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I am using the Matlab fitglm() function for a logistic regression based binary-classification on some data. I have a question regarding one of the optional arguments of fitgl() function. The argument 'Distribution' as mentioned here in the Matlab's fitglm() documentation, the optional argument Distribution for fitglm() specifies the distribution of the response variable. I dont understand this. Why we have to make an assumption about the distribution of response variable. I thought we can only make an assumption about the distribution of predictor variables for the two classes. What is wrong in my understanding ?

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We can indeed make assumptions about the response variable. Indeed, when you apply a regular linear regression model, by definition you are assuming a normal distribution of the response variable. When you want to use GLM to make predictions, your model inevitably will assign some noise to your predicted values. The assumption over the response variable will help your model to distribute that random noise more accurately. In addition, since GLM go beyond the traditional linear regression models, you are able to evaluate further models as for example logistic regression. If you change the assumed normal distribution in the response for a binomial distribution you will be actually using a logistic regression model (take a look at the very first example from the MATLAB's help page from your link!).

For a detailed explanation, take a look at this helpful lesson: https://onlinecourses.science.psu.edu/stat504/node/216

Hope this helps and good luck!

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