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.
Part One: Measurements
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. After measuring yourself,
Measure eleven additional people and record their arm spans and heights in inches.
Record your measurements below:
Name
Relationship to Student
Arm Span in Inches
Height in Inches
Part Two: Representing Data with Plots
Using GeoGebra to create a scatter plot of your data.
Step 1: Enter Arm Span and Heightin the Geogebra table
Step 2: Select 2 variable analysis
Step 3: Select Linear Regression
Enter the equation here:________________________________________
Create a box plot:
Step 1: Select only the arm span and height data
Step 2: Select 1 Multiple Variable Analysis
Note: Directions for downloading and using GeoGebra can be found in the "Course Information area."
And you can also call me for help on this.
Copy and paste your scatter plot and box 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) Which two points did you use to draw the line of best fit? (You used GeoGebra, so state the points
you would have used)
3) Write the equation of the line passing through those two points using the point-slope formula
y−y1=m(x−x1). Show all of your work. Remember to find the slope of the line first.
4) What does the slope of the line represent within the context of your graph? What does the yintercept represent?
5) 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
6) Use the line of best fit to help you to describe the data correlation:
Residual (Actual heightHeight from equation)
7) Using the line of best fit that you found in Part 3, Question 3, approximate how tall is a person
whose arm span is 66 inches:
8) According to your line of best fit, what is the arm span of a 74-inch-tall person:
9) What might cause the arm span and height not to be equal?
10) Explain why the equation you wrote to represent a human's arm span (measured across the
body with the arms extended) is a correlation and not causation.