Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 7, Part D:
Fitting Lines to Data (60 minutes)

In This Part: Trend Lines | Error | The SSE | More Lines | Summary

 In Parts A and B, you confirmed that there is a strong positive association between height and arm span -- short people tend to have short arms, and tall people tend to have long arms. In Part C, you investigated the nature of the relationship between height and arm span by graphing the line Height = Arm Span on a scatter plot of collected data. In Part D, using the same data you've been working with, you will investigate the use of other lines as potential models for describing the relationship between height and arm span, and you will explore various criteria for selecting the best line. Again, here is the scatter plot of the 24 people's data: Problem D1 Describe the trend in the data points -- in other words, how would you describe the general positioning of the points in the scatter plot? What does this trend tell you about the relationship between height and arm span?

 Now let's take another look at the scatter plot with the line Height = Arm Span graphed:

Problem D2

 a. Does this line generally provide an accurate description of the trend in the scatter plot? b. Do you think there might be a better line for describing this trend?

Let's consider two other lines for describing the relationship between Height and Arm Span:

 • Height = Arm Span + 1 • Height = Arm Span - 1

The following scatter plot includes the graphs of all three lines:

 Problem D3 Based on a visual inspection, which of these three lines does the best job of describing the trend in the data points? Explain why you chose this line.

 Session 7: Index | Notes | Solutions | Video