Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [logistic-regression]

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

In statistics, logistic regression is a regression model where the dependent variable is categorical.

We have $$Pr(Y=1|x, \theta) = \frac1{1+\exp(-\theta^Tx)}$$

278 questions
8
votes
4 answers

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 how I calculate this; I can't get the same result.…
RDJ
  • 207
2
votes
1 answer

How to determine labeled balls for logistic regression

I am studying this paper about logistic regression. In section 4.2 (Randomly Generated Problems) on page 1534, they say "Features of positive (negative) examples are independent and identically distributed, drawn from a normal distribution…
Saeed
  • 175
2
votes
1 answer

Intuition behind logistic regression, logit function?

I’m confused about the steps to go from a simple linear regression to logistic regression. If we have a dataset consisting of a column of x values and a column of y values (the values we want to predict), then we can run a simple linear regression…
King Squirrel
  • 2,607
2
votes
0 answers

Using Linear Regression for Classification

I am using Vowpal Wabiit to explore the power of different loss functions (e.g. squared, hinge, logistic, quantile) for classification. I've trained different models using each of these loss functions. Among many of LibSVM dataset, I have seen minor…
AmirC
  • 129
1
vote
1 answer

Laying out logistic function equation with Euler's number

Sorry for the incredibly basic question. I've not studied maths but need to understand the how to formulate an equation for something I'm revising. In the image below I cannot get the same result of 0.0924. I'm sure the result is correct but I…
Robertxc
  • 13
1
vote
0 answers

Derive logistic regression from multinomial logistic regression

The log-likelihood function of Multinomial logistic regression is given by: \begin{equation} l(w) = \sum_{j=1}^{n}\left(\sum_{i=1}^{m}{y_{j}}^{(i)}{w^{(i)}}^{T}x_{j} -…
qwerty
  • 65
1
vote
1 answer

Kolmogorov–Smirnov test in logistic regression

When applying KS-test (as goodness-of-fit test) on logistic regression (class: 0,1), where x-axis = probability of being classified as class 1, sorting ascendingly. Here are the 2 questions: 1. Why are the 2 curves to plot are TPR, FPR? AFAK,…
Wong
  • 143
1
vote
0 answers

How to do prediction in a binary classification with logistic regression when we care much more about type I error than type II error?

How to do prediction in a binary classification with logistic regression when we care much more about type I error than type II error? Which criteria should I use to select the threshold value and how should I show different altitude to type I…
XWei
  • 39
1
vote
1 answer

Using LDA decision boundary inequality to classify an observation X

I have a single regressor $X$ and response $y$, where $y=n_k/n$ if $X$ is of class $k$, and $k=1,2$. Let $n_k$ denote the number of observations in class $k$, and $n$ the total number of observations. Denote $\mu_k$ as the mean of class $k$, …
sk13
  • 49
1
vote
0 answers

Do logistic functions have to be symmetrical?

I'm attempting the find the equation of a graph i have plotted, which is S shaped similar to a logistic function. I want to use the logistic function equation to model it, but "top curve" of the S is longer than the first curve, meaning it isn't…
piptheninjafrog
  • 11
  • 1
1
vote
1 answer

How does the softmax function come about?

I'm unsure how the softmax function comes about. I understand that the sigmoid function is a result of phrasing the log-odds as a linear equation and then rearranging the formula to model for the probability of an event occurring, but I'm not sure…
tryingtolearn
  • 141
1
vote
0 answers

Why can the logit function be written as a linear function?

The logit function is $ ln \frac{F(x)}{1-F(x)} $. According to wikipedia and the variety of materials that I have read, we can write this in linear form ($\beta_0 + \beta_1x$) for purposes of logistic regression.…
Haim
  • 757
0
votes
0 answers

Moderate Effect Interpretation

Hello I'm studying the moderate effect of one continuous variable, family income, on the relationship between gender (dummy variable) and whether attending school (dummy variable). For the first model, I only put the dummy variable, gender…
Fox_Summer
  • 25
0
votes
0 answers

Can I use logistic regression models for all steps in a mediation analysis

I am learning mediation analysis now. I have a question about variable types for mediation analysis. Supposed I have a dependent variable, Y, an independent variable, X, and a mediating variable, M. My first question is that if they are all dummay…
Fox_Summer
  • 25
0
votes
0 answers

Cross-Entropy Loss for Logistic Regression

my book has the following short section about Logistic Regression: What can be done with a single sigmoid unit? Logistic regression! For a binary classification problem let us define the cross-entropy loss on an example $(\mathbf{x}, y \in \{0,…
xotix
  • 887
1
2