1. **State the problem:** We have data on opponent's height (H) and unreturned lobs (L) from five matches. We want to find: A. The dependent variable. B. The least-squares regression equation. C. The predicted number of unreturned lobs for an opponent 5.9 feet tall. 2. **Identify the dependent variable:** The dependent variable is the one we want to predict or explain. Here, it is the number of unreturned lobs (L) because it depends on the opponent's height. 3. **Calculate the least-squares regression line:** The regression line has the form $$L = a + bH$$ where $b$ is the slope and $a$ is the intercept. Given data: $$H = [5.0, 5.5, 6.0, 6.5, 5.0]$$ $$L = [9, 6, 3, 0, 7]$$ Calculate means: $$\bar{H} = \frac{5.0 + 5.5 + 6.0 + 6.5 + 5.0}{5} = \frac{28.0}{5} = 5.6$$ $$\bar{L} = \frac{9 + 6 + 3 + 0 + 7}{5} = \frac{25}{5} = 5.0$$ Calculate slope $b$: $$b = \frac{\sum (H_i - \bar{H})(L_i - \bar{L})}{\sum (H_i - \bar{H})^2}$$ Calculate numerator: $$(5.0 - 5.6)(9 - 5) + (5.5 - 5.6)(6 - 5) + (6.0 - 5.6)(3 - 5) + (6.5 - 5.6)(0 - 5) + (5.0 - 5.6)(7 - 5)$$ $$= (-0.6)(4) + (-0.1)(1) + (0.4)(-2) + (0.9)(-5) + (-0.6)(2)$$ $$= -2.4 - 0.1 - 0.8 - 4.5 - 1.2 = -9.0$$ Calculate denominator: $$(5.0 - 5.6)^2 + (5.5 - 5.6)^2 + (6.0 - 5.6)^2 + (6.5 - 5.6)^2 + (5.0 - 5.6)^2$$ $$= 0.36 + 0.01 + 0.16 + 0.81 + 0.36 = 1.7$$ So, $$b = \frac{-9.0}{1.7} \approx -5.29$$ Calculate intercept $a$: $$a = \bar{L} - b \bar{H} = 5.0 - (-5.29)(5.6) = 5.0 + 29.62 = 34.62$$ Thus, the least-squares regression equation is: $$L = 34.62 - 5.29H$$ 4. **Predict unreturned lobs for $H=5.9$ feet:** $$L = 34.62 - 5.29 \times 5.9 = 34.62 - 31.21 = 3.41$$ So, the best estimate is approximately 3.41 unreturned lobs. **Final answers:** A. Dependent variable is the number of unreturned lobs (L). B. Least-squares equation: $$L = 34.62 - 5.29H$$ C. Predicted unreturned lobs for opponent height 5.9 feet is approximately 3.41.