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From |
David Hoaglin <dchoaglin@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Interpreting coefficients of (logX)^2 variable in pooled OLS regression [SEC=UNOFFICIAL] |

Date |
Fri, 24 May 2013 22:11:04 -0400 |

Hi, Lucy. Apart from reporting that the coefficient of ldistsq is positive, I wonder whether it is necessary to give a separate interpretation to that coefficient. The relation is between lfare and a function of ldist (after adjusting for differences among the years), and that function involves both a quadratic term and a linear term. That is, the quadratic term and the linear term should be taken as a unit. It may be helpful to plot the fitted curves relating fare and dist (i.e., transform back from the log scale to the data scale), a separate curve for each year. I wonder whether the relation of lfare to ldist is truly quadratic. You have enough data to try a piecewise-constant model: Split the range of ldist into disjoint intervals, each containing, say at least 50 observations, choose one of those intervals as the reference category, and create an indicator variable for each of the other intervals. Then use that set of indicator variables as the predictors, instead of ldist and ldistsq. If you then plot the coefficient of each indicator variable against the value of ldist at the midpoint of its interval, you can get a good impression of the shape of the nonlinearity. It might, for example, resemble a linear spline. Also, what do you see when you look at the relation of lfare to ldist for each year separately? Would it be helpful to include interactions with year in your model? David Hoaglin On Fri, May 24, 2013 at 9:08 PM, DU,Lucy <Lucy.Du@deewr.gov.au> wrote: > Unofficial > Hi All > > I've been working on this research question using panel data set and am having difficulties interpreting my stata output. > > Dataset: airfare.dta available on http://www.stata.com/texts/eacsap/. > > Research question: How certain key variables affect airfares in the U.S. market. In the near future > > I ran a pooled OLS regression: regress lfare ldist ldistsq y98 y99 y00 > > Where: > lfare - log transformed airfare variable ldist - log transformed distance variable ldistsq - (ldist)^2 y98, y99, y00 - year dummy variables > > I understand how to interpret coefficients under a log-log transformed model, and coefficients where it's a quadratic model, but when it's a quadratic log transformed variable I'm completely stuck! > > My output is as follows: > > . regress lfare ldist ldistsq y98 y99 y00 > > Source | SS df MS Number of obs = 4596 > -------------+------------------------------ F( 5, 4590) = 581.09 > Model | 339.211826 5 67.8423653 Prob > F = 0.0000 > Residual | 535.882547 4590 .11675001 R-squared = 0.3876 > -------------+------------------------------ Adj R-squared = 0.3870 > Total | 875.094374 4595 .190444913 Root MSE = .34169 > > ------------------------------------------------------------------------------ > lfare | Coef. Std. Err. t P>|t| [95% Conf. Interval] > -------------+---------------------------------------------------------- > -------------+------ > ldist | -.783627 .1298635 -6.03 0.000 -1.038222 -.5290322 > ldistsq | .0897726 .0098112 9.15 0.000 .0705379 .1090072 > y98 | .024341 .0142555 1.71 0.088 -.0036067 .0522887 > y99 | .0350861 .0142555 2.46 0.014 .0071384 .0630338 > y00 | .0959191 .0142555 6.73 0.000 .0679714 .1238668 > _cons | 6.239633 .4270934 14.61 0.000 5.402325 7.076942 > ------------------------------------------------------------------------------ > > Can someone explain how I interpret the coefficients for ldist and ldistsq? * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Interpreting coefficients of (logX)^2 variable in pooled OLS regression [SEC=UNOFFICIAL]***From:*"DU,Lucy" <Lucy.Du@deewr.gov.au>

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