A test for the arbitrage pricing theory which employs a multivariate linear regression model is developed. Given a sample of return premiums for a set of N assets which includes a subset of k linearly independent portfolios, the k factor APT hypothesis is accepted if the intercept term is zero in the multivariate regression of the returns on the k portfolios. The test may be carried out simply, by using univariate multiple regression software. The relation of this test to the concept of performance potential and Sharpe's measure of performance is also discussed. If the performance potential of the k portfolios is not significantly less than the performance potential of the complete set of N assets, then the k factor APT hypothesis is accepted.