Can I use the interaction between a dummy variable and the variable it was derived from? I am trying to make a multiple linear regression model.   
I have a hypothesis that $x$ is a significant predictor of $y$ but only when $x > 0.5$  ($x$ ranges from -2 to + 2).
Is it acceptable to make a dummy variable $x_{Dum}$ for when $x > 0.5$ and from there create an interaction term  $x_{Dum}\cdot x$ in the model? I am very new to statistics, and have no formal training, but my thinking was that this would create the model in a way where the effect of $x$ is only attributed when $x$ is greater than $0.5$. 
Is this an acceptable way, or should I try and apply some sort of other transformation to my $x$ variable?
 A: The interaction term you propose would give you a predictor that is 0 for values of $x$ less than or equal to 0.5 and equal to $x$ for values above that. In principle there's nothing wrong with that formulation of a predictor variable in your regression.
That wouldn't, however, test your hypothesis that "$x$ is a significant predictor of $y$ but only when $x > 0.5$." For that you would have to compare models with and without that restriction.
I would suggest some other approaches. Unless you have solid theoretical reasons for the cutoff value of 0.5, you might be better off letting the data tell you whether there is some change in the relationship between $x$ and $y$ near there. One is to do a change-point analysis, on which there are 200 questions on this site. Another would be to use more flexible splines to model $x$ in your regression, to allow for (and potentially discover) a non-linear relationship between $x$ and $y$. 
If your study is important enough to do, it should be important enough to do the analysis well, too. As you are new to statistics it would be good to get the help of someone experienced in statistical analysis who can serve as your guide. It's certainly possible to get by without formal academic training in statistics if you have a solid background in probability, but without a guide you risk going down a lot of roads to nowhere.
