Use RStudio to perform the calculations for the homework assignment.

Data set sic$97$ in Rpackage gstat includes the rainfall measurements of a specific day in Switzerland at $467$ locations. After loading the data set, there should be two point pattern shapefiles: sic$\_$obs $($contains coordinates and rainfall for $100$ stations$)$ and sic$\_$full has coordinates and rainfall for all $467$ stations. There is also a spatial grid dataframe called demstd. This contains the elevation of a bounding box that covers all of Switzerland.

The goal of the homework is to create a spatial interpolation of rainfall across the demstd grid based on the $100$ stations in sic$\_$obs. You should validate the interpolation results on the remaining $367$ stations.

HINT: Create a validation data set by stating with sic$\_$full and removing any control points including in sic$\_$obs:

sic$\_$valid $<-$ sic$\_$full$[$is$.$element$($sic$\_$full$ID$,$ sic$\_$obs$ID$)==$ F$,]$

QUESTION:

Using the sic$97$ data set, fit an inverse distance weighting interpolation using inverse distance weighting powers of idp $=1,2,5,$ and $10.$ Which idp results in an interpolation most closely matches the validation data set? Show numerical and written justification.