Choose from the following the assumptions we make in fitting data using a GLM.
We assume a conditional distribution for Y given X.
We assume a link function g(\cdot ).
We assume a noise model that captures the relationship between \mathbf{X} and Y.
We assume a linear relationship between the predictors and the linear predictor.
The assumptions we make in fitting data using a Generalized Linear Model (GLM) are:
1. We assume a conditional distribution for Y given X: In GLM, we make an assumption about the distribution of the response variable Y given the predictors X. Typically, this assumption is that Y follows a specific distribution from the exponential family, such as normal, binomial, Poisson, etc.
2. We assume a link function g(\cdot): GLM assumes that there is a systematic relationship between the predictors X and the mean of the response variable Y. The link function g(\cdot) is used to define this relationship by transforming the mean of Y onto the linear scale. Examples of commonly used link functions include the logit, identity, log, and inverse.
3. We assume a noise model that captures the relationship between X and Y: GLM assumes that the observed response variable Y is not a perfect representation of the true underlying relationship between the predictors X and Y. Instead, there is an element of randomness or noise present in the data. The noise model accounts for this randomness and defines the distributional form of the residuals or errors in the model.
These assumptions help to specify the GLM and guide the estimation procedure for fitting the model to the data.