8/30/2023 0 Comments Vector newton raphson method![]() In most situations, you have some historical data with known results and use one of several techniques to find the values of beta that best fit the data. When using logistic regression, the primary problem is how to determine the b (often called beta) values for the LR equation. You can’t assume that the data you’re working with can be modeled by the sigmoid function, but many real-life data sets can in fact be accurately modeled by the function. The result of the function is a value between 0.0 and 1.0 as shown in Figure 1. The domain of possible values for z is all real numbers. The function 1.0 / (1.0 + e-z) is called the sigmoid function. The p value can loosely be interpreted as a probability, so in this case you’d conclude that the patient has a 0.7613 probability of dying within the specified number of years. And suppose you have somehow determined that b0 = -95.0, b1 = 0.4, b2 = -0.9 and b3 = 11.2. Let the predictor variables be x1 = patient age, x2 = patient sex (0 = male, 1 = female) and x3 = patient cholesterol level. For example, suppose you want to predict death from heart disease. The x variables are the predictors and the b values are constants that must be determined. Logistic regression assumes that problem data fits an equation that has the form p = 1.0 / (1.0 + e-z) where z = b0 + (b1)(x1) + (b2)(x2) +. ![]() Examples include predicting whether or not a patient will die due to heart disease within a certain number of years (0 = not die, 1 = die), based on the patient’s age, sex and cholesterol level, and predicting whether or not a baseball team will win a game (0 = lose, 1 = win) based on factors such as team batting average and starting pitcher earned run average. Logistic regression (LR) is a machine-learning technique that can be used to make predictions on data where the dependent variable to be predicted takes a value of 0 or 1. Volume 27 Number 09 Test Run - Coding Logistic Regression with Newton-Raphson
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