The rule of thumb for minimum sample size is 10 times of the number of items in the most complex variable (the variable with the largest number of items).
Please read Applied Regression Analysis and Other Multivariable Methods by Kleinbaum, Kupper and Muller for details.
Usually 30 is the minimum number of participants, however, you have to do some power test of the study to see how many are needed to consider results significant. http://www.3rs-reduction.co.uk/html/6__power_and_sample_size.html