BackIn a given dataset, you determine the value of the correlation coefficient to be . Find the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? What about the unexplained variation?
A retail analyst is studying the relationship between the number of in-store promotional displays (x) and weekly sales revenue (y) at 12 store locations. Use the data below and a calculator to find the coefficient of determination.
"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?
15. r = 0.642"
"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?
13. r =- 0.450"
The coefficient of determination r^2 is the ratio of which two types of variations? What does r^2 measure? What does 1 - r^2 measure?
What is the coefficient of determination for two variables that have perfect positive linear correlation or perfect negative linear correlation? Interpret your answer.
"In Exercises 7-10, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?
7. r =0.465"
"In Exercises 7-10, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?
8.r =- 0.328"
"In Exercises 7-10, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?
10. r =0.881"
"Old Vehicles In Exercises 31–34, use the figure shown at the left.
33. Coefficient of Determination Find the coefficient of determination r^2 and interpret the results."
"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 r^2 and interpret the result,
12. [APPLET] Median and Mean Hourly Wages The table shows the median and mean hourly wages (in dollars) in 10 states in a recent year. The equation of the regression line is y = 1.208x + 1.495. (Source: U.S. Census Bureau)
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"[APPLET] For Exercises 2–9, use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary library science teachers in the United States for 12 years. (Source: U.S. Bureau of Labor Statistics)
7. Find the coefficient of determination r^2 and interpret the result."
"[APPLET] For Exercises 2–9, use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary library science teachers in the United States for 12 years. (Source: U.S. Bureau of Labor Statistics)
8. Find the standard error of estimate Se and interpret the result."