Name the Relation, Part II For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion.

a. Number of cigarettes smoked by a pregnant woman each week and birth weight of her baby

b. Years of education and annual salary

c. Number of doctors on staff at a hospital and number of administrators on staff

d. Head circumference and IQ

e. Number of moviegoers and movie ticket price

Given a residual plot that shows a random scatter of points around the horizontal axis with no apparent pattern, which conclusion is most appropriate about the use of a linear model?

Given the following correlation coefficients, which value of $r$ would most likely correspond to a scatterplot showing a strong negative linear relationship between two variables?

Why is it important to report correlations together with scatter diagrams when analyzing the relationship between two quantitative variables?

Given a scatterplot of $price$ versus $mileage$ for $20$ used sedans, what type of correlation would you most likely expect to observe between $price$ and $mileage$ ?

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.”