TITLE:
On Minimizing the Standard Error of the Slope in Simple Linear Regression
AUTHORS:
Steven M. Crunk, Xinh Huynh
KEYWORDS:
Minimization; Variance; Coefficient; Beliefs about Statistics; Statistical Literacy
JOURNAL NAME:
Open Journal of Statistics,
Vol.4 No.3,
March
28,
2014
ABSTRACT: A common homework
problem in texts covering calculus-based simple linear regression is to find a
set of values of the independent variable which minimize the standard error of
the estimated slope. All discussions the authors have heard regarding this
problem, as well as all texts with which the authors of this paper are familiar
and which include this problem, provide no solution, a partial solution, or an
outline of a solution without theoretical proof and the provided solution is
incorrect. Going back to first principles we provide the complete correct
solution to this problem.