version 12.1
use https://www3.nd.edu/~rwilliam/statafiles/nonlinhw.dta, clear

********** Part 1.
* Plot of x1 with y1
estimates clear
scatter y1 x1, scheme(sj)
curvefit y1 x1, f(1 4)
* HW: Show another way to graph this model
* HW: Show how to estimate this model using regress and/or glm

********** Part 2.
* Plot of x1 with y2
estimates clear
scatter y2 x1
curvefit y2 x1, f(1 0)
* HW: Show how to estimate this model using regress and/or glm

********** Part 3.
* Plot of x1 with y3.
estimates clear
scatter y3 x1
mkspline xle0 0 xgt0 = x1, marginal
reg y3 x1
predict linear
reg y3 xle0 xgt0
predict spline
scatter y3 x1 || line linear x1 || line spline x1, sort scheme(sj)

******** Part 4.
* As this shows, a polynomial model would also be plausible for y3.
* In practice, it is often hard to tell just from the scatterplot what
* transformation is best, so theory is important.
estimates clear
curvefit y3 x1, f(1 4)