Variance Formula __full__ | Sxx

Sxx=∑x2−(∑x)2ncap S x x equals sum of x squared minus the fraction with numerator open paren sum of x close paren squared and denominator n end-fraction Why It Matters

: Compute ( (x_i - \barx)^2 ):

Here, . This reveals a profound truth:

The of the slope depends directly on Sxx: [ SE(\hat\beta 1) = \sqrt\frac\textMSES xx ] where MSE = mean squared error. Sxx Variance Formula

[ S_xx = \sum x_i^2 - n\barx^2 ]

. It is a foundational measure of variability that quantifies the total spread of data points around their mean. While often confused with variance itself, cap S sub x x end-sub Sxx=∑x2−(∑x)2ncap S x x equals sum of x