AP Statistics
Correlation Coefficient
Name: ___________________________________
Identify the direction and all possible interpretation of each of the following
correlations. Be sure to identify each example as positive, negative, or zero (not
correlated). Then give all possible interpretations for the results. Be cautious and
wary of reaching ‘causal conclusions’!
1. Professor Johansen finds that for every diet beverage someone drinks during the day, the
likelihood of heart attacks increases by 4 percent.
Examples of answers:
There is a weak, positive, linear relationship between the number of diet drinks consumed
each day and the likelihood of having a heart attack. (because of the nature of the problem,
you could potentially see more drinks relating to a compulsive eat or drinking problem
within the person, which could relate to stress or other underlying conditions)
There is no correlation between the number of diet drinks consumed each day and the
likelihood of having a heart attack. (people who drink diet drinks are typically more
concerned with their health, and more than likely workout. So, you would expect to see
little relationship between these two elements)
There is a strong, positive, linear relationship between the number of diet drinks consumed
each day and the likelihood of having a heart attack.
2. Margaret notices that the temperature in her office drops several degrees from July to
December. In a careful review of the budget she discovers that the company’s utility
expenses also drop from July to December.
Examples of answers:
There is a strong, negative, linear relationship between the use of the air conditioner and
the budget. (you would expect to see a direct correlation between the use of the air
conditioner/heater and the overall cost of electricity if you are in Texas)
There is a weak, non-linear relationship between the use of the air conditioner and the
budget. (If you live in a state that has high temperatures in the summer and freezing
temperatures in the winter, you would expect to see a parabolic function)
3. Fontaine who runs a gym has created a special exercise/weight lifting class for women
that are overweight. He finds that for two days a woman attends the class she loses ½ %
body fat.
There is a strong, positive, linear relationship between days spent in the exercise class and
losses in percentage of body fat. (this is assuming that no changes are made in caloric
intake on any of the individuals or they have decreased their caloric intake)
AP Statistics
Correlation Coefficient
Name: ___________________________________
There is a weak, positive, linear relationship between days spent in the exercise class and
losses in percentage of body fat. (You would expect to see variations as some people have
varying eating habits as well as different body types and lose weight at different rates which
will produce outliers created a lower correlation coefficient)
4. Many students in Professor Handel’s class express that they want a review session.
Professor Handel agrees to hold an open review session for two hours the day before the
exam. He then has his TA write down when each student arrives at the session and when
they depart. When the exams are graded, Professor Handel announces there will be no
more review sessions. The longer students spent at the review session the lower their score
on the exam.
There is a strong, negative, linear relationship between the hours spent at the review
session and the students test scores (this could occur because it has created information
overload, or additional stress about the test)
There is a strong, negative, linear relationship between the hours spent at the review
session and the students test scores (You would expect the results to vary greatly based on
the individuals and their needs. Some students benefit greatly from the study review
session while others are impact negatively)
5. Over a four week period a teacher watches elementary school children playing during
recess. She counts the number of times students slide down a recently added playground
slide. As the weeks progress she sees little change in sliding behavior over time.
There is a strong, non-linear relationship between the weeks the playground has been
present and the number of times children slide.
6. Ariel enjoys collecting Black and Decker tools. Her garage is filled with every gadget ever
made by Black and Decker. Her neighbors knowing this frequently borrow tools from her.
Ariel notes that her neighbors are better about returning the tools when they live on her
side of the street than when they live across the street.
This is a categorical situation which will be impossible to determine the relationship between location
and % of time returned.