Compare the US trade deficit with Japan with the yen/dollar exchange rate

A key determinant of exchange rates is a trade deficit or a trade surplus. Other things equal if the US has a trade deficit with Japan, the dollar should depreciate relative to the yen. Select a time period and compare the US trade deficit with Japan with the yen/dollar exchange rate during that period. Do the data support the theory? What other factors might be influencing the yen/dollar rate?