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For one of my questions on my test, we were to define the least squares criterion. I said: When we create a linear model we are attempting to minimize the distance between each of the data points plotted and our regression line. Our Least Squares Criterion is that we want our regression line to have the smallest possible value when you take all of the distances between the data points and the regression line squared. The smaller the value the better fit our regression line is.

Would anyone be willing to tweak my definition and define it in a superior way? Any help appreciated!

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Original: Our Least Squares Criterion is that we want our regression line to have the smallest possible value when you take all of the distances between the data points and the regression line squared. The smaller the value the better fit our regression line is.

Modified 1: The Least Squares Criterion (for linear regression) is to find a straight line such that the sum of the square of the distances between the data point and this straight line is minimum.

Modified 2: (Slightly more technical) The straight line which gives the best linear unbiased estimator (BLUE) of the coefficients. Gauss-Markov theorem guarantees that BLUE is given by ordinary least squares.

Note that the word straight line is important for linear regression here because if not then for non-linear regression, we can fit curve through he data points which may give us an even smaller sum of the square of the distances.

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  • $\begingroup$ Thank you for your help Nilotpal! $\endgroup$ – Trever Sep 30 '18 at 16:37

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