This paper estimates successfully a version of the monetary approach to foreign exchange rates applied to the US dollar for the post-1973 floating exchange rate period. Although this approach has lately fallen in disrepute, the statistical evidence is strongly in support of the model. The results conform to expectations. All coefficients have the correct sign and are highly significant statistically. The null hypothesis that the coefficient on the money stock variable is equal to +1 fails to be rejected in all four estimated regressions. This reflects money neutrality. The null hypothesis that the coefficient on the scale variable is equal to -1 fails to be rejected in all these four regressions. This means that there are neither economies nor diseconomies of scale for aggregate income. The joint null hypothesis that both of the above two constraints hold fails to be rejected at marginal significance levels much higher than 10% for the first two regressions and fails to be rejected at a marginal significance level higher than 2% for the last two regressions. Finally, the adjustment to the long run falls upon the real interest rate and probably upon the scale variable. There is evidence that the foreign exchange rate, the money supply, and the nominal interest rate are all weakly exogenous. One implication of this study is that businesses, economists, individual investors, central bankers and policy-makers should have a more benign look upon fluctuations in foreign exchange rates, and should become convinced that these fluctuations are determined by fundamental forces.