10-6. Exercises

1. BASIC

Ex 1. For the Basic and Application exercises in this section use the computations that were done for the exercises with the same number in Section 10.2 "The Linear Correlation Coefficient", Section 10.4 "The Least Squares Regression Line", and Section 10.5 "Statistical Inferences About ".

Ex 2. For the sample data set of Exercise 1 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=β1^SSxySSyyr^2 = \hat{β_1} \frac{SS_{xy}}{SS_{yy}}. Confirm your answer by squaring rr as computed in that exercise.

Ex 3. For the sample data set of Exercise 2 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=β1^SSxySSyyr^2 = \hat{β_1} \frac{SS_{xy}}{SS_{yy}}. Confirm your answer by squaring rr as computed in that exercise.

Ex 4. For the sample data set of Exercise 3 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=β1^SSxySSyyr^2 = \hat{β_1} \frac{SS_{xy}}{SS_{yy}}. Confirm your answer by squaring rr as computed in that exercise.

Ex 5. For the sample data set of Exercise 4 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=β1^SSxySSyyr^2 = \hat{β_1} \frac{SS_{xy}}{SS_{yy}}. Confirm your answer by squaring rr as computed in that exercise.

Ex 6. For the sample data set of Exercise 5 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=β1^SSxySSyyr^2 = \hat{β_1} \frac{SS_{xy}}{SS_{yy}}. Confirm your answer by squaring rr as computed in that exercise.

Ex 7. For the sample data set of Exercise 6 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=β1^SSxySSyyr^2 = \hat{β_1} \frac{SS_{xy}}{SS_{yy}}. Confirm your answer by squaring rr as computed in that exercise.

Ex 8. For the sample data set of Exercise 7 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=SSyy−SSESSyyr^2 = \frac{SS_{yy}−SSE} {SS_{yy}} . Confirm your answer by squaring rr as computed in that exercise.

Ex 9. For the sample data set of Exercise 8 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=SSyy−SSESSyyr^2 = \frac{SS_{yy}−SSE} {SS_{yy}} . Confirm your answer by squaring rr as computed in that exercise.

Ex 10. For the sample data set of Exercise 9 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=SSyy−SSESSyyr^2 = \frac{SS_{yy}−SSE} {SS_{yy}} . Confirm your answer by squaring rr as computed in that exercise.

Ex 11. For the sample data set of Exercise 9 of Section 10.2 "The Linear Correlation Coefficient" find the coefficient of determination using the formula r2=SSyy−SSESSyyr^2 = \frac{SS_{yy}−SSE} {SS_{yy}} . Confirm your answer by squaring rr as computed in that exercise.

2. APPLICATIONS

Ex 12. For the data in Exercise 11 of Section 10.2 "The Linear Correlation Coefficient" compute the coefficient of determination and interpret its value in the context of age and vocabulary.

Ex 13. For the data in Exercise 12 of Section 10.2 "The Linear Correlation Coefficient" compute the coefficient of determination and interpret its value in the context of vehicle weight and braking distance.

Ex 14. For the data in Exercise 13 of Section 10.2 "The Linear Correlation Coefficient" compute the coefficient of determination and interpret its value in the context of age and resting heart rate. In the age range of the data, does age seem to be a very important factor with regard to heart rate?

Ex 15. For the data in Exercise 14 of Section 10.2 "The Linear Correlation Coefficient" compute the coefficient of determination and interpret its value in the context of wind speed and wave height. Does wind speed seem to be a very important factor with regard to wave height?

Ex 16. For the data in Exercise 15 of Section 10.2 "The Linear Correlation Coefficient" find the proportion of the variability in revenue that is explained by level of advertising.

Ex 17. For the data in Exercise 16 of Section 10.2 "The Linear Correlation Coefficient" find the proportion of the variability in adult height that is explained by the variation in length at age two.

Ex 18. For the data in Exercise 17 of Section 10.2 "The Linear Correlation Coefficient" compute the coefficient of determination and interpret its value in the context of course average before the final exam and score on the final exam.

Ex 19. For the data in Exercise 18 of Section 10.2 "The Linear Correlation Coefficient" compute the coefficient of determination and interpret its value in the context of acres planted and acres harvested.

Ex 20. For the data in Exercise 19 of Section 10.2 "The Linear Correlation Coefficient" compute the coefficient of determination and interpret its value in the context of the amount of the medication consumed and blood concentration of the active ingredient.

Ex 21. For the data in Exercise 20 of Section 10.2 "The Linear Correlation Coefficient" compute the coefficient of determination and interpret its value in the context of tree size and age.

Ex 22. For the data in Exercise 21 of Section 10.2 "The Linear Correlation Coefficient" find the proportion of the variability in 28-day strength of concrete that is accounted for by variation in 3-day strength.

Ex 23. For the data in Exercise 22 of Section 10.2 "The Linear Correlation Coefficient" find the proportion of the variability in energy demand that is accounted for by variation in average temperature.

3. LARGE DATA SET EXERCISES

Ex 24. Large Data Set 1 lists the SAT scores and GPAs of 1,000 students. Compute the coefficient of determination and interpret its value in the context of SAT scores and GPAs.

Ex 25. Large Data Set 12 lists the golf scores on one round of golf for 75 golfers first using their own original clubs, then using clubs of a new, experimental design (after two months of familiarization with the new clubs). Compute the coefficient of determination and interpret its value in the context of golf scores with the two kinds of golf clubs.

Ex 26. Large Data Set 13 records the number of bidders and sales price of a particular type of antique grandfather clock at 60 auctions. Compute the coefficient of determination and interpret its value in the context of the number of bidders at an auction and the price of this type of antique grandfather clock.

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