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For a general linear equation, y = mx + b, it is assumed that the errors in the y-values are substantially greater than the errors in the x-values. The vertical deviation can be calculated using this formula: If the square of the deviations is minimized, the "best line" can be calculated: By the use of matrix algebra (determinants), the values of the slope (m) and the y-intercept (b) can be calculated. A short review of determinants: Given: Example: It is evaluated: Equals: Now, the values for m, b, and the deviation D can be determined by these matrices: Notice that this theory assumes the data are basically linear! If data for a curve is passed to this program, it still calculates a straight line. Deciding which type of regression fits best is the user's responsibility. [ Home | Statistics | Algorithm | Architecture | Application | Glossary ]