11. Correlation

"Old Vehicles In Exercises 31–34, use the figure shown at the left.

Scatter Plot Construct a scatter plot of the data. Show y and x on the graph."

"In Exercises 9 and 10, identify the explanatory variable and the response variable.

10. An actuary at an insurance company wants to determine whether the number of hours of safety driving classes can be used to predict the number of driving accidents for each

driver."

In Problems 9– 12, determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables.

In Problems 9– 12, determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables.

[DATA] Putting It Together: Paternal Smoking It is well-documented that active maternal smoking during pregnancy is associated with lower-birth-weight babies. Researchers wanted to determine if there is a relationship between paternal smoking habits and birth weight. The researchers administered a questionnaire to each parent of newborn infants. One question asked whether the individual smoked regularly. Because the survey was administered within 15 days of birth, it was assumed that any regular smokers were also regular smokers during pregnancy. Birth weights for the babies (in grams) of nonsmoking mothers were obtained and divided into two groups, nonsmoking fathers and smoking fathers. The given data are representative of the data collected by the researchers. The researchers concluded that the birth weight of babies whose father smoked was less than the birth weight of babies whose father did not smoke.

b. What is the explanatory variable? What is the response variable?

If the slope of a least-squares regression line is negative, what could be said about the correlation between the explanatory and response variable?

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

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.