Abstract
This paper shows how the dynamic program algorithm called the αQ algorithm can be used as an alternative algorithm to produce the coefficients of a least squares problem. It shows also how the output of the algorithm can be used to calculate various statistical quantities needed to evaluate linear models. In particular, we show how to calculate standard statistical quantities like the coefficient of determination R2, the t statistics, and the F statistics. These quantities serve as a measure of how well the model fits the data.
Similar content being viewed by others
References
Davidson, R., and Mackinon, J.G., Estimation and Inference in Econometrics, 3rd Edition, Oxford University Press, New York, NY, 1993.
Maindonald, J.H., Statistical Computation, John Wiley and Sons, New York, NY, 1984.
Kalaba, R. E., Natsuyama, H. H., and Ueno, S., Regression Analysis via Dynamic Programming, I: Theory, 30th ISCIE International Symposium on Stochastic Systems and Their Applications, Kyoto, Japan, 1998.
Kalaba, R. E., Natsuyama, H. H., and Ueno, S., Regression Analysis via Dynamic Programming, II: Computational Results, 30th ISCIE International Symposium on Stochastic Systems and Their Applications, Kyoto, Japan, 1998.
Bellman, R., and Kalaba, R. E., Dynamic Programming and Modern Control Theory, Academic Press, New York, NY, 1965.
Casella, G., and Berger, R. L., Statistical Inference, Duxbury Press, Belmont, California, 1990.
Green, W.H., Econometric Analysis, 3rd Edition, Prentice Hall, Upper Saddle River, New Jersey, 2000.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Johnson, J., Kalaba, R. Statistical Measures for Ordinary Least Squares Using the αQ Algorithm. Journal of Optimization Theory and Applications 117, 461–474 (2003). https://doi.org/10.1023/A:1023937419543
Issue Date:
DOI: https://doi.org/10.1023/A:1023937419543