sources
– incarceration: https://www.sentencingproject.org/the-facts/#map
– rural-urban: population density https://www.states101.com/populations
– agriculture income: https://data.ers.usda.gov/reports.aspx?ID=17839#P9dd070795569412d9525def18d45bde2_4_185iT0R0x0
– state GDP: https://apps.bea.gov/regional/downloadzip.cfm
method for "rural-urban" metric
– population density and agriculture income data values were converted to "standard scores", aka "z-scores":
z-score = (data value – mean)/SD
– the z-scores were added and divided by 2; result = the rural/urban metric z-score
– note1: 'urban' means "increasing population density"
'rural' means "increasing agriculture income as % of state GDP"
for the 'rural' metric to denote a "rural to urban" value,
the z-scores for agriculture income were 'reversed' by multiplying by "–1"
before adding to the population density z-scores
– note2: "NCE" is "normal curve equivalent" (see Wikipedia, "Normal curve equivalent")
tool: Mathematica

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– the ellipses are centered on the Rep/Dem means;
the standard deviations are represented by the ellipses' axes
– the 50 plot points represent the (rural-urban, incarceration) coordinates for each state;
and are colored according to their 2020 Electoral College vote
– "r" is the Pearson correlation value