Simple Logistic Regression

Logistics equation calculator. Graph A, below, shows the linear regression of the observed probabilities, Y, on the independent variable X. The problem with ordinary linear regression in a situation of this sort is evident at a glance: extend the regression line a few units upward or downward along the X axis and you will end up with predicted probabilities that fall outside the legitimate and meaningful range of 0.0 to 1.0, inclusive. Logistic regression, as shown in Graph B, fits the relationship between X and Y with a special S-shaped curve that is mathematically constrained to remain within the range of 0.0 to 1.0 on the Y axis. A. Ordinary Linear Regression. B. Logistic Regression. The mechanics of the process begin with the log odds, which will be equal to 0.0 when the probability in question is equal to .50, smaller than 0.0 when the probability is less than .50, and greater than 0.0 when the probability is greater than .50. The form of logistic regression supported by the present page involves a simple weighted linear regression of the observed log odds on the independent variable X. As shown below in Graph C, this regression for the example at hand finds an intercept of -17.2086 and a slope of .5934. C. Weighted Linear Regression of C. Observed Log Odds on X.