How to analyse point data as covariate for areal data

Question

I have two data sets:

a) a set of polygons with areal data variables.
b) point measures of various co-variates of interest (note I do not necessarily have a point for each polygon)

How do I correctly analyse this data set for correlations between an areal variable (dependent variable) and point measures (independent variable)?

Unsure what techniques I need to use. Working in R.

Edit on 7 July 2014:

What I'm really wondering is - if you have areal data i.e. some variable that depends on an area and not points - so something related to population density for example - and you want to analyze that versus a point measurement - rainfall at specific measurement points for example. What is the correct/best way to do this ? I've thought about it since and I see two approaches: 1) Krige the point data and get an average value for each polygon (I presume by picking multiple sample points within the polygon and getting an average) - then build polygon based models using the kriged estimates as covariates. 2) Treat the areal data as point estimates of a field taking the centroid of each polygon as the location for each point estimate, then build a geostatistical model using all data as point estimates. Both these approaches strike me as "incorrect" - what I'm asking really is which is least "incorrect" ?

Answer 1

For future reference, you likely did not get a previous response because your question was lacking adequate detail and a reproducible example. Often, folks like to see what your data looks like and what you have already tried.

If I understand you correctly, all you want is correlation between the attributes in a polygon and point feature class. You can relate the data using over() and then calculate a simple correlation matrix on the results.

require(sp)
require(rgeos)

######################################################################                          
# Create example data using meuse data in sp 
data(meuse)
coordinates(meuse) <- ~x+y

# Create polygon buffers, perturb data and subsample to 
#   create unequal problem
polys <- gBuffer(meuse, byid=TRUE, width=runif(nrow(meuse),30,100))
  polys@data <- data.frame( V1=polys@data[,1]*runif(nrow(polys)), 
                            V2=polys@data[,2]*runif(nrow(polys))^2,
                            V3=polys@data[,3]**2)
polys <- polys[sample(nrow(polys),100),]
######################################################################                          

# Use over to associated attrubutes spatially and then remove NA's
( cor.data <- data.frame(over(meuse, polys), meuse@data[,1:3]) )
  cor.data <- na.omit(cor.data)

# Create and plot correlation matrix
cor(cor.data)   
  pairs(cor.data)