= Solution
Let $Y_i$ be passenger count and use a <Poisson regression> with log mean, initially treating the response as a working daily count:
$$
\log\mu_i=\beta_0+\beta_B\log(\mathrm{Bmiles}_i)+\beta_F\mathrm{Fare}_i
+\beta_P\log(\mathrm{Pop}_i)+\beta_O\frac{\mathrm{Older}_i}{\mathrm{Pop}_i}
+\beta_L\mathrm{LIH}_i+\beta_V\mathrm{Poverty}_i+\beta_R\mathrm{MedRent}_i.
$$
Center and scale the continuous predictors before fitting, and compare a small set of defensible reduced models rather than saturating twenty observations. Household counts should not be called household proportions without a household denominator; population-scaled counts are alternative intensity covariates. Bus miles can be an estimated elasticity term rather than an <offset>, since proportionality of passenger numbers to bus miles has not been established.
For actual counts, the log-likelihood score is $X^T(Y-\mu)=0$, with $\mu_i=e^{x_i^T\beta}$. Fitting by <iteratively reweighted least squares> uses weights $\mu_i$ and working response $\eta_i+(Y_i-\mu_i)/\mu_i$. Compare nested means by a <likelihood-ratio test> only if the Poisson variance assumption is plausible; check the <Poisson deviance>, Pearson dispersion $\sum_i(Y_i-\widehat\mu_i)^2/\widehat\mu_i/(20-p)$, residuals, leverage and sensitivity to influential providers. Consider <Quasi-Poisson regression> or <negative binomial regression> if variance exceeds the mean.
The recorded response is actually a daily average, so <Poisson working models for averaged counts> need special care. If a provider was observed for $T_i$ days and total passengers were $C_i$, fit $C_i\sim\operatorname{Poisson}(T_i\mu_i)$ with <offset> $\log T_i$. If only the average and no observation duration are available, a Poisson mean model can still be explored, but its likelihood and standard errors are not automatically justified by integer-looking averages.
A one-unit increase in an untransformed predictor has fitted multiplicative mean effect $e^{\beta_j}$; a bus-mile elasticity $\beta_B$ gives a doubling effect $2^{\beta_B}$. \b[No numerical coefficient estimates or selected twenty-provider model are identifiable from the printed excerpt.] The full provider file and, ideally, the averaging periods are needed to execute these model comparisons.
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