A study was conducted to evaluate Vitamin D status among schoolchildren in Thailand. Exposure to sunlight allows the body to produce serum \(25(\mathrm{OH}) \mathrm{D}\), which is a marker of Vitamin D status; serum level is measured in units of \(\mathrm{nmol} / \mathrm{L}\) and having serum level below \(50 \mathrm{nmol} / \mathrm{L}\) is indicative of Vitamin D deficiency. The following model was fit to predict serum \(25(O H) D\) level from age, sex, and their interaction.

(a) Write the model equation.

(b) Interpret the model coefficients.

(c) Is there statistically significant evidence that the association between serum \(25(O H) D\) level and age differs by sex? Explain your answer.

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Estimate Std. Error t value Pr(>|t|) (Intercept) 97.7709 4.7732 20.48 0.0000 age -3.0156 0.4774 -6.32 0.0000 sexM -16.2848 7.0740 -2.30 0.0217 age:sexM 2.9369 0.7054 4.16 0.0000