I need to do multiple regression for my little research project. I have 4 continuous variables as x variables that are supposed to predict customer's satisfaction, which is measured on the scale 1 to 5: Very happy, Happy, Neither, Unhappy, Very unhappy.

I have records of about 10000 customers to use. I was going to do multiple linear regression, however, I am reading a research project that is almost identical to what I want to do, the y variable is measured on a similar scale, but the statistician there (and I know he is a statistician with a degree in statistics) used "multiple logistic regression"

I was under the impression that logistic regression is used only when 'y' variable is binary (yes or no, alive or dead...etc). Is it actually possible to use logistic regression for something like this??? if so, how???

Many thanks