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Understanding Logistic Regression

Logistic Regression is a statistical method used for binary classification tasks, where the goal is to predict the probability of an observation belonging to one of two possible classes. Despite its name, logistic regression is actually a classification algorithm rather than a regression algorithm.

The logistic regression model works by fitting a logistic curve to the observed data. This curve is an S-shaped curve that ranges from 0 to 1, which is suitable for representing probabilities. The logistic function, also known as the sigmoid function, is typically used to model this curve. The equation for the logistic function is:

P(y=1∣x)= 1/1+e^-z

Where:

• P(y=1∣x) is the probability of the dependent variable (y) being 1 given the independent variable (x).
• e is the base of the natural logarithm.
• z is the linear combination of the independent variables and their coefficients.

In logistic regression, the model parameters (coefficients) are estimated using maximum likelihood estimation. The coefficients are chosen to maximize the likelihood of observing the actual outcome given the predictor variables.

Once the model is trained, it can be used to predict the probability of an observation belonging to a certain class by plugging in the values of the predictor variables into the logistic function. Typically, a threshold of 0.5 is used to make a binary classification decision: if the predicted probability is greater than 0.5, the observation is classified as belonging to the positive class; otherwise, it is classified as belonging to the negative class.

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