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 dichotomous.

A dichotomous variable refers to a variable that is binary and mutually exclusive (e.g. gender, surgery/no surgery, success/failure, live/die).

Function

Comparison to other regressions

Simple linear regression involving two variables:

  • y is an arbitrary observed value of the continuous dependent variable
  • ϵ is the difference between observed y and the regression line

y=β0+β1x+ϵ

Logistic Regression

  • The observed value of Y is 𝜇y|x, the mean of a subpopulation of Y values for a given value of X
  • ϵ 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

μy|x=β0+β1x

References

1.
Daniel WW, Cross CL. Biostatistics: A Foundation for Analysis in the Health Sciences. 11th ed. Wiley; 2019.

Citation

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