On Minimizing the Standard Error of the Slope in Simple Linear Regression

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.

Cite this paper

Crunk, S. and Huynh, X. (2014) On Minimizing the Standard Error of the Slope in Simple Linear Regression.*Open Journal of Statistics*, **4**, 173-177. doi: 10.4236/ojs.2014.43016.

Crunk, S. and Huynh, X. (2014) On Minimizing the Standard Error of the Slope in Simple Linear Regression.

References

[1] Weisberg, S. (2005) Applied Linear Regression. 3rd Edition, John Wiley & Sons, Inc., Hoboken.

http://dx.doi.org/10.1002/0471704091

[2] Stewart, J. (2011) Calculus. 7th Edition, Thomson Brooks/Cole, Belmont.

[3] Greenberg, H. (1971) Integer Programming. Academic Press, New York.

[4] Li, D. and Sun, X. (2006) Nonlinear Integer Programming. Springer, New York.

[1] Weisberg, S. (2005) Applied Linear Regression. 3rd Edition, John Wiley & Sons, Inc., Hoboken.

http://dx.doi.org/10.1002/0471704091

[2] Stewart, J. (2011) Calculus. 7th Edition, Thomson Brooks/Cole, Belmont.

[3] Greenberg, H. (1971) Integer Programming. Academic Press, New York.

[4] Li, D. and Sun, X. (2006) Nonlinear Integer Programming. Springer, New York.