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

Suppose you are shown two scatterplots: Scatterplot A shows a strong upward trend with points closely clustered around a straight line, while Scatterplot B shows points widely scattered with no apparent pattern. Which of the following conclusions is best supported by the graphs?

"In Exercises 19-22, two variables are given that have been shown to have correlation but no cause-and-effect relationship. Describe at least one possible reason for the correlation.

19. Value of home and life span"

"[DATA] Influential Observations Zillow.com is a site that can be used to assess the value of homes in your neighborhood. The organization provides a list of homes for sale as well as a Zestimate, which is the price Zillow believes the home will sell for. The following data represent the Zestimate and sale price (in thousands of dollars) of a random sample of recently sold homes in Charleston, South Carolina.

a. Draw a scatter diagram of the data, treating the Zestimate as the explanatory variable and sale price as the response variable."

"In Exercises 19-22, two variables are given that have been shown to have correlation but no cause-and-effect relationship. Describe at least one possible reason for the correlation.

21. Ice cream sales and homicide rates"

Interpreting r

In Exercises 5–8, use a significance level of α = 0.05 and refer to the accompanying displays.

Bear Length and Weight The lengths (inches) and weights (pounds) of 54 bears are obtained from Data Set 18 “Bear Measurements” in Appendix B, and results are shown in the accompanying XLSTAT display. Is there sufficient evidence to support the claim that there is a linear correlation between length and weight?

Finding the Best Model

In Exercises 5–16, construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential, and power models.

Deaths from Motor Vehicle Crashes Listed below are the numbers of deaths in the United States resulting from motor vehicle crashes. Use the best model to find the projected number of such deaths for the year 2025.

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.

Graphical Analysis In Exercises 11–14, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

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

"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."

Writing Use an appropriate research source to find a real-life data set with the indicated cause-and-effect relationship. Write a paragraph describing each variable and explain why you think the variables have the indicated cause-and-effect relationship.

b. Other Factors: The relationship between the variables is caused by a third variable.