Simple Linear Regression

Y = A + B * X

B = (xy - x * y) / (x² - x * x)

A = (x² * y - x * xy) / (x² - x * x) = y - B * x

R =          (xy - x * y)
R = ¾¾¾¾¾¾¾¾¾¾¾¾¾¾
R =  Ö (x² - x * x)(y² - y * y)

  A - intercept, B - slope, R - correlation
    x - average of x values, x² - average of the x squared values
    y - average of the y values, y² - average of the y squared values
    xy - average of the x and y products

Example

1 - Data

2 - Data, Squared, and Product Values

3 - Averages

4 - A, B and R Values

B = (310.8333 - (3.5 * 67.5)) / (15.1667 - (3.5 * 3.5))
B = 25.57

A = 67.5 - (25.57 * 3.5)
A = -22.00

R = (310.8333 - (3.5 * 67.5)) / Ö(15.1667 - (3.5 * 3.5))(6648.1667 - (67.5 * 67.5))
R = +0.9548

5 - Linear Equation

Y = A + B * X

Y = -22.00 + 25.57 * X

6 - Actual and Estimated Linear Values