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The equation of the regression line is calculated so as to minimise the sum of the squares of the vertical distances between the observations and the line. The regression line represents the relationship between the variables if (and only if) that relationship is linear. The equation of this line ensures that the overall discrepancy between the actual observations and the predictions from the regression are minimised and, in that respect, the line is the best that can be fitted to the data set. Other criteria for measuring the overall discrepancy will result in different lines of best fit.
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An equation that makes a straight line when it is graphed. Often written in the form: y = mx+b