# Do the # of weights (non-intercept coefficients) in logistic regression = # of features

A simple question that I just want to clarify for understanding: In logistic regression, if we have $$n$$ input features, will there therefore be $$n$$ weights used for classification, one for each feature?

EDIT: I wanted to edit this so it will show up if others search. It seems that a more common terminology for what I called weights is "coefficients". What I call "bias" would also be a coefficient, just the intercept one.

• What would you define as a feature?
– Dave
Apr 26 at 3:45
• Say we are using height and weight to classify if someone is a male or female. I would say a feature is height and weight, so there are 2 features. Apr 26 at 3:48
• i have not come across the term "weight" in this context, but if it means "regression coefficient", then there will be $n+1$ weights, unless you have chosen to exclude the intercept. note that a feature which is $p$-categorical will actually result in $p-1$ features when turned wide form via 1-hot encoding Apr 26 at 4:34
We can have more features if we include the option of parameter expansion. As a very simple example, if we want to include a quadratic feature for $$x$$, then the input feature is just $$x$$, but then we create another term $$x^2$$ which gets it's own weight, so in a sense we have two weights that came from one input feature. Other examples of parameter expansion include interaction effects (features $$x, y$$ expanded to $$x, y, x \times y$$) and splines (piecewise continuous polynomials).