I do diagnostic research and am interested in determining how the probability of a patient having cancer is related to the concentration of different molecules in the blood. I have received conflicting information on what specifically counts as logistic regression. Some people say that it is regression when the outcome is categorical (eg. cancer vs not) while someone I work with says that it is when the relationship between the probability of the outcome and the measured variables is not linear and includes exponents.
ie they are saying that if the probability of cancer is a function of:
β0 + (β1* molecule x) + (β2* (molecule y)^2) +(β3* (molecule z)^0.5)
then this is logistic regression but if the probability is based off of:
β0 + (β1* molecule x) + (β2* molecule y) +(β3* molecule z)
Then I should use linear regression. (beta reefers to different constants). I am very confused.