How to write down a logistic regression formula for continuous and categorical variables?

Question

I have a logistic regression with five explanatory variables (x) and Y is binary. I will present a small work tomorrow on a powerpoint and wondering what the neatest way is to write my logistic regression?

my variables: x_1: categorical, with the categories: teachers, biomathematics, economics and mathematics. Mathematics is the reference variable.

x_2:age, continuous

x_3: gender(Woman=1, man=0)

x_4:preparatory course: (Yes=1, No=0)

x_5: calendar, continuous

I have received a total brain release and can not figure out how to write the nicely on the presentation. Could someone write down the formula to me?

Answer 1

The formalism used to write models in R can be quite handy, in this case with factor variables explicitly noted:

Y ~ age + calendar + factor(teacher) + factor(gender) + factor(prep_course)

You could expand to indicate more specifically that this is a logistic regression, and I suppose to indicate the reference levels of the factor variables (although that probably isn't so important for your presentation).

Answer 2

If you're going to explain the model as percent change of odds, I would use the same equation.

$$ \frac{\pi(x)}{1-\pi(x)} = e^{\alpha + \beta_1teacher + \beta_2biomathematics + \beta_3economics + \beta_4age + \beta_5woman + \beta_6prep + \beta_7calendar} $$

But given 5 dummy variables, I agree that this might be cumbersome for a powerpoint slide. Have you considered using an equation for just the continuous effects and creating a separate table for all the categorical effects?

$$ \frac{\pi(x)}{1-\pi(x)} = \gamma e^{\beta_4age+ \beta_7calendar} $$

                  mathematics teachers biomathematics economics
man    no prep     gamma_1
man    prep        gamma_2
woman  no prep     gamma_3
woman  prep        

Then fill out the entire table with the evaluated coefficients as percent increase over the equation. $$ \begin{align} \gamma_1 &= 100(e^\alpha-1)\%\\ \gamma_2 &= 100(e^{\alpha + \beta_6}-1)\%\\ \gamma_3 &= 100(e^{\alpha + \beta_5 + \beta_6}-1)\%\\\ ... \end{align} $$