9.4 EXERCISES 512 CHAPTER 9 Correlation and Regression For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. Interpret the meaning of the coefficient -8.2 in the multiple regression equation ny = 112.1 + 0.43x 1 - 8.2x2 + 29.5x3. 2. Compare the numbers of dependent and independent variables in a multiple regression equation and a single regression equation. Predicting y-Values In Exercises 3–6, use the multiple regression equation to predict the y-values for the values of the independent variables. 3. Cauliflower Yield The equation used to predict the annual cauliflower yield (in pounds per acre) is ny = 24,791 + 4.508x 1 - 4.723x2 where x1 is the number of acres planted and x2 is the number of acres harvested. (Adapted from United States Department of Agriculture) (a) x1 = 36,500, x2 = 36,100 (b) x1 = 38,100, x2 = 37,800 (c) x1 = 39,000, x2 = 38,800 (d) x1 = 42,200, x2 = 42,100 4. Sorghum Yield The equation used to predict the annual sorghum yield (in bushels per acre) is ny = 80.1 - 20.2x 1 + 21.2x2 where x1 is the number of acres planted (in millions) and x2 is the number of acres harvested (in millions). (Adapted from United States Department of Agriculture) (a) x1 = 5.5, x2 = 3.9 (b) x1 = 8.3, x2 = 7.3 (c) x1 = 6.5, x2 = 5.7 (d) x1 = 9.4, x2 = 7.8 5. Black Cherry Tree Volume The volume (in cubic feet) of a black cherry tree can be modeled by the equation ny = -52.2 + 0.3x 1 + 4.5x2 where x1 is the tree’s height (in feet) and x2 is the tree’s diameter (in inches). (Source: Journal of the Royal Statistical Society) (a) x1 = 70, x2 = 8.6 (b) x1 = 65, x2 = 11.0 (c) x1 = 83, x2 = 17.6 (d) x1 = 87, x2 = 19.6 6. Elephant Weight The equation used to predict the weight of an elephant (in kilograms) is ny = -4016 + 11.5x 1 + 7.55x2 + 12.5x3 where x1 represents the girth of the elephant (in centimeters), x2 represents the length of the elephant (in centimeters), and x3 represents the circumference of a footpad (in centimeters). (Source: Field Trip Earth) (a) x1 = 421, x2 = 224, x3 = 144 (b) x1 = 311, x2 = 171, x3 = 102 (c) x1 = 376, x2 = 226, x3 = 124 (d) x1 = 231, x2 = 135, x3 = 86
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