, has abdominal circumference of 90 inches, and bmi of 26 (use the relevant information from this description). Compare and discuss the answers from the two lines.

1. Using the regression line, estimate the body fat of a man who is very atypical for the explanatory variable you identified. What do you get? What do you think of your results?

1. Using the regression line, estimate the body fat of a man who has a value of 0 for the explanatory variable you identified (i.e. the value of the response variable will be the intercept). What does this tell you?

1. To whom can these results be generalized? To whom can they not be generalized? Explain.

Report instructions:

The report must be typed and double-spaced; no more than 3 pages including graphics. Include all figures, summaries and computer output used in your analysis.

The write-up will include the following (labeled) sections:

I. Problem Statement: include pertinent definitions and descriptions

II. Methods: Description, justification, comparison of methods used; computer output.

III. Conclusions: Statement and justification of conclusions

IV. Discussion: Shortcomings, future directions, further insights

I. Problem Statement: In this section, the author will describe the question(s) being addressed in the analysis and any relevant background that is helpful to understanding the question. (1-2 paragraphs)

II. Methods: In this section, the author will indicate the methods used, describe the question addressed by each method, and interpret relevant computer output.

III. Conclusions: In this section, the author will describe overall conclusions and the justification for these conclusions from the work done. In particular, how would you answer the original question posed?

IV. Discussion: In this section, the author will discuss the limitations of his/her analysis did (e.g. did you have to make any particular assumptions? Was there missing information? ), describe additional questions that would be of interest to investigate with the data, and offer any final insights into the question under consideration.

Grading Rubric:

To get full credit for completion the report will include all required sections and responses to prompts.

Taking the analysis and report from ‘good’ to ‘excellent’ or from ‘excellent’ to ‘exceptional’ does not necessarily mean adding more (graphics, words, etc.) – though this might be part of it, rather it means conducting a more thoughtful and careful analysis and preparing a more organized and informative report on your work.