Adjusted Confidence Intervals for The Slope of A Simple Regression Line

Abstract

Nanayakkara and Cressie [1] have presented a confidence interval for the slope (β₁) in the regression model (1) when the error term has non constant variance. For the case of a single predictor and the error terms are normally distributed with variance which is a function of the predictor variable. Their simulation results show that the proposed confidence interval, is preferable to the confidence interval based on the ordinary least squares, OLS method. Later, Wilcox [2] found that confidence intervals based on bootstrap techniques can improve Nanayakkara and Cressie’s (NC) method. However, the simulation results show only a comparison of coverage probabilities of confidence intervals for the slope. Unlike Nanayakkara and Cressie and Wilcox, this paper presents a comparison of confidence intervals for the slope of a simple regression using OLS and NC methods when these confidence intervals have minimum coverage probability 1-α. The ratio of the expected lengths of these confidence intervals are compared using Monte Carlo simulation. The conclusion is that the confidence interval for β₁ based on the NC method is less efficient than the confidence interval for β₁ based on the OLS method for some cases. These results are not similar to those of Nanayakkara and Cressie and Wilcox.

Keywords: Simple linear regression model, Heteroscedasticity, Ordinary least-squares method, Coverage probability, Expected length

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