Project Option 1—Individually
Intro:
There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because as one measurement increases, so does the other measurement.
You will discover through this project whether a human's arm span (measured across the body with the arms extended) is correlated to his height.

You will need to collect data from 11 people, which will give you 12 data points including your own personal data. You will turn in and answer questions regarding only one scatter plot if doing the project alone. You may use the sample data provided in Part One if you do not have 11 people to measure.

Part One: Measurements
1. Measure your own height and arm span (from finger-tip to finger-tip) in inches. You will likely need some help from a parent, guardian, or sibling to get accurate measurements. Record your measurements on the “Data Record” document (bottom of this document). Use the “Data Record” to help you complete Part Two of this project.
2. Measure 11 additional people and record their arm spans and height in inches. You may use the sample data provided in the table if you do not have 11 people to measure.
Arm Span (inches)
Height (inches)
58
60
49
47
51
55
19
25
37
39
44
45
47
49
36
35
41
40
46
50
58
61
Myself 67 68

Part Two: Representing Data with Plots
1. Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit and sketch it on your graph.
2. Copy and paste your scatter plot below:

Part Three: The Line of Best Fit
1) Which variable did you plot on the x-axis and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.

2) Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
A) Pick any two point on your line of best fit. Write the coordinates of your two points below:
Point 1 ( , ) Point 2 ( , )

B) Using the two point above find the slope using the formula

C) Plug in your slope and one of the two points above into point-slope form

D) Change above equation into slope-intercept form y = mx + b. (See page 5 in lesson 5.06).

3) What does the slope of the line represent within the context of your graph? What does the
y-intercept represent?

4) Test the residuals of two other points to determine how well the line of best fit models the data.
Arm Span
Height
Height from equation
Residual (Actual height-Height from equation)

5) Use the line of best fit to help you to describe the data correlation:

6) Using the line of best fit that you found in Part 3, Question 2, approximate how tall is a person whose arm span is 66 inches:

7) According to your line of best fit, what is the arm span of a 74-inch-tall person:

Data Record:
Name
Relationship to Student
Arm Span in Inches
Height in Inches