During the first few days of the new unit students explore relationships in the data we had collected about the class.

### Back to the Class Data

Looking at class data gives us the chance to ask questions about relationships among the variables. Here are some questions my students came up with:

- Is arm span really equal to height?

The easiest way to dig into this question is to look at a scatter plot of the data. So, we plotted the variables, along with the line height = arm span.

We noted that two people were on the line, two others were very close, and the rest were either above or below the line. What do those points above the line mean about height and arm span for those people? What about the points below the line?

- If my hand span is longer than my wrist circumference, then shouldn’t I be able to wrap my hand around my wrist and touch my pinky to my thumb?

One hundred percent of students had longer hand spans than wrist circumference, but only a couple of students could wrap their hands around their wrists.

- Is the age (in months) related to any other measure?

It would seem that none of the other variables is a good predictor for age in months. It also seems as if age vs height has a negative association. Huh?

### Digging a Little Deeper

If the line height = arm span doesn’t describe, or predict, that relationship well, then what would do a better job? We added a “movable line” and adjusted it until it looked about right.

Our line predicted that height = 0.85 * arm span + 26 cm. Wait, what? Height is 85% of arm span? And what is that +26 cm all about? It made for an interesting conversation, especially this question from a student: “How can a person who has an arm span of 0 cm be 26 cm tall?” Which prompted: “What does an arm span of 0 cm even mean?” I certainly don’t have definitive answers to these questions. What I *can* do is encourage the curiosity, the conversation, and point out that the relationship we discovered is for these measurements. Does it make much sense to use our calculated relationship to make predictions about heights for arm spans that are relatively far away from the data we collected?

### Correlation, Causation, Outliers, Influential Points

All of these topics follow from this initial discussion about the class data. Ultimately, students once again find their own variables of interest and complete an analysis demonstrating what they’ve learned. This time topics included unemployment rates, marriage rates, divorce rates, distances & temperatures of celestial objects, height & weight, obesity rate & life expectancy, and mean snowfall & mean low temperature.

Once again, the variety of topics that interested my students is greater than what I could have come up with. More importantly, because they chose their own variables, they were interested in analyzing the data and answering their own questions.