= Solution
With Control as the reference group, the fitted <normal linear model> has mean
$$
\mathbb E[\mathrm{Weight}]
=\beta_0+\beta_{\rm Time}t+\beta_{\rm Treat}I_{\rm Treat}
+\beta_{\rm Int}tI_{\rm Treat}+\text{cage effect}.
$$
Thus the control-group rate is $\beta_{\rm Time}$, while the treatment-group rate is $\beta_{\rm Time}+\beta_{\rm Int}$. The estimates are
$$
\boxed{\widehat{\text{control slope}}=-0.006023,}
$$
and
$$
\boxed{\widehat{\text{treatment slope}}
=-0.006023-0.173515=-0.179538}
$$
weight units per day. The control slope has $t=-0.477$ and $p=0.63334$, so \b[there is no statistically significant evidence of weight loss over time in the control group] at conventional <significance level>[significance levels].
The plotted <regression residuals> for each mouse form smooth time patterns rather than an unstructured cloud: nearby observations on the same mouse have similar residuals, and the mice also show persistent individual offsets. This is strong evidence of <autocorrelation> and omitted mouse-level variation. The ordinary linear model treats all 400 measurements as independent after accounting for cage, so it commits <pseudoreplication> and will generally underestimate the coefficient <standard error>[standard errors]. The reported $t$-tests and $p$-values should therefore \b[not be trusted]. A <random-intercept linear mixed model> with a within-mouse correlation structure would respect the repeated-measures design.
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