CHAPTER 10 Review Exercises 571 4.Fixed Percentage If a restaurant were to change its tipping policy so that a constant tip of 20% of the bill is added to the cost of the dinner, what would be the linear regression equation relating the cost of the dinner 1x2 and the amount of the tip 1y2? 5.Switched Variables Which of the following values change if the two variables of dinner cost and amount of tip are switched: the value of r = 0.846, the P-value of 0.008, the critical values of {0.707? 6.Change in Scale Exercise 1 stated that for the given paired data, r = 0.846. How does that value change if all of the amounts of dinners are left unchanged but all of the tips are expressed in cents instead of dollars? 7.Values of r If you had computed the value of the linear correlation coefficient to be 1.200, what should you conclude? 8. Predictions The sample data result in a linear correlation coefficient of r = 0.846 and the regression equation yn = -0.00777 + 0.145x. What is the best predicted amount of tip, given that the cost of dinner was $84.62? How was the predicted value found? 9. Predictions Repeat the preceding exercise assuming that the linear correlation coefficient is r = 0.132. 10.Explained Variation Given that the linear correlation coefficient r is found to be 0.846, what is the proportion of the variation in tips that is explained by the linear relationship between amounts of dinner and amounts of tips? What is the proportion of the variation that cannot be explained by that linear relationship? Review Exercises 1.Casino Size and Revenue Listed below are sizes (in thousands of square feet) and revenue (in millions of dollars) from casinos in Atlantic City (based on data from the New York Times). Is there sufficient evidence to conclude that there is a linear correlation between size and revenue of casinos? Can a casino increase its revenue by enlarging its physical size? Size 160 227 140 144 161 147 141 Revenue 189 157 140 127 123 106 101 2.Casino Size and Revenue Use the same paired data from the preceding exercise. a. Find the linear regression equation. b. What is the best predicted amount of revenue for a casino with a size of 200 thousand square feet? Is it likely that the best predicted amount of revenue will be accurate? 3. Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball. a. Find the value of the linear correlation coefficient r. b. Based on the result from part (a), what do you conclude about a linear correlation between time and height? c. What horrible mistake would be easy to make if the analysis is conducted without a scatterplot? Time (sec) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Height (m) 0.0 1.7 3.1 3.9 4.5 4.7 4.6 4.1 3.3 2.1
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