Logistic Regression

Authors

Affiliations

Nate Yomogida, B.S., SPT

Doctor of Physical Therapy

B.S. in Kinesiology

Chloë Kerstein, B.S., SPT

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
• $ϵ$ is the difference between observed $y$ and the regression line

$$y={\beta }_0+{\beta }_{1}x+ϵ$$

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

$${\mu }_y|x={\beta }_0+{\beta }_{1}x$$

References

1.

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