Complete the following exercises before the submission deadline. In addition to the points detailed below, 5 points are assigned to the quality of the annotation, as well as to the ‘cleanliness’ of the code and resulting pdf document.

Exercise 1 – 1 point

We will again be working with the BC Parks dataset, which contains information on the locations of Provincial Parks in British Columbia. The parks belong to 5 different regions. There is also information on elevation (in m) and percent forest cover contained within the dataset.

  • Import the BC park locations dataset and convert the data to a ppp object (for today you can exclude information on regions). – 1 point(s)

Note: You will need to load the maptools package and make use of the as.owin() function.

Exercise 2 – 4 points

  • Estimate and plot \(\rho\) for the locations of parks as a function of both elevation and forest cover (be sure that the x-axis for elevation does not go below 0). – 2 point(s)
  • Check for collinearity between elevation and forest cover (you will need to consider NA values). – 1 point(s)
  • Based on these initial analyses, write down the expected form of the model. Provide justification for this starting point. – 1 point(s)

Note: Estimating rho can be slow (\(\sim\) 1-2 min). Be sure to leave enough time for the document to knit.

Exercise 3 – 4 points

  • Fit the model you have defined in exercise 2 and inspect the model output. – 1 point(s)
  • Fit a null, intercept only model. – 1 point(s)
  • Use AIC and a likelihood ratio test to determine if the model you defined is a better fit than the intercept only model. – 1 point(s)
  • Write down the equation for the selected model. – 0.5 point(s)
  • Use this equation to estimate the intensity of parks at 500m elevation and 50% forest cover.

Exercise 4 – 4 points

  • Visualise the fitted model. Note: log scale the estimated intensity when plotting, ignore the standard error. You can use the n argument to adjust the resolution – 1 point(s)
  • Plot the effects of the individual coefficients. Note: use the median value(s) of the other coefficients. – 2 point(s)
  • Visually, do you think the model predictions are a good match to the data? – 1 point(s)

Exercise 5 – 1 point

  • Test whether the observed data deviate significantly from the model predictions. – 1 point(s)

Exercise 5 – 2 points

  • Calculate and plot the model residuals. – 1 point(s)
  • Based on the residuals, do you think the model performing well? – 1 point(s)

Exercise 6 – 3 points

  • Calculate the partial residuals as a function of both elevation and forest cover. – 1 point(s)
  • Do you think that the terms are accurately capturing trends in the data? – 1 point(s)
  • Do you have enough information to further refine the model and improve it’s accuracy? – 1 point(s)

Exercise 7 – 1 points

  • Based on these analyses, what have you learned about the spatial distribution of parks in BC? – 1 point(s)