# Questions tagged [logistic-regression]

For questions about logistic regressions, a regression model where the dependent variable is categorical.

139 questions
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### What is e in this equation, and how do I solve it?

Apologies for the rudimentary question. I haven't studied math and can't find an answer to this online. Is the '$e$' in this equation for logistic regression Euler's number? If so, it doesn't matter ...
2answers
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### Invert the softmax function

Is it possible to revert the softmax function in order to obtain the original values $x_i$? $$S_i=\frac{e^{x_i}}{\sum e^{x_i}}$$ In case of 3 input variables this problem boils down to finding $a$, ...
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### How to estimate of coefficients of logistic model

Consider model $logit(p)=a+bx$. I would like to get a analytic formula of $a$ and $b$ like in linear regression. In linear regression, we can get a formula of estimates of $a$ and $b$. I tried using ...
2answers
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### Show that logistic regression with squared loss function is non-convex

How would you show that if you do logistic regression with a squared loss function, it is not a convex optimization problem (in parameters)? In other words, your loss function for an individual ...
3answers
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### Logistic regression: Prove that the cost function is convex

I'm reading this You can do a find on "convex" to see the part that relates to my question. Background: $h_\theta(X) = sigmoid(\theta^T X)$ --- hypothesis/prediction function $y \in \{0,1\}$ ...
1answer
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### Find the MLE of a GLM

(Note this is not an assignment, but revision for a topic from Cambridge past exam papers) I have been trying to attempt the below question, and I am struggling with part (b). For (a) it is ...
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### What do the parameters of a multinomial logistic regression correspond to?

I've recently started learning about data science/statistics and learned how to derive such models as linear regressors and logistic regressors. What I don't understand, however, is what the ...
1answer
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### Likelihood function for logistic regression

In logistic regression, the regression coefficients ($\hat{\beta_0}, \hat{\beta_1}$) are calculated via the general method of maximum likelihood. For a simple logistic regression, the maximum ...
0answers
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### Vehicle Routing Problem that minimizes Total Time instead of Total Cost, with a few alterations

A company has to collect waste for different customers, at different locations, using two vehicles both with a certain capacity. The vehicles have to begin and end at the depot and when the capacity ...
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### Monotonic transformation to smooth the probabilities

I am studying some event for a set of objects that can be plotted on a square $[0, 100] ^ 2$. I have used logistic regression to calculate probabilities that event occur for different objects and the ...
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### Fitting logistic regression models

I am studying The Elements of Statistical Learning book and I have a question. On pages 120-121 the logistic regression problems is rewritten in the form of matrix and vectors products as follows:(4....
1answer
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### why do we use logistic function to build logistic regression.

Why do we use logistic function to build logistic regression. I know the output value for logistic function bounds between 0 & 1, and bcos of this we can express as probability. Is this the reason ...
1answer
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### Logistic regression - Transposing formulas

I am trying to understand the math behind Logistic regression. I am confused about transposing one formula to another. Here is what I have: Our regression formula $$\ y = b_0 + b_1x$$ Our sigmoid ...
2answers
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### If logistic is the log odds ratio, what's softmax?

I recently saw a nice explanation of logistic regression: With logistic regression, we want to model the probability of getting success, however you define that in the context of the problem. ...
1answer
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### Solving the logistic equation [closed]

I need to solve the logistic equation $$\frac{dP}{dt} = P(a-b\ln P)$$ How do I go about solving this?
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### Simple Logistic Regression - how do I use real data?

Binomial Logistic Regression to predict probability Confusion Point 1: I think I'm right in saying one of the steps of Logistic Regression is to get: $$\log(\mathrm{Odds})$$ Now take this very ...
1answer
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### Logistic curve through three points

I need to find a logistic curve that passes through three points exactly. This means I cannot do a best fit but rather must use simultaneous equations. Essentially this is used to model population ...
1answer
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### Deriving the odds ratio of a 3-way interaction logistic regression model

Suppose a logistic regression model has three binary explanatory variables $x_1$, $x_2$ and $x_3$ used to estimate the probability of success. This model includes all three main effects, the three $2$-...
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### Non-linear regression for cumulative distribution function

I have twenty probability distributions based on a simulation. The corresponding cumulative distribution plot for one distribution looks like this: Simulated result I believe that most of the ...
1answer
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### What is the relationship between the logistic function and the logistic loss function?

The standard logistic function is : $$f(x) = \frac{1}{1+e^{-x}}$$ But the logistic loss function is typically defined as : $$l(w^{\top} \cdot x) = \ln(1 + e^{-y(w^{\top} \cdot x)})$$ I ...
1answer
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