Sample variance ( s^2 = S_xx / (n-1) = 14.8 / 4 = 3.7 ) Sample standard deviation ( s = \sqrt3.7 \approx 1.9235 )
( n = 5 ) ( \sum x_i = 4 + 8 + 6 + 5 + 3 = 26 ) Sxx Variance Formula
But what exactly is , and why is it called the "variance formula"? Sample variance ( s^2 = S_xx / (n-1) = 14
( \sum x_i^2 = 16 + 64 + 36 + 25 + 9 = 150 ) ( (\sum x_i)^2 / n = 26^2 / 5 = 676 / 5 = 135.2 ) ( S_xx = 150 - 135.2 = 14.8 ) ✅ 5. Sxx in Linear Regression In simple linear regression (model: ( y = \beta_0 + \beta_1 x + \epsilon )), Sxx plays a starring role. The of the slope depends directly on Sxx:
The of the slope depends directly on Sxx: [ SE(\hat\beta 1) = \sqrt\frac\textMSES xx ] where MSE = mean squared error.
From now on, when you see variance, think Sxx first. Need more help? Practice calculating Sxx with random datasets — it’s the fastest way to internalize these formulas. Use the computational formula for speed and the definitional formula for conceptual clarity.
The of these values is: [ \barx = \frac1n \sum_i=1^n x_i ]