By augmenting a bivariate data set with one point, the correlation coefficient and/or the slope of the regression line can be changed to any prescribed values. For the target value of the correlation coefficient or the slope, the coordinates of the new point are found as a function of certain statistics of the original data. The location of this new point with respect to the original data is investigated.
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David L. Farnsworth, “The effect of a single point on correlation and slope,” International Journal of Mathematics and Mathematical Sciences, vol. 13, no. 4, pp. 799-805, 1990. doi:10.1155/S0161171290001107
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