11. Correlation

Obesity In a study published in the Journal of the American Medical Association, researchers found that the length of time a mother breast-feeds is negatively associated with the likelihood a child is obese. In an interview, the head investigator stated, “It’s not clear whether breast milk has obesity-preventing properties or the women who are breast-feeding are less likely to have obese kids because they are less likely to be obese themselves.” Using the researcher’s statement, explain what might be wrong with concluding that breast-feeding prevents obesity. Identify some lurking variables in the study. 201

Crime Rate and Cell Phones The linear correlation between violent crime rate and percentage of the population that has a cell phone is −0.918 for years since 1995. Do you believe that increasing the percentage of the population that has a cell phone will decrease the violent crime rate? What might be a lurking variable between percentage of the population with a cell phone and violent crime rate?

Explain what is wrong with the following statement: “We have concluded that a high correlation exists between the gender of drivers and rates of automobile accidents.” Suggest a better way to write the sentence.

Faulty Use of Correlation On the basis of the scatter diagram below, explain what is wrong with the following statement: “Because the linear correlation coefficient between age and median income is 0.012, there is no relation between age and median income.”

"In studies of monozygotic (identical) twins, the correlation between intelligence (IQ) scores is 0.85.

a. Who are the individuals in this study?"

Why is it important to perform graphical as well as analytical analyses when analyzing relations between two quantitative variables?

What is the difference between univariate data and bivariate data?

The variable is the variable whose value can be explained by the value of the explanatory variable.

What does it mean to say two variables are positively associated? Negatively associated?

True or False: Correlation implies causation.

Suppose you work a part-time job and earn \$15 per hour. Draw a scatter diagram that might represent the relation between your gross pay and hours worked. Is this a deterministic relation or a probabilistic relation?