9.3 EXERCISES 504 CHAPTER 9 Correlation and Regression For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary Graphical Analysis In Exercises 1–3, use the figure. (xi, y) (xi, yi) x y x (xi, yi) y = y y 1. Describe the total variation about a regression line in words and in symbols. 2. Describe the explained variation about a regression line in words and in symbols. 3. Describe the unexplained variation about a regression line in words and in symbols. 4. The coefficient of determination r2 is the ratio of which two types of variations? What does r2 measure? What does 1 - r2 measure? 5. What is the coefficient of determination for two variables that have perfect positive linear correlation or perfect negative linear correlation? Interpret your answer. 6. Two variables have a bivariate normal distribution. Explain what this means. In Exercises 7–10, use the value of the correlation coefficient r to calculate the coefficient of determination r2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation? 7. r = 0.465 8. r = -0.328 9. r = -0.957 10. r = 0.881 Using and Interpreting Concepts Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 11–20, use the data to (a) find the coefficient of determination r2 and interpret the result, and (b) find the standard error of estimate se and interpret the result. 11. Stock Offerings The numbers of initial public offerings of stock issued and the total proceeds of these offerings (in millions of dollars) for 12 years are shown in the table. The equation of the regression line is ny = 222.346x + 5001.340. (Source: University of Florida) Number of offerings, x 42 101 82 104 162 225 Proceeds, y 13,307 30,742 27,750 32,065 39,093 46,967 Number of offerings, x 125 79 118 143 115 165 Proceeds, y 22,296 13,234 24,044 34,027 39,479 61,860
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