8.1 a The regression line is weight = 123.05 - 8.94 smokes
b. The coefficient of smokes represents the difference in the birth weight (in ounces) of babies who are born to mothers that smoke. Mothers who don't smoke have babies weighing 123.05 ounces at birth (on average), while mothers who smoke have babies weighing 114.11 ounces (on average).
c. The difference in birth weights is equal to the slope of the smokes variable and this is significantly different from zero (p = 0).
8.2 a The regression line is weight = 120.07 - 1.93 parity.
b. The average weight of the first-born child is 120.07 ounces and the subsequent children have an average weight of 118.14 ounces.
c. There is not a statistically significant difference in birth weights between the first-born and other children since the coefficient of the parity function cannot be distinguished from zero (p > 0.10).
8.3 a The fitted regression line is
weight = -80.41 +0.44*gestation - 3.33*parity -0.01*age +1.15*height +0.05*weight - 8.40 smoke
b. For each extra day that the baby gestates it gains (on average) 0.44 ounces of birth weight and for each year that the mother ages the birth weight of the baby drops by 0.01 ounces.
c. The coefficient of parity is different because of the effect of the other variables in the model.
d. The model predicts a birth weight of
-80.41 +0.44*284 - 3.33 * 0 -0.01*27 +1.15*62 +0.05*100 - 8.40*0 = 120.58 ounces.
Since the baby actually weighed 120 ounces, the residual is -0.58 ounces.
e. The variance explained by the model is (332.57-249.28) so
\( R^2 \) = (332.57-249.28)/(332.57) = 0.2504435. The adjusted \( R^2 \) is
\( R^2_{adj} = 1 - (249.28/332.57) \times (1236-1)/(1236-6-1) = 0.2467842 \).