Logistic Regression

Authors
Affiliations

Doctor of Physical Therapy

B.S. in Kinesiology

Doctor of Physical Therapy

B.A. in Neuroscience

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: