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:WAGE: = Bo + B₁ EDUC; + &iwhere WAGE; is the hourly wage of person i (i.e., any specific person) and EDUC; is the number of years of education for that same person. Theresidual ₂ 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:WAGE;= -10.7+ 3.1 EDUC;If the standard error of the estimate of B₁ is 1.04, then the true value of B₁ lies betweengrows, you would expect this range toin size.and. As the number of observations in a data set

The standard error of the regression is a measure of how far the observed values fall from the…

Answered: If the standard error of the estimate…

If the standard error of the estimate of 3₁ is 1.04, then the true value of ₁ lies between grows, you would expect this range to in size. and As the number of observations in a data set

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4A: Problems In Applying The Linear Regression Model

Section: Chapter Questions

Problem 1E

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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:
WAGE: = Bo + B₁ EDUC; + &i
where WAGE; is the hourly wage of person i (i.e., any specific person) and EDUC; is the number of years of education for that same person. The
residual ₂ 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:
WAGE;= -10.7+ 3.1 EDUC;
If the standard error of the estimate of B₁ is 1.04, then the true value of B₁ lies between
grows, you would expect this range to
in size.
and
. As the number of observations in a data set

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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 EDUCiEDUCi is the number of years of education for that same person. The residual εiεi 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=−12.3+4.4 EDUCi If the standard error of the estimate of β1 is 1.29, then the true value of β1 lies between (2.465, 3.11, 3.755, 1.82) and (5.69, 6.98, 5.045) . As the number of observations in a data set grows, you would expect this range to (INCREASE OR DECREASE) in size.
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