MATH 116 ACTIVITY 6: Understanding Relationships between data - scatterplots and correlation
WHY: Much of the use of statistics involves relationships between variables. It is important to understand the terms and
ideas involved in describing such relationships in the same way that it is important to understand the terms and
ideas used in describing distributions of single variables.
LEARNING OBJECTIVES:
1. Learn the terminology and ideas for looking at association between two quantitative variables
2. Be able to find and interpret the correlation coefficient for a set of bivariate (two-variable) data.
3. Work as a team, using the team roles.
CRITERIA:
1. Success in completing the exercises.
2. Success in working as a team and in filling the team roles.
RESOURCES:
1. The Statistics Handbook chapter on Organizing an Describing data - especially p.6
2. The notes on "Association between variables" attached (as pages 4 & 5)
3. Your calculators and the sheet with instructions for your calculator (different for different individuals)
4. The team role desk markers (handed out in class for use during the semester)
5. 40 minutes
PLAN:
1. Select roles, if you have not already done so, and decide how you will carry out steps 2 and 3
2. Read through the handout defining the basic terms and work through the examples given there [Note: the examples do not
show how to find a general solution.]
3. Complete the exercises given here - be sure all members of the team understand and agree with all the results in the
recorder's report.
4. Assess the team's work and roles performances and prepare the Reflector's and Recorder's reports including team grade .
EXERCISES:
1. In a study of diet and exercise, data have been collected on the lean body mass (in kilograms- body mass excluding all fat) and
metabolic rate (calories burned per 24 hours) of 12 women . The researchers hope to show that lean body mass [which is
relatively easy to measure] is useful in predicting metabolic rate [which is harder to measure]. The data are given here:
Subject # Mass Rate Subject# Mass Rate
1 40.3 1189 7 41.2 1204
2 33.1 913 8 50.6 1502
3 36.1 995 9 42.0 1256
4 54.6 1425 10 42.4 1124
5 48.5 1396 11 34.5 1052
6 42.0 1418 12 51.1 1347
a.) Which variable (metabolic rate, lean body mass) should be considered the explanatory variable, and which should be
considered the response, [or does this distinction not make sense in this situation]?
b.) Plot the data. Be sure to label the axes, indicating which variable is on which axis (Mass ranges from about 30 Kg to about
55 Kg. Rate ranges from about 900 calories to about 1600 calories).
c.) Describe the association between the variables:
Is it positive or negative?
What is the form (linear, curved, complicated)?
Does the association appear to be strong (a clear pattern, points close to a line or curve) or weak (no clear
pattern or lots of scatter away from the pattern)?
d.) Find the correlation coefficient r [use your calculator - do not work from the formula] . Does the value seem reasonable for
the graph?
