Bluman A.G. Elementary Statistics- A Step By Step Approach

574 Chapter 10 Correlation and Regression3. Which number is the slope of the regression line?4. Which number is the y intercept of the regression line?5. Which number can be found in a table?6. Which number is the allowable risk of making a type I error?7. Which number measures the variation explained by the regression?8. Which number measures the scatter of points about the regression line?9. What is the null hypothesis?10. Which number is compared to the critical value to see if the null hypothesis should berejected?11. Should the null hypothesis be rejected?See page 590 for the answers.Exercises 10–31. What is meant by the explained variation? How is itcomputed? Explained variation is the variation due to therelationship. It is computed by (y y) 2 .2. What is meant by the unexplained variation? How is itcomputed? Unexplained variation is the variation due tochance. It is computed by (y y) 2 .3. What is meant by the total variation? How is itcomputed?4. Define the coefficient of determination.5. How is the coefficient of determination found?6. Define the coefficient of nondetermination. It is thepercent of the variation in y that is not due to the variation in x.7. How is the coefficient of nondetermination found? Thecoefficient of nondetermination is found by subtracting r 2 from 1.For Exercises 8 through 13, find the coefficients ofdetermination and nondetermination and explain themeaning of each.8. r 0.80 R 2 0.64; 64% of the variation of y is due to thevariation of x; 36% is due to chance.9. r 0.75 R 2 0.5625; 56.25% of the variation of y is due to thevariation of x; 43.75% is due to chance.10. r 0.35 R 2 0.1225; 12.25% of the variation of y is due to thevariation of x; 87.75% is due to chance.11. r 0.42 R 2 0.1764; 17.64% of the variation of y is due to thevariation of x; 82.36% is due to chance.12. r 0.18 R 2 0.0324; 3.24% of the variation of y is due to thevariation of x; 96.76% is due to chance.13. r 0.91 R 2 0.8281; 82.81% of the variation of y is due to thevariation of x; 17.19% is due to chance.14. Define the standard error of the estimate for regression.When can the standard error of the estimate be used toconstruct a prediction interval about a value y?15. Compute the standard error of the estimate forExercise 13 in Section 10–1. The regression line equationwas found in Exercise 13 in Section 10–2. 629.486216. Compute the standard error of the estimate forExercise 14 in Section 10–1. The regression lineequation was found in Exercise 14 in Section 10–2.12.03* (TI value 12.06)17. Compute the standard error of the estimate for Exercise 15in Section 10–1. The regression line equation was foundin Exercise 15 in Section 10–2. 94.22*18. Compute the standard error of the estimate forExercise 16 in Section 10–1. The regression lineequation was found in Exercise 16 in Section 10–2.The standard error should not be calculated.19. For the data in Exercises 13 in Sections 10–1 and 10–2and 15 in Section 10–3, find the 90% prediction intervalwhen x 200 new releases. 365.88 y2925.04*20. For the data in Exercises 14 in Sections 10–1 and 10–2and 16 in Section 10–3, find the 95% prediction intervalwhen x 60. The prediction interval should not be calculated.21. For the data in Exercises 15 in Sections 10–1 and 10–2and 17 in Section 10–3, find the 90% prediction intervalwhen x 4 years. $30.46 y $472.38*22. For the data in Exercises 16 in Sections 10–1 and 10–2and 18 in Section 10–3, find the 98% prediction intervalwhen x 47 years. The prediction interval should not becalculated.*Answers may vary due to rounding.10–42