Linear Regression
Linear regression uses the general linear equation Y=b0+∑(biXi)+ϵ where Y is a continuous dependent variable and independent variables Xi are usually continuous (but can also be binary, e.g. when the linear model is used in a t-test) or other discrete domains. ϵ ϵ is a term for the variance that is not explained by the model and is usually just called "error". Individual dependent values denoted by Yj can be solved by modifying the equation a little: Yj=b0+∑(biXij)+ϵj
Logistic Regression
Logistic regression is another generalized linear model (GLM) procedure using the same basic formula, but instead of the continuous Y , it is regressing for the probability of a categorical outcome. In simplest form, this means that we're considering just one outcome variable and two states of that variable- either 0 or 1.
In other words, Y is a categorical variable, Xi are usually continuous
The equation for the probability of Y=1 looks like this:
P(Y=1)=11+e−(b0+∑(biXi))