An exercise physiologist used skinfold measurements to estimate the total body fat, expressed as a percentage of body weight, for 19 participants in a physical fitness program. The body fat percentages and the body weights are shown in the table.36

Actually, participants 1 to 10 are men, and participants 11 to 19 are women. A summary and graph of the data for men, women, and both sexes combined into a single sample follow.

(a) Compute the regression equations for the males and females separately.
(b) The equation to the fitted regression line for both sexes combined, which is shown on the plot, is Å· = 26.88 + 0.021*. How does the slope of this line compare to the slopes you computed in part (a)? Can you explain the discrepancy? (c) Examine the correlation coefficients for (i) the males, (ii) the females, and (iii) both sexes combined. Do these values agree with your reasoning provided in part (b)?

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Weight Fa Weight Fat Participant X(kg) Y(%)| Participant X(kg) Y(%) 89 28 88 27 66 24 59 23 93 29 73 25 82 29 77 25 9 100 30 67 23 12 13 14 15 16 17 18 19 57 2 68 32 69 35 59 31 62 29 59 26 56 28 66 33 72 33 3 10 Men (n10) Women (n9) Both sexes (n 19) T 63.1 71.68 у 28.37 y 26.30 x 13.2430 sx 5.7975 s 2.6269 2.8723 r # 0.9352 у 30.67 13.1320 sy 3.4835 r 0.0780 0.8132 a Men .Women 30- 28 26 24 70 80 90 100 60 Weight (kg