550 CHAPTER 10 Correlation and Regression StatCrunch 9. Testing for Correlation Use the information provided in the display to determine the value of the linear correlation coefficient. Is there sufficient evidence to support a claim of a linear correlation between weights of large cars and the highway fuel consumption amounts? 10.Identifying Total Variation What percentage of the total variation in highway fuel consumption can be explained by the linear correlation between weight and highway fuel consumption? Statistical Literacy and Critical Thinking 1. se Notation Using Data Set 1 “Body Data” in Appendix B, if we let the predictor variable x represent heights of males and let the response variable y represent weights of males, the sample of 153 heights and weights results in se = 16.27555 cm. In your own words, describe what that value of se represents. 2.Prediction Interval Using the heights and weights described in Exercise 1, a height of 180 cm is used to find that the predicted weight is 91.3 kg, and the 95% prediction interval is (59.0 kg, 123.6 kg). Write a statement that interprets that prediction interval. What is the major advantage of using a prediction interval instead of simply using the predicted weight of 91.3 kg? Why is the terminology of prediction interval used instead of confidence interval? 3. Coefficient of Determination Using the heights and weights described in Exercise 1, the linear correlation coefficient r is 0.394. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide? 4. Standard Error of Estimate A random sample of 118 different female statistics students is obtained and their weights are measured in kilograms and in pounds. Using the 118 paired weights (weight in kg, weight in lb), what is the value of se? For a female statistics student who weighs 100 lb, the predicted weight in kilograms is 45.4 kg. What is the 95% prediction interval? Interpreting the Coefficient of Determination. In Exercises 5–8, use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. 5.Times of Taxi Rides and Tips r = 0.298 (x = time in minutes, y = amount of tip in dollars) 6. Distances of Taxi Rides and Tips r = -0.114 (x = distance in miles, y = amount of tip in dollars) 7. Distances of Taxi Rides and Faresr = 0.986 (x = distance in miles, y = fare in dollars) 8.Times of Taxi Rides and Faresr = 0.953 (x = time in minutes, y = fare in dollars) Interpreting a Computer Display. In Exercises 9–12, refer to the display obtained by using the paired data consisting of weights (pounds) and highway fuel consumption amounts (mi , gal) of the large cars included in Data Set 35 “Car Data” in Appendix B. Along with the paired weights and fuel consumption amounts, StatCrunch was also given the value of 4000 pounds to be used for predicting highway fuel consumption. 10-3 Basic Skills and Concepts
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