Sxxn−1the fraction with numerator cap S sub x x end-sub and denominator n minus 1 end-fraction The average squared distance from the mean.
s squared equals the fraction with numerator cap S x x and denominator n minus 1 end-fraction A Quick Example If your data is correlation coefficient
Because $S_xx$ is the denominator, it represents the spread of your x-values. If $S_xx$ is small (x-values are clustered tightly), the slope becomes very sensitive to changes. If $S_xx$ is large (x-values are spread out), the slope estimate is more stable. Sxx Variance Formula
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(∑xi)2n=2024=4004=100the fraction with numerator open paren sum of x sub i close paren squared and denominator n end-fraction equals the fraction with numerator 20 squared and denominator 4 end-fraction equals 400 over 4 end-fraction equals 100 Sxxn−1the fraction with numerator cap S sub x
Sxx is not the final variance value; it is the numerator used to find variance. Sample Variance ( s2s squared
Square each of those differences. This ensures all values are positive. Sum of Squares ( cap S cap S Add all those squared numbers together. If $S_xx$ is large (x-values are spread out),
[ S_xx = \sum x_i^2 - \frac(\sum x_i)^2n ]
In regression analysis, you map the relationship between an independent variable ( ) and a dependent variable ( ). To find the slope ( ) of the best-fit line, you must use Sxxcap S sub x x end-sub alongside its counterpart, Sxycap S sub x y end-sub (the sum of products):