Here's how you can make a map colored by log10 of Population Density (2000), which is the variable color_value below. You can change that metric to whatever you want, and the rest of the code is the same.
ax = usamap('conus');
load coastlines
geoshow(ax, coastlat, coastlon,...
'DisplayType', 'polygon', 'FaceColor', [.45 .60 .30])
states = shaperead('usastatelo', 'UseGeoCoords', true)
% - color the states by PopDens2000, since we have that data here in the
% "states" struct array
% - throw out DC since its population density is much higher (~9000) than
% all the actual states (~1.1 to ~1100)
% - throw out Alaska and Hawaii since they won't show up on the map
% (which shows the continental US) - in particular, Alaska's
% population density is the lowest of all the states, and you don't want
% it determining the colors of the other states if Alaska is not even
% shown on the map
states(ismember({states.Name},{'District of Columbia' 'Alaska' 'Hawaii'})) = [];
% use a log color scale:
color_value = log10([states.PopDens2000]);
% pick a colormap to use:
color_map = parula();
% get the min and max color_value:
color_limits = [min(color_value) max(color_value)];
% convert color_value into an index in color_map:
% - minimum color_value goes to 1
% - maximum color_value goes to size(color_map,1)
color_idx = round((color_value-color_limits(1))/(color_limits(2)-color_limits(1))*(size(color_map,1)-1))+1;
% index into color_map using color_idx to
% get the colors to use for each state
faceColors = makesymbolspec('Polygon',{ ...
'INDEX',[1 numel(states)], ...
'FaceColor',color_map(color_idx,:)});
% show the states
geoshow(ax,states,'DisplayType','polygon','SymbolSpec',faceColors);
% make a colorbar
colormap(color_map);
colorbar('YAxisLocation','left');
clim(10.^color_limits);
