I have a Pearson correlation of r=.30 between two variables - x and y. Now, I want to see whether this relationship changes as a function of variable z. I then calculated the following regression y~x+x:z (using lm in R). The standardized beta coefficient for the effect of x jumps to 1.07, and the x:z interaction coefficient is -.70. I am a bit worried that these numbers are unrealistic. That is, given that the relationship between x and y is low, it sounds too good to have such a high standardized regression coefficient. Any reason I should be worried about this analysis? The correlation between x and z is r-.06. I don't know if that means anything.
Thank you, Nitzan.