The use of user-friendly interactive regression software enables undergraduate engineering students to reach a high level of sophistication in regression, correlation and analysis of data. In order to interpret correctly the results, the students must be familiar with potential causes for poor fits in correlations, should be able to recognize a poor correlation and improve it if possible. They should also be aware of the practical consequences of using a correlation which has no statistical validity. In this paper, the harmful effects of numerical error propagation (resulting from collinearity among the independent variables) are explained and demonstrated. Simple methods for minimizing such error propagation in polynomial regression are introduced. This material can be presented, for example, as part of 3rd year undergraduate mathematical modeling and numerical methods course.