Quiz Question Soln Maximimizing Log-likelihood in Logistic Regression

#1

Q4. Log-likelihood statistic

Large values of the log-likelihood statistic indicate:

  1. That there are a greater number of explained vs. unexplained observations.
  2. That the statistical model fits the data well.
  3. That as the predictor variable increases, the likelihood of the outcome occurring decreases.
  4. That the statistical model is a poor fit of the data.

My assumption is that the log likelihood is the function, which we are trying to maximize to minimize the error, so in that case the higher value of log-likelihood would point to less error. So I am not getting how the option 4 is right here.

#2

Quiz: Suppose instead of using negative of log-likelihood as the loss, you decide to use least square loss which is defined as Σ(y - y_pred)^2, assuming binary classification, which of the following statements is true about the loss How can we prove the shape of the graph? Whether it would be convex or concave or kind of mix of them, so multiple minima and maxima will be present

#3

Hey @tisandas2011, always raise a new thread for new question. I am answering the first one here, for the second one plz raise a new doubt.

Actually in the log likelihood stastic, it is pre assumed that we are talking about negative of log likelihood. This is the ambiguity within terms, and it is completely understandable, that you were misguided. So 4. option is correct, as we are talking about negative of log likelihood.

Hope this resolved your doubt.
Plz mark the doubt as resolved in my doubts section. :blush:

#4

Thanks for the help…