a$)$First$,$load the data and pick out every other data point in the x and y directions. I.e$.,$you should have data points $[0,0],[0,2],[0,4],...,[2,0],[2,2],[2,4],...$You can look atthe lectrure notes on Gaussian Process Regresison for an example how to do this. Youwill use this data set to make the interpolation, and the other data points for comparison.b$)$First$,$do a $2$D linear interpolation on the reduced $($even$)$data points. Use the functionscipy.interpolate.RegularGridInterpolator$().$Then reconstruct a new version of the entiredata set $($all points$)$using this interpolation. Make a plot of row $300$for both the origionaldata and the interpolated data. On average, how far off is the interpolated data? Do thesame thing for row $301.$Why is the data in this row farther off?c$)$Repeat part b$)$using cubic interpoalation. You can still usescipy.interpolate.RegularGridInterpolator$()$with the option method$=$'cubic'.d$)$Now repeate part b$)$using gaussian proces regression. Be sure to include the errors inyour plot using the sigma returned by the GPR and the fill$\_$between$()$function$.$How doesthe accuracy compare to cubic interpolation? How does the actual error compare to thesigma from the GPR$?$Note: For GPR to work, you'll probably need to use a smaller number of data points. Forexample, you may need to use every $6$th or $10$th point, rather than every$-$other point. Oryou may need to use every$-$other row between $250$and $350.$Or you might need to justrandomly pick $10,000($or less$)$data points out of the $500,000$or so you start with $-$thisshould work find for GPR$.$I$\text{'}$m not sure what will work or will work best, but give it a try.e$)$Finally$,$repeate part d$),$but include an error on each point of $0\mathrm{.}005,$the rounding erroron the data. Compare the sigma returned by the GPR and the difference between the real and interpolated values in parts d$)$ and e$).$

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