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When does logistic regression of X and Y make sense?
Just to be clear: it seems the question makes sense only in the case where (a) there is a single predictor X (in addition to the implicit constant) and (b) X is a binary variable. Otherwise, logistic regression of X against Y cannot be done. – whuber ♦ Aug 3 ’13 at 18:48 Thanks for contributing an answer to Cross Validated!
How is the likelihood ratio used in logistic regression?
The likelihood ratio test is used to test the null hypothesis that any subset of the ‘s is equal to 0. The number of ‘s in the full model is k+1, while the number of ‘s in the reduced model is r+1. (Remember the reduced model is the model that results when the ‘s in the null hypothesis are set to 0.)
What is the shape of a logistic regression model?
The denominator of the model is (1 + numerator), so the answer will always be less than 1. With one X variable, the theoretical model for has an elongated “S” shape (or sigmoidal shape) with asymptotes at 0 and 1, although in sample estimates we may not see this “S” shape if the range of the X variable is limited.
Which is an algebraically equivalent equation for logistic regression?
There are algebraically equivalent ways to write the logistic regression model: which is an equation that describes the odds of being in the current category of interest. By definition, the odds for an event is π / (1 – π) such that P is the probability of the event.
Is it possible to formulate similar equations in logistic regression?
My question is whether something similar holds in the case of logistic regression and whether it is possible to formulate similar equations for the regression coefficients in logistic regression for when Y is used as a predictor of X. @gung thanks for the reference!
What’s the difference between logistic regression and Pearson’s regression?
An important distinction here is that Pearson’s product-moment correlation, the linear regression of Y on X, and the linear regression of X on Y (assuming X is continuous) are all linear models. On the other hand, logistic regression is a nonlinear model / an instance of the generalized linear model.
Can you treat y as a predictor of X?
To be sure, it is possible to treat Y as a predictor of X instead of treating X as a predictor of Y by using the following equations: