univariate logistic regression analysis
Univariate logistic regression is a statistical technique used to model the relationship between one independent variable (predictor variable) and a binary dependent variable (response variable) using logistic regression.
In univariate logistic regression, only one independent variable is considered. The goal is to estimate the effect of this variable on the probability of a particular outcome occurring, given the presence of the independent variable.
The logistic regression model estimates the probability of the outcome using the logits (natural logarithm of the odds ratio) of the dependent variable. The model equation can be written as:
logit(p) = β0 + β1X1
Where:
-
logit(p) represents the natural logarithm of the probability of the outcome variable (p) being 1 (successful, positive, etc.).
- β0 is the intercept or constant term of the model.
odds
- β1 is the regression coefficient or slope of the independent variable (X1).
- X1 is the value of the independent variable.
To estimate the regression coefficients (β0 and β1), maximum likelihood estimation is commonly used. The logistic regression model outputs odds ratios, confidence intervals, and p-values to determine the significance of the independent variable's effect on the outcome.
Univariate logistic regression is useful for assessing the relationship between a single predictor and a binary response variable. It can help in understanding the impact of an independent variable on the odds of a particular outcome and can serve as a starting point for more complex multivariate logistic regression analyses.

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