= Solution
The comparison is a <nested-model F-test> of the three time-by-diet interaction coefficients, with null hypothesis that all are zero. The reduced <linear regression> model has a common time slope and four diet-specific intercepts; the full model permits four slopes. It has eight fitted coefficients and $579-8=571$ residual degrees of freedom.
$$
F=\frac{(34.381-31.589)/3}{31.589/571}\approx16.823,
\qquad \boxed{F\sim F_{3,571}\text{ under the null}}.
$$
The rounded sums of squares give the displayed approximation; the software reports $F=16.824$ using unrounded values. The quoted <p-value> $1.744\times10^{-10}$ gives overwhelming evidence against equal log-weight growth slopes across diets under the <normal linear model> assumptions. Thus \b[reject the common-slope hypothesis]. Because repeated measurements on the same chicken may be correlated, the exact reference distribution requires independent, homoscedastic Gaussian errors; the displayed ordinary regression output by itself does not establish that assumption.
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