how to get covariance of the estimated coefficients using excel

[Moohwan]

I would like to report the estimated variances and covariances of the
estimated coefficients from regression using excel.
How could I do that?

[robert111]

If you know the statistical formulas for these, write appropriate formulas. I know Excel does linear regression and has slope and intercept functions but not sure about multiple regression, check tools add-ins.

[Jerry W. Lewis]

Standard errors of estimates (square root of variances) are given by LINEST
with the optional 4th argument set to TRUE. Covariances are not natively
available, but can be calculated from first principles.

For simple linear regression, the covariance between slope and intercept
estimates is
=-1/sqrt(1+CVx^2)
where CVx is =STDEVP(xdata)/AVERAGE(xdata)

For more general models that are linear in the unknowns, the covariance
matrix for estimates is
MINVERSE(MMULT(TRANSPOSE(xmatrix),xmatrix))*S^2
where S is the standard deviation given by LINEST with the optional 4th
argument set to TRUE. As a calculation, this can run into numerical problems
with complicated models. If you have Excel 2003, compare the variance of
estimates from this calculation with what LINEST returns; if they do not
agree, then this approach needs more numeric precision than is available in
Excel (Excel like most software uses IEEE double precision).

Jerry

"Moohwan" wrote:

> I would like to report the estimated variances and covariances of the
> estimated coefficients from regression using excel.
> How could I do that?
>

[Jerry W. Lewis]

For truth in advertising, note that -1/sqrt(1+CVx^2) is the correlation, not
the covariance between slope and intercept estimates.

Jerry

"Jerry W. Lewis" wrote:

> Standard errors of estimates (square root of variances) are given by LINEST
> with the optional 4th argument set to TRUE. Covariances are not natively
> available, but can be calculated from first principles.
>
> For simple linear regression, the covariance between slope and intercept
> estimates is
> =-1/sqrt(1+CVx^2)
> where CVx is =STDEVP(xdata)/AVERAGE(xdata)
>
> For more general models that are linear in the unknowns, the covariance
> matrix for estimates is
> MINVERSE(MMULT(TRANSPOSE(xmatrix),xmatrix))*S^2
> where S is the standard deviation given by LINEST with the optional 4th
> argument set to TRUE. As a calculation, this can run into numerical problems
> with complicated models. If you have Excel 2003, compare the variance of
> estimates from this calculation with what LINEST returns; if they do not
> agree, then this approach needs more numeric precision than is available in
> Excel (Excel like most software uses IEEE double precision).
>
> Jerry
>
> "Moohwan" wrote:
>
> > I would like to report the estimated variances and covariances of the
> > estimated coefficients from regression using excel.
> > How could I do that?
> >

[Jerry W. Lewis]

LINEST does multiple regression, as does the Regression tool in the Analysis
ToolPak. Neither gives the covariance of estimates.

Jerry

"robert111" wrote:

>
> If you know the statistical formulas for these, write appropriate
> formulas. I know Excel does linear regression and has slope and
> intercept functions but not sure about multiple regression, check tools
> add-ins.
>
>
> --
> robert111
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