Session 7, Part C:
Modeling Linear Relationships (35 minutes)

In This Part: How Square Can You Be? | Analyzing the Differences | Using a Scatter Plot

 In Parts A and B, you confirmed that there is a strong positive association between height and arm span. In Part C, we will investigate this association further. Note 2 The drawing below suggests that a person's arm span should be the same as her or his height -- in which case, a person could be considered a "square." Is this correct? Do most people have heights and arm spans that are approximately the same? That is, are most people "square?" Problem C1 Why is this not the same as establishing an association between height and arm span?

We'll use the same set of measurements for 24 people:

Person #

Arm Span

Height

 1 156 162 2 157 160 3 159 162 4 160 155 5 161 160 6 161 162 7 162 170 8 165 166 9 170 170 10 170 167 11 173 185 12 173 176

Person #

Arm Span

Height

 13 177 173 14 177 176 15 178 178 16 184 180 17 188 188 18 188 187 19 188 182 20 188 181 21 188 192 22 194 193 23 196 184 24 200 186

 Problem C2 Compare the measurements for the six heights and arm spans you collected, including your own. How many people are "squares" -- i.e., their arm spans and heights are the same? For how many people are these measurements approximately the same?

 To measure the differences between height and arm span, let's look at the numerical differences between the two. In these problems, we will use "Height - Arm Span" as the measure of the difference between height and arm span.

Problem C3

Consider the difference:

Height - Arm Span

 a. If you know only that this difference is positive, what does it tell you about a person? What does it not tell you? b. If you know that this difference is negative, what does it tell you? What does it not tell you? c. If you know that this difference is 0, what does it tell you?

 Session 7: Index | Notes | Solutions | Video