One research question of public health interest is to determine the extent to which high blood pressure is a genetic phenomenon. In 20 families, the systolic blood pressure of the mother, father, and first-born child in the family were measured (in units of \(\mathrm{mm} \mathrm{Hg}\) ). A multiple linear regression model using \(Y=\) child's blood pressure, \(X_{1}=\) mother's blood pressure, and \(X_{2}=\) father's blood pressure led to the following estimate of a least squares line: \(E(Y)=-15.69+0.415 X_{1}+0.423 X_{2}\). The standard errors associated with \(b_{0}, b_{1}\), and \(b_{2}\), respectively, are \(23.65,0.125\), and 0.119 . The least squares fit produced \(R^{2}=0.597\) and \(M S E=113.8\).

(a) What proportion of the variability of a child's systolic blood pressure is explained by this model?

(b) Does the least squares line indicate statistically significant associations between each of the parent's systolic blood pressures and that of the child? Explain your answer.

(c) What is the predicted systolic blood pressure for a child whose mother's and father's systolic blood pressure is \(125 \mathrm{~mm} \mathrm{Hg}\) and \(140 \mathrm{~mm} \mathrm{Hg}\), respectively?

(d) A colleague tells you that something must be wrong with your model because your fitted intercept is negative, but blood pressures are never negative. How do you respond?

(e) Briefly describe three different plots for assessing the appropriateness or fit of the above regression model.