The sign of the coefficient of correlation indicates whether the data are

# The sign of the coefficient of correlation indicates

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The sign of the coefficient of correlation indicates whether the data are positively correlated (i.e., the larger values of X are typically paired with the larger values of Y) or negatively correlated (i.e., the larger values of X are typically paired with the smaller values of Y). ***The existence of a strong correlation does not imply a causation effect. It only indicates the tendencies present in the data.*** Exercises Q1 An article (J. Clements, Why Investors Should Put up to 30% of Their Stock Portfolio in Foreign Funds, The Wall Street Journal, November 26, 2003, p. D1) that discussed investment in foreign stocks stated that the coefficient of correlation between the return on investment of U.S. stocks and international large cap stocks was 0.80, U.S. stocks and international small cap stocks was 0.53, U.S. stocks and international bonds was 0.03, U.S. stocks and emerging markets stocks was 0.71, and U.S. stocks and emerging markets debt was 0.58. a) What conclusions can you make about the strength of the relationship between the return on investment of U. S. stocks and each of these five other types of investments? b) Compare the results of (a) . Q2 The data in the file coffeedrink.xls represent the calories and fat, in grams, of 16-ounce iced coffee drinks at Dunkin Donuts and Starbucks. a) Compute the coefficient of correlation. b) What conclusions can you reach about the relationship between calories and fat?
11 Answer Q1 (a)You can say that there is a strong positive linear relationship between the return on investment of U.S. stocks and the international large cap stocks, U.S. stocks, and emerging market stocks; a moderate positive linear relationship between U.S. stocks and international small cap stocks, U.S. stocks, and emerging market debt stocks; and a very weak positive linear relationship between U.S. stocks and international bonds. (b) In general, there is a positive linear relationship between the return on investment of U.S. stocks and international stocks, U.S. bonds and international bonds, U.S. stocks and emerging market debt, and there is a very weak negative linear relationship, if any, between the return on investment of U.S. bonds and international stocks. Q2 (a) r = 0.720 Descriptive Statistics Mean Std. Deviation N Calories 380.00 113.137 7 Fat 15.786 7.2678 7 Correlations Calories Fat Calories Pearson Correlation 1 .720 Sig. (2-tailed) .068 N 7 7 Fat Pearson Correlation .720 1 Sig. (2-tailed) .068 N 7 7 (b) There is a strong positive linear relationship between calories and fat.