# What is the difference between least squares line and the regression line?

It is common to plot the line of best fit on a scatter plot when there is a linear association between two variables. One method of doing this is with the line of best fit found using the least-squares method. Another method would be to use a regression line that, which can be written as (y-mean(y))/SD(y) = r*(x-mean(x))/SD(x). What is the difference between these two models? I don't understand when to use one over the other. We also learned that the regression line always passes through the averages of the conditional y distributions of the data is football-shaped when plotted. Is this also the case for the least-squares line?

I do not follow what you’ve written about a football, but the least squares regression line passes through $$(\bar{x},\bar{y})$$, yes.
• When you see people post the equation $\hat{\beta}=(X^TX)^{-1}Xy$, that’s the full ordinary least squares regression equation using matrices. If that looks like “huh?” right now, that’s okay. You’ll get there if you continue studying statistics, but you’ll come across that plenty if you hang on on Cross Validated much.