= Solution
The first command fits independent <Poisson random variables> with means $\mu_j$ and a <log link>. For concentration $x$ and strain indicator $s$, its fitted <linear predictor> is
$$
\log\widehat\mu=4.14443-1.47253x+0.33667s-0.12534xs.
$$
The <interaction> allows different concentration slopes in the two strains. At $x=0$ the second strain's mean is multiplied by $e^{0.33667}$; its slope is $-1.47253-0.12534$. These are multiplicative changes in counts, not changes in probabilities.
The <maximum-likelihood estimates> use the <Poisson regression> likelihood. With <design matrix> $X$, estimated information $X^T\operatorname{diag}(\widehat\mu_j)X$ gives the inverse <covariance matrix>; diagonal square roots give the <standard errors>. The printed <Wald tests> use approximately standard-normal coefficient-to-error ratios. Fuel and strain effects are strong, whereas the <interaction> has $p=0.182$, suggesting a common slope.
$H_2$ removes just the <interaction>; $H_3$ also removes strain. Their parameter counts are four, three and two. Under the usual large-sample <likelihood-ratio test>, $D_2-D_1=1.78089$ is compared with $\chi^2_1$ and is below $3.841459$, so the <interaction> is not required at 5%. By contrast, $D_3-D_2=32.61857$ is far above that threshold, so the strain main effect should remain. Comparing $H_3$ directly with $H_1$ uses $D_3-D_1$ and two <degrees of freedom>.
For an approximate absolute goodness-of-fit test, compare $D_1=84.59557$ with $\chi^2_{70-4}$; its upper-tail probability is about $0.061$. For $H_2$, $D_2=86.37646$ on $67$ <degrees of freedom> has $p\approx0.056$. \b[The additive model $H_2$ is the preferred parsimonious fit] at 5%, subject to the independent <Poisson distribution> and large-sample assumptions. The printed nine rows are only a subset; the supplied fitted output refers to all 70 observations.
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