In ( y = a + bx ):
The standard deviation is simply the square root of the variance. This brings the metric back into the original units of measurement.
While it is frequently associated with calculating variance and standard deviation, Sxxcap S sub x x end-sub Sxx Variance Formula
The relationship between Sxx and sample variance is clear: (S_xx) is the of the sample variance formula.
is being compared against itself. This distinguishes it from Syycap S sub y y end-sub (the sum of squares for variable Sxycap S sub x y end-sub (the sum of products, used to measure how vary together in regression analysis). The Two Formulas for Sxxcap S sub x x end-sub There are two primary ways to write and calculate the Sxxcap S sub x x end-sub In ( y = a + bx ):
[ b = \fracS_xyS_xx ] [ S_xy = \sum (x_i - \barx)(y_i - \bary) ]
Sxx=∑xi2−(∑xi)2ncap S sub x x end-sub equals sum of x sub i squared minus the fraction with numerator open paren sum of x sub i close paren squared and denominator n end-fraction Key Components : Individual data points in your set. : The sample mean (calculated as is being compared against itself
Sxx=∑x2−(∑x)2ncap S sub x x end-sub equals sum of x squared minus the fraction with numerator open paren sum of x close paren squared and denominator n end-fraction : The sum of each squared individual value. : The square of the total sum of all values. : The total number of data points (sample size). Step-by-Step Calculation Example