Answered: The measure of standard error can also…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The measure of standard error can also be applied to the parameter estimates resulting from linear regressions.

For example, consider the following linear regression equation that describes the relationship between education and wage:

WAGEi=β0+β1EDUCi+εi

where WAGEi is the hourly wage of person i (i.e., any specific person) and EDUCi is the number of years of education for that same person. The residual εi encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero.

Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates:

WAGEi=−11.5+6.1 EDUCi

If the standard error of the estimate of β1 is 1.32, then the true value of β1 lies between(4.78, 4.12, 3.46, 5.44) and (6.76, 7.42, 8.74) . As the number of observations in a data set grows, you would expect this range to (DECREASE , INCREASE) in size.

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