Using the data in Question 1 (but omitting the proposed distance variable), choose a value of p to minimise the standard error of the estimate associated with the following quantities, specifically comparing y referring to honey and x the number of bees:
y* = y - p sigma{j=1 to n} wij yj
x* = x - p sigma{j=1 to n} wij xj
Define the weight wij = 1 for all neighbors within 2 units of the hive and 0 otherwise.
We use the spatial data to determine the set of neighbors within 2 units of each hive, and take the sum
of their values. Then we can explore with a range of p values, finding such standard errors as follow:
Of these, p = 0 minimizes the standard error, although the r2
is low. Thus, the model collapses back
into a linear regression, and we conclude that the number of bees in the hive does not seem
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