# Height vs Arm span Algebra Scatter Plots

Project Option 1—Individually

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.

Look at whether a human's arm span (measured across the body with the arms extended) is correlated to his height.

There needs to be collected data from 11 people, which will give you 12 data points including your own personal data.

Part One: Measurements

Measure your own height and arm span (from finger-tip to finger-tip) in inches. Measure eleven additional people, and record their arm spans and heights in inches.

Part Two: Representing Data with Plots

Create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph. Then make a box plot.

Part Three: The Line of Best Fit

Answers the following questions:

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.

Which two points did you use to draw the line of best fit?

Write the equation of the line passing through those two points using the point-slope formula y−y1=m(x−x1).

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

Test the residuals of two other points to determine how well the line of best fit models the data.

Use the line of best fit to help you to describe the data correlation.

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?

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

What might cause the arm span and height not to be equal?

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.

https://brainmass.com/math/linear-algebra/height-vs-arm-span-algebra-scatter-plots-590089

#### Solution Preview

Part One: Measurements

Data Record

Height vs. Arm Span

Height (x) in. Arm span ( y) in.

71 73

62 63

63 66

72 70

66 66

64 64

67 70

60 64

65 67

66 64

67 65

Part Two: Representing Data with Plots

Please refer to the attached document for the graphs.

Part Three: The Line of Best Fit

Using excel, the two points that were used to draw the lines of best fits were (62, 63 ) and (70, 72 ).

Write the equation of ...

#### Solution Summary

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. Another example is the human's arm span (measured across the body with the arms extended) is correlated to his height. This will be explored further by scatter plot and box data from 11 people.