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Graphics Processing Units (GPUs) have a large and complex design space that needs to be explored in order to optimize the performance of future GPUs. Statistical techniques are useful tools to help computer architects to predict performance of complex processors. In this study, these methods are utilized to build a model which predicts the GPU performance efficiently. The design space of targeted Fermi GPU has more than 8 million points which cause exploring this huge design space a challenging process. In order to build an accurate model, we propose a two-tier algorithm in our algorithm which builds a multiple linear regression model from a small set of simulated data. In this algorithm the Plackett–Burman design is used to find the key parameters of the GPU, and further simulations are guided by a fractional factorial design for the most important parameters. Our algorithm is able to construct a GPU performance predictor which can predict the performance of any point in the design space with an average prediction error between 1% and 5% for different benchmark applications. In addition, in comparison to other methods which need a large number of sampling points, the accuracy in our method is achieved by only sampling between 0.0003% and 0.0015% of the full design space. [ABSTRACT FROM AUTHOR]