Stat 411/511

# Data Analysis 3

##### Due on canvas Dec 4th @ midnight

The dataset fat in the faraway package contains body measurements for 252 men, including a body fat measurement based on an underwater weighing technique. Read the help file for the dataset for more information.

You will need to install the faraway package first (install.packages("faraway")), then

Reasearchers are interested in the relationship between age and body fat percentage. In particular, predicting an individuals bodyfat percent (brozek) from just their age (age) using the following simple linear regression model:
$\mu \{\text{Body fat} \, | \, \text{Age}\} = \beta_0 + \beta_1 \text{Age}$

• Is there evidence that mean bodyfat depends on age?

• Interpret estimates and confidence intervals for slope and intercept parameters of the above linear regression model.

• What is dangerous about interpreting the intercept?

• Is the above linear regression model appropriate?

• Based on the above linear regression model, provide and interpret both a confidence interval for the mean body fat percentage, and a prediction interval for the body fat percentage, of a man who is 28.

• Explain why the prediction interval obtained may not be accurate to predict the body fat percentage of a randomly sampled American who is 28.

Your report should include the following sections:

• Introduction Give a brief overview of the data, a little bit of background and the questions of interest. Keep this concise, understandable to someone outside of this class, free of statistical jargon and to the point. You should provide a summary graphic of the data involved and some basic summary statistics.

• Methods Describe your reasoning for the procedures you have chosen to answer the questions. State the assumptions of the procedures, and show or describe why you think they are reasonable assumptions in this case (or why the test might be robust to violations of the assumptions). Explain any changes, transformations or other modifications you make to the data.

• Summary Provide a brief non-technical summary of your findings that answers the questions of interest (like the statistical summaries we have been writing). Make sure you include some indication of the scope of inference (Can population inference be made? To what population? Can causal inference be made?)