You can calculate a regression equation by using the same number of data points as you have equation coefficients. However, the regression equation will not be as universal as a regression equation calculated using three times the number of data points as equation coefficients.
To correct the R2 for such situations, an adjusted R2 takes into account the degrees of freedom of an equation. When you suspect that an R2 is higher than it should be, calculate the R2 and adjusted R2. If the R2 and the adjusted R2 are close, then the R2 is probably accurate. If R2 is much higher than the adjusted R2, you probably do not have enough data points to calculate the regression accurately.
Adjusted R2 = 
where n is the number of data points and m is the number of independent variables.