| Concept | Formula | Role | |---------|---------|------| | Sxx (definition) | ( \sum (x_i - \barx)^2 ) | Total squared deviation from mean | | Sxx (computational) | ( \sum x_i^2 - (\sum x_i)^2/n ) | Numerically stable calculation | | Variance | ( S_xx / (n-1) ) | Average squared deviation | | Regression slope | ( S_xy / S_xx ) | Change in y per unit change in x | | SE of slope | ( \sqrts_e^2 / S_xx ) | Precision of slope estimate | | Correlation | ( S_xy / \sqrtS_xx S_yy ) | Standardized covariance |
Sxx=56−1443cap S sub x x end-sub equals 56 minus 144 over 3 end-fraction Sxx Variance Formula
There are two ways to write this formula: the (easier to understand) and the Calculation Formula (easier to compute). | Concept | Formula | Role | |---------|---------|------|
The Pearson correlation coefficient ( r ) can be expressed as: Sxx Variance Formula