Correlation coefficient and R squared in Google Earth Engine

Question

I want to calculate the correlation coefficient and R squared between two bands for two different images. How should I proceed?

    var s1_float = ee.ImageCollection("COPERNICUS/S1_GRD_FLOAT")
        .filterMetadata ('resolution_meters', 'equals', 10)
        .filter (ee.Filter.eq ('instrumentMode', 'IW'))
        .filter (ee.Filter.eq('orbitProperties_pass', 'ASCENDING'))
        .filterDate('2020-01-02', '2020-01-04')
        .filterBounds(geometry) 
        .first()
        .clip (geometry)
    
    //second image from my assets 
    var grd = ee.Image ("users/bene96detta/SLC_to_GRD_orb_TC").clip(geometry);

    //difference between the two bands 
    var diffBandVV = grd.select('b2').subtract(s1_float.select('VV')) 
    //std deviation 
    var stdevVV = diffBandVV.reduceRegion({ 
    reducer: ee.Reducer.stdDev(),
    scale: 30,
    maxPixels: 10e9
    });

Answer 1

I was also looking to calculate R2 between two images, and couldn't find a reducer to do this -- only for the Pearson correlation coefficient. Here is my current solution showing both (Pearson correlation coefficient and coefficient of determination, i.e. R2)).

Hopefully there is either a reducer that I missed, or a more elegant solution that someone can share.

https://code.earthengine.google.com/9b66ed88a7c0d581c6d484f16dac70c1

var geometry = 
    ee.Geometry.Polygon(
        [[[-117.24411029815674, 40.07684302769587],
          [-117.24411029815674, 40.06830460341872],
          [-117.23411102294922, 40.06830460341872],
          [-117.23411102294922, 40.07684302769587]]]);

var image = ee.Image("LANDSAT/LC08/C01/T1_TOA/LC08_041032_20140108")
var image1 = image.select("B2")
var image2 = image.select("B3")

Map.addLayer(image1.clip(geometry),{min:0,max:0.3},"B2")
Map.addLayer(image2.clip(geometry),{min:0,max:0.3},"B3")
Map.centerObject(geometry,15)

image = image.select(["B2","B3"])
var values = image
.reduceRegion(ee.Reducer.toList(), geometry, 30)
print("Values: ", values)


// Pearson correlation coefficient:
var pearsonR = image.reduceRegion(
{
geometry: geometry,
reducer: ee.Reducer.pearsonsCorrelation(),
scale:30  
})
print("Pearson R(B2,B3):", pearsonR.get("correlation"))


// Coefficient of determination:
function R2(image, fitted, geometry, scale){
  image = image.rename("constant")
  fitted = fitted.rename("constant")
var SSres = image.subtract(fitted).pow(2)
.reduceRegion({
  geometry:geometry,
  reducer:ee.Reducer.sum(),
  scale:scale
})
var imageMean = image.reduceRegion({
  geometry:geometry,
  reducer:ee.Reducer.mean(),
  scale:scale
}).toImage(["constant"]);
var SStot = image.subtract(imageMean).pow(2)
.reduceRegion({
  geometry:geometry,
  reducer:ee.Reducer.sum(),
  scale:scale
})
var coeff = ee.Number(1).subtract(
  ee.Number(SSres.get("constant"))
  .divide(ee.Number(SStot.get("constant"))))
return coeff
}


// R2 using B2 as y_true and B3 as y_fitted:
var coeff = R2(image1,image2,geometry, 30);
print("R2(y_true=B2, y_fitted=B3): ", coeff)