The following quote is from the paper “Evaluation of the Accuracy of Different Methods Used to Estimate Weights in the Pediatric Population” (Pediatrics [2009]: e1045–e1051):

As expected, the model demonstrated that weight increased with age, but visual inspection of an age versus weight plot demonstrated a nonlinear relationship unless infants and children were analyzed separately.

The linear coefficient for age as a predictor of weight was to 3.48 in children.

This quote suggests that when a scatterplot of weight versus age was constructed for all 1011 children in the study described in the paper, the relationship between y weight and x age was not linear. When the 1011 children were separated into two groups—infants (age birth to 1 year) and children (age 1 to 10 years)—and separate scatterplots were constructed, the relationship between weight and age appeared linear in each scatterplot. The slopes reported in the given quote (referred to as “the linear coefficient”) are expressed in kg/year. Briefly explain why the relationship between weight and age in the scatterplot for the combined group would appear nonlinear.

1. Age and the measure of flexi bil ity just described will be measured for a group of individuals. Our goal is to determine whether there is a relationship between age and this measure of flexi bil ity. What are two reasons why it would not be a good idea to use just the students in your class as the subjects for your study?
2. Working as a class, decide on a reasonable way to collect data on the two variables of interest.
3. After your class has collected appropriate data, use them to construct a scatterplot. Comment on the interesting features of the plot. Does it look like there is a relationship between age and flexi bil ity?
4. If there appears to be a relationship between age and flexi bil ity, fit a model that is appropriate for describing the relationship.
5. In the context of this activity, write a brief description of the danger of extrapolation.