The US gained its independence on the 4th of July of 1776. During this time the world's economic system was based on commerce. Hence the author choosing to portray Minerva, the goddess of commerce, for a painting about America's independence. Commerce was key to a country's economy and in order to succeed in being an independent country. Also, one can see the ship that is painted in the picture's background.
On the other hand, wisdom was key to the formation and success of an independent nation. Minerva was also the goddess of wisdom. The country needed the wisdom to decide how to run themselves, make their own laws, and create a government.
Minerva was also the goddess of crafts. Crafts represented tradable goods that could impulse the country's economy. A successful country was one that was able to produce elaborate goods that had added value to them: instead of just exporting primary goods. Therefore, crafts were key for a successful and strong economy.