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Regression Line vs Line of Best Fit

Regression Line vs Line of Best Fit,understand the difference between the two concepts of Linear Regression
Regression Line vs Line of Best Fit

The regression line (curve) consists of the expected values of a variable (Y) when given the values of an explanatory variable (X). In other words it is defined as E[Y|X = x]. To actually compute this line we need to know the joint distribution of X and Y, which in many cases we don’t know.

The line of best fit can be thought of as our estimate of the regression line. “Best fit” is not a precise term, since there are many ways to define it (ie using a least squares criterion, minimizing the absolute values of the residuals etc.).

One desirable property for the line of best fit to have is for it to converge to the regression line as our number of observations increase. And in the case of the variables X and Y having a bivariate normal distribution (which is often assumed) and selecting the ordinary least squares line as best fitted can be proven to occur.

The above answer was shared by Michael Zahir.

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