Let us read the fuel efficiency data that ships 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 fairly linear relationship

. twoway scatter gphm weight

. graph export auto.png, width(500) replace
(file auto.png written in PNG format)

. ![Fuel Efficiency by Weight](auto.png)

zsh:1: bad pattern: [Fuel

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 pounds more than another requires on average an extra 1.4 gallons to travel 100 miles.

That's all for now!