The prevalence of childhood obesity in industrialized nations is constantly rising. Since between 30% and 60% of obese children maintain their obesity into adulthood, there is great interest in better understanding the reasons for this rising trend. In one study, researchers looked at the relationship between a child's percent fat mass and several explanatory variables.4 These were the percent of energy intake at dinner, each parent's body mass index (BMI), an index of energy intake validity (EI/BMR), and gender. The following table summarizes the results of the multiple regression analysis:
b s(b)
Intercept 5.13 3.03
Gender (M = 0, F = 1) 4.69 0.51
Dinner (%) 0.08 0.02
EI/predicted BMR -1.90 0.65
Mother's BMI (kg/m2 ) 0.23 0.07
Father's BMI (kg/m2 ) 0.27 0.09
In addition, it is reported that R = 0.44 and F(5, 524) = 25.16.
(a) How many children were used in this study?
(b) What percent of the variation in percent fat mass is explained by these explanatory variables?
(c) Interpret the sign of each of the regression coef?cients given in the table. For EI/predicted BMR, data values ranged between 1.4 and 2.8 with a low value associated with underreporting of energy intake.
(d) Construct a 95% con?dence interval for the difference in predicted percent fat mass when energy intake at dinner differs by 5% (assume all other variables are the same).