Statistical inferences for linear regression models when the covariates have functional relationships: polynomial regression
Liu, W., Wynn, H. P.
& Hayter, A. J.
(2008).
Statistical inferences for linear regression models when the covariates have functional relationships: polynomial regression.
Journal of Statistical Computation and Simulation,
78(4), 315-324.
https://doi.org/10.1080/00949650601100981
& Hayter, A. J.
(2008).
Statistical inferences for linear regression models when the covariates have functional relationships: polynomial regression.
Journal of Statistical Computation and Simulation,
78(4), 315-324.
https://doi.org/10.1080/00949650601100981
In many linear regression models, there are functional relationships among the covariates. The usual (partial) F tests for these models do not utilize these functional relationships, however, and so have certain undesirable properties. Improvements over these F tests are proposed in this article, and they are based on simultaneous confidence bands. For ease of illustration of the ideas, we focus on the polynomial regression model.