558 CHAPTER 10 Correlation and Regression TABLE 10-6 Heights (inches) of Fathers, Mothers, and Their Children Height of Father Height of Mother Height of Child Sex of Child (1 = Male) 66.5 62.5 70.0 1 70.0 64.0 68.0 1 67.0 65.0 69.7 1 68.7 70.5 71.0 1 69.5 66.0 71.0 1 70.0 65.0 73.0 1 69.0 66.0 70.0 1 68.5 67.0 73.0 1 65.5 60.0 68.0 1 69.5 66.5 70.5 1 70.5 63.0 64.5 0 71.0 65.0 62.0 0 70.5 62.0 60.0 0 66.0 66.0 67.0 0 68.0 61.0 63.5 0 68.0 63.0 63.0 0 71.0 62.0 64.5 0 65.5 63.0 63.5 0 64.0 60.0 60.0 0 71.0 63.0 63.5 0 Using a Dummy Variable as a Predictor Variable EXAMPLE 3 Table 10-6 is adapted from Data Set 10 “Family Heights” in Appendix B and it is in a more convenient format for this example. Use the dummy variable of sex (coded as 0 = female, 1 = male). Given that a father is 69 in. tall and a mother is 63 in. tall, find the multiple regression equation and use it to predict the height of (a) a daughter and (b) a son. YOUR TURN. Do Exercise 19 “Dummy Variable.” SOLUTION Using the methods of multiple regression from Part 1 of this section and computer software, we get this regression equation: Height of child = 36.5 - 0.0336 1Height of father2 + 0.461 1Height of mother2 + 6.14 1Sex2 where the value of the dummy variable of sex is either 0 for a daughter or 1 for a son. a. To find the predicted height of a daughter, we substitute 0 for the sex variable, and we also substitute 69 in. for the father’s height and 63 in. for the mother’s height. The result is a predicted height of 63.2 in. for a daughter. b. To find the predicted height of a son, we substitute 1 for the sex variable, and we also substitute 69 in. for the father’s height and 63 in. for the mother’s height. The result is a predicted height of 69.4 in. for a son. The coefficient of 6.14 in the regression equation shows that when given the height of a father and the height of a mother, a son will have a predicted height that is 6.14 in. more than the height of a daughter. Icing the Kicker Just as a kicker in football is about to attempt a field goal, it is a common strategy for the opposing coach to call a time-out to “ice” the kicker. The theory is that the kicker has time to think and become nervous and less confident, but does the practice actually work? In “The Cold-Foot Effect” by Scott M. Berry in Chance magazine, the author wrote about his statistical analysis of results from two National Football League (NFL) seasons. He uses a logistic regression model with variables such as wind, clouds, precipitation, temperature, the pressure of making the kick, and whether a time-out was called prior to the kick. He writes that “the conclusion from the model is that icing the kicker works—it is likely icing the kicker reduces the probability of a successful kick.” J in is a f is s
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