. The book website provides data on the temperature–pressure profile of the Martian atmosphere, as measured by the Mars Global Surveyor spacecraft in 2003 using a radio occultation technique [638]....

.
The book website provides data on the temperature–pressure profile of the Martian atmosphere, as measured by the Mars Global Surveyor spacecraft in 2003 using a radio occultation technique [638]. Temperatures generally cool with increasing planetocentric radius (altitude).

a.
Smooth temperature as a function of radius using a smoothing spline, loess, and at least one other technique. Justify the choice of span for each procedure.

b.
The dataset also includes standard errors for the temperature measurements. Apply reasonable weighting schemes to produce weighted smooths using each smoother considered in part (a). Compare these results with the previous results. Discuss.

c.
Construct confidence bands for your smooths. Discuss.

d.
These data originate from seven separate orbits of the spacecraft. These orbits pass over somewhat different regions of Mars. A more complete dataset including orbit number, atmospheric pressure, longitude, latitude, and other variables is available in the file mars-all.dat at the book website. Introductory students may smooth some other interesting pairs of variables. Advanced students may seek to improve the previous analyses, for example, by adjusting for orbit number or longitude and latitude. Such an analysis might include both parametric and nonparametric model components.