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From |
Roger Newson <roger.newson@kcl.ac.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: Rescaling |

Date |
Mon, 09 Aug 2004 18:25:51 +0100 |

At 18:03 09/08/2004, Nick Cox wrote (in reply to Cordula Stolberg):

I think what Cordula really wants might be centring, rather than scaling. If you extract a constant X_0 from an X-variate before fitting the regression model, and therefore regress Y with respect to X-X_0, then the intercept will be the expected value of Y if X==X_0, instead of the expected value of Y if X==0. This often causes the intercept to make more sense, although, as Nick says, the intercept is still expressed in Y-units.The units of the intercept are the same as those of the response. As I understand it, you can restate in other units exactly as convenience or whim dictates. No statistical issue arises.

For instance, in the -auto- data we might do the example:

. sysuse auto, clear

(1978 Automobile Data)

. replace weight=weight-2000

(74 real changes made)

. regress mpg weight foreign

Source | SS df MS Number of obs = 74

-------------+------------------------------ F( 2, 71) = 69.75

Model | 1619.2877 2 809.643849 Prob > F = 0.0000

Residual | 824.171761 71 11.608053 R-squared = 0.6627

-------------+------------------------------ Adj R-squared = 0.6532

Total | 2443.45946 73 33.4720474 Root MSE = 3.4071

------------------------------------------------------------------------------

mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

weight | -.0065879 .0006371 -10.34 0.000 -.0078583 -.0053175

foreign | -1.650029 1.075994 -1.53 0.130 -3.7955 .4954422

_cons | 28.50393 .9630195 29.60 0.000 26.58372 30.42414

------------------------------------------------------------------------------

.

The intercept is then the miles per gallon expected in a realistic US-made car weighing 2000 pounds (1 US ton), instead of the miles per gallon expected in a fantasy US-made car with zero weight, and the standard error will be reduced because the line is not being extrapolated off the edge of the paper.

If we typed our -replace- statement as

. replace weight=(weight-2000)/2000

then we would have computed a regression coefficient for -weight- equal to a decrease in mileage per incremental US ton, which might be easier to explain than a decrease in mileage per incremental pound.

I hope this helps.

Roger

--

Roger Newson

Lecturer in Medical Statistics

Department of Public Health Sciences

King's College London

5th Floor, Capital House

42 Weston Street

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United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648

Fax: 020 7848 6620 International +44 20 7848 6620

or 020 7848 6605 International +44 20 7848 6605

Email: roger.newson@kcl.ac.uk

Website: http://www.kcl-phs.org.uk/rogernewson

Opinions expressed are those of the author, not the institution.

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**Follow-Ups**:**Re: st: RE: Rescaling***From:*Roger Newson <roger.newson@kcl.ac.uk>

**References**:**st: RE: Rescaling***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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