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Statistics Rough Solutions to the Additional Practice Problems

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Rough Solutions to the Additional Practice Problems 4.2. The sample size 𝑛 = 200. The estimated regression equation is 𝑊𝑒𝚤𝑔ℎ𝑡 = −99.41 + 3.94𝐻𝑒𝑖𝑔ℎ𝑡, 𝑅 = 0.81, SER = 10.2. (a) Substituting 𝐻𝑒𝑖𝑔ℎ𝑡 = 70, 65, and 74 inches into the equation, the predicted weights are 176.39, 156.69, and 192.15 pounds. (b) 𝛥𝑊𝑒𝚤𝑔ℎ𝑡 = 3.94 × 𝛥𝐻𝑒𝑖𝑔ℎ𝑡 = 3.94 × 1.5 = 5.91. (c) We have the following relations: 1 𝑖𝑛 = 2.54 𝑐𝑚 and 1 𝑙𝑏 = 0.4536 𝑘𝑔. Suppose the regression equation in centimeter-kilogram units is 𝑊𝑒𝚤𝑔ℎ𝑡 = 𝛾 + 𝛾 𝐻𝑒𝑖𝑔ℎ𝑡. The coefficients are ˆ 0  9941 04536  45092 kg; ˆ1  394  024536 54  07036 kg per cm. The 𝑅 is unit free, so it remains at 𝑅 = 0.81. The standard error of the regression is 𝑆𝐸𝑅 = 10.2 × 0.4536 = 4.6267 𝑘𝑔. 4.3. (a) The coefficient 9.6 shows the marginal effect of Age on AWE; that is, AWE is expected to increase by $9.6 for each additional year of age. 696.7 is the intercept of the regression line. It determines the overall level of the line ...
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