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Could you please tell me what is the exact meaning of this pattern? (I tried to mention meanings that I think could be relevant)

e.g.He does everything so I am very lucky in that regard.
1) because of that
2) in that case

He is studying law and in that regard he is doing very well.
1) in that case

We will take care of supplying the food, so you have nothing to worry about in that regard.
1) just 'that'

Mitt Romney: I will preserve and protect a woman’s right to choose, and am devoted and dedicated to honoring my word in that regard.
1) in that case
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He does everything so I am very lucky in that regard. 1) because of that 2) in that case

Neither. You are lucky on that one particular way. You need a comma before "so".

He is studying law and in that regard he is doing very well. 1) in that case

No. I think you meant something other than what it says, because it says that the fact that his study of law is one aspect of his life that could be said to be going well.

We will take care of supplying the food, so you have nothing to worry about in that regard. 1) just 'that'

Comments  
Thank you enoon.
Do you have any idea, how could I learn the proper usage of that phrase (in that/this regard)? Could you help me to use it properly?