Project | Algebra homework help
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. Record your measurements on the “Data Record” document. Use the “Data Record” to help you complete Part Two of this project.
- Measure eleven additional people, and record their arm spans and heights in inches.
Part Two: Representing Data with Plots
- Using GeoGebra or graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph. Then, use the software to make a box plot.
Note: Directions for downloading and using GeoGebra can be found in the “Course Information area.”
- Copy and paste your scatter plot and box plot into a word processing document.
Part Three: The Line of Best Fit
Include your scatter plot, box plot, and the answers to the following questions in your word processing document, and submit to your instructor. Be sure to review how to save your files before getting started.
- 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). Show all of your work. Remember to find the slope of the line first.
- 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.