comparing R-squared and F-stat I am doing multiple regression with Gas production (l/d) as response variable, and flow rate (l/h) and COD influent (g/l) as explanatory variables in R. I made two models. 
mod1 <- gas ~ flow + COD 

r^2 = 0.64

f stat= 56.62(2,64) with 0.0000.... p value.

mod2 <- gas ~ flow*COD

r^2 = 0.81

f stat = 89.14 (3,63) with also very low p value.

Now for both cases, what the r^2 says and the f stat says?
I did the anova test of the both models. how to interpret them? 
Model 1: Gas ~ Flow + CODin

Model 2: Gas ~ Flow * CODin

Res.Df   RSS Df Sum of Sq      F    Pr(>F)    
1     64 24307                                  
2     63 12835  1     11472 56.311 2.631e-10 ***

 A: The $R$-squared are 0.64 and 0.81 for models 1 and 2, respectively. It means that in model 1 around 64% of the variation in the gas production can be explained by including the main effects of flow rate and COD influent in the model. In model 2, it mean that, around 81% of the variation in the gas production can be explained by including the effects of flow rate and COD influent as well as the interaction effect between low rate and COD influent. You normally add this interaction term, if you suspect that the flow rate effect on gas production may depend on COD influent.   
The $F$- tests for both models are significant.
In model 1, it means that you reject $H_0: \beta_1=\beta_2=0$ vs. $H_1:$ At least one of the $\beta_j \ne0, j=1,2$, where $\beta_1, \beta_2$ are regression parameter associated to flow and COD in model 1. 
In model 2, it means that you reject $H_0: \beta_1=\beta_2=\beta_3=0$ vs. $H_1:$ At least one of the $\beta_j \ne0, j=1,2,3$, where $\beta_1, \beta_2$ and $\beta_3$ are regression parameter associated to flow, COD and the interaction effect term between low rate and COD in model 2.
The anova, is actually testing if the reduction in the residual sum of square errors due to adding the interaction term is significant enough or not. In other words, it is testing $H_0:$ model 1 is the preferred model against $H_1:$ model 2 is the preferred model. It has another name, we sometimes call it partial $F$-test, since the test statistics has F distribution.   
Now, here the partial F-test is significant. It means that adding the interaction term reduces the sum of of square errors significantly.
