Least-Squares Line Slope from Data

Equation: least-squares slope m = Sxy/Sxx, with Sxy = Σ(x − x̄)(y − ȳ) and Sxx = Σ(x − x̄)². Values: points (1,2), (2,4), (3,5), (4,7); x̄ = 2.5, ȳ = 4.5. Step 1: deviations x − x̄ = −1.5, −0.5, 0.5, 1.5 and y − ȳ = −2.5, −0.5, 0.5, 2.5. Step 2: Sxy = 3.75 + 0.25 + 0.25 + 3.75 = 8; Sxx = 2.25 + 0.25 + 0.25 + 2.25 = 5. Step 3: m = 8/5 = 1.60. 1.67 is the slope between the end points; 2.00 uses the first two points; 1.25 inverts the ratio.