9 Chapter Quiz 520 CHAPTER 9 Correlation and Regression Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book. For Exercises 1–8, use the data in the table, which shows the average annual salaries (both in thousands of dollars) for secondary and elementary school teachers, excluding special and vocational education teachers, in the United States for 11 years. (Source: U.S. Bureau of Labor Statistics) Secondary school teachers, x Elementary school teachers, y 56.0 54.3 56.8 55.3 57.8 56.1 58.3 56.3 59.3 56.8 60.4 57.7 61.4 59.0 62.9 60.8 64.3 62.2 65.9 63.9 67.3 65.4 1. Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation? Explain. 2. Calculate the correlation coefficient r and interpret the result. 3. Test the significance of the correlation coefficient r that you found in Exercise 2. Use a = 0.05. 4. Find the equation of the regression line for the data. Draw the regression line on the scatter plot that you constructed in Exercise 1. 5. Use the regression equation that you found in Exercise 4 to predict the average annual salary of elementary school teachers when the average annual salary of secondary school teachers is $63,500. 6. Find the coefficient of determination r2 and interpret the result. 7. Find the standard error of estimate se and interpret the result. 8. Construct a 95% prediction interval for the average annual salary of elementary school teachers when the average annual salary of secondary school teachers is $63,500. Interpret the results. 9. Stock Price The equation used to predict the stock price (in dollars) at the end of the year for a restaurant chain is ny = -86 + 7.46x 1 - 1.61x2 where x1 is the total revenue (in billions of dollars) and x2 is the shareholders’ equity (in billions of dollars). Use the multiple regression equation to predict the y@values for the values of the independent variables. (a) x1 = 27.6, x2 = 15.3 (b) x1 = 24.1, x2 = 14.6 (c) x1 = 23.5, x2 = 13.4 (d) x1 = 22.8, x2 = 15.3
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