Regression on fractional data I'm writing a piece of research into the death rate of minorities on tv shows, as there's been a lot of outcry over the deaths of queer women in media but very little actual analysis on the topic. I've done multivariate data analysis in the past but nothing needing regression; I'm a second-year undergraduate statistics student.
In order to control for the correlation between total number of characters and number of deaths, I'm intending to express the deaths per year as a fractional value. Aside from a simple linear regression, are there any regression models that would be appropriate? I've looked into binomial regression (which might works, but I'm unsure) and Poisson regression already, which certainly wouldn't work as it's not integer data.
 A: You say you cannot use a poisson regression on the count variable deaths directly, because there might be some influence of exposure (number of characters that year) with the number of deaths, presumably because with too many characters the film company's need to get rid of more of them ... (?). 
But I think that we can take care of that within the glm framework, I will first discuss a poisson regression (with log link). Let $Y_t$ be the number of deaths year $t$, the exposure $E_t$ the total number of characters, and possibly $x_t$ other covariates (in intensive form, see Goodness of fit and which model to choose linear regression or Poisson). Then $Y_t \sim \cal{P}(\lambda_t)$, $\lambda_t = \exp(\beta_0+1\cdot \log E_t + \beta^T x_t)$ where the log exposure $\log E_t$ is used as an offset (see Difference between offset and exposure in Poisson Regression). This is a baseline model which is not modelling any interaction between exposure and number of deaths.  Then to see if there is any such interaction, extend the model as 
$\lambda_t = \exp(\beta_0+1\cdot \log E_t + s(\log E_t) + \beta^T x_t)$ where $s(\cdot)$ represents a smooth term, maybe a spline, or more simply a linear term. Then the estimate of the new term indicates if there is such an interaction.  If there is overdispersion all this can be done within a negative binomial model. 
One could argue (since the number of deaths $Y_t$ is bounded above by the exposure) that a binomial likelihood is more natural. That would have to be used with a log link, see for instance Log binomial regression with a case-control sample
