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Determining the Least Squares Line

Least squares would be a tedious process if we had to draw four of five lines of best fit and then determine which line had the least sum of squares. Even if we did this, we still would have no way of knowing whether the line we had chosen was truly the best out of all possible lines.

Consider the data in the following figure. The least squares formulae automatically provided the slope and y-intercept where the sum of squares (and therefore the Standard Error of Estimate) is smallest.