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Peter Flom's observation only makes sense if your y is not a probability. Check plot(density(y));rug(y) at different buckets of $x$ and see if you see a changing Beta distribution or simply run betareg. Note that the beta distribution is not an exponential family distribution and thus cannot be modeled with glm in R and you should use Peter's suggestion.

Peter Flom's observation only makes sense if your y is not a probability. Check plot(density(y));rug(y) at different buckets of $x$ and see if you see a changing Beta distribution or simply run betareg. Note that the beta distribution is also an exponential family distribution and thus it should be possible to model it with glm in R.

Peter Flom's observation also makes sense given that y is already magically [0,1]. Check plot(density(y));rug(y) at different buckets of $x$ and see if you see a changing Beta distribution or simply run betareg. Note that the beta distribution is not an exponential family distribution and thus cannot be modeled with glm in R and you should use Peter's suggestion.

Peter Flom's observation only makes sense if your y is not a probability. Check plot(density(y));rug(y) at different buckets of $x$ and see if you see a changing Beta distribution or simply run betareg. Note that the beta distribution is not an exponential family distribution and thus cannot be modeled with glm in R and you should use Peter's suggestion.

Assume you are looking at the probability of someone agreeing to a proposal ($y=1$ agree, $y=0$ disagree) given an incentive $x$ between 0 and 10 (could be log transformed, e.g. remuneration). There are two people proposing the offer to candidates ("Jill and Jack"). The real model is that candidates have a base acceptance rate and that increases as the incentive increases. But it also depends on who is proposing the offer (in this case we say Jill has a better chance than Jack). Assume that combined they ask 1000 candidates and collect their accept (1) or reject (0) data.

Given that "The y values are probabilities of being of a certain class, obtained from averaging classifications done manually by people," I strongly recommend doing a logistic regression on your base data. Here is an example:

Assume you are looking at the probability of someone agreeing to a proposal ($y=1$ agree, $y=0$ disagree) given an incentive $x$ between 0 and 10 (could be log transformed, e.g. remuneration). There are two people proposing the offer to candidates ("Jill and Jack"). The real model is that candidates have a base acceptance rate and that increases as the incentive increases. But it also depends on who is proposing the offer (in this case we say Jill has a better chance than Jack). Assume that combined they ask 1000 candidates and collect their accept (1) or reject (0) data.