I'm having a difficult time getting my head around the idea that B and A in the regression equation
Y= BX + A are statistics and that their signifcance can be estimated. Where is the sample of Bs and As, from which the standard error of each estimate is derived? I'd prefer an explanation that I can visualize. For instance, I'm thinking that on a scatterplot, the sample of As are points (derived from B) on the Y axis and connected to each of the data points by lines with the same slope as the regression line. Is that correct?

Thanks in advance

B (as you're calling it) is the slope of the line of best fit that goes through your scatter plot. And A (as you're calling it) is the y-intercept of that same line. The reason I keep saying "as you're calling it" is because most textbooks generically indicate the regression line as y = Ax + B, not Bx + A as you've indicated. No one way is technically more correct than the other, just a matter of convention.

Interesting. It turns out that different disciplines use different notations; but they all mean the same thing. Thanks for pointing that out. I'm still wondering about the standard error of these estimates, though.