Please use complete sentences
for your responses.
1. The scatterplot shows
x = internet users
per 1,000 people
y = life expectancy
(years)
for the 20 countries with the largest population for 2009.
(World Almanac Book of Facts, 2009)
Describe what the data point (2, 62.5) tells about Bangladesh.
2. In this group of 20 countries does an increase in the density of internet users (i.e., the number of internet users per 1,000 people) tend to be associated with an increase or a decrease in life expectancy?
3. The correlation coefficient is 0.62. The value of the correlation coefficient indicates a fairly strong positive linear relationship. Based on this observation, someone might suggest that an easy way to increase a country’s life expectancy would be to get more people online. Do you think this is a reasonable conclusion? Why or why not?
It is easy and fun to construct silly examples of correlations that do not result from causal connections. Here are some examples from John Allen Paulos, a mathematics professor at Temple University who is well known for his popular books on mathematical literacy.
4. Read this excerpt from A Mathematician Reads the Newspaper[1] by Paulos. Identify the explanatory, response, and confounding (lurking) variables in Paulos’ examples.
Ex. 1: A more elementary widespread confusion is that between correlation and causation. Studies have shown repeatedly, for example, that children with longer arms reason better than those with shorter arms, but there is no causal connection here. Children with longer arms reason better because they’re older!
Ex 2: Consider a headline that invites us to infer a causal connection: BOTTLED WATER LINKED TO HEALTHIER BABIES. Without further evidence, this invitation should be refused, since affluent parents are more likely both to drink bottled water and to have healthy children; they have the stability and wherewithal to offer good food, clothing, shelter, and amenities.
Making a practice of questioning correlations when reading about “links” between two variables is a good statistical habit.
Example 1
Explanatory variable:
Response variable:
Confounding variable:
Example 2
Explanatory variable:
Response variable:
Confounding variable:
5. Paulos also writes a column for ABCNews.com called Who’s Counting? In his February 1, 2001, column, Paulos discusses the idea that correlation does not imply causation. He points out that the consumption of hot chocolate is negatively correlated with crime rate. Obviously, drinking more hot chocolate does not lower the crime rate.
For this situation assume that the data describe large cities in the United States.
A What is the explanatory variable?
B What is the response variable?
C Identify a plausible confounding variable in this scenario
6. Describe a scenario with two quantitative variables that are probably highly correlated due to a third confounding variable.
[1]Paulos, J.A. (1995). A mathematician reads the newspaper (p. 137). New York: Basic Books.