To answer this question, provide your R code, R outputs

Use data sic.100 from the package geoR. This data set contains rainfall locations (in kilometres) and measurements (in millimetres).

a. Produce a quick numeric summary of the data. What are (round the answer with 3 decimal places)

Minimum distance between data points =

Maximum distance between data points =

(0.5 mark)

b. Visualize the locations (using 4 plots) of the data in the x and y planes. (1 mark)

c. What is the approximate y coordinate of a point with the largest data value? (0.5 mark)

(i) 0

(ii) 100

(iii) 400

(iv) 600

d. Plot a sample variogram on the interval [0,300] using 11 bins. (0.5 mark)

e. Fit the exponential variogram to the sample variogram from (d) by using ordinary least squares and maximum likelihood methods. Use the initial values (1000,10) and nugget = 10000. (1 mark)

f. Plot the fitted variograms against the sample variogram. Compare the fitted ordinary least squares and maximum likelihood curves. Which of these curves better fits points of the empirical variogram? (0.5 mark)

g. Plot the empirical directional variogram for 30 degrees with a tolerance angle 20 degrees. Use the line plot. (0.5 mark)

h. Plot a multidirectional empirical variogram (computed for 0, 45, 90, and 135 degrees). (0.5 mark)

i. make a data frame from sic.100 using the command

df <- data.frame(sic.100$coords, data = sic.100$data)

make a SpatialPointsDataFrame from df. (0.5 mark)

j. Assume an anisotropic exponential model. Apply the likfit function with

coords =coordinates(df) and data =df$data

and the initial values

ini = c(1000,10) and nug = 10000

Based on the obtained results, is this model isotropic? Justify your answer. (1 mark)

k. Produce a 2D variogram plot for the model

data ~ 1 with cutoff = 200 and width = 10

(0.5 mark)