Logistic Regression
Logistic regression is used when the independent variables are ____ and the dependent variable (outcome) is dichotomous1.
A dichotomous variable refers to a variable that is binary and mutually exclusive (e.g. gender, surgery/no surgery, success/failure, live/die)1.
Function
Comparison to other regressions
Simple linear regression involving two variables:
- \(y\) is an arbitrary observed value of the continuous dependent variable
- \(\epsilon\) is the difference between observed \(y\) and the regression line
\[ y = \beta_0 + \beta_1 x + \epsilon \]
Logistic Regression
- The observed value of Y is 𝜇y|x, the mean of a subpopulation of Y values for a given value of X
- \(\epsilon\) is 0 (therefore not included in the formula)
- the difference between the observed Y and the regression line (see Figure 9.2.1) is zero, and we may write Equation 11.4.1 as
\[ \mu_y|x = \beta_0 + \beta_1 x \]
References
1.
Daniel WW, Cross CL. Biostatistics: A Foundation for Analysis in the Health Sciences. 11th ed. Wiley; 2019.
Citation
For attribution, please cite this work as:
Yomogida N, Kerstein C. Logistic Regression. https://yomokerst.com/The
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