The correlation of human height with foot length is a popular school science project because it requires little special equipment. It also has applications far beyond the classroom -- forensic investigations can gain information about a suspect based on evidence in the form of footprints that were left at a crime scene. A mathematical analysis of height versus foot length can provide a formula that can be used to predict one of these measurements from the other.

- Skill level:
- Moderate

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### Things you need

- People to measure
- Measuring tape
- Pen or pencil
- Paper
- Graph paper or graphing program
- Calculator

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## Instructions

- 1
Measure the length of the bare foot of your first subject in inches. Record this number on your paper. Measure the height of your first subject in inches, and record this number as well. Repeat with all study subjects. The greater the number of subjects included in your study, the smaller your margin of error will be and the more valid your results will be.

- 2
Lay out a graph with foot length in inches along the x axis, or horizontal axis, and height in inches along the y axis, or vertical axis. Plot each individual data point on your graph.

- 3
Look for a line of best fit among your data points, or use your graphing software to find the line of best fit. A line of best fit is the line that best describes all the data points, meaning a single, straight line that goes through the data points with as little distance as possible between the line and the points. Draw the line of best fit on your graph with a ruler.

- 4
Identify the direction in which the line is moving and how close the data points are to your line of best fit. If the line of best fit goes up, then a positive correlation has been found. If the line goes up only a little and is close to horizontal, then a weak positive correlation has been found. If the line goes up sharply, then a strong positive correlation has been found.

- 5
Find the equation for your line of best fit using two data points that lie directly on your line of best fit. If no data points are directly on your line, then plot two imaginary points on your line and use these points. Write your data points as x,y coordinates, such as 9, 60. Your two data points will be called (x1, y1) and (x2, y2). Calculate the value of m, or the slope, using the equation: (y2-y1)/(x2-x1). Calculate the equation of your line using the equation y-y1=m(x-x1). This equation can be used to determine the height of an individual given their foot length, or vice versa.

#### Tips and warnings

- There are many methods for measuring foot length, such as standing or measuring the foot while it is not supporting the weight of the body. Be sure to use the same measuring methods consistently for all subjects.
- If there is no correlation between human height and foot length in your particular sample size, then no line of best fit will be found.