[ s_x = \sqrt\fracS_xxn-1 ]
Where:
The total SST is precisely ( S_xx ) for the entire response variable. And the variance estimate within groups is based on SSW/df, which is analogous to Sxx within each group summed. Sxx Variance Formula
is very small, our data points are bunched together, making our prediction of the slope very unstable. If cap S sub x x end-sub [ s_x = \sqrt\fracS_xxn-1 ] Where: The total
cap 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 2. Step-by-Step Calculation If you have a small data set, like , here is how you find cap S sub x x end-sub using the definitional method: Find the Mean ( Subtract Mean from each point: Square those results: Sum them up ( cap S sub x x end-sub cap S sub x x end-sub vs. Sample Variance ( It is important to note that cap S sub x x end-sub is not the final variance . It is the numerator used to find it. To get the Sample Variance ( , you divide cap S sub x x end-sub To get the Population Variance ( sigma squared , you divide cap S sub x x end-sub In our example above ( Sample Variance: 4. Why "Squared"? If cap S sub x x end-sub cap
The standard error of the slope ( SE(b_1) ) also depends critically on Sxx:
This version is the most intuitive because it shows exactly what variance is : the average of the squared deviations.