@vishal_prof_gmail_com . Sorry I could not reply earlier. Had a busy day. Rick_SAS and PaigeMiller have already given you the answer. I have nothing new to add. I am answering only because the question was referring to me. 1. Chi Square statistics = ((Beta - 0)/ Std error)^2, here beta is the coefficient which we are testing against the null hypothesis that it is 0. The part of formula (Beta - 0)/ Std error), is same as for t-statistics. I agree to the point that target variable is discrete , however Beta is coming from a population which is continuous (can be -ve/+ve) that's why it is standardized. Why don't we then compare to a t distribution, rather than squaring it and then comparing it to Chi square distribution (which is the square of a random number). You are right when you say that X^2 is (Beta/Std.Error)^2 and it looks very much like t-statistics, except for the square term. So much so that square root of X^2 is also called Psuedo t-ratio (see here)! But why Pesudo when they actually look very similar and why can't one use t-statistics for logisitic regression? You have an excellent question! My answer would go like this. The assumptions about the population should go before we carry out any statistical procedure. I don't think it is a good idea to reverse the flow of logic (that is carry out a test first and then do assumptions about population later. I guess that is how the statistics work). The assumption with t-statistics is that the population is approximately normal looking (which is actually t-distribution) and the population parameters are unknown. However when you are doing Logistic regression, the population parameters are known (actually it can be shown that variance and its related mean are known). For example in binary logistic regression, the expected value E(Y) = n*p and Var(Y) = n*p*(1-p), where n=number of data-points, p=probability of success (in case of coin flip for example it is 0.5 but it can be anything between 0 and 1). This seemingly simple difference put different constraints on the tests that we can carry out. What you are saying in the point 'You use Chi-square statistics when the observations are coming from a Chi-square distribution while you use t-statistics when the observations are coming from a t-distribution.' is true for target variable , however we are checking the coefficients which not necessarily maybe from a Chi-square distribution. and 2. Even in Logistic regression the target variable is transformed using Logit function in to a continuous variable (-infinity to infinity). It is actually a generalized linear model. The transformation that you are talking about helps us to fit and visualize the data. To begin with we do not have a continuous data. As in binary logisitic regression, it is only 0 or 1 (or dead/alive, cancer/not cancer, loan defaulted/not defaulted etc.). Transformations helps us to understand and predict but it does not alter the underlying original data and thus the distribution. Coefficients are associated with that transformation. I tried to keep things simple but I am sorry if I made it confusing rather. Best wishes,
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