Suppose a researcher studying the incidence of cardiovascular disease estimates a regression model by including information on each person’s cholesterol level (as an independent explanatory variable). If the researcher fails to also include information on whether the person is a smoker, will the estimated regression coefficient on cholesterol be biased? If so, will the bias be positive or negative?
Are cholesterol level and smoking correlated? If they are not, then your regression coefficient will not be biased. Otherwise you have so called omitted variable bias: http://en.wikipedia.org/wiki/Omitted-variable_bias