a) By looking at the Estimate column in the summary table, we can create the

regression line as follows:

\[ \hat{bwt} = -80.41 + 0.44 * \hat{gestation} - 3.33 * \hat{parity} - 0.01 * \hat{age} + 1.15 * \hat{height} + 0.05 * \hat{weight} - 8.40 * \hat{smoke} \]

b) For gestation, we can interpret the slope of it by holding all other variables

constant and note that for every day the mother is in pregnancy, the baby weight

goes up by a factor of 0.44.

Likewise for the age variable, the older the mother, the baby weight is expected

to go down by a factor of -0.01.

c) Since we have added new variables to the model, the model is adjusted and

re-fitted and the parameter estimates change to create the model.

d) The residual of the first observation is calculated as follows:

\[ $\hat{e_1} = bwt_1 - \hat{bwt_1} = 120 - (-80.41 + 0.44 * 284 - 3.33 * 0 - 0.01 * 27 + 1.15 * 62 + 0.05 * 100 - 8.40 * 0) = -0.58 \]

e) We can calcuate \(R^2\) and \(R^2_{adj}\) by using the information given and the

formulas below:

\(R^2 = 1 - (var(e_{i}) / var(y_{i}))\) and

\(R^2_{adj} = R^2 * (n-1 / n-k-1)\)

In this case, n = 1236, k = 6 (6 predictors)

\(var(e_{i}) = 249.28\) and \(var(y_{i}) = 332.57\)

Plugging in the numbers gives us

\(R^2 = 1 - (249.28 / 332.57) = 0.25\) (rounded to two decimal places)

\(R^2_{adj} = 0.25 * (1235 / 1229) = 0.25\)