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Ian r squared value .294 is very low. dimension A is NOT the primary driver of Dimension B. If you look at the scatter diagram you can clearly see this. I know you want to 'prove' that A causes B, but it doesn't...
perhaps if we understood the process and what the dimensions were we could provide more insight. it is possible that A does cause B and your study design is flawed.
Good point about R^2. As Ellis Ott said: "Plot the data!"
I disagree about the comment on proving a relationship. What you stated is correct for observational data. However, experimental data that has been replicated can essentially prove a relationship. For example, I only have to flip the light switch on and off a few times to essentially prove that it causes the light to turn on and off.