Logistic Regression for Binary Outcomes

Logistic Regression Prediction Tool (Simplified)

Logistic Regression Prediction Tool

Define Pre-Trained Model & New Observation

This tool uses a pre-trained logistic regression model. You need to provide the intercept and coefficients. It does not train a model from data.

Model Coefficients (Pre-Trained)

New Observation Data (Values for X variables)

Prediction Settings

Prediction Output

Input model coefficients and new data, then click "Predict Probability".
Logit (z = β₀ + Σ βᵢXᵢ): N/A
Predicted Probability P(Y=1 | X): N/A
N/A
Awaiting Prediction...

Understanding Logistic Regression & Export

Logistic Regression for Binary Outcomes

Logistic Regression is a statistical method used to model the probability of a binary outcome (an event with two possible results, e.g., yes/no, pass/fail, win/lose) based on one or more predictor (independent) variables.

Unlike linear regression which predicts a continuous value, logistic regression predicts a probability, which is always between 0 and 1.

The Logistic Function (Sigmoid):

The core of logistic regression is the logistic function (or sigmoid function), which takes any real-valued number and maps it to a value between 0 and 1:

P(Y=1) = 1 / (1 + e-z)

Where:
  • P(Y=1) is the probability of the outcome being 1.
  • e is the base of the natural logarithm (Euler's number, approx. 2.71828).
  • z is the linear combination of the input variables and their coefficients (also known as the logit or log-odds):
    z = β₀ + β₁X₁ + β₂X₂ + ... + βnXn
    • β₀ is the intercept (bias).
    • β₁, β₂, ..., βn are the coefficients for the predictor variables X₁, X₂, ..., Xn. These coefficients are typically learned from data using a training process (not performed by this simplified tool).

Interpretation:

  • The output P(Y=1) is the estimated probability that the event of interest will occur given the specific values of the predictor variables.
  • This probability can then be used to make a classification by comparing it to a threshold (commonly 0.5). If P(Y=1) > threshold, the outcome is classified as 1; otherwise, it's classified as 0.

Note: This tool requires you to provide the intercept (β₀) and coefficients (βᵢ) from an already trained logistic regression model.

Export Prediction

© Logistic Regression Prediction Tool (Simplified). For educational purposes.