Question

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

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. Use the "Data Record" to help you complete Part Two of this project.

2. Measure 11 additional people, and record their arm spans and heights in inches.

Part Two: Representation of 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 into a word processing document.

Part Three: The Line of Best Fit

Include your scatter plot and the answers to the following questions in your word processing document.

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.

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.

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 Three, 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?

Answer 1

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. Use the "Data Record" to help you complete Part Two of this project.

Name	Relationship to Student	Arm Span in Inches	Height in Inches
Me	self	70	68
Mom	mother	72	70
Dad	father	79	76
Camellia	sister	68	67
Alex	grandfather	74	72
Jeryl	grandmother	65	64
Tyler	classmate	68	66
Carrie	classmate	64	64
Ethan	classmate	68	67
Josie	classmate	61	60
Erica	classmate	65	62
Dylan	classmate	68	66

1. Measure 11 additional people, and record their arm spans and heights in inches.

Part Two: Representation of 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 into a word processing document.

Arm Span of People

Height in Inches of People

Part Three: The Line of Best Fit

Include your scatter plot and the answers to the following questions in your word processing document.

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. I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.
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. I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.
3. What does the slope of the line represent within the context of your graph? What does the y-intercept represent? The slope represents the rate of change arm span based on height. The y intercept is the arm span.
4. Test the residuals of two other points to determine how well the line of best fit models the data. Using point (66,68) and point (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

          

1. Use the line of best fit to help you to describe the data correlation. Based on this data, for every inch in height, the arm span increases by 1.1 inches.
2. Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches? 66 = 1.1x – 5 or 71 = 1.1x divide each side by 1.1 and y = 64.55 inches is the height.
3. According to your line of best fit, what is the arm span of a 74-inch-tall person? Y = 1.1(74) – 5 or y = 76.4 inches.