Which family in glm() in R is most appropriate for a response variable of proportions? I currently have a data set where my dependent variable is a proportion (ex: the percent of a success). I currently have it set up where my y-values are between 0 and 1 (ex: 54.6% is 0.546). I decided to use logistic regression because my y-variable is between 0 and 1. However, since my y-variable is not binary, I assume I cannot use the family "binomial" in glm() R.
It is also worthy to note that I am doing a class project so dispersion value is important as well as AIC. When I use the binomial family, R automatically makes the dispersion value as 1, which does not help me figure out if my data is overdispersed.
Questions:

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*Is logistic regression appropriate to use in this scenario?

*If the binomial family (link = logit) is appropriate as well for logistic reg, how should I scale/change the weight so that I can get an accurate dispersion value, as opposed to the assumed "1"?

I am open to other methods for going about this. Thanks!
UPDATE: I was able to do some more research, and one of my independent variable "total population" is the total for the percentage proportion (had to calculate it myself to make sure it aligns). My y-variable is still the percentage/proportion of success that the event happened within the population.

As far as I know, you can use the binomial family if you make use of the weights argument. However, this only makes sense, if your dependent variable comes from a binomial distribution and is already weighted by the number of trials. A similar discussion can be found here: How to apply binomial GLMM (glmer) to percentages rather than yes-no counts?.
Alternatively, you could use a fractional logit model, where the dependent variable is a fraction. A reference on that can be found here: ECONOMETRIC METHODS FOR FRACTIONAL RESPONSE
VARIABLES WITH AN APPLICATION TO 401 (K) PLAN
PARTICIPATION RATES. For the glm model type this can be implemented by changing the family to quasibinomial.
And regarding your 2nd question: I think the usual approach is looking at the deviance residuals. As far as I know, the ratio of the deviance residuals and the degrees of freedom is a decent approximation for the dispersion parameter. However, I cannot provide a reference for this right now.
