Let us read the fuel efficiency data that is shipped with Stata
. sysuse auto, clear
(1978 Automobile Data)
To study how fuel efficiency depends on weight it is useful to transform the dependent variable from “miles per gallon” to “gallons per 100 miles”
. gen gphm = 100/mpg
We then obtain a more linear relationship
. twoway scatter gphm weight || lfit gphm weight ///
> , ytitle(Gallons per Mile) legend(off)
The regression equation estimated by OLS is
. regress gphm weight
Source | SS df MS Number of obs = 74
-------------+---------------------------------- F(1, 72) = 194.71
Model | 87.2964969 1 87.2964969 Prob > F = 0.0000
Residual | 32.2797639 72 .448330054 R-squared = 0.7300
-------------+---------------------------------- Adj R-squared = 0.7263
Total | 119.576261 73 1.63803097 Root MSE = .66957
------------------------------------------------------------------------------
gphm | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | .001407 .0001008 13.95 0.000 .001206 .0016081
_cons | .7707669 .3142571 2.45 0.017 .1443069 1.397227
------------------------------------------------------------------------------
Thus, a car that weighs 1,000 lbs more than another requires on average an extra 1.4 gallons to travel 100 miles.
That’s all for now!