Punching like this is correct?

Question

when I throw my right hand I let my hips pull my upper body then I release my punch. is this correct?

Answer 1

Don't just pull your arm backward in order to punch,  you have to let your waist to bring your shoulder, then, your arm to go forward to punch out along with the footwork.  It will give you the best quality of punches, more powerful and less energy consumed than just punch out by only moving with your arm.

For some reasons,  many hispanic fighters can't make use of their waists and shoulders when punching and I only see mostly black and white fighters do that.  

Answer 2

Assuming you are right handed and therefore stand left foot forward, right foot back, left hand for jabs, right hand for power, then you should throw the punch beginning with extending the arm and twisting your right back foot in the "squishing a bug" motion, like you learn in baseball when your swinging the bat. It should be quick and powerful, with a slight twist in the hips.

I hope that helped, it's alot easier to show then to type, but I did my best.