Display fpfit equation in a twoway scatter plot || fpfit

[Felipe de Mussy]

I am trying to get the relationship between Life Expectancy and GDP (Preston curve). I already have plotted a twoway scatter plot and a fpfit line, that fit well with the relationship, but I do not know how to get the fpfit equation. Happy if somebody knows how can I do it.

[Andrew Musau]

You are just fitting a fractional polynomial, and the default is degree 2.

webuse grunfeld, clear
regress invest c.mvalue#c.mvalue
predict investhat, xb
tw scatter investhat mvalue, msize(tiny) mcolor(red)
gr save gr1.gph, replace
tw scatter invest mvalue|| fpfit invest mvalue, leg(off)
gr save gr2.gph, replace
gr combine gr1.gph gr2.gph

Res.:

[Felipe de Mussy]

Thanks Andrew for your comment. I am doing that. What I needed was to get the equation of the fractional polynomial fit curve. Finally I got it transforming the GNI to ln(GNI) and then a lineal regression.

[Andrew Musau]

The model in #2 is

$$\text{invest}_{i}= \beta_{0}+ \beta_{1}\text{mvalue}_{i}^{2} + u_{i}$$

where \(i\) is the observation of a firm in a given year. It is estimated using OLS and we obtain the predicted outcome

$$\widehat{\text{invest}}_{i}= \hat{\beta_{0}}+ \hat{\beta_{1}}\text{mvalue}_{i}^{2}$$


So the graph on the left hand side is a scatter plot of \(\widehat{\text{invest}}\) and mvalue.