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Session 7, Part C:
Modeling Linear Relationships (35 minutes)
In This Part: How Square Can You Be? | Analyzing the Differences | Using a Scatter Plot
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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?"
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Problem C1 |  |
Why is this not the same as establishing an association between height and arm span?
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We'll use the same set of measurements for 24 people:
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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?
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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.
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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? |
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