Question: An economist is studying the relationship between the incomes of
An economist is studying the relationship between the incomes of fathers and their sons or daughters. Let x be the annual income of a 30-year-old person and let y be the annual income of that person’s father at age 30 years, adjusted for inflation. A random sample of 300 thirty-year-olds and their fathers yields a linear correlation coefficient of .60 between x and y. A friend of yours, who has read about this research, asks you several questions, such as: Does the positive value of the correlation coefficient suggest that the 30-year-olds tend to earn more than their fathers? Does the correlation coefficient reveal anything at all about the difference between the incomes of 30-year-olds and their fathers? If not, what other information would we need from this study? What does the correlation coefficient tell us about the relationship between the two variables in this example? Write a short to your friend answering these questions.
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