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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: RE: Rescaling |

Date |
Mon, 9 Aug 2004 18:32:46 +0100 |

This reminds me that Sir David Cox in various places emphasises treating regression of y on x as y = mean of y + b(x - mean of x) Nick n.j.cox@durham.ac.uk Roger Newson > At 18:03 09/08/2004, Nick Cox wrote (in reply to Cordula Stolberg): > >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. > > 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. > > 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. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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