= Solution
Writing $Y_i=\operatorname{medv}_i$, $L_i=\operatorname{lstat}_i$, and $A_i=\operatorname{age}_i$, the fitted <normal linear model> is
$$
Y_i
=\beta_0+\beta_1L_i+\beta_2A_i+\beta_3L_iA_i+\varepsilon_i,
\qquad
\varepsilon_i\stackrel{\rm iid}{\sim}N(0,\sigma^2).
$$
The R formula `lstat * age` includes both main effects and their <interaction term>.
Three notable features are:
* The fitted model is highly significant overall: its $F$ statistic is $209.3$ on $(3,502)$ degrees of freedom with $p<2.2\times10^{-16}$. Its $R^2=0.5557$, however, means that about $44\%$ of the observed response variation remains unexplained, and the residual standard deviation is about $6.15$ house-value units.
* At fixed age, the fitted slope with respect to lstat is
$$
-1.3921+0.004156\,A.
$$
The large negative main coefficient is strongly significant. The positive interaction is significant at the $5\%$ level ($p=0.0252$), indicating that this negative association becomes slightly weaker for older housing tracts.
* The age main-effect estimate is essentially zero with $p=0.9711$, but it is the age effect specifically at $L=0$ and should not be interpreted separately from the significant interaction. The diagnostic plots also show curved residual structure, increasing spread, a heavy upper tail with observations 215, 372, and 373, and substantial influence from observation 215. These features cast doubt on linearity, constant variance, and Gaussian residual assumptions.
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